THE EFFECT of STEAM INJECTION on the ELECTRICAL CONDUCTIVITY of SAND and CLAY by DAVID BUCHANAN BUTLER
THE EFFECT OF STEAM INJECTION ON THE ELECTRICAL CONDUCTIVITY OF SAND AND CLAY by DAVID BUCHANAN BUTLER
B. Sc., Applied Science, Queen's University, 1986 M. Sc., Geophysics, University of British Columbia, 1990
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF GEOPHYSICS AND ASTRONOMY
We accept this thesis as conforming to the required standards
UNIVERSITY OF BRITISH COLUMBIA November 1995 © David Buchanan Buder, 1995 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.
Department of
The University of British Columbia Vancouver, Canada
Date
DE-6 (2/88) ABSTRACT
To interpret electrical surveys used to monitor subsurface steam-injection projects, one needs to know whether steam zones are resistive or conductive relative to initial conditions. This can be determined through laboratory measurements of the effects of steam injection on the electrical conductivity of sand. Experiments presented in chapter 2 measured the combined effects of the salinity of the boiler feedwaters and the steam quality - the fraction of the injected flux that is vapour. The injection of low quality steam, boiled from a saline solution, into clean sand saturated with the same solution, resulted in a net de• crease in conductivity, and a constant equilibrium conductivity in the steam zone. The in• jection of high-quality steam, using the same solutions, resulted in conductivity dropping first to a minimum, and then increasing to an equilibrium value similar to that seen in the low quality injection. This localized conductivity minimum became progressively less conductive with time, and travelled with the steam front. The appearance of the conductivity minimum at the steam front can be attributed to the formation of a dilution bank, which temporarily decreases the local salinity. This suggests that many steam injections will create steam zones with electrically resistive fronts, which can be used to track the steam. The effects of clay on the electrical conductivity of steam zones is further investigated in chapter 3. Experimental and numerical results indicate that clay-bearing steam zones can be electrically conductive relative to initial conditions, in part due to water saturations in the steam zones that are higher than those in comparably steam-flooded clean sands. However, it is still likely that high quality steam injections will result in resistive leading edges of the steam zones. In low quality steam injections, where dilution banks do not form around the front, it is more likely that steam zones are entirely conductive relative to initial conditions, particularly in fresh water environments.
ii TABLE OF CONTENTS
Abstract ii
List of figures V List of tables vii Acknowledgements viii Chapter 1: Introduction 1 Motivation 1 The definition of steam 2 The physical effects of steam injection 3 The electrical effects of steam injection 3 Overview of the thesis 6 Chapter 2: The effects of saline steam liquid and steam quality on the electrical conductivity of steam-flooded sands 9 Introduction 9 Parameters affecting electrical conductivity 10 Experimental apparatus 15
Procedure 17 Results 18 Discussion 21 Interpretation of the measured data 22 Numerical test of the high steam-quality interpretation 29
Summary 34 Chapter 3: The effect of clay content on the electrical conductivity of steam-flooded sands 55 Introduction 55 The electrical conductivity of clay 56
iii Experimental apparatus and procedures 59 Experimental results 62 Discussion 66 Numerical investigation of experimental data 69 Numerical extension of results to higher clay contents and higher salinities 73 Summary 80 Chapter 4: Conclusions 95 References 99 Appendix A: Details of experimental apparatus 104 Fluid system 104 Temperature measurement and control system 106 Electrical measurement system 107
iv LIST OF FIGURES
1.1 Schematic of an idealized steam flood 8
2.1 Electrical conductivity as a function of sodium chloride concentration 36 2.2 The effect of temperature on electrical conductivity 37 2.3 Laboratory steam-flood apparatus 38 2.4 Measurement locations within the conductivity cell 39 2.5 Temperature and conductivity records from experiment #1 40 2.6 Selected conductivity profiles from experiment #1 41 2.7 Surface plots of temperature and conductivity data from experiment #1 42 2.8 Temperature and conductivity records from experiment #2 43 2.9 Selected conductivity profiles from experiment #2 44 2.10 Surface plots of temperature and conductivity data from experiment #2 45 2.11 Temperature and conductivity records from experiment #3 46 2.12 Selected conductivity profiles from experiment #3 47 2.13 Surface plots of temperature and conductivity data from experiment #3 48
2.14 Interpreted physical property changes occurring in experiment #1 49
2.15 Interpreted physical property changes occurring in experiment #2 50 2.16 Interpreted physical property changes occurring in experiment #3 51 2.17 Approach used to simulate electrical conductivity response 52 2.18 Comparison of measured and modelled conductivity records 53
2.19 Comparison of measured and modelled conductivity profiles 54
3.1 Electrical conductivity of sand and clay, versus pore-fluid conductivity 81
3.2 Distribution of sand and clay inside conductivity cell 82 3.3 Effect of temperature on measured conductivity values in sand and clay 83
v 3.4 Temperature and conductivity records from steam-flood experiment 84 3.5 Selected conductivity profiles from steam-flood experiment 85 3.6 Surface plots of temperature and conductivity data from experiment 86 3.7 Calculated and observed conductivities of sand and clay, versus salinity 87 3.8 Effect of high quality steam injection on clean sand 8 8 3.9 Comparison of measured and modelled temperature records 89 3.10 Comparison of measured and modelled conductivity records in clean sand 89 3.11 Comparison of measured and modelled conductivity profiles from cell 90 3.12 Comparison of measured and modelled conductivity records in clay layer 91 3.13 Simulated conductivity responses of representative reservoirs during high quality steam injection 92 3.14 Schematic of temperature, salinity, water saturation, and conductivity changes that are observed during high quality injections 93 3.15 Simulated conductivity responses of representative reservoirs during low quality steam injection 94
A.l Schematics of thermocouple feedthroughs 109 A.2 External thermocouple multiplexer 110 A.3 External heating coil control circuit 111 A.4 Conductivity multiplexer circuit 112
vi LIST OF TABLES
2.1 Experimental parameters for three steam injections into clean sand 18 2.2 Input parameters for numerical simulation of high quality injection 33
3.1 Experimental parameters for a steam injection into sand and clay 61 3.2 Input parameters for numerical simulation of injection 71 3.3 Parameters used to simulate electrical responses of example reservoirs 74 3.4 Summary of electrical and reservoir parameters for nine simulations of high quality injections 76 3.5 Summary of electrical and reservoir parameters for six simulations of low quality injections 79
vii ACKNOWLEDGEMENTS
There are many people without whom it would have been impossible to finish this thesis. The most important of these is my wife, Sandy Stewart. She has put up with my work-related absences for many years, spending many evenings, most weekends, and even some vacations on her own, so that I could puzzle my way through my work. She has been a great source of encouragement and equanimity, keeping me on a reasonably even keel throughout my time here. She has even listened to me whenever I prattle on about steam, sand, or any other work-related topic of dubious entertainment value. I am of course grateful to my supervisor, Rosemary Knight. Her insight, guidance, optimism, and boundless enthusiasm have all been very helpful. Perhaps the aspect I appreciated the most was her ability to remain calm as I broke, melted, fried, vaporized, contaminated, or otherwise destroyed numerous integral pieces of laboratory equipment. I have been lucky to have as pleasant a place to work as the Rock Physics Lab. In " particular, Paulette Tercier, Jane Rea, and Kevin Jarvis have been a invaluable for their technical expertise, and their senses of humour. Financial support was provided by an NSERC postgraduate scholarship, and a Tri- Council (NSERC, MRC, SSHRC) Eco-Research fellowship. Funding for the laboratory research was provided initially by Mobil Exploration and Production Services, and Mobil Research and Development. Additional funding was obtained from an NSERC operating grant to Rosemary Knight.
Finally, I would like to thank Guiseppe Marinoni. I have benefitted greatly from his expertise.
viii CHAPTER 1:
INTRODUCTION
Motivation
Subsurface steam injection has been used for over 30 years in enhanced-oil- recovery operations (Doscher and Ghassemi, 1981). In recent years it has also proven to be a very effective technique for the removal of certain types of nonaqueous-phase-liquid contaminants from the near surface (Stewart and Udell, 1988). Despite its long history of use, however, it is not yet possible to predict how steam will travel through a rock or soil. Since the overall effectiveness of an injection depends on how much of the subsurface is treated, it is necessary to track the motion of the steam. Monitoring wells provide accurate information at isolated positions, but do not usually provide the necessary density of coverage. Thus, to ensure that all oil- or contaminant-bearing regions are treated, a reliable remote mapping technique is required. Electrical methods are potentially well suited to the steamflood monitoring problem, as they can detect remote changes in reservoir electrical conductivity, which is a function of the three reservoir properties with the largest potential for change due to steam injection - temperature, pore-water salinity, and water saturation. There are three stages in the electrical monitoring process: data collection, data processing, and finally, data interpretation. Routine data collection techniques for electrical methods have existed for many years (Beck, 1981; Dobrin, 1976). Data processing, long relying on crude methods such as the plotting of apparent conductivities in pseudo-sections (Telford et al., 1976), has recently progressed to the point where data inversion techniques are now capable of recovering multidimensional subsurface conductivity structures (Oldenburg and Li, 1994). This thesis concentrates on improving the interpretation of steam-flood electrical monitoring surveys, a topic that has received relatively httle attention. A few published field
1 surveys, discussed later, have been successfully used to detect steam-induced subsurface conductivity changes, but only rudimentary interpretations of the data were presented. In this thesis, the approach taken to improve the interpretation is to directly measure the conductivity of geologic materials during controlled laboratory steam injections, and to compare the changes to measured or inferred changes in temperature, salinity, and water saturation. It is thus possible to determine the relative contributions of these parameters to the conductivity, and to determine whether those contributions change as a steam flood progresses. The relationships observed in the experiments can then be used to better interpret field surveys, and to better track steam in the subsurface.
The definition of steam
The terminology used in steam injection projects can be confusing, since the term
"steam" is used to refer to a number of different states of water. The confusion most likely results from two definitions existing in common usage. The American Heritage Dictionary
(Morris, 1969) defines steam as either the vapour phase of water, or the mist formed by cooling water vapour. The Concise Oxford Dictionary (Allen, 1991) defines it as either the gas into which water is changed by boiling, or a mist of liquid particles of water formed by the condensation of this gas. Thus both dictionaries define steam as either a liquid or a gas.
In many steam injection projects, as in this thesis, a slightly different meaning is used: steam refers to a two-phase mixture of hot water vapour which is produced by boiling, and of equally hot liquid water. There is a subtle difference between this definition and the ones above: it defines steam as both vapour and liquid, neither just vapour nor just liquid. The definition results from the boiling procedure commonly used. Many of the boilers consist of a single-pass, flow-through water tube. The tube is heated, but not enough to boil all of the water. The resulting mixture of hot water vapour and equally hot liquid water is then pumped directly into the subsurface. Therefore the liquid phase of steam occurs due to incomplete boiling. The two phases in the mixture, which is sometimes
2 referred to as wet steam, are referred to as steam vapour, the vapour phase of steam, and steam liquid, the liquid phase of steam.
The physical effects of steam injection Injecting steam into the subsurface induces many changes in a reservoir, as noted in Figure 1.1. In oil-industry applications, the reservoir initially contains liquid water and oil. In the case of a near-surface clean-up operation, the ground contains water and a contaminant. The region immediately surrounding the injection well, soon after injection starts, is hot enough for steam vapour to exist and be stable. This region is the steam zone. It contains steam vapour, steam liquid, some left-over oil, some original reservoir water, and some steam condensate, which is condensed steam vapour. The condensate forms at the steam front - the leading edge of the steam zone - where it mixes with whatever liquid water is nearby. This mixture, over time,comprise s varying amounts of steam condensate and original reservoir water. The steam front moves forwards as the reservoir is heated, replacing much of the liquid with steam vapour, but leaving some water and oil behind. Just ahead of the steam front, the reservoir is warm, and contains both oil and some of the mixture of steam condensate and original pore water. Farther still downstream, the reservoir contains only the original fluids, and is at the original temperature. How the reservoir changes from steam conditions, right next to the borehole, to initial conditions far from the front, is not entirely known. It is the nature of all these changes - the changing temperature, the motion of the steam front, and the motions of all the original and injected fluids - that dictates how the conductivity will change. Investigating, understanding, and describing these changes is what this thesis is all about.
The electrical effects of steam injection Conductivity depends on three main parameters: temperature, salinity, and water
3 saturation. Therefore to fully comprehend the steam-induced electrical response, one must understand, first, the physical response: how steam moves through a reservoir, how temperature responds, what pore-fluid movements are induced, and how those movements affect salinity and water saturation. Second, one must know how conductivity depends on temperature, salinity and water saturation. Previous work in understanding the electrical effects of steam injection has followed one of three methods, or a combination of them. One involves the numerical simulation of the physical effects of steam injection to determine the resulting temperature, salinity, and water-saturation distributions. Empirical relationships between conductivity and these three parameters can then be used to calculate the resulting conductivity distributions. Another method consists of measuring in the field the electrical conductivity at various times over a steam-injection project. The third method determines the effects experimentally by injecting steam into porous materials and measuring the electrical response. Numerical simulation of the movement of steam, water, and oil through a rock requires the solution of the nonisothermal multiphase flow problem. The problem is further complicated by the need to incorporate phase change effects. Many publicly available techniques exist for the isothermal problem: for a detailed description of the techniques, see Peaceman (1977), and Aziz and Settari (1979). These techniques, however, generally do not allow for phase changes. Substantially fewer techniques exist publicly for the simulation of the nonisothermal problem, but there are some. A numerical model of steam injection into one-dimensional water-saturated reservoirs was developed by Menegus and Udell (1985). The model calculates the pressure, temperature, and water-saturation fields that result from the injection of steam into a water-saturated porous medium. Stewart and Udell (1988) expanded this to include the effects of an oil phase, and obtained good agreement between model calculations and experimental measurements. Pruess and Narasimhan (1985) developed a model for the nonisothermal two-phase flow of water in a
4 multidimensional fractured porous medium. Falta et al. (1992a) then presented a multi• dimensional model that simulated the three-phase flow of air, water, and a nonaqueous- phase liquid. All of these simulators calculate temperature and water-saturation profiles in a steam-flooded reservoir. Although they do not calculate salinity variations, presumably such calculations can be added to the routines. Therefore they could be used to calculate steam-induced conductivity changes. This technique was used by Vaughan et al. (1993), who included the effects of salt transport in Menegus's and Udell's (1985) simulator, and calculated the conductivity distribution that develops from the injection of steam into a one- dimensional water-saturated medium. Their numerical results matched their experimental data, which were collected using initially water-saturated clean quartz sands, and using distilled water as the source for the steam. They found the steam-flooded sand to be strongly resistive compared to initial conditions. At the beginning of the writing of this thesis, these were the only published numerical and laboratory steam-flood conductivity results. They can be considered an important first contribution to the interpretation of steam-flood data. Only a few field electrical surveys over steam-injection projects have been published. From these, an interesting disagreement has surfaced as to whether steam zones are resistive or conductive, relative to initial conditions. An interpretation of controlled- source magnetotelluric data collected over an enhanced-oil-recovery steam flood suggested that the steam zone was resistive (Wayland et al., 1987). That interpretation was discounted by Mansure and Meldau (1990), who stated that steam zones can either be resistive or conductive. More recently, a comparison of borehole-resistivity logs to temperature logs found steam zones to be conductive (Ranganayaki et al., 1992), as did a borehole-to- borehole resistivity-tomography study (Ramirez et al., 1993).
In this thesis, the emphasis is placed on investigating the steam-induced conductivity response through laboratory experiments. A systematic* approach is used
5 throughout the work, starting with simple injections, and progressing to more complicated systems as the simple ones are understood. Experiments are used to determine the effects of different boiler-water salinities, different types of porous material, and different initial saturating fluids on the steam-flood electrical behaviour of a reservoir. Interpretations of the results are given in terms of physical changes taking place in the sand. These are then supported by numerical simulations of particular experiments.
Overview of the thesis This thesis is motivated in part by the disagreement over field results noted above. A central objective, therefore, is to determine whether steam zones are resistive or conductive, relative to starting conditions, and more importandy, what makes them so. It is a recurring theme, addressed in chapters 2 and 3. As mentioned above, injecting steam will cause many changes in a reservoir. To fully understand how conductivity is affected, it is necessary first to know how it depends on temperature, salinity, and water saturation. Therefore the beginning of chapter 2 is a detailed discussion of these relationships. A comprehensive summary of this nature does not exist elsewhere, and it is useful in understanding much of the work presented herein. This is largely an experimental thesis. Therefore following the initial discussion in chapter 2, the apparatus designed and built to measure the electrical response is summarized. It is further detailed in appendix A.
As noted in my definition of steam, the injected steam is a mixture of water vapour and liquid water. The mass fraction of the mixture that is steam vapour is referred to as the steam quality. Since vapour is resistive, and liquid conductive, it has long been presumed that the quality can have an effect on the electrical conductivity of a reservoir, since it is a measure of the amount of liquid being injected. Chapter 2 presents a series of experiments designed to investigate this effect. An important dependence on steam quality is presented, and the results are explained using a simplified numerical approach developed in the latter
6 part of the chapter. Chapter 2 shows that steam zones in clean sands are resistive. However, a number of oil reservoirs and most near-surface environments undergoing steam injection do not involve clean sands, and contain appreciable amounts of clay. Clays complicate the electrical response, because they add an additional conduction mechanism along their surfaces. Clay effects have often been invoked to explain the difference between laboratory and field electrical responses, since previous laboratory measurements used no clay. Chapter 3 therefore investigates the effects of clay. It follows the format of chapter 2: it first summarizes the electrical effects of clay, and then experimentally determines the steam- flood electrical response. To my knowledge, these are the first electrical measurements made in the laboratory on steam-flooded clays. Due to design limitations, only very small amounts of clay could be investigated. The numerical approach presented in chapter 2 is therefore modified to allow the low-clay-content results to be extended to more meaningful high-clay-content scenarios.
Chapter 4 is a summary of the thesis. It contains the major conclusions from the two previous chapters, tying them together so as to revisit the question of why steam zones become resistive or conductive.
7 T7T7771T777777T77/ ^Impermeable Rock/y //////////////// Porous Reservoir
steam zone:; ;;;;;; Mixed Zone: Undisturbed Zone: -hot warm region - cold - contains steam contains oil, steam vapour, steam liquid, contains oil condensate, and original oil, original pore original pore water water, steam pore water condensate
//////'//'/////// Impermeable Roc
Steam Front
Fig. 1.1: Simple schematic of an idealized steam flood. Injecting steam heats up the reservoir, and forces fluids to move trhrough the pore space. CHAPTER 2:
THE EFFECTS OF SALINE STEAM LIQUID AND STEAM QUALITY ON
THE ELECTRICAL CONDUCTIVITY OF STEAM-FLOODED SANDS
Introduction If electrical methods are to be useful monitoring tools, the effects of steam injection on a reservoir's electrical conductivity must be well understood. Otherwise, the interpretation of the electrical data will be suspect. Currently, these effects are not fully known; only a very few examples of steam-flood electrical surveys have been published, and as noted in chapter 1, some of these disagree as to whether a steam-flooded reservoir is resistive or conductive. Interpretation is further complicated by the as-yet unknown effects of certain steam-injection parameters, such as the salinity of the boiler feedwaters, and in particular, the steam quality. Clearly there is a need for the careful investigation of the electrical response. This chapter addresses three issues: whether steam zones are resistive or conductive, what makes them so, and whether steam quality affects the conductivity. Currently only one laboratory study of the steam-induced electrical response has been published: Vaughan et al. (1993), in an experimental and numerical study, investigated the effects on conductivity caused by the injection of steam boiled from distilled water into a salt-water-saturated sand pack. The study illustrated the impact on conductivity of the distilled steam condensate that forms at the steam front. The conductivity measurements showed how the dilution of salt water by the condensate dominated the electrical response.
There is an additional factor that must be considered in many field applications where salt water, rather than fresh, is used as the feedwater. Specifically, the transport of salt in the steam liquid must be taken into account. The presence of saline liquid in the steam zone can have a large effect on the electrical conductivity. The amount and the
9 salinity of the injected steam liquid is determined in part by the steam quality. The quality also affects the speed at which the steam liquid moves through the steam zone, relative to the steam front. For example, an increase in steam quality leads to an increased steam-front speed, and a decreased steam-liquid speed. This relative speed has a strong effect on the specific temporal and spatial conductivity changes seen in a steam zone. Detection of the steam front is most useful for monitoring purposes. The experiments reported here clearly show how steam quality, which is linked to salt transport in the steam liquid, strongly affects the electrical conductivity both in, and ahead of, the steam zone.
Parameters Affecting Electrical Conductivity
The electrical conductivity of clean (clay-free) sands and sandstones can be de• scribed using Archie's equation (Archie, 1942):
m Of = c)) S£o-W) (2.1)
where Of is the formation conductivity, <(> is porosity, Sw is the water saturation, ow is the conductivity of the pore fluid, and m and n are the cementation and saturation exponents. Archie (1942) found that m is approximately 1.8 to 2.0 for consolidated sandstones, and 1.3 - the value used in this study - for clean, unconsolidated sands. Steam injection can af• fect the electrical conductivity by changing the liquid water saturation in the reservoir, by changing the salinity of the pore fluid, and by increasing the temperature. Secondary influ• ences include steam-induced changes in fluid pressure and matrix wettability.
The water saturation will vary during a steam flood as a result of the displacement
by steam of water, oil, or contaminant. Original Sw levels in a reservoir can vary widely, as can water saturations in a steamed region. Numerical studies showed that a decrease in water saturation occurs in a narrow zone immediately behind the steam front (Menegus and Udell, 1985; Stewart and Udell, 1988; and Falta et al., 1992b). Minimum water saturations in a steam zone are not likely to be less than 0.10 to 0.15. This level is supported both by
10 theoretical considerations (Menegus and Udell, 1985), and field estimates (Mansure and
Meldau, 1990). Menegus and Udell (1985) found that the residual steam-zone water saturation depends in part upon the geometry of the injection process, with the minimum saturation obtained when steam is injected into the top of a formation, forcing fluids downwards. They also show that increasing the steam quality can decrease the steam-zone water saturation. The effect of water-saturation variations is included explicitly in Archie's
n law! in the term Sw . The saturation exponent n, over saturations ranging from 0.15 to 1.0, was determined by Archie (1942) to be approximately 2.0, the value used in this study.
Other researchers have found n values in water-wet rocks that range from 1.3 to 2.6
(Longeron et al., 1989; Sprunt et al., 1988; de Waal et al., 1991).
j There can potentially be very large salinity contrasts occurring due to the injection of steam. Oil reservoir salinities can be as high as 3.1 mol/L (Worthington et al., 1990); while the minimum salinity depends upon the salinity of the injected water. Figure 2.1 i shows the dependence of conductivity on salinity at 20 degrees Celsius: since conduction in
! rocks is predominantly ionic, an increase in salinity increases the number of available charge carriers, resulting in increased conductivity. The increase is approximately linear in i salinity for low concentrations, but becomes non-linear at higher salinities, as interference effects between dissolved ions lessen the ability of individual ions to carry current
efficiently. The conductivity, cw, of a very dilute solution of a single ion can be described as (Ellis, 1987):
3 2 ! ow=l0 c(|Z|F) ^ (2.2) I
In all equations shown here, a is given in S/m, and c, the ionic concentration, in mol/L
(M). Z is the valence of the ion, and F is Faraday's constant, 9.648* 104 C/mol. The absolute mobility of an ion, u., is defined as the terminal velocity of the ion through the fluik when subjected to a force. The units of u. are (m/s)/N. A more useful formula uses the i similarly defined electrical mobility, u.', which is the terminal velocity of an ion when subjected to an electric field. Its units are (m/s)/(V/m). Extending the formula to include i i 11 different ions:
3 ow=10 FX|Zil CiHV (2.3) i Equation (2.3) is accurate to within five percent for concentrations less than 0.005 M. Robinson and Stokes (1965) developed a nonlinear equation for the equivalent conductivity, defined as A = o7(10c), of dilute NaCl solutions:
A = Ao_B^A%B2 (24) 1 + 4BVc
The first term on the right, A°, refers to the limiting equivalent conductivity of a solute at very low concentrations, where there are no interactions between dissolved ions. The second term attempts to account for interference effects between ions; the negative sign indicates that this interference decreases the equivalent conductivity as salinity increases.
The parameters A0, Bi, B2, and B were tabulated as functions of temperature. Equation (2.4) is accurate to within 0.1 percent for concentrations up to 0.1 M NaCl. The most widely applicable formulae for calculating the conductivity of NaCl solutions are three empirical relations given by Worthington et al. (1990) for the salinity ranges 10"4 M to 0.1 M, 0.09 M to 1.4 M, and 1.0 M to 5.35 M. The equation for the dilute range is
log a = 0.942203 + 0.888900 log c - 2.72398* lO'^log cf - 2.25682* 10"3(logc^ + 1.46605* 10-5(logcf * ('}
Their three equations were shown to fit measured data to within 0.1 percent. The injection of steam will clearly cause an increase in reservoir temperature. A theoretical study reported by Stewart and Udell (1988) showed that steam injection produced a narrow heated zone ahead of the steam front. Therefore the effect of increased temperature on conductivity is restricted to regions within or very close to the steam zone. Increasing the temperature of a reservoir increases its electrical conductivity, due mainly to changes in the conductivity of the pore water. The temperature variation of conductivity was measured by Ucok (1979), for a number of concentrations; the data are shown in
Figure 2.2. Conductivity increases with temperature up to approximately 300 degrees
12 Celsius, at which point it starts to decrease. This behaviour is caused by the decrease with temperature of water's viscosity, density, and dielectric permittivity (Quist and Marshall, 1968). The dominant effect at lower temperatures, the decreasing viscosity of water, results in an increased ionic mobility, and therefore increased conductivity. However, Quist and Marshall (1968) noted that above 300 degrees Celsius, both the density and dielectric permittivity of water continue to decrease, while viscosity becomes reasonably constant. This results in a lower salinity and a decreased dissociation of the ions. Therefore the conductivity starts to decrease above 300 degrees Celsius. Steam injection in oil reservoirs is unlikely to cause temperatures to exceed 300 degrees Celsius (Mansure and Meldau, 1990), and therefore most temperature corrections account only for increases in conductivity. Temperature corrections are most commonly made using Arps' law (Arps, 1953 ):
02 = (T2 + 21.5)
Oi (Ti+21.5)f (2.6) where T is in degrees Celsius. This is a least-squares linear fit to the conductivity of NaCl solutions at temperatures between 0 and 156 degrees Celsius. It tends to overestimate the conductivity of more concentrated solutions at temperatures above 120 degrees Celsius
(Sen and Goode, 1992). A less commonly used correction is Heiland's equation (Heiland,
1940):
cJT = ai8[l+p(T-18)]> (2.7) where Ois is the conductivity of solutions at 18 degrees Celsius, and (3 is approximately
0.022. Another less commonly used correction is an exponential equation given by Llera et al., (1990):
aw = a0exp(^). (2.8)
In this equation, U is the activation energy of viscous flow, while k is Boltzmann's con• stant, and T is absolute temperature. Equations (2.7) and (2.8) attempt to account only for changes in viscosity; this was shown to overestimate the thermal increase in the
13 conductivity of numerous dissolved solutes (Robinson and Stokes, 1965).
A number of other researchers have developed equations for conductivity that simultaneously consider salinity and temperature. Vaughan et al. (1993) expressed the four free parameters of equation (2.4) as cubic functions of temperature, to determine the conductivity of solutions of salinities up to 0.1 M NaCl, and for temperatures to 100 degrees Celsius. Sen and Goode (1992) used an empirical formula for salinities between
0.09 M and 4.74 M NaCl, and temperatures less than 200 degrees Celsius:
2 Ow = (5.6 + 0.27T - 1.5*10-4 T ) M-^+ 0.09gTMi.s (2.9)
1.0 + 0.214M where M is the molarity and T is temperature (degrees Celsius). This was shown to be more accurate than Arps' law. Ucok (1979) developed empirical equations for NaCl, KC1, and CaCl2 solutions that accounted for the drop in conductivity at higher temperatures. The
equations determined aw for salinities from 0.5 M to 3.9 M, and for temperatures between
20 and 400 degrees Celsius. The equations, also shown to be superior to Arps' law, correctly predict decreased conductivities at higher temperatures.
Wettability can have a strong effect on fluid distribution and therefore conductivity.
Anderson (1986) discusses how wettability affects the conductivity through Archies saturation exponent n. He emphasized that Archie's law assumes that all the brine in a rock is connected, but that that actually occurs only in strongly water-wet cases. He concluded that n is essentially independent of wettability at very high saturations, but that it can reach values of 10 or more at low saturations in oil-wet rocks.
Given the complicated dependence of conductivity on all these parameters, it was decided to experimentally measure the electrical behaviour in the laboratory. Any previously unknown links between saline feedwater, steam quality, and the resulting electrical conductivity, if they constitute an important mechanism that must be considered when interpreting electrical data, would presumably then appear in the results. The laboratory apparatus discussed below was developed to determine how saline steam liquid and steam quality affect the conductivity of steam-flooded sands. 14 Experimental Apparatus The steam injection apparatus is shown in Figure 2.3. The electrical conductivity cell consists of a 32.5 cm long, 13.9 cm diameter ceramic tube, sealed at both ends with stainless-steel plates, and filled with Ottawa sand. Greater than 99 percent of the sand is quartz; the grains are spherical to sub-spherical, and are well rounded. Steam is produced by pumping water from a reservoir, through a preheater, then through a steam generator (a boiler). When the steam is injected at the top plate, it heats the system, and forces fluid out the bottom of the vessel. Eleven thermocouples, inserted through the ceramic wall, measure temperature every 2.5 cm along the axis of the cell. Two others measure the temperature upstream and downstream of the steam generator. Heating coils and thermocouples attached to the outside of the cell (not shown) are used to set the external temperature distri• bution equal to the internal distribution, to minimize heat losses and promote 1-D fluid and current flow. Electrical conductivity is measured using a four-electrode technique; the steel plates act as the current electrodes, and the thermocouple sheaths act as the potential electrodes. A 10 V square wave is passed across a series arrangement of the sand pack and a precision resistor, which is used to determine the current passing through the sand. The alternating current is necessary for the removal of electrochemical voltages set up between the thermocouples and the endplates. A frequency of 100 Hz is used since few capacitive effects are produced, and the sampling rate is fast enough to capture all conductivity changes. Assuming 1-D current flow, the conductivity of the sand between successive thermocouples is °=^V • <2-10>
where L is the distance between a neighbouring pair of thermocouples, Vp is the voltage
across the precision resistance Rp, A is the cell's cross-sectional area, and V is the voltage
15 measured between thermocouples. This cell is a modification of a design described by Vaughan et al. (1993), that used a 5.08 cm diameter, approximately 75 cm long, horizontal glass tube. Vaughan et al. (1993) reported that a steam override likely occurred in the experiments, because of the cell's horizontal orientation. In the experiments reported here, the conductivity cell was ori• ented vertically in order to better promote the stable advance of a 1-D steam front. The di• mensions of the cell were also changed in order to improve the resistive measurement limit of the cell. Since any four-electrode technique used to monitor electrical resistivity has a system-dependent maximum resistance that can be measured, the diameter of the cell was increased, and the length shortened. This lowered the overall resistance of the sand, making it possible to increase the resistivity of solutions that can be measured.
Figure 2.4 is an enlarged sketch of the conductivity cell, used to show where measurements are made. Both temperatures and conductivities are measured approximately every 2.5 s. Temperatures inside the sand are measured at 11 thermocouple tips, which are equally spaced along the axis of the cell. These are referred to later in the text as temperatures Ti through Tn, with Ti measured at the top of the cell, and Tn measured at the bottom. (These labels are also used to refer to the thermocouples themselves.) Conductivities are average measurements made between neighbouring thermocouple sheaths. Thus there are ten conductivity measurements, referred to later as
An important aspect of the system is the steam generator: it was constructed by wrapping the 3.2 mm stainless-steel fluid tubing around a cartridge heater, insulating the tubing, and pressing it into a dewar flask. Since it is a one-pass boiler, whatever fluids pumped into the boiler are then injected into the cell. Any salt in the feedwater remains in the steam liquid. By adjusting the heater's input electrical power, the steam quality can be set to any desired value between zero and one. Volumetric flow rates into the boiler are kept constant throughout an experiment. The mass flux leaving the boiler, and entering the sand,
16 is equivalent to that entering the boiler from the pump. The steam quality therefore deter• mines the steam-vapour and steam-liquid mass-injection rates. Much of this apparatus was machined in house. Additional details of the pore-fluid, temperature-measurement, electrical-measurement, and temperature-control systems can be found in Appendix A.
Procedure
At the start of an experiment, the cell is carefully filled with dry Ottawa sand. The sand is sieved using mesh sizes 25 and 42, to obtain grain sizes from 0.7 to 0.35 mm. The filling is done slowly, and the cell is repeatedly agitated in order to settle the sand and obtain a strong packing. The technique results in a repeatable porosity of 33%, and a stable pack that does not settie with the injection of fluids. Therefore the sand pack can be used repeatedly for numerous experiments. Before saturating the sand, a vacuum line is first attached to the top of the cell. Saturating fluid is allowed in from the bottom as far as the downstream valve. The valve is then closed, and the system evacuated for three hours. Fluid is then allowed to flow into the cell. The vacuum line is disconnected, and drain tubing attached to the top. The cell is then flushed with three pore volumes of saturating solution. Once the sand is saturated, the reservoir is filled with the appropriate displacing fluid, and the pump and pore-fluid lines flushed. The pore-fluid line is then connected to the top of the cell.
To begin a displacement, the pump is set for the desired flow rate, the preheater set to the desired temperature, and the steam generator set for the appropriate power input. The pump and heaters are then turned on, and the flow is shunted past the measurement cell. When the required power level is reached by the boiler's heating circuits, and the fluid leaving the boiler has reached an equilibrium temperature, the monitoring and control systems are started. Ten minutes later, the steam is diverted into the sand. The injection
17 continues until steam nears the downstream end of the cell, at which point the heaters are turned off, and the monitoring stops. The cell is then flushed with cold water until the internal temperature has dropped below 40 °C.
Results A series of experiments were conducted to determine the effects of feedwater salin• ity and steam quality on the electrical conductivity of unconsolidated sand. A displacement of salt-water-saturated sand with low quality steam, which was boiled from distilled feedwater, served as a test of the cell, and as a baseline for further experiments. The second experiment was a repeat of the first, except that saline feedwater was used. The third experiment was a repeat of the second, except that high quality steam was used. Parameters describing the experiments are summarized in Table 2.1. All experiments used identical initial pore-fluid salinities and identical volumetric flow rates into the boiler. The flow rate of 15.9 ml/min was chosen because it was found to produce a stable, one-dimensional, steam front advance. Volumetric flow rates into the sand increased in the third experiment, due to the higher steam quality.
Table 2.1. Experimental parameters for the three steam injections: q is the
volumetric flow rate into the boiler, CD is the salinity of the boiler feedwaters,
and Csat is the initial pore-fluid salinity.
# q (ml/min) Co (mol/L) Csat (mol/L) Quality 1 15.9 distilled 0.01 0.17 +/- 0.02 2 15.9 0.01 0.01 0.17 +/- 0.02 3 15.9 0.01 0.01 0.62 +/- 0.02
In the first experiment, the sand was initially saturated with 0.01 M NaCl and the quality of the injected steam was 17 percent. The boiler feedwater was distilled, so the injected two-phase mixture consisted of vapour and distilled liquid. The results are shown in Figures 2.5a and 2.5b.
18 The individual temperature records in Figure 2.5a correspond to the locations
shown in Figure 2.4. Only Ti and Tn are labelled, as T2 through T10 follow in sequence after Ti. At each thermocouple, temperature began at approximately 20 degrees Celsius, then increased with the approach of the steam front. Arrival of the steam front at a thermo• couple is marked by the point where the temperature reaches the boiling point, which in this experiment is near 100 degrees Celsius. The conductivity data in Figure 2.5b are also labelled according to Figure 2.4. Here only ai and c?io are labelled, as c>2 through 09 also follow in sequence after G\. The sand initially had a uniform conductivity of 0.022 S/m, which can be seen in Figure 2.5b as the starting point for all conductivity traces. Conductivity in the uppermost region of the sand (corresponding to conductivity trace 01) increased very slightly soon after injection began, but then fell rapidly by more than two orders of magnitude. Deeper regions in the sand displayed similar behavior. Some traces showed a temporary conductivity increase before the arrival of the steam front, followed by a decrease as the steam front passed through the region. After steam swept through the sand, conductivities approached equilibrium values below 10-4 S/m. Figure 2.5b shows conductivities measured at specific positions as functions of time. Another view of the data is a "time snap-shot" - conductivity as a function of position, at a specific time. Six such snap-shots are shown in Figure 2.6. The first corresponds to the initial conductivity distribution, and the rest correspond to the times when the steam front reached the first, third, fifth, seventh, and ninth thermocouples respectively. The top left of the diagram shows a uniform initial conductivity of 0.022 S/m. The top right of the diagram, at 2580 s, shows that by the time the steam front reached the first thermocouple, conductivity decreases could be seen well forward into the sand. The later snapshots show that the conductivity of the steam zone (represented by those values to the left of the arrows in each plot) remained reasonably constant with time and position. The plots for 3220 s and 3750 s show that conductivities 3.8 cm ahead of the steam front
19 were anomalously high compared to the values in the rest of the sand. These relatively high values correspond to the temporary increases in conductivity that are shown between 3000 s and 4200 s in Figure 2.5b. To complete the picture, the data are shown in Figures 2.7a and 2.7b as three- dimensional surfaces, which plot temperature and conductivity against depth in the cell, and against time. The steam zone is indicated by the triangular, flat temperature region at the right of Figure 2.7a. Undisturbed conditions are indicated by the flat conductivity region at the left of Figure 2.7b. The second experiment injected 17 percent-quality steam boiled from 0.01 M NaCl, identical to the saturating fluid. The temperature and conductivity results for this experiment are shown in Figures 2.8a and 2.8b. The temperature response at all positions in the cell was nearly identical to that seen in the first experiment. Conductivity in the uppermost region (trace Oi) first increased by a factor of two, then dropped as the steam approached, and reached an equilibrium value of 0.04 S/m, significantly more conductive than in the first experiment. The other regions behaved similarly, except that the initial increase was gradually reduced over the length of the cell, reaching a factor of 1.4 at the downstream end. All regions reached a stable steam-zone conductivity of 0.04 S/m. It can be seen in Figure 2.9 that after 2700 s, the shape of the conductivity profile remained reasonably fixed, relative to the position of the steam front. This can also be seen in the surface plots of temperature and conductivity in Figures 2.10a and 2.10b.
The third experiment was a repeat of the second, except that the injected steam quality was increased to 62 percent. Results are shown in Figures 2.1 la and 2.11b. The steam penetrated much more quickly into the sand, reducing by half the time required for the steam front to reach the end of the cell. Temperature did not increase in the sand until just before the arrival of the steam front. Conductivities in the upper three regions of the sand (represented by traces Oi, G2, and 03) again increased as the temperature increased, although the magnitudes of the increases were less than in the previous experiment, and
20 increases were not seen in regions farther into the sand. Unlike the second experiment, all positions in the steam zone showed conductivities that varied with time. For example, 05 started to decrease at 1525 s, 100 s before steam arrived at thermocouple T5, and continued to decrease until 1750 s, when steam reached thermocouple T6. Thereafter, 05 increased slowly for the remainder of the experiment. Each region followed this behaviour: with the approach of the steam front, conductivity decreased, continued to decrease to a minimum as steam reached the downstream edge of the region, then started to increase again towards an steady value. The magnitude of the minimum decreased from one measurement region to the next. This is best seen in Figure 2.12, which clearly shows how the shape of the conductivity profile, relative to the position of the steam front, changed with time. The minimum deepened as it travelled, so that the region near the steam front became progressively less conductive as the front moved through the sand. In a perspective view, as in Figure 2.13b, this appears as a deepening conductivity "valley", which follows the path of the steam front.
Discussion
The electrical data presented above are analysed here in two parts. The first part comprises interpretations of how steam injection affects electrical conductivity through changes in temperature, salinity, and water saturation. These are summarized in schematics which show the effects of steam on idealized reservoirs. The interpretations are based on the measured data, and are therefore correlated with the data wherever possible. This discussion highlights the major effects of steam quality on electrical conductivity. The second part of the analysis is a theoretical test of the interpretation. A numerical model is developed that describes the flow of gas, liquid, heat, and dissolved salt, and calculates the resulting conductivity. It is applied to the experimental conditions, and the resulting theoretical data compared to the experimental results.
21 Interpretation of the measured data The following is a summary of the interpretations of the electrical data. The interpretations relate conductivity to the physical conditions within the reservoir, and will be tested later against theory through the numerical modelling of the steam-injection process. The measured electrical responses of the first experiment can be understood by considering the physical changes which would take place in an idealized reservoir as a result of steam injection. Figure 2.14a contains three time snapshots: each shows predicted movements of water and gas as steam works its way through sand. By time ti, soon after the start of steam injection, a small steam zone has expanded outwards a short distance from the injection point. The zone contains both gas and liquid. The gas, injected steam vapour, moves rapidly from the injection point to the steam front, and condenses into distilled water. The liquid, a mixture of injected steam liquid, steam condensate, and original pore fluid, also moves from the injection point to the steam front, although more slowly than the gas. It is important to understand that the gas and liquid can coexist in the pores: the liquid moves along the grain surfaces, and the gas moves quickly through the central portions of the pores. Just in front of the steam front is a mixed zone, a fully liquid- saturated region where steam condensate mixes with and displaces the original pore fluid. Farther ahead is an undisturbed zone, where the pore-fluid composition has not changed from initial conditions. The first experiment injected steam boiled from distilled water into salt-water- saturated sand. Figure 2.14b shows how, under such circumstances, temperature, water saturation, salinity, and hence conductivity are predicted to vary in the steam zone and the mixed zone. Temperature is predicted to remain at the boiling point throughout the steam zone, then decrease to the initial value across the mixed zone. Water saturation remains constant at a residual value throughout much of the steam zone, and then rapidly reaches 100 percent immediately upstream of the steam front. Ahead of the front, the sand is fully
22 saturated with liquid water. Salinity at the injection point is fixed at the steam-liquid value, which under these circumstances is distilled. Since the steam liquid moves faster than the steam front, the salinity of the entire steam zone is very close to that of distilled water. Ahead of the steam front the salinity climbs quickly to the initial value at the downstream edge of the mixed zone. The conductivity response of this idealized reservoir depends upon the relative magnitudes of the changes in these three parameters. In the steam zone, it is low compared to initial conditions, since the combined effects of low water saturation and low salinity outweigh the effects of increased temperature. Approaching the steam front from within the steam zone, one can see from the schematic that conductivity increases primarily due to an increase in water saturation. In the mixed zone, conductivity is dominated by the increase in salinity in the downstream direction, and increases accordingly. Although temperature decreases, it has comparatively little effect, due to the overwhelming salinity change. This situation is representative of the actual conditions in the sand during the first experiment, near the injection point, and early in time. One can see from the data in Figure 2.5 that by the time steam reached the first thermocouple at 2500 s, conductivity trace c>i had decreased to one hundredth its initial value. Thus a resistive steam zone was develop• ing at this time. Ahead of the steam front, even though temperature was decreasing with depth, conductivity increased with depth, as shown between 3 cm and 16 cm on the t = 2580 s time slice of Figure 2.6. This region represents the mixed zone. The undisturbed zone is seen between 16 cm and 27 cm, where conductivity remained at the initial value.
At t2 in Figure 2.14a, a later picture of the idealized reservoir is shown. By this time, the steam zone has expanded outwards. It has pushed ahead of it the mixed zone, which has also expanded and has pushed the undisturbed zone even farther downstream. The same physical processes that occurred at ti are still occurring: the steam zone expands slowly outwards, replacing most of the liquid in the pores with steam vapour, steam vapour moves rapidly to the steam front, where it condenses; injected steam liquid moves through
23 the steam zone, passes the steam front and enters the mixed zone; and the steam condensate moves ahead of the steam front and mixes with the original pore fluid. Looking at X2 in Figure 2.14b, temperature remains unchanged in the steam zone, and again falls through the mixed zone to the original value. Water saturation remains at a small but constant value throughout most of the steam zone, and begins to climb to 100 percent only very near the steam front. Salinity is unchanged from the value in the earlier steam zone, and the liquid water in this region is mostly distilled. An important change should now occur in the mixed zone: a small region should develop immediately ahead of the steam front where salinity changes very little. This occurs since the continual condensation of distilled water has flushed all of the salt away from the steam front. Farther ahead, salinity starts to climb to the initial value.
Aside from its expanded size, the steam zone in this schematic appears very similar to the early-time one, with temperature, salinity, and water saturation profiles that are nearly identical to their earlier versions. Accordingly, the conductivity in the steam zone is predicted to remain unchanged from the earlier scenario. In the experiment, evidence of this constant steam-zone conductivity is best seen in the third (t = 3220 s) and fourth (t = 3750 s) time slices, where conductivity in the steam zone at both times is 5 x 10-4 S/m. Looking again at the schematic, since salinity is now nearly constant immediately in front of the steam front, the effects of decreasing temperature can be seen. Conductivity therefore drops slightly in the mixed zone. Evidence of this effect can be seen in the data in the t = 3220 s slice of Figure 2.6, between 11 cm and 14 cm, and in the t = 3750 s slice between 16 cm and 19 cm. It is also clearly seen in traces 04 through Os in Figure 2.5b, between 3100 s and 4100 s. Looking once more at the schematic in Figure 2.14b, at the point where salinity starts to increase, the effects of increasing salinity again outweigh the effects of decreasing temperature, and conductivity starts to increase. Thus a short period of time after injection begins, a small conductivity "bump" appears, and travels just ahead of the steam front. This effect is seen best in the surface plot of the data (Figure 2.7b), where a
24 small conductivity ridge is shown near the bottom of the conductivity slope, running parallel to and just ahead of the steam zone in Figure 2.7a. The final time-sliceschematic , at t3 in Figure 2.14a, represents a time when much of the physical pattern has been established. Temperature and saturation profiles are very similar to the earlier ones. The salinity profile is also similar to the earlier one, except that the flat section ahead of the steam front has widened. As a result, conductivity appears much the same as in the t2 slice. In the measured data, temperature signals from T5 to Tn in Figure 2.5a show a fixed shape after approximately 3000 s. Conductivity traces (J5 to a 11 are also similar to one another. This experiment, which used distilled boiler feedwaters, was conducted to test the ability of the apparatus to detect steam-induced changes in conductivity, and was intended to act as a baseline against which other results could be compared. The sand-pack porosity, injection mass flux, and initial pore-fluid salinity were similar to those used in run 106 of Vaughan et al. (1993), while the steam quality was lower (17 percent vs. 48 percent). The reproduction of their results is viewed as a validation of the experimental set-up. Whenever salt exists in the boiler feedwaters, the interpretation of electrical conductivity data must pay careful attention to the movement of that salt. This is emphasized by the results of the second experiment. The initial conditions of this experiment were identical to those of the first one, as were the injection rate and the steam quality. A comparison of Figure 2.5a and 2.8a shows that the temperature responses of the two experiments were very similar. The conductivity responses were, however, quite different, as a result of the salt movement.
Figure 2.15a shows the predicted movements of water and gas for an idealized reservoir, for the conditions of the second experiment. The movements are identical to those in Figure 2.14a, which corresponds to the first experiment. Figure 2.15b shows the predicted temperature, water-saturation, salinity, and conductivity profiles. The temperature and water-saturation profiles are identical to those of Figure 2.14b. The salinity profile,
25 however, is substantially different than in Figure 2.14b. In this case, salinity is slightly higher in the steam zone than in the undisturbed zone. This occurs because the boiler feedwater and the original pore fluid are equal in salinity, and the steam generator vaporizes a fraction (f, the steam quality) of the feedwater, concentrating the salt in the steam liquid by a factor of l/(l-f). Since, as in the case of the first experiment, the steam liquid flows faster than the steam front, the steam-zone salinity is constant. When the steam liquid reaches the steam front, it recombines with the condensed steam vapour, producing water in the mixed zone whose salinity is very nearly that of the original pore fluid. Thus a drop in the salinity occurs at the steam front, from the steam zone to the mixed zone, which is very nearly equal in salinity to the water in the undisturbed zone.
Conductivity in such a system is predicted to be constant throughout much of the steam zone, as shown in the ti schematic in Figure 2.15b. This response is observed in the data in Figure 2.8b, where all traces approach the same value at later times. Looking at the schematic, as one approaches the steam front from within the steam zone, conductivity increases as the water saturation increases. Looking at the data in the t = 2700 s time slice in Figure 2.9, this increase is observed 1 cm to 2 cm ahead of the steam front. The shift of the location of this increase to ahead of the front is not a serious disagreement with the predicted scenario. I believe it is related to a small initial air saturation, probably caused by an imperfect evacuation of the cell prior to initial saturation. (Air is stable at temperatures and pressures that would cause steam vapour to condense. Therefore an air phase can develop ahead of the steam front As a result, the water saturation can be reduced by air just ahead of the steam front, instead of by steam vapour just behind the steam front.) Ahead of the steam front, in the mixed zone, the schematic shows that conductivity decreases downstream to its initial value, due to decreasing temperature. This is clearly seen from 9 cm to 20 cm at t = 2700 s in Figure 2.9.
The second and third time-slice schematics in Figure 2.15a emphasize that the temperature, water-saturation, and salinity profiles in the vicinity of the steam front do not
26 change much with time. Hence the conductivity profile does not change much with time. This is observed in the conductivity data from the second experiment: it shows best in the last five time slices in Figure 2.9, and in the relatively constant shape seen in the surface plot of Figure 2.10b. There is a very important difference in the electrical responses of the second and third experiments, which differed only in their steam qualities: the low-quality injection resulted in a uniform conductivity everywhere in the steam zone, and this conductivity remained constant over time;wherea s in the high-quality injection, the conductivity in the steam zone changed with position and time. The key to the way in which steam quality affects the physical and electrical responses in a steam injection is how it affects the relative speeds of the steam front and the steam liquid. The steam front moves more slowly than the steam liquid in a low quality injection. It moves more quickly than the steam liquid in a high quality injection. This increase in the relative speed of the steam front in a high quality injection is caused by the increased steam quality: since more steam vapour is injected, more heat is delivered to the steam front. The reservoir is therefore heated more quickly, and the steam front advances more rapidly. At the same time, there is less steam liquid injected (since more of the feedwater is vaporized), so it moves more slowly than in a low-quality injection. The idealized high quality electrical response is explained in the schematics of Figures 2.16a and 2.16b. The steam front moves more quickly than in the low quality injection, so the steam zone is larger at ti in Figure 2.16a than it is in the schematics in Figures 2.14a or 2.15a. Two sections now exist in the steam zone - a steam-liquid section and a steam-condensate section. Liquid water in the former is predominantly injected steam liquid, which moves more slowly through the steam zone and never reaches the steam front. Liquid in the latter is a mixture of steam condensate and original pore fluid that is left behind as the steam front advances. Ahead of the steam front is the mixed zone, where steam condensate mixes with the original pore fluid. Farther downstream is the undisturbed
27 zone. At ti in Figure 2.16b, temperature in the steam zone is constant at the boiling point, and drops quickly ahead of the steam front to the initial value. Saturation, as in the previous experiments, is at a residual level in most of the steam zone, and quickly approaches 100 percent near the steam front. Salinity in the steam-liquid section of the steam zone is constant. In the steam-condensate section, salinity drops to a minimum at the steam front, where steam vapour condenses to form distilled water. Ahead of the steam front, salinity increases through the mixed zone, and reaches the initial value in the undisturbed zone. The schematic shows that at this early time, conductivity remains flat in the steam- liquid section, and climbs slightly towards the steam front in the steam-condensate zone. This is a result of saturation effects outweighing salinity effects. Temperature effects are predicted to dominate in the mixed zone, causing the conductivity to drop slightly in the downstream direction. This drop is observed in the data in the t = 1070 s slice in Figure 2.12, between 4 cm and 9 cm. Later, at t2, the steam zone and the mixed zone have expanded; so too have the steam-liquid section and the steam-condensate section. As in the scenarios for the two previous experiments, the temperature and water-saturation profiles are predicted to keep their shapes, and move with the steam front. As timeprogresses , the amount of distilled water (condensed steam vapour) on both sides of the steam front, as a fraction of the total liquid present, increases. Therefore, although salinity has the same general shape as at ti, the minimum value at the steam front decreases.
Conductivity is now predicted to show a very interesting response: it remains flat in the steam-liquid section; initially drops in the steam-condensate section as salinity effects dominate; increases just upstream of the steam front, as saturation effects dominate; and continues to increase ahead of the steam front as salinity effects again dominate. Temperature effects are essentially unseen. This predicted conductivity response is plainly evident in the data, in the last three time slices of Figure 2.12.
28 At t3, the physical picture of the reservoir, and the associated temperature and saturation profiles are predicted to be very similar to those of t2. However, the continued condensation of distilled water at the steam front continues to depress the salinity in that region. As a result, the minimum conductivity seen near the steam front continues to drop. The data display this behaviour in Figure 2.12 at 11 cm and 1630 s, 17 cm and 1880 s, and 22 cm and 2100 s. The result, a deepening conductivity "valley" that travelled just behind the steam front, can best be seen in the surface plot of Figure 2.13b. The high steam-quality results thus suggest that a unique and easily identifiable electrical signature, caused by the development of a distilled condensate bank, can be associated with the steam front. The occurrence of the conductivity minimum depends on the relative speeds of the steam front and the steam liquid: if the steam front moves more quickly, then a minimum will occur, if instead the speed of the steam liquid exceeds that of the steam front, no minimum will occur, as the injected salt will keep up with the steam front, thereby masking the dilution effects of the distilled condensate.
Numerical test of the high steam-quality interpretation
The validity of the above interpretations can be tested by numerically modelling the steam-injection process. In order to calculate the conductivity response, the temperature, salinity, and water saturation responses must first be determined. This can be accomplished by viewing the steam front as a moving boundary, and treating the regions behind and ahead of the front separately. This approach is developed below for a high quality injection, although it can be used to reproduce the results of all three experiments.
The steam injection process can be simulated, as shown in Figure 2.17, by splitting the reservoir into two parts - a liquid zone and a steam zone. The parameters in the diagram are explained below. The liquid zone consists of the mixed zones and undisturbed zones shown in Figures 2.14, 2.15, and 2.16. In it, the transport of heat, liquid water, and solute ahead of the steam front are modelled. The steam zone is also broken into two parts: a
29 steam-liquid section, where the transport of injected steam liquid and salt are modelled; and a steam-condensate section, where the movement of liquid water, as well as the progressive dilution of original pore fluid by steam condensate at the steam front, are modelled. Once the temperature, salt-concentration, and water-saturation profiles are calculated for the steam and liquid zones, the profiles are joined at the steam front, and the entire conductivity profile calculated. The liquid zone is considered in a moving reference frame attached to the steam front, travelling at the steam front velocity Vf. Both the salt transport and heat transport in this reference frame are described by advective-dispersive equations:
^ 92c 9c 9c ,,. D Vww—= —, (2.11) 9u2 9u 9t 9*T 9T 9T a Q(3 — = —, (2.12) 9u2 9u 9t where u is the distance ahead of the steam front, c is the salt concentration, T is the tem• perature, D is the ionic dispersion coefficient, and a and P control the dispersive and
advective heat fluxes. The pore-water velocity relative to the steam front, vw, is:
Vww = — - Vf Sw, (2.13) A<|>
where q is the volumetric pump rate, and S'w is the residual water saturation in the steam zone. The terms a and p* are defined as follows:
a = kT/[p $ Cp + (l-<|>) ps cj, (2.14)
p = vww p Cp <() /[p 0 Cp + (M>) ps Cs], (2.15) where kj is the water-saturated sand's thermal conductivity, p is the density of the water,
ps is the density of the sand grains, Cp is the heat capacity of the water, and Cs is the sand-
grain heat capacity. The initial salinity, Qnit, is set to Csat, the original pore-fluid salinity, and the boundary conditions are:
«0,.)-J^^U -Cu, (2.16) Vww 9u
30 c(~,t) = Qnit, (2.17) where Qnj, the salinity of water injected at the steam front, is set to a value that represents the conductivity of condensate, i.e., distilled water. The corresponding solution is given by
Kreft and Zuber, (1978):
(2.18) + Wj("-Vwwtf Vin/TCDtT \ 4D4Dtt
The initial temperature, Tinjt, is set to room temperature. Thermal boundary conditions are:
T(0,t) = Tinj, (2.19)
l(oo,t) = Tinit, (2.20) where Tjnj is set at the boiling temperature. The solution is (Ogata and Banks, 1961):
y "J"* 4erfM) + lexp(HerfM| . (2.21) T^j-Tinit 2 l2Vatl 2 ^a/ l2Vat/
Thus the liquid-zone salinity and temperature distributions can be calculated analytically. In the steam zone, temperature is fixed at that of the injected steam. The residual steam-zone water saturation is determined experimentally by measuring the volumetric difference between the total outflow from the cell and the total inflow into the boiler, at the time when steam broke through the end of the cell. Assuming that the initial water saturation in the cell before the experiment is 100 percent, the volumetric difference, as a
fraction of the total pore volume of the cell, gives the average steam saturation, Ssteam. and
S'w = 1.0 - Ssteam- The saturation distribution close to the steam front is then estimated using the method of Menegus and Udell (1985). An approximation to the salt-concentration profile can be obtained by splitting the steam zone into two parts, as shown in Figure 2.17b. One part looks downstream from the injection port, and in it, salt transport in the steam-liquid section is modelled. Salt transport in original pore fluid is modelled in the
31 other part, which looks upstream from the steam front. This original pore fluid has been progressively diluted by steam condensate, and has been left behind in the steam- condensate zone. Looking downstream from the injection port, the steam-liquid section is treated in a fixed reference frame, and the initial pore-fluid salinity throughout the section is set to zero.
The injection salinity is set to Q, / (1-f), where f is the steam quality, and C0 is the boiler-
feedwater salinity. The steam-liquid speed is set as vi = q(l-f) / (A <|> S'w). Salt transport in this situation has an analytical solution of the form of equation (2.18). Looking upstream from the steam front, the steam-condensate section, like the liquid section with which it shares the steam front as a boundary, is treated using a moving
reference frame attached to the steam front. The initial concentration is set to Csat, and the
pore-water velocity, v2, directed backwards from the front towards the injection port, is the difference between the steam-front speed and vi. The salinity boundary condition at the front, at any time, is set equal to the solution of equation (2.18) at u = 0. Due to the time- varying boundary concentration, this problem does not have an analytical solution, and is therefore solved using a 1-D finite-difference calculation. The salinity in the steam zone is, to a first approximation, the sum of the steam-liquid and steam-condensate solutions, over the region between the injection port and the steam front The liquid- and steam-zone solutions are then combined to obtain profiles of salin• ity, temperature, and water saturation as functions of time and distance along the cell. These profiles are then used with equations (2.1), (2.5), and (2.6), and the geometry of the cell electrodes, to produce predicted conductivity curves.
Table 2.2 shows the values used for the numerical modelling of the third experiment. The arrival times of the steam front were chosen at each thermocouple as the point where the temperature became constant with time. A least-squares fit of the arrival- times-versus-distance was used to obtain the front velocity. The theoretical results are compared to all of the data in Figure 2.18, and to selected time slices in Figure 2.19.
32 Modelled curves have been offset to the right by 250 s in Figure 2.18 to account for an initial period during which the steam heated the top plate of the cell before advancing into the sand. The results show good agreement with the laboratory data: the modelled conduc• tivity averages in Figure 2.18 reach a minimum, and then climb to a stable equilibrium value. The match is not as good at the top of the cell, but this is to be expected, as the flow regime close to the inlet is unlikely to be 1-D. The modelled time slices in Figure 2.19 also show the deepening conductivity valley seen in the data.
Table 2.2. Input parameters used in the numerical simulation of the third experiment
A 0.0152 m2
0.33 4.0 W/m/K kT
P 998 kg/m3 Ps 2650 kg/m3 4220 J/kg/K cP 2000 J/kg/K Cs
7 D 2.7 x 10- m2/s
q 15.9 ml/min f 0.65
Vf 2.0 x 10^ m/s
Sw (steam zone; minimum) 0.14
Qnj. (water zone) 6.0 x 105 mol/L NaCl
Csat 0.01 mol/L NaCl
C0 0.01 mol/L NaCl
This numerical technique was used to test whether the characteristic electrical
33 signature in the third experiment was caused by the separation of the steam zone into two sections - one containing steam liquid and one containing steam condensate. The good agreement between the measured and modelled results can be viewed as a confirmation of the separation.
The modelling approach is a vastly simplified representation of the steam-injection process. Its chief limitation is that it does not allow for heat losses that affect the propaga• tion of the steam front. The steam-front speed is calculated as an average over the whole experiment; as such it does not account for the relatively slow progress of the front at the beginning of the experiment. Therefore the model overemphasizes the separation of dis• tilled condensate and saline steam liquid in the early part of the injection, thereby underes• timating the conductivity. This error cannot be completely corrected by shifting the modelled results in time. The technique of splitting the ion transport in the steam zone into two parts also leads to ionic dispersion errors, since the calculation in the steam-liquid section is unaware of ions present due to the calculation in the steam-condensate section. This results in an overestimation of the steam-zone ionic gradients, and a resulting overes- timation of ionic dispersion effects. Nevertheless, it is a useful technique for explaining ob• served laboratory results.
Summary Steam injection in these experiments, using clean, water-saturated sands, resulted in a net decrease in conductivity. This is in direct contrast to the increased conductivities seen in field experiments (Ranganayaki et al., 1990; Ramirez et al., 1993). The difference may be due to the effects, in the field, of clay and nonconducting fluids such as oil. Clay is known to both increase the effects of temperature, and decrease the effects of changes in water saturation (Waxman and Thomas, 1974), thereby strongly increasing the conductivity of a steam zone. Steam will also preferentially penetrate the most permeable parts of a reservoir, leaving clay lenses with high water saturations, and correspondingly
34 high conductivities. Therefore the resistive effects of steam injection may be overem• phasized in these clean sand laboratory displacements. With this in mind, a logical next step would be to investigate the effects of clay. This leads me to chapter 3.
35 100 ~i I— !
.001 .01 .1 1 10
Concentration (mol/L NaCl)
Fig. 2.1. Electrical conductivity as a function of sodium chloride concentration. Data shown as solid circles are from Lide (1990-1991); those shown as open triangles are from Carrnichael (1989).
36 150 -1—1—'—1—* ' J — * | i i 1 1 O O E 125 0 O a O
V i 100 5 > O O o | O IT T> 75 - * |E-""J c A A A o A O ,..| • 1 50 CO O | o j A \_ O • • • -*—' p n 0 o 25 o • 0) A* ..." " HI 0 50 100 150 200 250 300 350 400
Temperature (°C)
Fig. 2.2. The effect of temperature variations on the electrical conductivity of sodium chloride solutions. Data are from Ucok, (1979). Concentrations are three percent by mass NaCl (squares), 10 percent (triangles), and 20 percent (circles).
37 Preheater Steam Generator
, - ~ .... 10 Volts ••>;*-:-;-:-;;/-:-&y 8 Temperatures > - - — I * -y.-y.
y^y/yWyW:5 y-:y:y:y::
Voltmeter Conductivities
Fig. 2.3. Laboratory apparatus used to measure the electrical conductivity of un• consolidated material undergoing steam injection.
38 Fig. 2.4. Measurement locations inside the conductivity cell. Temperatures are point measurements made along the axis of the cell, while conductivity values are average measurements made between neighbouring thermocouples.
39 20 0 1000 2000 3000 4000 5000 Time (s) b.
0 1000 2000 3000 4000 5000 Time (s)
Fig. 2.5. Temperature (a) and electrical conductivity (b) distributions resulting from the injection of 17 percent-quality steam, boiled from distilled water, into sand initially saturated with 0.01 M NaCl. Curve labelling corresponds to Figure 2.4.
40 ^ Steam Ft ont t = 2580 s
E io-'- E 55 e/>
o 3 10" o
5 10 15 20 25 30 10 15 20 25 30
Depth (cm) Depth (cm)
Steam Front Steam Front
— 10" E E en >. 5 10"
O o lO"4 O O
10" 11 11 I • 10 15 20 25 30 0 5 10 15 20 25 30
Depth (cm) Depth (cm)
Steam Front Steam Front 10"
E E 0) en
10'
O O O O 10'
10' 10 15 20 25 30 0 5 10 15 20 25 30
Depth (cm) Depth (cm)
Fig. 2.6. Conductivity as a function of position at six different times during the first experiment. Each point represents an average conductivity, measured from 1.27 cm above the plotted position to 1.27 cm below.
41 3000
Time (s) 4000
|TTTTriTny7TrfyT^ i f |- r r i"r|f T"TT-| i i I r 10 20 30 40 50 60 70 80 90 Temperature (°C)
b.
1000 2000 3000
Time (s) 4000
TTrt rn-.M,,-,-,; J -5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 Log [Conductivity (S/m)]
Fig. 2.7. Temperature (a) and electrical conductivity (b) distributions from the first experiment, shown as functions of depth and time. The viewing angle is identical in both plots.
42 0 1000 2000 3000 4000 5000 Time (s)
Fig. 2.8. Temperature (a) and electrical conductivity (b) distributions from the second experiment. The sand was initially saturated with 0.01 M NaCl, and was flushed with 17 percent-quality steam boiled from 0.01 M NaCl.
43 Steam Front t = 2700 s
E co
.01
oo
10 15 20 25 30
Depth (cm)
^ Steam Front Steam Front
E
o o
.001 5 10 15 20 25 30 1 0 1 5 20 25 3 0
Depth (cm) Depth (cm)
Steam Front Steam Front t = 4410 6 J:
E CO
XI c oo
10 15 20 25 30 10 15 20 25 30
Depth (cm) Depth (cm)
Fig. 2.9. Conductivity as a function of position at six different times during the second experiment.
44 10 20 30 40 50 60 70 80 90 TEMPERATURE (°C)
yfffrps^^ i j | rT.ri ! ] -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 LOG [CONDUCTIVITY (S/M)]
Fig. 2.10. Temperature (a) and electrical conductivity (b) distributions from the second experiment, shown as functions of depth and time. The viewing angle for both plots is identical to that of Figure 2.7.
45 a.
500 1000 1500 2000 Time (s)
Fig. 2.11. Temperature (a) and electrical conductivity, (b) distributions from the third experiment. The sand was initially saturated with 0.01 M NaCl, and was flushed with 62 percent-quality steam boiled from 0.01 M NaCl.
46 Steam Front
.01
•D .001-
10 15 20 25 30 5 10 15 20 25 30 Depth (cm) Depth (cm)
Steam Front Steam Front , = 1630 8
E
o o
10 15 2 0 3 0 0 5 10 15 20 25 30
Depth (cm) Depth (cm)
Steam Front
.01
.001
.0001 5 10 15 20 25 30 10 15 20 25 30
Depth (cm) Depth (cm)
Fig. 2.12. Conductivity as a function of position at six different times during the third experiment.
47 1000 1500 TIME (S) 2000
10 20 30 40 SO 60 70 80 90 TEMPERATURE (°C)
-3.4 -3.2 -3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 LOG [CONDUCTIVITY(S/M)]
Fig. 2.13. Temperature (a) and electrical conductivity (b) distributions from the third experiment, shown as functions of depth and time. The viewing angle for the temperature is the same as in Figure 2.10a. The angle in (b) has been changed to show the development of a conductivity valley.
48 Fig. 2.14. Schematics of (a) affected regions in a steam-flooded reservoir, and (b) the
associated changes in water saturation (Sw), temperature (T), salinity (c), and conductivity (a). These schematics are specific for the injection of low quality steam, which was boiled from distilled water, into a saline-water- saturated reservoir a. b.
Fig. 2.15. Schematics of (a) affected regions in a steam-flooded reservoir, and (b) the
associated changes in water saturation (Sw), temperature (T), salinity (c), and conductivity (o). These schematics are specific for the injection of low quality steam, which was boiled from saline water, into a saline-water-saturated reservoir Fig. 2.16. Schematics of (a) affected regions in a steam-flooded reservoir, and (b) the
associated changes in water saturation (Sw), temperature (T), salinity (c), and conductivity (o). These schematics are specific for the injection of high quality steam, which was boiled from saline water, into a saline-water-saturated reservoir (a) Steam Zone Liquid Zone
"inj r • Cjnit - ^sat
Tinj > f d.H2 Tinit = 20 °C
Vf u = 0
(b)
Steam-Liquid Section / / / , Cinj = C0/(1-f)^ /= ^\/////^ = V '
V1 = q(1-f)/(A<|>S'w) 22222
Vf
ISteam-Cbridehsate Section! Cinj = C(u = 0, t) Cjnit : 1 = tinji -4—! V2 = Vf - v-|
Fig. 2.17. A simplified approach to modelling the electrical conductivity response seen in the laboratory experiments, (a) Solutions for water- saturation, temperature, and salt-concentration profiles are calculated separately for both the steam zone and the liquid zone. The input pa• rameters for the modelling include the steam-front speed, Vf; the total mass injection rate, which is the product of the room-temperature density of water, p, and the volumetric pump rate, q; the salinities of
the initial saturating fluid, Csat, and of the steam generator feedwater,
C0; the initial temperature, T^; the injected steam temperature, T^; and f, the steam quality. The salinity of distilled water (d. H2O) is an equivalent NaCl salinity that has the same electrical conductivity as distilled water, (b) The steam zone is split into two parts, to model the transport of salt both in the steam liquid, and in original pore fluid left behind in the steam zone. Shading in the diagram reveals the regions of Figure 2.16 that are modelled in each part of the process.
52 500 1000 1500 2000 2500 Time (s)
Fig. 2.18. A comparison of the data from the third experiment and the corresponding model results. Conductivities are shown as functions of time, for the measurement locations of Figure 2.4. Each window contains two sets of experimental data (solid lines) and model predictions (dashed lines). The upper window shows conductivity traces Oi and 02, the lowest one shows 09 and O"io, and 03 through 0$ are shown in between.
53 10 -2
? 10 -3
10' -2
10 -3 p n 10 -2
-3
o n 10 o -2 Id 10 o •r-H 10 -3 o CD 10 -2
10 -3 0 0.05 0.1 0.15 .0.2 0.25 0.3 Depth in Cell (m)
Fig. 2.19. A comparison of measured data (crosses) and corresponding model results (solid lines) for the third experiment, showing conductivities as functions of position, at specific times.
54 CHAPTER 3:
THE EFFECT OF CLAY CONTENT ON THE ELECTRICAL CONDUCTIVITY OF STEAM-FLOODED RESERVOIRS
Introduction The electrical conductivity of a steam-flooded clean sand, as shown in chapter 2, varies in a predictable fashion as a result of steam-induced changes in temperature, salinity, and water saturation. Accordingly, electrical methods can be used to monitor and thereby optimize the use of steam injection for enhanced-oil-recovery operations, groundwater remediation projects, or steam extraction for geothermal power generation. However, many oil reservoirs, near-surface soils, and geothermal regions do not consist solely of clean sand; they contain appreciable amounts of clay, which can have a large effect on conductivity. In fact, while in chapter 2 the conductivities of clean sand steam zones were measured and found to be resistive relative to initial conditions, field experiments in clay- bearing regions have delineated conductive steam zones (Ranganayaki et al., 1992; Ramirez et al., 1993). Thus it is imperative, for electrical monitoring purposes, to understand how steam injection affects the conductivity of clay-bearing sands. This chapter concentrates on two issues: how the presence of clay alters the steam-induced electrical response of clean sand, and what parameters determine whether a clay-bearing steam zone is resistive or conductive relative to initial conditions. This is done by comparing, both experimentally and numerically, the electrical responses of sand and clay.
As noted in the previous chapter, the electrical conductivity of clay-free porous geologic material depends primarily on the amount and conductivity of the contained water. This is the basis for Archies law (Archie, 1942):
m ob = <|> Swaw , (3.1)
where oD is the bulk conductivity of the material, § is the porosity, Sw is the water
55 saturation, and aw is the conductivity of the water. The constant m is referred to as the cementation exponent, and n is the saturation exponent. Steam injection can affect
conductivity by changing both Sw and aw, while changes in $ are minor and are comparatively unimportant. Laboratory measurements of the effect of steam injection on electrical conductivity have, to date, used clean, initially water-saturated sands (Vaughan et al., 1993; Butler and Knight, 1995). To mimic field scenarios, the injected steam in these studies was a mixture of steam vapour and hot unboiled water (steam liquid). In the study by Vaughan et al. (1993), where distilled water was used as the steam liquid, the steam zone was found to be approximately 25 times as resistive as initial conditions. In the study by Butler and Knight (1995), boiler feedwaters equal in salinity to the initial pore water were used. While the shape of the conductivity response depended on the steam quality, the resulting steam zone was five times as resistive as initial conditions. In these two laboratory studies, salinity and water-saturation decreases, which tend to decrease conductivity, outweighed the conductivity increases due to temperature, thereby resulting in resistive steam zones. In distinct contrast to these laboratory results, there are now a number of field studies which suggest that steam zones, as a result of the presence of clay, are conductive (Mansure et al., 1990; Newmark and Wilt, 1992; Ramirez et al., 1993). They suggest that clay accentuates the temperature effects, which then outweigh the effects of decreases in salinity and water saturation.
The electrical conductivity of clay
The manner in which clay affects the conductivity of geologic materials has been studied by, among others, Patnode and Wyllie (1950), Winsauer and McCardell (1953), Hill and Milburn (1956), Waxman and Smits (1968), Clavier et al. (1984), and Sen and Goode (1992). For the purposes of this study, the effects of clay on the bulk conductivity can be described using the Waxman and Smits equation (Waxman and Smits, 1968):
56 m ab =
This equation treats conduction as the sum of two interacting parallel mechanisms; the first term in the brackets represents bulk-pore-fluid conduction, while the second represents
clay-surface conduction. The cation concentration, Qv, a constant for a particular rock, can range from zero to approximately 1.0 meq/cm3. It describes the number of cations, which are in addition to the ions in the saline pore fluid, that are loosely attached to the negatively charged clay surface sites. These cations are free to move along the surface and can therefore conduct, with an equivalent electrical conductance, B, which in turn depends on
aw. Thus the magnitude of the clay conduction depends on the cation density, which is related to clay content, and on the ease with which these cations can move. As in clean sands, conduction in clay is affected by steam-induced changes in salinity, water saturation, and temperature. The salinity behaviour is illustrated in Figure
3.1, by comparing the relationship between o*b and crw both for water-saturated clay- bearing sands and for water-saturated clean sands. In all cases, the clay-sand conductivity, represented by the dashed line, is greater than that of the clean sand, represented by the solid line. The difference represents the clay-surface conduction. Small at very low values
of Gw, it increases with aw to a maximum value, and then remains constant with any
further increases in aw. Waxman and Smits (1968) incorporated this behaviour into B. They reasoned that conduction can occur through the migration of a single cation in an electric field from one fixed exchange site to another, or through the movement of a cation from the first site into the electrolyte followed by the movement of another ion from the electrolyte into the second site. The efficiency of the second method would be greatly increased by increases in salinity, up to some relatively high concentration, above which further salinity increases would make little difference in cation mobility. Waxman and
Smits' (1968) salinity correction is
B = B0 (l.O - 0.83 exp (^-)), (3.3)
57 where B0 is the maximum, high salinity value of B, and aw is measured at 25 °C. BQ was determined to be 3.83 (S/m) / (meq/cm3). In an oil reservoir, salinity can vary during a steam flood from approximately 3.1 mol/L (Worthington et al., 1990) to less than 0.001 mol/L in areas containing condensed steam (distilled water). Waxman and Smits (1968) estimated the boundary between the linear and nonlinear regions of Figure 3.1 to be approximately 0.3 mol/L. Thus in a particular steam-flood scenario, if salinity varies only in the region above 0.3 mol/L, the magnitude of the conductivity changes would be no different in clay-bearing sand than in clean sand. Below 0.3 mol/L, however, conductivity changes would be larger in clay-bearing sand than in clean sand.
Clay conduction is not as strongly affected by water saturation as is conduction through the bulk pore fluid. This is reflected in the form of the clay term: although the clay cations actually remain clustered near the clay surfaces, and thus are relatively unaffected
by changes in water saturation, Qv is expressed as an average concentration over the entire
pore volume. Accordingly, Sw appears in the denominator of the clay term, effectively keeping the number of available clay cations constant regardless of saturation. Since the
saturation exponent applied to the clay term is reduced from n to n-1, the effect of Sw changes on the conductivity of very clay-rich sand is significantly less than in clean sand. Temperature affects the equivalent conductance of the clay cations (Waxman and Thomas, 1974; Sen and Goode, 1992). As temperature increases from 20 to 100 degrees Celsius, B increases approximately by a factor of four, thereby increasing the magnitude of the clay conduction by a factor of four. The net effect on bulk conductivity depends upon the relative magnitudes of the pore-fluid conductivity and the clay conductivity. Mansure et al. (1990) gave an approximate temperature correction, which fits the data of Waxman and Thomas (1974) to within 20 percent:
B = BQ (0.04 T), (3.4) where T is in degrees Celsius. I suggest that there is a fourth mechanism by which clay alters the electrical
58 response: the presence of clay will presumably lessen the water-saturation decrease which occurs as steam advances through the sand. This should lead to higher steam-zone residual water saturations in clay-bearing sands than in clean sands, and may play an important role in the electrical response of clay.
This experimental study was designed to investigate how steam injection affects the electrical response of a clay-bearing region. In particular, the effects of temperature, water saturation, salinity, and residual water saturation were compared, to determine which of these four parameters dominate the response, and when they dominate it. Steam was injected into sand and clay, and the electrical responses of the two measured and compared. The experimental results showed that a clay-bearing steam zone can be resistive compared with its initial state, but conductive compared with clean sand regions subjected to the same steam-flood scenario. Numerical investigation of the results showed that a clay-induced increase in the steam-zone residual water saturation is a significant factor in determining the steam-zone conductivity. The experimental results were confined to low clay contents and low salinities. They were then extended numerically to higher clay contents and higher salinities, again to determine the relative contributions of the four parameters to the conductivity of the steam zone. The numerical analysis illustrated that at higher clay contents, steam zones do become conductive relative to initial conditions, as a result of accentuated temperature effects and significantly increased steam-zone residual water saturations. However, in most high quality injections, steam zones initially become resistive, regardless of whether they eventually become conductive. Steam zones that are always conductive relative to initial conditions only occur in a low steam-quality injection.
Experimental Apparatus And Procedures
The laboratory apparatus used in this experiment was described in chapter 2, and illustrated in Figure 2.3. As discussed in chapter 2, the apparatus measures the temperature and conductivity distributions in the cell, as a function of timedurin g a steam flood.
59 The focus of this study is a comparison of the steam-flood responses of clay and clean sand. Clean Ottawa sand and two clay regions were placed in the cell, as shown in Figure 3.2. The lower clay region, composed of 90 percent Ottawa sand and 10 percent kaolinite clay, extended from just above thermocouple six (T6 in Figure 3.2) to thermocouple seven (T7). The upper region, pure kaolinite, was a 7 cm by 4 cm lens, extending from just above thermocouple three to thermocouple four. This cell measures the average conductivities between neighbouring thermocouple pairs. Therefore, given the distribution of sand and clay as shown in Figure 3.2, 03 and 0*6 will be most strongly affected by clay conduction; 02 and 05 may show minor clay effects; and 01,04, 07, as, 09, and aio will show only the response of clean sand. In order to quantify the effect of temperature on the conductivity of the sand and clay, the conductivities of the different layers in the cell were measured as functions of temperature alone. First, the cell was saturated with a solution of a particular salinity, and the conductivity distribution measured at room temperature. Next, the external heaters were used to raise the internal temperature to 25 °C. Once the entire inside of the cell reached this value, conductivity was measured again. The heaters were then used to raise the internal temperature in increments of 10 °C. At each step, temperature was allowed to come to equilibrium, and conductivity was then measured. This process was repeated up to an internal temperature of 75 °C. In order to quantify the effect of salinity, the above procedure was performed twice, using pore-fluid salinities of 0.01 M NaCl and 0.05 M NaCl. Therefore the effect of salinity variations within this range can be obtained from a comparison of the two data sets.
It is not possible to measure the effect of saturation on the conductivity of the individual clay and sand regions in the cell. An average saturation over the entire cell can be measured, but saturation will vary with distance in the cell. Equation (3.2) is therefore used to quantify the effect of saturation, assuming a saturation exponent of 2.0.
The steam-zone residual water saturations in the clay and sand regions are of
60 particular interest in this study. As mentioned above, they cannot be measured directly. However, they can be inferred from the conductivity measurements using equation (3.2), once the effects of temperature and salinity are removed. I am most interested in whether the residual saturations in the clay regions are greater than those of the clean sand regions. If the saturation in a clay region is inferred to be greater, then the use of equation (3.2) is checked against the data of Knoll and Knight (1994), to ensure that the saturation in the clay is, if anything, underestimated rather than overestimated. Knoll and Knight (1994) provided laboratory measurements of the effect of saturation on the conductivity of sand- clay mixtures at room temperature and pressure. The steam-injection experiment started with the evacuation of the conductivity cell. The cell was then saturated with 0.01 M NaCl, and the pump and fluid lines filled with this solution as well. When the pump, pore-fluid preheater, and steam generator were started, the flow was first diverted past the conductivity cell for approximately ten minutes, until the steam generation system reached the boiling temperature. At this point, monitoring of the temperatures and conductivities began, and ten minutes later, steam was injected into the cell. The injection and monitoring continued until steam broke through the end of the cell. Table 3.1 lists the experimental parameters for the steam flood. The injection rate into the boiler and the steam quality were chosen because they were found to produce a stable, one-dimensional steam-front advance. The salinity of both the initial pore fluid and the boiler feedwater was chosen to approximate that of a fresh-water oil reservoir.
Table 3.1. Experimental parameters corresponding to data shown in Figure 3.4.
q 4.23 ml / min boiler injection rate Co 0.01 M NaCl initial pore-fluid salinity 0.01 M NaCl boiler feedwater salinity f 0.75 steam quality
61 Experimental Results The effects of temperature on conductivity are shown in Figure 3.3: part a shows the response measured when the cell was saturated with 0.01 M NaCl, and part b shows the 0.05 M results. Each graph shows, with the open circles, the response of the sand-and- clay layer, which lies between thermocouples T6 and T7, and with closed squares, the average response of the clean sand. It can be seen from the data that, for both salinities, there is little difference between the sand response and the clay response. The steam-flood data are shown in Figure 3.4. The temperatures, measured at specific locations as functions of time, are shown in part a. They are point measurements made along the axis of the cell, at the tips of the 11 thermocouples. Each trace illustrates the data from one thermocouple. The left-hand trace, labelled Ti, corresponds to thermocouple Ti in Figure 3.2, and the right-handtrace , labelled Tn, corresponds to thermocouple Tn. The rest of the traces from thermocouples T2 to T10 are not labelled, as they follow in sequence after Ti. The temperatures, initially uniform at 25 °C, increase at each point as the steam front approaches. Arrival of the steam front at a thermocouple is marked by the point where the temperature becomes constant. This temperature, approximately 110 °C, is the boiling temperature at the cell's internal pressure, which was set by the pressure-relief valve attached to the outlet of the cell. For instance, the steam front reached thermocouple Ti at approximately 3600 s, and at Tn at 6950 s. Between 4100 s and 4500 s, the temperature of the steam increased slightly to 115 °C, and then decreased again to 110 °C by 5200 s; this was caused by minor adjustments to the pressure-relief valve.
Figure 3.4b shows the conductivity data. Again, each trace is labelled according to the sketch in Figure 3.2 (traces as and 09 are not labelled due to a lack of space, but they follow in sequence after 07). Most of the traces start at approximately 0.025 S/m, except 03, which starts at 0.036 S/m. The responses can be separated into two categories: those from clean sand and those from clay. Trace Oi shows a typical clean sand response. It begins at 0.026 S/m, remains
62 constant until 1200 s, and then gradually increases as temperatures Ti and T2 increase. It continues to increase, with increasing temperature, until 3200 s, when it reaches approximately 0.042 S/m. From the temperature data, it can be seen that steam will soon arrive at the top of this conductivity-measurement region. Conductivity then decreases rapidly to 0.006 S/m at 3900 s, which, as shown in Figure 3.4a, is the time when steam reaches T2, the thermocouple at the bottom of o{s measurement region. Following this, c>i continues to decrease at a more gradual pace, reaching a minimum conductivity of 0.0026 S/m at 4800 s. It then increases gradually again, and levels off at 0.004 S/m at approximately 6000 s. This pattern is repeated by all of the clean sand regions. For example, 04 increases gradually as temperatures increase at T4 and Ts> and reaches a maximum of 0.05 S/m at 4400 s, which is just before the arrival of steam at T4. Next, it drops rapidly to 0.003 S/m at 4950 s, which is when steam reaches T5, and then decreases more gradually, to 0.0016 S/m at 5700 s. Finally, 04 increases slowly for the remainder of the experiment. Traces C7, a%, Go, and O"io also follow the pattern, but the experiment was terminated while they were still decreasing. The pattern slowly evolves, as the minimum conductivity obtained decreases slowly with increasing depth in the sand. The 05 minimum is slightly high, but this region contains a small amount of clay at its bottom edge. The clean sand regions also tend towards similar final conductivities, near 0.004 S/m. The clay-sand responses are shown by 03 and Os- Trace CJ3 starts at 0.036 S/m, and remains constant until 1800 s. Like the clean sand conductivities, it then slowly increases with increasing temperature, reaching a maximum of 0.06 S/m at 4000 s, just before the arrival of steam at T3, at the top of the measurement region. It then decreases rapidly to 0.01 S/m at 4700 s - the point when steam reaches T3, at the bottom of the measurement region. Next, it decreases more gradually, dropping to 0.0075 S/m by 5200 s as steam continues to move downwards. Conductivity trace 06 behaves in a similar fashion: it increases gradually until 4100 s, slightly before the arrival of steam at T6; decreases rapidly until 5700 s, when steam reaches T7; decreases more slowly to 0.008
63 S/m at 61 OX) s, and then increases slightly until the end of the experiment. The major difference between these two responses and the clean sand responses is that the clay regions have more conductive steam zones. Figure 3.4b displays the conductivity data as values at specific locations, as functions of time. An alternate method is to view them as functions of position, at specific times. Six such "snap-shots" are shown in Figure 3.5. The first snap-shot, in the upper left corner, corresponds to the starting condition, and shows conductivity as a function of depth in the cell. The ten data correspond to the ten measurement regions of Figure 3.2, and are plotted at the midpoints between thermocouple locations. In this first graph, the initial conductivities are nearly equivalent at approximately 0.025 S/m, except for the third datum from the left, 03, which is slightly more conductive and represents the upper clay lens. The remaining five snap-shots correspond to the times when the steam front reached the first, third, fifth, seventh, and ninth thermocouples. In the second snap-shot, at 3585 s, the steam front is at the first thermocouple, at the top of Oi's measurement region. Conductivity Oi has begun to decrease, while 02 and 03, at the next two locations, have increased. Deeper than 10 cm into the sand, the conductivities remain close to their original values. In the third snap-shot, the steam front has reached the top of the clay lens. Conductivities in the steam zone (those data to the left of the arrow) have decreased considerably. Conductivity ahead of the steam front (to the right of the arrow) increases with depth, reaching a maximum 4.5 cm ahead of the front. In the next graph, at 4950 s, the steam front has reached thermocouple T5. In the steam zone, the anomalously high conductivity of the clay lens (03, third datum from the left) is apparent, and is situated between two more resistive sand regions. Ahead of the steam front, a similar profile exists as did in the earlier graph, with conductivity reaching a maximum 4.5 cm ahead of the front, then decreasing farther into the sand. This panel shows the first indication of a conductivity minimum forming in the steam zone, at a depth of 6.5 cm, and a magnitude of 0.002 S/m. The last two snap-shots shows that this minimum moves with the steam front,
64 and decreases in magnitude over time. At 5680 s, the minimum is 0.0015 S/m at 11.5 cm, and at 6380 s it is 0.00095 S/m at 19 cm. Thus the steam front is always located downstream of the conductivity minimum, and upstream of the conductivity maximum. The last snap-shot also clearly shows that the two clay regions , at 8.5 cm and 16.5 cm, have conductivities in the steam zone that are much' higher than in the surrounding sands. A third method of displaying the data is as three-dimensional surface plots, which display spatial and temporal variations simultaneously, as in Figure 3.6. Part a illustrates how the temperature profile in the cell changed throughout the experiment. Undisturbed temperatures are shown by the flat triangular region, at 25 °C, at the left of the diagram. The steam zone is represented by the flat triangle of elevated temperatures at the right of the diagram. These data can then be compared to Figure 3.6b, which shows how the conductivity profile in the cell changed throughout the experimenL The flat region at the left of the diagram represents undisturbed conditions. The steep slope on the surface, just to the right of the centre of the plot, shows a drop in conductivity that moves through the cell. This drop corresponds to the temperature increase shown in Figure 3.6a. The section identified in Figure 3.6a as the steam zone shows in Figure 3.6b as being substantially less conductive than the initial conditions. Also evident in part b are the anomalously conductive clay-rich steam zones, which appear as two triangular ridges of elevated steam-zone conductivities that parallel the time axis, at 8.5 cm and 16.5 cm.
The average residual water saturation in the steam zone, Swres, was determined to be 0.14 +/- 0.07. This was estimated by measuring the volumetric difference between the total outflow from the cell and the total inflow into the boiler, at the time when steam broke through the end of the cell. The initial water saturation in the cell before the experiment was assumed to be 100 percent. The volumetric difference, as a fraction of the total pore volume
an of the cell, gives the average steam saturation, Ssteam» d Swres = 1.0 - Ssteam-
65 Discussion
As a result of steam injection, the clay regions in this experiment became resistive relative to initial conditions. To determine why this occurred in this case, and when a clay -bearing steam zone will be conductive relative to initial conditions, one must know how the presence of clay alters the dependence of conductivity on temperature, salinity, and water saturation. As well, one must understand how residual steam-zone water saturation is affected by clay content. Clay-induced alterations of these relationships can be determined by comparing the conductivity responses of the clay to those of the sand. To fully understand the responses, six requirements must be met. The first is that the effect of temperature on the conductivity of both sand and clay must be known. This effect was measured: as shown in Figure 3.3, temperature does not affect the clay much differently than the sand. This is undoubtedly due to the fact that the clay content is small, and so has little effect on the temperature response. The second requirement is that the temperature changes that occurred must be known. These also were measured for both sand and clay. The third requirement is that the effect of salinity on the conductivity of the sand and clay must be known. This was measured in conjunction with the temperature effects. As the comparison in Figure 3.7 indicates, there is little difference between the measured conductivities of the sand and clay and the conductivities calculated using equation (3.2). As well, the calculated curves indicate that conductivities of the sand and clay would not be significantly different above 0.001 M NaCl. The fourth requirement is that one knows how salinity changed in the sand and clay during the experiment. The numerical model developed in chapter 2 is used to evaluate the salinity changes. By matching the modelled conductivity data to the measured data from the clean sand regions, salinity changes in the sand can be inferred. The same salinity changes are then assumed to have occurred in the clay regions. The fifth requirement is that the effect of saturation on the conductivity of sand and clay be known. This effect is calculated for the sand using equation (3.1), and for the clay using equation
66 (3.2). The final requirement is that the residual steam-zone water saturation be known in the sand and clay. The value of Swres in the sand and in the clay is also inferred using the numerical modelling process, by matching the modelled and measured data. The difference in Swres between sand and clay is expected to be an important electrical effect. Since the conductivity responses of the clay are to be compared to those of the sand, it is worthwhile summarizing the clean sand conductivity response. In Figure 3.8a are shown some of the data, from chapter 2, collected during a steam flood of a clean sand. The steam quality in this experiment was 62 percent. The sand was initially fully saturated with 0.01 M NaCl, and was injected with steam produced from water of the same salinity. The conductivity data are plotted against depth in the cell for three times during the flood. Figure 3.8b is a schematic of the zones which develop during the steam-flood process. Figure 3.8c illustrates the corresponding changes in temperature, saturation, salinity and conductivity. The steam front, labelled on all figures, is defined as the point where steam vapour condenses. It forms the leading edge of the steam zone. Consider the first time, labelled as ti in Figure 3.8. In the experimental data, the steam front, as indicated by the temperature data, is at a depth of 2 cm. Conductivity decreases ahead of the steam front towards the undisturbed section deeper in the cell. Figure 3.8b illustrates how a high quality steam flood progresses through clean sand. At time ti, a small steam zone has expanded outwards a short distance from the injection point. The zone contains both gas and liquid. The liquid, mostly injected steam liquid, moves slowly through the reservoir, forming a steam-liquid section at the back of the steam zone. The gas, injected steam vapour, moves rapidly from the injection point to the steam front, where it condenses into distilled water. This forms a section at the front of the steam zone that contains a mixture of steam condensate and original pore fluid. Just in front of the steam front is a mixed zone - a fully liquid-saturated region where condensed steam vapour (distilled water) mixes with and displaces the original pore fluid. Farther ahead is an undisturbed zone, where the pore-fluid composition matches initial conditions.
67 In Figure 3.8c are shown the predicted temperature (T), water saturation (Sw), and salinity or salt concentration (c) at this early time ti. Temperature remains at the boiling point throughout the steam zone, then in the mixed zone rapidly approaches the original value. Water saturation remains at an equilibrium level throughout much of the steam zone, and then rapidly reaches 100 percent immediately upstream of the steam front. Ahead of the front, the sand is fully water saturated. Salinity in the steam-liquid section of the steam zone is constant. Although the boiler feedwater has the same salinity as the initial pore fluid in the undisturbed zone, the steam liquid is more saline than the initial pore fluid because part of the injected water is vaporized, thus increasing the salt concentration in the liquid portion. In the steam-condensate section, salinity drops to a minimum at the steam front, where steam vapour condenses to form distilled water. Ahead of the steam front, salinity again increases through the mixed zone, and reaches the initial value in the undisturbed zone.
The predicted conductivity response (a) at time ti is also shown in Figure 3.8c. Conductivity remains flat in the steam-liquid section, and climbs slightly towards the steam front in the steam-condensate zone, a result of saturation effects overwhelming salinity effects. At this early time, temperature effects dominate in the mixed zone, and the conductivity drops slightly in the downstream direction. As can be seen, referring back to
Figure 3.8a, this scenario describes the observed conductivity response.
At the next time, r.2, the experimental data present a much more complex variation with depth in the cell. This is best explained with reference to the schematics in Figures
3.8b and 3.8c. By t2, the steam zone and the mixed zone have expanded; so too have the steam-liquid and steam-condensate sections. The temperature and water-saturation profiles have the same form, and have moved with the steam front. Over time, the amount of distilled water on both sides of the steam front, as a fraction of the total liquid present, has increased. Therefore, although salinity has the same general shape as at ti, the minimum value at the steam front has decreased.
68 The corresponding conductivity response is shown in Figure 3.8c. Conductivity is predicted to remain flat in the steam-liquid section; initially drop in the steam-condensate section as salinity effects dominate; increase just before the steam front, as saturation effects dominate; and continue to increase ahead of the steam front as salinity effects again dominate. Temperature effects are essentially unseen. This conductivity response is in good agreement with what we observe in the experimental data. At t3, the physical picture of the reservoir in Figure 3.8b and the associated temperature and saturation profiles in Figure 3.8c are very similar to those at t2. However, the continued condensation of distilled water at the steam front continues to depress the salinity in that region. As a result, the conductivity seen near the steam front continues to drop, as shown at 22 cm in the t3 time slice of Figure 3.8a. We clearly see a pronounced minimum in conductivity associated with the steam front. Thus the response of clean sand to steam injection is well understood. By carefully comparing it to the clay response, the mechanisms by which clay alters that response can be determined. The sand-and-clay layer between thermocouples T6 and T7 is ideally suited for comparison: since it was subjected to the same steamflood conditions as the clean sands, it experienced the same temperature and salinity variations. The clay lens between thermocouples T3 and T4 will be neglected in this analysis, as it was initially packed dry, and became heavily fractured upon saturation.
Numerical investigation of experimental data
As noted above, the conductivities of the sand and clay in this experiment depend on temperature in a similar fashion, and are also similarly affected by salinity. Therefore any major differences in the steam-flood electrical response are presumably saturation- related. Temperature changes were measured in the cell during the experiment. To
69 determine the salinity and saturation changes that occurred, the conductivity in the clean sand must first be numerically modelled. This is done using the approach described in chapter 2. The one-dimensional simulation accounts for mass, heat, and salt transport in both an expanding steam zone, and in a water zone ahead of the steam. Archie's law is then used to calculate the conductivity distribution. By matching the measured conductivity data, we can infer the salinity and water-saturation changes that occurred during the experiment. Consider first the temperature data. To start, known parameters in the mass and heat equations are set to the experimental values: these include the speed at which the steam front advances, the volumetric flow rate into the boiler, the steam quality, and the steam- zone temperature. The thermal conductivity of the model is then adjusted to obtain a good fit to the temperature data. The measured and modelled temperature data are shown in Figure 3.9. In the experiment, a preheating interval of 3130 s is required for the top steel plate to be heated to steam temperature, before steam can move through the sand. The model does not simulate the heating; instead it produces a temperature distribution, which is closer to a step function, that would occur if no steel plate existed. The modelled data are therefore shifted in time by 3130 s. The temperatures from the deeper regions in the cell are better matched, as the effect of the steel plate decreases with distance. The steam-front speed, boiler flow rate, and steam quality are also known input parameters for the conductivity modelling. In addition, the original pore-fluid salinity and the boiler-feedwater salinity are fixed at the experimental values. The two unknowns are the sand's coefficient of ionic dispersion, D, and the steam-zone water saturation. The dispersion coefficient is a measure of how easily the distilled water condensing at the steam front mixes with the original pore fluid. In the modelling process, it controls the degree of curvature of the salinity profile, and thus to some extent the curvature of the conductivity profile, near the steam front. Therefore the appropriate value for the sand is inferred by matching this curvature. The water saturation in the steam zone is estimated by matching
70 the conductivity in the steam zone. This value is then checked to ensure it compares well to the value determined at the end of the experiment. The modelled results are compared to the measured conductivities cji, 02, 04, 07, o"g, Go, and C10 in Figure 3.10. Trace 05 was not included since it seemed to be affected by clay. Selected time slices from the measured data are superimposed on modelled time slices in Figure 3.11. The parameters used in the numerical model are summarized in Table 3.2. The modelled conductivities match well the initial increases prior to the steam front's arrival, the decreases that coincide with the passage of the steam front, and the final equilibrium value in the steam zone. It can be assumed from this match that the model correctly estimates salinity variations and the steam-zone water saturation. There are some disagreements between the measured and modelled data. First, the initial increase in measured conductivity, before the arrival of the steam front, occurs long before the modelled increase does. This is caused by the model's inability, as shown in Figure 3.9, to account for a preheating stage. Second, the large drop in conductivity occurs earlier in the measured data than in the modelled response. I suggest that this is due to a small amount of air in the sand, probably caused by an imperfect evacuation of the cell prior to initial saturation. Air is stable at temperatures and pressures that would cause steam vapour to condense. Therefore an air phase can develop ahead of the steam front, reducing the saturation at a given position before the steam front arrives. Neither of these failings of the model will affect its ability to correctly predict the equilibrium conductivity in the steam zone.
Table 3.2. Parameters used in the numerical simulation of the experiment
A 0.0152 m2 cross-sectional area of cell
pw 958 kg/m3 water density
71 Ps 2650 kg/m3 solid density
Cpw 4220 J/kg/K heat capacity of water 2000 J/kg/K heat capacity of solid a 0.025 dispersivity of system f 0.75 steam quality
5 Vf 7.4 x 10" m/s steam front speed
Sw 0.12 steam-zone water saturation
Co 0.01 M NaCl initial pore-fluid salinity Qnj 0.01 M NaCl boiler feedwater salinity Qv 0.01 meq/cm3 sand-clay cation exchange capacity
The effects of the changes in temperature, salinity, and water saturation on the conductivity of the sand-clay layer can now be calculated. Equation (3.2), in conjunction both with laboratory-confirmed temperature and salinity corrections for B, and with the experimental value of Qv, is used to calculate the conductivity of region six. Figure 3.12 compares the measured conductivity response (solid line) to the modelled response of the sand-and-clay layer (dotted line). The model matches the initial conductivity, as well as the magnitude of the temperature-related response seen near 5000 s. However, it seriously underestimates the steam-zone conductivity. The steam-zone residual saturation used in the model calculations was 0.12, the value determined for the clean sand regions. Since the effects of both temperature and salinity have been accounted for, this saturation level must be too low. To match the measured steam-zone conductivity for region six, a water saturation of 0.18 is required.
Therefore the residual water saturation in the clay-bearing part of the steam zone in this experiment was significantly greater than the saturation in the sand. It was the dominant factor responsible for the increased conductivity, relative to the clean sand, in the steam zone. The clay content in this layer was small. This resulted in a clay conduction
72 term which was small in comparison to the bulk conduction term. Whether increases in residual steam-zone water saturation become important at higher clay contents or at higher salinities remains to be determined. This is the subject of the next section.
Numerical extension of results to higher clay contents and higher salinities The clay-bearing steam zones in this experiment were resistive compared to their initial conditions. Obviously, to determine how much clay is required for a steam zone to be conductive relative to initial conditions, the clay content in the layer must be increased. Using a large amount of clay in this cell, however, presents a potentially serious safety problem: adding clay decreases the permeability of the sand, and will lead to higher internal pressures. The increased pressure, by itself, is not a problem, but the associated increase in boiling temperature is. Most of the seals in the cell are only reliable below 140 °C. Therefore I was unwilling to increase the clay content in a continuous layer. The experimental results can, however, be extended to higher clay contents and higher salinities numerically. By calculating the theoretical conductivity responses of a number of different types of reservoirs, one can determine under what circumstances a steam zone will be conductive relative to initial conditions. Specifically, one can determine whether they become conductive primarily as a result of reservoir parameters, such as increased relative importance of clay conduction, or increased residual steam-zone water saturation; or whether it is the result of the effects of an injection parameter, such as the steam quality.
To investigate the electrical responses at higher clay contents, three examples of clay-bearing materials are studied. The first is a mixture of 90 percent sand and 10 percent kaolinite, like that used in my laboratory experiment. The other two are commercial hydrocarbon-bearing reservoir rocks: Noxie sandstone, and Torpedo sandstone. The porosities, clay contents, cation concentrations, and permeabilities for these materials are given in Table 3.3.
73 Table 3.3. Reservoir parameters for media used in numerical investigation of the relationship between clay content and steam-flood conductivity response. The porosity, clay content, and permeability of the sand-clay mixture were determined in the laboratory. For the two sandstones, porosity, clay content, cation concentration, and permeability were taken from Lake (1989). The irreducible water saturations were calculated using equation (3.6).
Porosity Clay Content Qv Permeability Irreducible (meq/cm3) (m2) Water Saturation sand-clay 0.33 10% 0.01 1.7 x 10-12 0.18 mixture laolinite Noxie 0.27 5% kaolinite, 0.07 4.2 x 1013 0.26 sandstone 1% chlorite, 7% illite, as pore lining clays Torpedo 0.245 6% kaolinite, 0.25 9.4 x 10-14 0.40 sandstone 7% illite, as pore- bridging clays
The numerical modelling process requires an estimate of the residual steam-zone water saturation. Darcy's law can be used to show that the residual water saturation in a steam zone depends, among other parameters, on permeability (Vaughan et al., 1993). This approach requires a relationship between effective permeability and water saturation. This relationship is usually derived empirically for a given reservoir, and can vary significantly between reservoirs. Instead, I use a direct empirical correlation between a reservoir's permeability and its irreducible water saturation, which is the minimum obtainable residual saturation, and which does not depend on parameters such as injection rate or steam quality. The correlation was given by Timur (1968): ,1.26 where Swirr and <|> are in percent, and k is in millidarcies. This equation was used to calculate the irreducible water saturations in Table 3.3. The numerical steam-flood conductivity model was then used to determine the
74 electrical response of these example reservoirs under particular injection conditions. Using a high steam quality, as in the laboratory experiment, each of the examples was subjected to three different steam floods, using initial pore-fluid salinities of 0.01, 0.1, and 1.0 mol/L NaCl. Since steam zones can always be made conductive if the boiler feedwaters are more saline than the original pore fluid, a less than instructive scenario, I kept boiler-feedwater and original pore-fluid salinities equal. The injection rate into the boiler was kept identical throughout all simulations. The porosities and irreducible water saturations in Table 3.3 result in different steam-front velocities, which are calculated by balancing heat flows across the steam front (Menegus and Udell, 1985). Simulation results are given in Figure 3.13. The parameters used in these simulations are summarized in Table 3.4. Each panel shows conductivity, normalized to the starting conductivity, as a function of distance at successive times during the flood. The panels are arranged so that clay content increases to the right, and salinity increases downwards. Panels a, b, and c display results of the 0.01 M NaCl calculations for sand and clay, Noxie sandstone, and Torpedo sandstone, respectively. Panel a shows that the section of the steam zone, which is to the left of the arrow, that is close to the front is very resistive (the conductivity ratio is less than unity). As the steam flood progresses, through snapshots ti to t.5, the minimum conductivity moves with the front. The equihbrium steam- zone conductivity, shown at the left of each snapshot, although greater than that just upstream of the front, is still resistive. In panel b, which represents the Noxie sandstone, a notably resistive section still appears just upstream of the steam front. Equilibrium conditions in the steam zone, however, are slightly more conductive than the starting value. The conductivity minimum still travels with the steam front, but by snapshot U has reached a stable value. In snapshot ts, the conductivity minimum does not deepen, but begins to broaden. In the Torpedo sandstone (panel c), the steam-zone conductivity near the front is nearly equivalent to the starting value. Eventually the steam zone becomes more conductive, as shown by the left edges of the each of the time slices. The major differences
75 in results between panels a, b, and c are that as clay cation concentration increases from a to c, clay conduction increases, and more importantly, steam-zone water saturation increases.
Table 3.4. Parameters used in numerical modelling of results shown in Figure 3.13.
Panel a: Panel b: Panel c: sand and clay Noxie sandstone Torpedo sandstone 3 3 3 Qv = 0.01 meq/cm Qv = 0.07 meq/cm Qv = 0.25 meq/cm Salinity = 0.01 M NaCl Salinity = 0.01 M NaCl Salinity = 0.01 M NaCl <]) = 0.33 <)) = 0.27 <|> = 0.24 Swirr = 0.18 Swirr = 0.26 Swirr = 0.40 5 5 vf = 3.1 x 10-5 m/s vf=2.6x lO" m/s vf = 2.6 x lO" m/s
Panel d: Panel e: Panel f: sand and clay Noxie sandstone Torpedo sandstone 3 3 3 Qv = 0.01 meq/cm Qv = 0.07 meq/cm Qv = 0.25 meq/cm Salinity = 0.1 M NaCl Salinity = 0.1 M NaCl Salinity = 0.1 M NaCl ()> = 0.33 <|> = 0.27
Panel g: Panel h: Panel i: sand and clay Noxie sandstone Torpedo sandstone 3 3 3 Qv = 0.01 meq/cm Qv = 0.07 meq/cm Qv = 0.25 meq/cm Salinity = 1.0 M NaCl Salinity = 1.0 M NaCl Salinity = 1.0 M NaCl (|> = 0.33
Panels d, e, and f use the same three example reservoirs, but the simulations are for
0.1 M NaCl. The profiles in panel d are very similar to those in a, except that the steam- zone conductivity ratios are substantially lower, particularly close to the steam front. This reflects the increased salinity contrast between the original pore fluid and distilled water, which condenses at the steam front and drastically lowers the surrounding conductivity. It also reflects that the magnitude of the bulk conduction term, relative to the clay conduction term, is greater in this simulation than in panel a. The clay-induced increases in relative steam-zone conductivity that occur from panels a to panel c are also evident between panels
76 d, e, and f. In panel f, the steam zone is eventually more conductive than the initial conditions, but a substantially resistive portion appears near the steam front. The bottom three panels illustrate the 1.0 M NaCl simulations. They further illustrate how increasing salinity increases the relative importance of the bulk conduction term, thereby accentuating the development of a steam-zone conductivity minimum close to the steam front. As well, increasing the salinity further reduces the relative conductivity of the steam zone, so that only the Torpedo sandstone has a conductive steam zone. Half of these simulations produce conductive steam zones. However, all but one show at least part of the steam zone to be more resistive than initial conditions. The resistive section grows with time, reflecting the growth of a distilled water bank at the steam front that dilutes the pore-fluid salinity. Thus regardless of the clay content, a conductivity minimum almost always appears at the front of the steam zone. In chapter 2,1 showed that the appearance of a distilled water bank is related to the injection steam quality. A high quality injection produces a steam front that travels more quickly than the steam liquid, thus allowing a distilled water bank to form, as shown in Figure 3.8a. A low quality injection, however, produces a steam front that travels more slowly than the steam liquid. This produces a scenario like that in Figure 3.14. The steam liquid, slightly more saline than the boiler feedwaters due to partial boiling, travels through the steam zone to the steam front, where it remixes with condensing distilled water. The resulting salinity profile is seen in Figure 3.14b: in the steam zone it is constant, at the steam-liquid value; then, after remixing occurs at the front, the water moving into the mixed zone is nearly as saline as the original pore fluid (in a case where boiler water and original pore fluid were identical), and so the resulting salinity profile ahead of the front is very nearly constant. Temperature and saturation profiles are similar to those of a high quality injection. The resulting conductivity profile is flat through most of the steam zone, increases close to the steam front as water saturation increases, and then decreases ahead of the front as temperature decreases. No minimum appears in the conductivity profile,
77 because no distilled water bank forms. The implication for the conductivity of a clay-bearing steam zones is obvious: a low quality injection would not result in a conductivity minimum forming near the front. To investigate this, the simulations for the Noxie and Torpedo sandstones were repeated, using a steam quality of 25 percent, and a correspondingly lower steam-front speed. These parameters are given in Table 3.5. The conductivity profiles at various times are displayed in Figure 3.15. All of the simulations produce profiles that remain flat throughout most of the steam zone, increase slightly at the steam front due to increasing water saturation, and fall ahead of the steam front due to decreasing temperature. In panels c and f, the steam zone is entirely conductive. It is instructive to compare panel b in Figure 3.13 to panel b in Figure 3.15. In the former, the steam zone is eventually more conductive than initial conditions. In the latter, it is resistive, despite the absence of a distilled water bank. The difference is due solely to the different salinities in the steam zone. In the high quality (75 percent), 0.01 M NaCl injection, the steam-liquid salinity, due to partial boiling, is 0.04 M NaCl; in the 25 percent injection, the salinity is 0.0133 M NaCl. Thus it appears that steam zones can indeed be more conductive than initial conditions as a result of clay being present in the medium. This high conductivity can occur either due to high amounts of clay conduction, or high steam-zone water saturations. In high quality injections, it is unlikely that a steam zone is entirely conductive, except for situations where there are very high clay contents and very low salinities. Entirely conductive steam zones can occur in low quality injections, where slow moving steam fronts disallow the formation of a distilled water bank. However, lower steam qualities lead to lower steam-liquid salinities, resulting in correspondingly lower steam-zone conductivities. Therefore reservoirs that are partially conductive in high quality injections may not necessarily be completely conductive in low quality injections.
78 Table 3.5. Parameters used to numerically model results shown in Figure 3.15.
Panel b: Panel c: Noxie sandstone Torpedo sandstone
3 3 Qv = 0.07 meq/cm Qv = 0.25 meq/cm Salinity = 0.01 M NaCl Salinity = 0.01 M NaCl <|> = 0.27 <|> = 0.24
Swirr = 0.26 SWirr = 0.40 vf = 2.6 x 10"5 m/s vf = 2.6 x 10"5 m/s
Panel e: Panel f: Noxie sandstone Torpedo sandstone
3 3 Qv = 0.07 meq/cm Qv = 0.25 meq/cm Salinity = 0.1 M NaCl Salinity = 0.1 M NaCl
Panel h: Panel i: Noxie sandstone Torpedo sandstone Qv = 0.07 meq/cm3 Qv = 0.25 meq/cm3 Salinity = 1.0 M NaCl Salinity = 1.0 M NaCl ((> = 0.27 ((> = 0.24 Swirr = 0.26 Swirr = 0.40 Vf = 1.14 x 10"5 m/s vf = 1.14 x 10"5 m/s
This may explain the disagreement between laboratory experiments, which until now have measured resistive steam zones (Vaughan et al., 1993; Butler and Knight, 1995), and field observations, which have noted conductive ones. In the case of some experiments (Mansure et al., 1990; Ranganayaki et al., 1992), measurements were made only before steam injection, and well afterwards. Thus they may have missed any resistive stages in the
79 steam zones. In other field measurements (Ramirez et al., 1993; Newmark and Wilt, 1992), no mention of steam quality is made. Steam fronts in these floods may have moved more slowly than the steam liquid, thus producing completely conductive steam zones. However, these injections took place in fresh water environments, which, in high clay content areas, can result in conductive steam zones even at high injection qualities.
Summary This study shows that steam-flooded materials with small amounts of clay will have steam zones which are less conductive than undisturbed zones, but more conductive than clean sand steam zones. The conductivity increase is primarily a result of an increased residual steam-zone water saturation. Materials with higher clay contents can have steam zones that are more conductive than initial conditions as a result of enhanced clay- conduction effects, as well as increased residual steam-zone water saturations. Steam quality can strongly affect the appearance of the conductivity profile in the steam zone, as was shown in chapter 2 using clean sands. In the case of clay-bearing steam zones, it can determine whether a steam zone will appear entirely conductive at all times, or whether a resistive leading edge of the zone can be used to track the steam front. This study's laboratory experiments and numerical simulations are meant to be a guide to how reservoirs respond electrically to steam injection. In light of the vast variability of physical properties between reservoirs, the conductivity profiles are not intended as fixed maps of a steam flood's conductivity response. The approach presented here, however, can be used on individual reservoirs to gain a firm understanding of what type of electrical responses are expected from steam injection. It is important to note that investigations such as this can avoid potentially costly misinterpretations of electrical data.
80 Water Conductivity
Fig. 3.1: Schematic showing the electrical conductivity of water-saturated sand and clay, as a function of pore-fluid conductivity.
81 W?m Sand
KX> Fig. 3.2: Distribution of sand and clay (kaolinite) inside conductivity cell, and location of temperature and conductivity measurements. 82 e tn 8 O a 8 c 2 0 30 40 50 60 70 BO Temperature (°C) b. 2.5 o 3 2.0 -o c o O « N 1.5 "3 E 1.0 ' • • i • • ' ' i 1 20 30 40 50 60 70 80 Temperature (°C) Fig. 3.3: The measured effect of temperature on the conductivity of clean sand in the cell (solid squares) and clay regions (open circles). Conductivities are normalized by the values at 21 °C. (a) Pore-fluid salinity of 0.01 M NaCl. (b) Pore-fluid salinity of 0.05 M NaCl. 83 a. 0 1000 2000 3000 4000 5000 6000 7000 Time (s) Fig. 3.4: Temperature (a) and electrical conductivity (b) distributions resulting from steam injection. Curve labelling corresponds to Figure 3.2. 84 B • • • • / X. • • / • a • / / I 01 / / / / / / / / / / o / •D .001 / / c / o / / / o / / / / / 10 15 20 25 30 5 10 IS 20 25 30 Depth (cm) Depth (cm) Steam Front t= 4310 s I Steam Front . ,_ / />"" a 7^ / a X- a a a / a / / / •y E / / / / CO / / / / •o 001 / / c / / / o / / o / / / / / / .0001 10 1 5 .20 25 30 5 10 15 2 0 2 5 3 0 Depth (cm) Depth (cm) Steam Front Steam Front / / / a / / a / B / a / / E .0 1 / 1 / co /* ^* CIO -° < / B • / • / a / V B " / V a / B xi .001 x> .001 / „ O / / O / o / / / o / / / / .OOOI / / .0001 / 5 10 15 20 25 30 1 0 1 5 20 25 30 Depth (cm) Depth (cm) Fig. 3.5. Conductivity as a function of depth in the cell, at six times in the experiment. 85 50 60 70 80 TEMPERATURE (°C) 2000 TIME (S) 6000 I -3.0 -2.5 -2.0 LOG [CONDUCTIVITY (S/M)] Fig. 3.6: Temperature (a) and electrical conductivity (b) distributions from the steam-injection experiment, shown as functions of depth and time. Viewing angles are identical. 86 E .1 CO o .01 3 •a c o • Sand, Calculated O + Clay, Calculated .001 O Sand, Observed m A Clay, Observed .0001 -i— i— .0001 .001 .01 .1 1 NaCl Concentration (mol/L) Fig. 3.7: Comparison of calculated and observed conductivities of sand and clay regions, as a function of salinity. Calculated values are from equation (3.2). 87 Fig. 3.8: The effect of high steam quality steam injection on clean sand, (a) Measured conductivities from chapter two. (b) Four regions that develop in the sand, (c) Corresponding changes in water saturation, temperature, salinity, and conductivity. 20 2000 3000 4000 5000 6000 7000 Time (s) Fig. 3.9: A comparison of measured (solid lines) and calculated (dashed lines) temperatures for the steam flood experiment. Temperatures are shown as functions of time, for the 11 thermocouples in the cell. 2000 3000 4000 5000 6000 7000 Time (s) Fig. 3.10: A comparison of measured (solid lines) and calculated (dashed lines) conductivities in the clean sand regions of the cell. Conductivities are shown as functions of time, for the measurement locations of Figure 3.2. 89 = 1 1 1 1 1 1 1 1 1 1 1 1 I l 1 1 1 1 5 X X . X X X X x *— A __ 10" -3 10 s~i i 1 1 1 1 1 1 llll llll llll i i i = i i 1 1 1 1 1 1 1 1 llll Mils . X X X X -2 — X / — 10 I X =—— — -3 >•> 10 1 1 1 11 1 1 11 1 1 1 1 1 1 11 1 1 1 =' i 1 1 1 11 1 1 11 1 1 11 1 1 1l l 1 1 l-s -t-> __x_ X— X • I—I I n In i - - 10" X >O 10" 1 1 1 11 1 1 11 1 I | t 1 1 1 1 1 1 1 Cs 5 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [ 1 1111 = o -—.X. X— X T*. • -2 X / 3 10 X -= X 10 3 ^1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 I 1 1 1 i Cs E 1 1 1 1 1 11 1 1 I 1 1 1 11 1. 1 11 1 1111 = X _ - 10" — X X -= - X - 10" 1 1 1 1 , 1 1 I I 1 1 1 1 1 1 , 1 I Cs 0 0.05 0.1 0.15 0.2 0.25 0 .3 Depth (m) Fig. 3.11: A comparison of measured conductivities (crosses) and corresponding model results (solid lines), showing values as functions of position, at specific times. 90 2000 3000 4000 5000 6000 7000 Time (s) Fig. 3.12: A comparison of measured (solid line) and calculated (dashed line) conductivities in the sand-and-clay layer. Conductivities are shown as functions of time, for the measurement location o"6 in Figure 3.2. 91 M-n-j-f w -i-j-i H-4-j-i-H-t-|-H-44 |H I-H3 •m-t-JH-H-j-j HH-I j i-m-| H-iij.i-ii > -1-fH-J-t H -(-j-tHH-l-j-tHH-t-JH-HH-j-i-^-nJ WH-t-|-H-H-|-4-H-f-j-H-(-t-JH-t-H-j-i-t I H-i-^4HH-j-M-M44HHH-)HHH-i-H-H-^ H-(H-|H-t-l-4-j-M-4H-)H-tH4-}-llH-)-JH- ^j-H-H-j-M-H-Jn-H-HJ-M- ] r__ L 111111.. i..,-,,, i,,,, i,,, ,.i , m 0 0.00 0.1 0.15 0.2 0.2f» 0.3 0 0 Of) 0,1 O.IG 0 2 0.25 0.:i 0 0.05 0.1 0.15 0.2 0 25 0.3 Dopth (m) DepUi {">) 0 0.05 0.1 0.15 0.2 0.25 0 3 0 0.05 0,1 0.15 0.2 0 25 0 5 0 0.05 0.1 0.15 0.2 0 25 0.11 Ocplh (ni) Depth (m) Depth (m) 0 0.05 0 1Ocpl 0.1h 5 (m)0. 2 0 25 0.3 o 0.05 0.1 |)cpU0.1l 5 (,„)0. 2 0.25 0.3 0 0.05 01 Ocpl0.1h5 (m) 0.2 0.25 0.3 Fig. 3.13: Simulations of conductivity versus time and depth in the cell. Simulations are for 90% sand and 10% kaolinite (a), (d), (g); Noxie sandstone (b), (e), (h); and Torpedo sandstone (c), (f), (i). Clay content increases to the right; salinity increases downwards. Associated model parameters are given in Table 3.3. Data are plotted as the logarithm of the ratio of conductivity to initial conductivity. 92 LEARRIS; . MIXED. -a ^ ZONE |! . ZONE. UNDISTURBED ZONE •c „ STEAM FRONT- - G • MIXED. UNDISTURBED ZONE - C S ZONE ZONE STEAM FRONT—1 • a - • _ " MIXED' UNDISTURBED ZONE' ZONE • c - ZONE: : STEAM FRONT Fig. 3.14: Spatial distributions of temperature, salinity, water saturation, and conductivity that are observed in the laboratory when low quality steam is injected into clean sand. Depth (ni) Depth (m) 0 0.05 0.1 0.15 0.2 0.25 D.3 0 0.05 0.1 0.15 0.2 0.25 0-3 Depth (m) Depth (m) Fig. 3.15: Simulations of low steam-quality injections into Noxie sandstone (b), (e), (h); and Torpedo sandstone (c), (f), (i). Data are plotted as the logarithm of the ratio of conductivity to initial conductivity. 94 CHAPTER 4: CONCLUSIONS In this thesis, I have studied whether the injection of steam into sand and clay causes the conductivity of the material to increase or decrease. I have shown that it is inappropriate to assume a priori that a steam zone will be resistive, or that it will be conductive. In fact it can easily be either, or both. The correct prediction of the response requires a careful analysis of the competing effects of changes in temperature, salinity, and water saturation. This laboratory study has shown that the electrical response of steam-flooded sands is significantly affected by the salinity of the injected steam, and by the steam quality. A high steam-quality injection can cause a dilution bank to form ahead of the steam front, resulting in a distinctive electrical behavior. The bank will form whenever the steam front moves more quickly than the steam liquid. This condition will be satisfied by high steam- quality injections, but not by low-quality injections. The bank will move with the steam front and can dominate the development of the steam-zone electrical conductivity, even when there is no bulk difference in salinity between the injected fluid and the initial pore fluid. The conductivity minimum deepens with distance and time, as a result of the increasing dilution over time of the pore fluid ahead of the front. The salinity at a given position reaches a minimum as the steam front passes that position, since the condensation and resulting dilution cease once the front passes by. The salinity at that position then immediately begins to increase as the more saline upstream water flows past. The conductivity at the steam front will continue to drop until the local salinity equals that of the condensing steam. At this point the minimum will begin to broaden, as the distance between the steam front and the steam liquid increases. The observed dependence on steam quality suggests that injection parameters could be selected so as to optimize the electrical 95 signature associated with the steam front. For example, the conductivity minimum seen at the steam front in this study with high-quality steam would be easier to detect than a steadily decreasing conductivity. Laboratory steam-injection experiments of this kind have typically been made on clean sands. Partly as a result of this, they have measured steam zones that are resistive relative to initial conditions. These measurements can be misleading if they are used to interpret field surveys without considering the effects of clay. In this study, when clay was added to the system, results showed clay-bearing steam zones to be more conductive than nearby clean sand zones, although still resistive relative to initial conditions. A significant reason for the increase was the increased residual steam-zone water saturation. Further numerical work demonstrated that if sufficient clay is added, the steam zones will be, at later times, conductive relative to initial conditions, particularly for high clay contents and low salinities. However, even for high-clay-content reservoirs, resistive sections of steam zones can develop. Only when the injected steam quality is low, can the reservoirs be completely conductive. The numerical model presented in this thesis was initially developed as a verification tool. It was used to ensure that my understanding of the underlying causes of the conductivity responses was correct. Very good matches were obtained between the measured and modelled data, using a minimum of empirical adjustments to the model parameters. These good matches justified using the model as a predictive tool. As noted in chapter three, I used it to investigate the effects of clay, and found it to provide quick and useful insight into how clay alters the electrical response. Future Research Future research in this field should follow two directions. First, to obtain results more representative of field conditions in enhanced oil recoveries and contaminant remediations, these experiments should be performed on oil-saturated sand. Oil is a 96 resistive liquid, immiscible in water. As a result, oil-saturated sand should produce conductivity responses, particularly ahead of the steam front, that differ from those responses presented here. A particularly useful study would use heavy crude oil. This oil can break up into lighter, resistive components that move far ahead of the steam front, and heavier, potentially conductive residual components that remain in the steam zone. The results should again be interpreted in terms of the physical processes occurring in the sand. A steam-water-oil numerical model should also be developed to verify those interpretations. Second, one must recognize that the real world is heterogeneous and three- dimensional. The experiments discussed in this thesis were designed so that the steam floods would be one-dimensional. The numerical techniques were also developed for a one-dimensional flood. This is appropriate for some injections into particularly homogeneous reservoirs. However, to understand many other injections, three- dimensional results are required. Limited laboratory experiments, particularly those with cylindrical or spherical steam fronts, or those with horizontal injection geometries, would provide useful results. However, it would be more appropriate to use numerical techniques rather than laboratory experiments to address the effects of heterogeneities. This is due primarily to the significant effort involved in building a laboratory apparatus, and to the infinite number of heterogeneous scale-model reservoirs that could be created. Therefore the simulator presented herein must be modified to solve the multidimensional, heterogeneous problem. There is no reason to expect that this cannot be done. Careful laboratory experiments using simple geometries can be used to test the validity of the simulator's calculations. Once proven to be accurate, the simulator can then be used to predict the electrical responses of actual reservoirs. The ultimate utility of laboratory experiments such as these is that they ground-truth our hypotheses of how the exploitation of a reservoir affects its geophysical responses. The experiments in this thesis will help to interpret electrical data collected over a steam-flooded reservoir. Electrical techniques are not the only ones used to monitor reservoirs. Seismic 97 techniques have also been used for many years. However, good laboratory measurements of the dynamic seismic response of a steam-flooded reservoir are rare. In future, piezoceramic elements will be inserted into the steam-injection cell, to measure the seismic response of a steam-flooded reservoir. 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S., and Wilt, M. J., 1993, The effects of steam injection on the electrical conductivity of an unconsolidated sand saturated with a salt solution: J. Geophys. Res., 98, No. Bl, 509-518. de Waal, J.A., Smits, R.M.M., de Graaf, J.D., and Schipper, B.A., 1991, Measurement and evaluation of resistivity-index curves: The Log Analyst, 32, 583-595. Waxman, M. H., and Smits, L. J. M., 1968, Electrical conductivities in oil-bearing shaly sands, Soc. Petr. Eng. J., 8, 107-122. Waxman, M. H., and Thomas, E. C, 1974, Electrical conductivities in shaly sands -1. The relation between hydrocarbon saturation and resistivity index; U. The temperature coefficient of electrical conductivity: J. of Petroleum Technology, 26, 213-225. 102 Wayland, J. R., Jr., Lee, D. O., and Cole, T. J., 1987, CSAMT mapping of a Utah tarsand steamflood: Trans., A. I. M. E., 283, 345-352. Winsauer, W. O., and McCardell, W. M., 1953, Ionic double-layer conductivity in reservoir rocks: Trans., A. I. M. E., 198, 129-134. Worthington, A. E., Hedges, J. H., and Pallatt, N., 1990, SCA guidelines for sample preparation and porosity measurement of electrical resistivity samples: The Log Analyst, 31, 20-28. 103 APPENDIX A: DETAILS OF EXPERIMENTAL APPARATUS There are three main interconnected systems in the apparatus: the fluid pumping and heating system, the temperature monitoring and control circuits, and the electrical monitoring circuits. These are described below. Fluid System The fluid system is comprised of a reservoir, an HPLC (high pressure liquid chromatography) pump, a preheater, steam generator, discharge beakers, and various valves and fluid lines. Steam is produced by pumping fluid at known flow rates from a reservoir, through a preheater, which heats the fluid to near boiling, and then through a boiler, which is set to vaporize a predetermined fraction of the flux. The steam, a mixture of the water vapour and the unboiled liquid, is then injected at the top plate, heating the system, and forcing fluid out the bottom of the vessel. The pump is designed to produce highly accurate, selectable flow rates from 1 to 30 ml/minute at pressures up to 1500 psi. At the low fluid pressures (a few tens of psi, at most) used in these experiments, however, the pump must be carefully calibrated, as the true flow rate can differ from the selected rate by up to 10%. Taking these calibrations into account allows the volumetric flow rate injected into the heaters to be calculated to within 1%. Discharge rates from the sand are measured using graduated cylinders placed below the apparatus. The pore-fluid preheater consists of 1/8" stainless steel tubing coiled around the inside wall of a 3.81 cm diameter heated ceramic tube. The tube, 30 cm long, is wrapped on the outside with nickel-chromium heating wire, and is encased in 5 cm of mineral wool insulation and 5 cm of urethane insulation. Power to the heating wire, and therefore the 104 temperature of the steel tubing, is regulated using a temperature controller and a platinum RTD (resistive temperature detector) placed on the inside of the ceramic tube. Water flows from the pump through the steel tubing, where it is heated to the desired temperature. The steam generator also consists of 1/8" stainless-steel tubing, wrapped instead around a high-power (2500 W) cartridge heater, which is 1.9 cm in diameter and 15 cm long. The tubing and cartridge heater are tightly encased in fibreglass insulation, and the whole assembly pressed into a dewar flask. The power leads are connected to the output of a 120 V variable auto-transformer. A precision power resistor is also wired in series with the cartridge heater. The power delivered to the heater, Pin, is calculated as: Pin = (A.1) where Vpr and Rpr are the voltage and resistance across the power resistor, respectively, and Vh is the voltage across the heater leads. The efficiency of the generator, e, is determined by comparing the temperature increase in a liquid flowing through the tubing to the input electrical power (A.2) where p is the density of the liquid, q is the volumetric flow rate, Cp is the liquid's heat capacity, and Ti and T2 are the inlet and outlet temperatures. Efficiency is a function of flow rate: the longer the liquid is in contact with imperfectly insulated surfaces, the more heat that can be lost to the surroundings. The steam quality - that portion of the liquid flux that is boiled - is then determined using the input power and the efficiency: (A.3) AH is the enthalpy of vapourization of the liquid. Since the steam generator is a one-pass boiler, any solids dissolved in the feedwaters will also be present in the two-phase mixture that is injected into the sand. The 105 salinity of the liquid portion of the steam will be more concentrated than the original fluid by a factor of 1/(1 -f). Temperature Measurement and Control System The temperature system monitors the internal temperature distribution, the external temperature distribution, and the steam generator inlet and outlet temperatures. It also controls the external heating coils. The internal temperatures are measured along the centre line of the sand pack using commercially available type-J thermocouples (iron-constantan measuring junctions). Eleven thermocouples, encased in a 1/8" diameter stainless-steel protective sheaths, were inserted through holes cut 2.54 cm apart in the ceramic wall. The holes were sealed by modifying standard Swagelok bulkhead feedthroughs (see Figure A.l), so that the thermocouples could pass through them into the sand. Viton o-rings are used to seal the body of the fittings against the cylindrical ceramic wall. Inlet and outlet steam generator temperatures were also measured using steel-sheathed J-type thermocouples, inserted with T-junctions into the fluid line. Each of the steel-sheathed thermocouple wires were connected directly to an input channel on an analog-to-digital (A/D) converter inserted in the computer. It is important to achieve a one-dimensional flood to ensure the correct determination of conductivity. To help achieve that, the outside of the ceramic sleeve is fitted with six independent sets of thermocouples and heater coils that work to create an external temperature profile equal to the internal one. The external thermocouples were created by welding iron and constantan wires together using an argon-atmosphere arc welder. The measuring junctions are embedded in electrical resistor cement, and are spaced every 5.08 cm along the tube. Each heater coil is 5.08 cm wide, and is centred around a thermocouple. The eleven interior thermocouples and the steam generator inlet and outlet thermocouples use 13 of the 16 available input channels on the computer's A/D board. 106 Therefore the six exterior thermocouples are connected through a thermocouple multiplexer to a single analog input on the A/D board. Thermocouple signals are typically not multiplexed, since the signals are based upon the small temperature-dependent voltages created by junctions of two dissimilar metals. To avoid additional corrupting thermoelectric voltages, the thermocouple wires normally run uninterrupted from the measuring junction to the channel's input. In this case, the limited number of input channels precluded that technique. Figure A.2 shows the simple reed-relay multiplexer designed for the task. TTL voltages from digital output channels on the A/D board turn on sequentially one of the six pairs of relays. The connection of the thermocouple metal with the left side of the relay produces a thermoelectric voltage that corrupts the desired temperature signal. However, the connection of the right side of the relay with the same thermocouple metal also produces a thermocouple voltage: since the multiplexer is isothermal, the two voltages are roughly equal in magnitude and opposite in sign. Therefore the relay-induced errors essentially cancel, and the resulting signals are accurate to within a few degrees Celsius. This is adequate for the purposes of achieving a one-dimensional temperature profile inside the sand. The external heating system is designed to set the external temperature profile equal to the internal one. Therefore if the external temperatures are below the internal ones, the heating coils are turned on, using the circuit shown in Figure A.3. Control is provided by six independent TTL-level digital output channels on the A/D board. A high voltage on a digital line (~ 4V) closes a reed relay, in turn causing 33 V dc to be placed across the coil of a corresponding power relay. This closes the power relay, and the heater draws power from a 36 V dc battery bank. The relays open, and the heaters turn off, when the TTL voltage goes low (~ IV). Electrical Measurement System The electrical monitoring system measures the voltages across the precision resistor 107 and between successive pairs of the eleven internal thermocouple sheaths. These signals are multiplexed onto one analog input channel on the A/D board using the circuit shown in Figure A.4. This multiplexer was designed to allow the sequential reporting of each of the 11 signals to the computer. The computer selects the required signals by sending two single-byte control words out its serial port. These bytes are then converted to two parallel bytes, which are connected to the channel-select pins of two one-of-sixteen analog multiplexing chips. The outputs from the two chips are then connected to a single input channel on the A/D board. Collection of the eleven square-wave signals is synchronized using a TTL-level trigger created by the square-wave source. The trigger line is connected to a digital input channel on the A/D board. The computer first selects the required signal using the multiplexer shown above, then continuously monitors the trigger line. Upon receiving a positive trigger, a predetermined number of voltage samples are made along the positive half-period of the square-wave. Upon receiving a negative trigger, an equal number of samples are taken along the negative half period. For a d.c. conductivity measurement, the late-time samples are averaged on both the positive and negative traces, and the difference between the two values stored in a file. The computer then selects another signal, and repeats the process. 108 Fig. A.l: Modification of Swagelok bulkhead feedthroughs, to allow thermocouples to be inserted into the sand. Standard fittings (a) were bored out to an inside diameter of 0.125 in., the outside diameter of the thermocouples. They were then fitted with Viton o-rings (b), which provided a seal against the curved ceramic wall of the conductivity cell. Constantan AID Input ° Iron Ft 5Yc 3 5Y 3 ft .Iron ,—v 3 o Ft 2 IFt IFt Ft 5V C • 5V iFt. c 3 3 3 3 1 3 3; o 3 Ft 2 3 Ft do 400 fi Ft J o -4 q co 3 oO in Ft Constantan K- d1 400o <« • \- 'oo 3 c z W Si LU d2 400 fi • V- 3 1 common 5Y* Fig. A.2: External thermocouple multiplexer. TTL voltages from channels dO, dl, and d2 are isolated from the multiplexer by 4N38 optical isolators. The voltages select one channel on each of the two one-of-sixteen MC14067B multiplexer chips. The selected channels close two of the reed relays, thereby connecting one of the external thermocouples to the analog-to-digital converter in the computer. 110 300 o 36Vdc ? 1 Heater Coil 1 36 Vdc 300 Q St Heater Coil 2 36 Vdc 300 Q co p n J Z Heater Coil 3 36 Vdc 300 n 'oo 3 it Heater Coil 4 300 Q 36 Vdc 11 Heater Coil 5 36 Vdc 300 Q PI Z Heater Coil 6 6 O 33 V 5YC 3 5Y 10kO c • c ft r_ • c 2 3 1 -C O • c 2 1 -c 3 -c 10kQ dO © d1 ©- d2 ® Fig. A.3: External heating coil control circuit. Three digital output lines from the computer (dO, dl, d2) are used in conjunction with a multiplexing chip (MC14067B) to turn on or off six optical isolators (4N38). The isolators open or close power relays, in turn operating the six external heating coils. Ill W • \r- • V- -C OD A3 400 B3 400 Hn10k CO • •—v- 3 • V- • V- 3 A1 400 2 5- B1 400 ^k10k -Viok •—y- •—v- A0 400 2 r C -3" H- -VlOk B0 400 5V 5V Fig. A.4: Conductivity multiplexing circuit. Two sets of four digital output lines from the computer (AO to A4, and BO to B4) are used to control the switching system. The computer lines are isolated from the switching circuit by eight optical isolator chips (4N38). Each thermocouple sheath is connected to an input channel on each of two one-of-sixteen multiplexer chips (MC14067B). The output from the multiplexer chips is connected to an analog-to-digital input on the computer, 112