ANNUAL TRANSACTIONS OF THE NORDIC RHEOLOGY SOCIETY, VOL. 20, 2012 Rheology of Petroleum Fluids Hans Petter Rønningsen, Statoil, Norway ABSTRACT NEWTONIAN FLUIDS Among the areas where rheology plays In gas 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 viscosity 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 fluid 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 pressures 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 gases also exist dissolved mixtures of hydrocarbon compounds, in liquid reservoir oils and thereby impact ranging from the simplest gases, like the fluid viscosity and productivity of these methane, to large asphaltenic molecules 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 viscosities, 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 solid- 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 density at 15°C (g/cc) 15 10 Shear stress,Pa Shear Figure 2. Correlation between density 18 5 and viscosity of North Sea crude oils . 0 0 20406080100 Shear rate, 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 water. 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 rheometers 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 yield stress, Apparent viscosity (mPa s) i.e. a certain threshold shear stress that has 0 to be imposed in order to start breaking the 0 100 200 300 400 500 600 gel structure and make it flow, the crude oil Shear rate (s-1) gels exhibit a complex time-dependent rheology. Due to lack of reversibility, the Figure 3. Shear-thinning behaviour of term thixotropy, 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 deformation, similar approach as modelling of the followed by a creep 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 plastic behaviour of such gelling oils has been 13 rheological equation of state: 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 pressure), 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 rheometer 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.