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Rheology of Petroleum Fluids

Rheology of Petroleum Fluids

ANNUAL TRANSACTIONS OF THE NORDIC SOCIETY, VOL. 20, 2012

Rheology of Petroleum

Hans Petter Rønningsen, Statoil, Norway

ABSTRACT NEWTONIAN FLUIDS Among the areas where rheology plays In reservoirs, the flow properties of an important role in the oil and gas industry, the simplest petroleum fluids, i.e. the focus of this paper is on crude oil hydrocarbons with less than five carbon rheology related to production. The paper atoms, play an essential role in production. gives an overview of the broad variety of It directly impacts the productivity. The rheological behaviour, and corresponding of single compounds are well techniques for investigation, encountered defined and mixture viscosity can relatively among petroleum fluids. easily be calculated. Most often reservoir gas viscosity is though measured at reservoir INTRODUCTION conditions as part of reservoir studies. Rheology plays a very important role in The behaviour is always Newtonian. The the petroleum industry, in drilling as well as main challenge in terms of measurement and production. The focus of this paper is on modelling, is related to very high crude oil rheology related to production. (>1000 bar) and/or high temperatures (170- Drilling and completion fluids are not 200°C) which is encountered both in the covered. North Sea and Gulf of Mexico. Petroleum fluids are immensely complex Hydrocarbon also exist dissolved mixtures of hydrocarbon compounds, in reservoir oils and thereby impact ranging from the simplest gases, like the fluid viscosity and productivity of these methane, to large asphaltenic reservoirs. Reservoir oils are also normally with molecular weights of thousands. This Newtonian fluids, but the variation in chemical variation is reflected in a large viscosity can be extremely large, both as a variation in , ranging from result of chemical variation, ranging from fractions of a centipoise to millions of light, low-viscous gas condensates to highly centipoise, and rheological behaviour, from viscous heavy oils, and temperature perfectly Newtonian to highly non- variation, which always has a large, and Newtonian, visco-elastic and nearly - fairly predictable impact on the Newtonian like. Description and rheological viscosity. Fig. 1 shows an example of a characterization of petroleum fluids thus rather heavy North Sea oil with nearly requires a broad variety of experimental perfectly Newtonian behaviour, even at a techniques and modelling approaches. low temperature. This is quite typical also of much heavier oils. The mentioned temperature variation of the viscosity of

11 these Newtonian fluids, is most often very representative of the fluid at real field well described by a so-called Arrhenius conditions. relation, i.e. a linear relationship between the logarithm of the viscosity  and the 25 inverse temperature1: 30°C 20 40°C s) 50°C 15 60°C

(mPa (1) 70°C 80°C 10 90°C where Ea is the flow activation energy.

Viscosity 5 6608/10-6 30 0

25 0.7 0.76 0.82 0.88 0.94

20 Crude oil at 15°C (g/cc) 15 10 Shear ,Pa Shear Figure 2. Correlation between density 18 5 and viscosity of North Sea crude oils . 0 0 20406080100 , 1/s NON-NEWTONIAN FLUIDS

Figure 1. Example of perfectly The more ‘interesting’ rheological Newtonian behaviour of a 21 °API North behaviour of petroleum fluids is found Sea crude oil at 5 °C. among fluids containing either solid paraffin waxes or dispersed . Depending on the At a given temperature, there is also volume fraction of dispersed, solid wax normally a simple relationship between the particles or water droplets, such fluids viscosity and the average molecular weight2 exhibit all degrees of non-Newtonian or density of the fluid18. The graph in Fig. 2 behaviour, which is described in some detail shows a useful correlation between density below. and Newtonian viscosity of North Sea crude As soon as paraffin (wax) crystals start oils, valid above the wax appearance to precipitate in a crude oil, the behaviour temperature of the oils. It has been found to starts to deviate from the Newtonian provide viscosity estimates typically within behaviour described above. In fact, the 10-15%, which may be acceptable as a first onset of deviation from simple Arrhenius estimate in many cases. temperature dependency is one method to Although they are typically Newtonian detect the onset of wax crystallization, or the and rheologically fairly simple, viscosity wax appearance temperature. The first wax measurements with heavy oils are not crystals have though a limited impact on trivial. There is no strict definition of viscosity and rheology. But as soon as the ‘heavy oil’, but here is meant an oil with a volume fraction of particles has reached a density higher than about 950 kg/m3. The few tenths of a per cent, significant shear sample preparation and pretreatment w.r.t. rate dependency can be observed, gas saturation and stabilization prior to characteristic of non-Newtonian behaviour. measurements with such oils, has to be Fig. 3 shows a typical example of carried out very carefully in order to obtain pronounced shear-thinning behaviour of a measured viscosities which are waxy North Sea crude oil at different temperatures below the wax appearance

12 temperature. studied for decades. One milestone work is 6 2000 that of Davenport and Somper more than forty years ago, where they studied gelled 5°C 10° oil behaviour in both lab-scale 1500 15°C 20°C and a large-scale pipeline. Various aspects 30°C of gelling and restart behaviour of waxy 1000 North Sea oils have since been studied extensively7-9. 500 In addition to developing a stress,

Apparent viscosity (mPa s) i.e. a certain threshold that has

0 to be imposed in order to start breaking the 0 100 200 300 400 500 600 structure and make it flow, the crude oil Shear rate (s-1) exhibit a complex time-dependent rheology. Due to lack of reversibility, the Figure 3. Shear-thinning behaviour of term , though often used, is not waxy North Sea crude oil. actually the right word to describe this behaviour, rather time-dependent shear Modelling and predicting non- degradation. Newtonian viscosities is much harder than When subjected to a given shear stress, Newtonian, and few non-Newtonian the rheological response is characterized by viscosity models exist. However, using a an initial, transient elastic , similar approach as modelling of the followed by a flow period at very low viscosity effect of dispersed water in crude shear rate, the length of which depends on oil, a semi-empirical non-Newtonian the shear stress, then a fairly rapid collapse viscosity model based on experimental data of the gel towards an equilibrium shear rate, for a large number of North Sea crude oils, characteristic for a given temperature. This has been developed3. The viscosity model is is illustrated in Fig. 4. directly linked to a thermodynamic model for calculating the fraction of solid wax as function of temperature and pressure4.

CRUDE OIL GELS AND TIME- DEPENDENT RHEOLOGY Several subsea North Sea oil fields produce highly paraffinic, high pour point oils. In addition to the wax deposition challenges with these fluids, there are additional challenges related to transient operations such as shut-downs, cool-down and pipeline restart, due to their gelling Figure 4. Time development of shear tendency. The origin of this tendency is the rate when a gelled oil is subjected to a interaction between wax crystals in the constant shear stress7. crude oil upon cooling. When the volume fraction of solid wax particles exceeds about As shown by Rønningsen7, and recently four per cent5, these interactions cause a confirmed by Schüller et al.9, this overall three-dimensional network to form under behaviour can be expressed mathematically quiescent conditions. The properties and by a time-dependent Bingham behaviour of such gelling oils has been

13 rheological : One feature of waxy crude oil gels that complicates the experimental (2) characterization, is the dependency of yield stress and gel breakdown not only on the where  is the shear stress. The Bingham actual temperature (and ), but also on the thermal and shear history prior to the viscosity (B) is essentially constant and the measurement conditions5,11. This has its Bingham yield stress (y) breaks down according to a second-order rate equation origin in a complex interplay of various (Fig. 5), indicating that the progressive chemical constituents in the oil which is breakdown process, to a good only partly understood. The prevailing approximation, can be represented by a theory is that some of the polar constituents series of linear and parallel flow curves with of an oil act as a kind of natural wax progressively lower yield stress7. Schüller structure modifiers, similar to synthetic pour et al.9 also devised a method for using a point depressants, and that the effect of modern to obtain the time- these substances in terms of their ability to dependent yield parameters, incl. the time interact with wax crystals, strongly depend constant for yield stress breakdown. on their solubility state, and hence on the

160 history of heating and cooling. The (A-B)/(1+C*x)+B similarity to synthetic wax modifiers has 150 been demonstrated in several studies5,8. In 140 A = 141.0 Pa B = 61.0 Pa any case, the sensitivity to history may be -1 130 k = 0.07 min very large. It is also often referred to as the 120 minimum-maximum gelling point (or pour

110 point) phenomenon, since the gelling

100 temperature may be higher or lower

Yield stress (Pa) depending on the thermal history as well. 90 This puts very high requirements on the pre- 80 conditioning methodology and skill of 70 operators in order to produce reproducible 60 rheological data of high quality. 0 20 40 60 80 100 120 140 160 180 Time (minutes) In relation to real oil production systems, Figure 5. Breakdown of gelled oil yield there are some additional factors that need to stress of a North Sea crude oil9. be taken into account. First, oil well streams contain dissolved gas which has a positive A very interesting observation is that the impact on the wax solubility4 as well as the restart behaviour observed by Davenport rheology in general and the gelling and Somper6 in a large scale (78 mm) flow behaviour specifically. As an example, loop, is very similar to the behaviour increasing the saturation pressure of an oil observed by Rønningsen7 in a completely from 1 bar (gas-free oil) to 100 bar, typical different geometry, i.e. a small scale cone- for many multiphase pipelines, has been and-plate rheometer, confirmed by Schüller found to reduce the yield stress by 60- et al.9 and also observed by Paso et al.10 in 70%8,12. Furthermore, a free gas phase in a similar modern type rheometers. Overall, pipeline reduces the effective contact area there seems to be good evidence in support between gelled oil and pipe wall in a of the adequacy of a time-dependent shutdown situation, and thereby the required rheological equation of state of this kind for restart or pressure. The pressure describing shear-induced breakdown of required to initiate movement of a gelled oil waxy crude oil gels. plug effectively depends on these two

14 parameters, i.e. the so-called ‘break-away’ vary a lot, but normally water-in-oil (w-i-o) yield stress and the contact area. The further dispersions are formed as long as the water progress of the restart depends on the more volume fraction (water cut) is not too high. detailed time-dependent rheology, as Stable dispersions, i.e. dispersions which are described above. A multiple plug pipeline stable for a long period without continuous restart model presented by Nossen et al.13 energy input from shear or , are might form basis for a more sophisticated often called . When the water cut future multiphase gelled oil restart model. exceeds a certain value, the inversion point, This is currently an important area of the changes to an oil-in-water (o- research in many oil companies. In a i-w) type with water as the continuous multiphase pipeline, a water phase may have phase. In fact, rather than a specific water a significant additional impact on viscosity fraction, the transition from w-i-o to o-i-w and gelling properties, as discussed below. normally occurs over a range, the inversion Some researchers have applied range. Predicting when the inversion takes oscillatory shear experiments to study the place for a specific crude and a specific viscoelastic properties of crude oil gels. production system, is highly important and a Vinogradov14 stated that the yield stress was major challenge in many oil production close in magnitude to the storage modulus systems, especially heavy oil systems. The measured at low frequency of oscillation. reason is that as the produced water cut Hou and Chang15 recently applied increases, the inversion point (or range) oscillatory measurements to study the effect determines the maximum viscosity of the of thermal and shear history on the well stream and hence the transport capacity of some Chinese crude oils. for a given design. Experimental Although the general picture of the crude determination of realistic inversion oil gel breakdown process seems to be behaviour is thus a highly prioritized area of reasonably well understood, and confirmed research at the moment. by several independent studies, there is still A recent paper by Zhilin et al.16 a way to go both to have really reliable and describes how such realistic flow loop reproducible experimental methods for experiments, taking into account variables determination of the rheological parameters, related to flow as well as pump energy and a coherent modelling framework, input, can be carried out. Primary focus in enabling detailed calculations of the restart this work was to determine the transition of gelled oil multiphase pipelines. from oil continuous to water continuous flow and thereby the maximum viscosity to WATER-IN-CRUDE OIL DISPERSIONS be designed for. Transport of unprocessed well stream, Although a number of factors has an impact i.e. mixtures of oil, gas and produced water, on the actual viscosity of a water-in-oil is very common in oil field developments. dispersion, such as the oil viscosity, droplet The effective viscosity of the transported size distribution etc., it turns out, that the fluid mixture is an important parameter for relative viscosity of such dispersions, up to pipeline capacity and sizing evaluations. the maximum point, can be expressed by Due to energy input from turbulence or some fairly simple models with surprisingly pumps, oil-water mixtures will tend to form large robustness and general validity. The dispersions of droplets of one phase in the simplest of these is probably the so-called other. Depending on the fluid , Brinkman formula17: specifically the content of polar, ‐2.5 interfacially active compounds in the oil, the r = (1 – ) (3) type and stability of such dispersions can

15 where r is the relative viscosity and  is the formula is believed to give somewhat more volume fraction of dispersed water. Zhilin realistic predictions than the empirical et al.16 found that a large number of correlation, which is not based on experimental flow loop data could be experimental data below 10% water cut. represented well by this simple formula, which needs no input on dispersion 20 characteristics other than volume fraction of 18 16 water. 14 Based on a large set of experimental 12 rheometer viscosity data for dispersions 10 with different North Sea crude oils, another 8 6 simple, empirical correlation was Relative viscosity 18 4 established by Rønningsen , also taking 2 into account the effect of temperature and 0 shear rate. The ‘high’ shear rate version of 0 20406080100 this correlation (500 s-1) is most often used Water cut (volume%) in pipeline simulations. This is one option for dispersion viscosity in the commercial 20°C 40°C 60°C flow simulator OLGA. It has the general 80°C Brinkman form: Figure 6. Correlations for relative lnr = k1 + k2T + k3  + k4 T (4) viscosity of water-in-crude oil emulsions. Black lines show the Rønningsen where T is temperature (°C) and  is correlation18 at different temperatures and volume% water. The coefficients from ref. shear rate 500 s-1. The grey line shows the 18 are shown in Appendix A. This Brinkman formula17. correlation is based on the well-known exponential relationship between relative The robustness of these correlations 19 viscosity and water cut of Richardson . towards variations in flow conditions, Fig. 6 shows the correlation graph for shear droplet sizes etc. seems to be surprisingly -1 rate 500 s and various temperatures large. It is fairly safe to assume that the together with the Brinkman correlation. relative viscosity of a water-in-crude oil 20 Johnsen and Rønningsen tested this dispersion is about 5-6 at 50% water cut and and other correlations against experimental about 8-9 at 60% water cut. Often, these are data for ‘live’, pressurized water-in-crude good enough estimates for oil dispersions in a wheel-shaped flow purposes. More important, and more simulator and found reasonable agreement challenging experimentally, is to predict up to a water volume fraction of at least 60- accurately where inversion will occur, or 65% in most cases. In fact, this appears to more precisely, the water cut of maximum be the most interesting range of water cuts viscosity. An important area of research since real crude oil dispersions very often where more work is needed, is thus to be tend to invert at volume fractions not higher able to measure realistic phase inversion than this. It can be noted in Fig. 6 that the behaviour, that can be transformed into Rønningsen correlation is very similar to the wellbore and pipeline transport conditions, Brinkman formula up to a volume fraction using small scale laboratory equipment. of about 55%. At very low water fractions This is important since very often, limited (less than about 5 vol%), the Brinkman sample volumes does not allow large scale

16 experiments to be carried out in early phase 3. Realistic meeasurement and of field design. prediction of phase inversion Finally, when waxy crude oils are co- (maximum viscosity water fraction) produceed with formation water, and in water-crude oil systems using subjected to cool-down in a transport small-scale equipment. system, two complex phenomena are combined, creating even more complexity, in form of waxy crude oil gels. ACKNOWLEDGMENTTS The properties of such gels have been The permission by Sttatoil to publish this studied recently by several groups21,22, material is highly acknowledged. showing that highly stable emulsions with very high viscosities and yield stresses, and APPENDIX strong non-Newtonian behaviour, are formed. An example of the effect of water Table A1. Coefficients of the correlation for cut on the yield stress of two waxy North relative viscosity of wateer-in-oil dispersions, Sea crude oils is shown in Fig. 7. Eq. (4)18.

100

Oil 2 80 Oil 1

60 REFERENCES 40 1. Rønningsen, H.P. (1993), "The rheology Yield stress (N/m²) 20 of crude oils", Nordic Rheology Conference, Gothenburg, Sweden, 19--20 August. 0 0 10 20 30 40 50 60 70 Volume% water 2. Rønningsen, H.P. (19993), ‘’Prediction of viscosity and of North Sea petroleum fluids by using the average Figure 7. Effect of dispersed water on 8 molecular weight”, Energy and Fuels, 7, yield stress . No. 5, 565-573.

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