Sac

PAPER 2006-052

Controlling VLLE Equilibrium with a Cubic EoS in Heavy Oil Modeling

K. KREJBJERG Calsep, Inc.

K. S. PEDERSEN Calsep A/S

This paper is to be presented at the Petroleum Societys 7th Canadian International Petroleum Conference (57th Annual Technical Meeting), Calgary, Alberta, Canada, June 13 15, 2006. Discussion of this paper is invited and may be presented at the meeting if filed in writing with the technical program chairman prior to the conclusion of the meeting. This paper and any discussion filed will be considered for publication in Petroleum Society journals. Publication rights are reserved. This is a pre-print and subject to correction.

Abstract The paper presents experimental PVT data of reservoir

fluid mixtures with API gravities ranging from 8 to 30. As can be seen from the presented data, heavy oils may under influence of gas injection split out an extra liquid phase, for which type of system a VLLE approach would be necessary to fully describe the phase equilibrium. Reservoir simulators are largely set up with 2-phase flash calculation algorithms that are capable of handling VLE, but not VLLE systems. The majority of todays reservoir simulators are therefore unable to fully represent the phase behavior of heavy oils in fields with gas injection. The paper outlines a heavy oil fluid characterization procedure that allows the user to get 2-phase flash results for VLLE systems that are approximately right with respect to gas/liquid ratio and saturation points. It is further shown how the characterization can be modified to give the full VLLE picture.

Introduction PVT simulations on heavy reservoir oil mixtures have

traditionally been carried out using black oil correlations expressing the fluid properties in terms of easily measurable

quantities like API oil gravity, gas gravity and gas/oil ratio. With the application of secondary recovery techniques like gas injection and thermal stimulation, it has become more interesting, also for heavy reservoir oils, to make compositional equation of state based simulations

A heavy oil has a high density at standard conditions. Crude oils are essentially mixtures of paraffinic (P), naphthenic (N) and aromatic (A) compounds. The densities of aromatics are higher than that of naphthenes and paraffins of the same molecular weight. This is consistent with chemical analyses showing that heavy oil mixtures are rich in aromatic compounds. The density of an oil at standard conditions is conventionally expressed as API gravity

............(1)

SG is the 60 oF/60 oF specific gravity, which is defined as mass ratio of equal volumes of oil and water at the appropriate temperature. As the density of water at 60 oF is close to 1 g/cm3, the specific gravity of an oil sample will take approximately the same value as the density of the oil sample in g/cm3. The term

131.5SG

141.5API =

PETROLEUM SOCIETYCANADIAN INSTITUTE OF MINING, METALLURGY & PETROLEUM

2

heavy oil may be used for oil mixtures of an API gravity below 30.

The C10+ aromatics present in a crude oil mixture will be components containing one or more aromatic ring structures with paraffinic side branches. The melting temperature of that type of compound is low as compared with that of normal and slightly branched paraffins of approximately the same molecular weight. For this reason wax precipitation is unlikely to take place from a heavy oil mixture. The fact that high molecular weight compounds may be kept in solution in the oil at low temperatures has the side effect that the viscosity of heavy oil mixtures can be very high indeed at production conditions and even at reservoir conditions. Lindeloff and Pedersen (2004) have reported viscosities as high 8,500 cP for a heavy reservoir fluid.

Gas injection is often applied to heavy oil reservoirs. If the gas is dissolved in the oil, it will lower the oil viscosity and facilitate production and possibly also enhance the recovery rate. The injection gas may have the side effect that the oil splits into two liquid phases. This is undesirable because the heavier liquid phase may be highly viscous and sticky and therefore difficult to recover. Presence of two liquid phases also means that a conventional reservoir simulator will not be able to give a true picture of the reservoir fluid behavior for the simple reason that the reservoir simulators standard used in the oil industry cannot handle more than one hydrocarbon liquid phase. This raises the question of what is an optimum fluid characterization for a heavy oil in a reservoir with gas injection.

Heavy Oil Reservoir Fluid Compositions Tables 1-3 show three heavy oil compositions. The API

gravity of the reservoir fluid composition in Table 1 is 28. This oil is at the very light end of what is classified as a heavy oil. Table 2 shows the composition of the liquid from a flash of a heavy reservoir oil to standard conditions (1.01 bar and 15 C). Its API gravity is 18. Finally Table 3 shows the composition of a reservoir fluid with an API gravity of 10.

Based on extensive compositional data for reservoir fluids from regions covering most of the world Pedersen et al. (1983, 1984, 1992) have shown that most reservoir fluids for carbon numbers (CN) above C6 exhibit an approximately linear relationship between carbon number and the logarithm of the corresponding mole fraction, zN

.. (2)

Figure 1 shows a plot of the C7+ mole %s (logarithmic scale) versus carbon number for the reservoir fluid in Table 1. As is indicated by the dashed line an approximately linear relation is seen consistent with Equation (2). Figure 2 shows a similar plot for the oil mixture in Table 2. For this oil mixture linearity according to Equation (2) starts at around C11 and the mole %s of the fractions from C7-C10 are far below the best-fit line through the C11-C40 mole %s (dashed line in Figure 2). For the mixture in Table 3 linearity starts at around C17 as may be seen from Figure 3 and the concentrations of C7-C10 are almost negligible.

Figures 2 and 3 add pieces to the picture of a heavy oil. The two figures suggest a trend saying that the lower the API, the lower the concentration of the lighter C7+ components. These components may have disappeared from the reservoir over a long period of time as a result of biodegradation, leaving a

reservoir fluid behind consisting of a heavy end essentially containing C11+ hydrocarbons and a light end dominated by C1. Limited miscibility is often seen for mixtures with a discontinuous molecular weight distribution and that could well be the case for heavy reservoir fluids low in C7-C10 components.

PVT Data for Heavy Oil Mixtures Figures 4-6 show plots of differential liberation results for

the oil mixture in Table 3. Oil formation volume factors (Bo) are plotted in Figure 4, solution gas/oil ratios (Rs) in Figure 5 and oil densities in Figure 6. The differential liberation experiment was carried out at a temperature of 52 C.

Figures 7 and 8 show saturation points measured in two swelling experiments on the oil mixture in Table 1. Both experiments were carried out at a temperature of 74 C, one using CO2 as injection gas and the other one using the gas in Table 4 .

Figure 9 shows a measured phase diagram for the oil mixture in Table 2, which has initially been recombined with C1 to a gas/oil ratio of 29.7 Sm3/m3. An equimolar mixture of C1, C2, C3 and nC4 was added to the resulting mixture and saturation pressures measured for various mixing ratios at a temperature of 24 C. For an injection gas concentration of around 34 weight %, the liquid phase is seen to split into two and the pressure band with 2 liquid phases widens with increasing injection gas concentration. A lower region (VLLE) is seen with 3 phases, one gas (or vapor) phase (V) and two liquid phases (L). Above this area is one with two liquids in equilibrium (LLE).

In addition to the data mentioned in this paper, conventional PVT data for 25 heavy oil mixtures with API gravities ranging from 8 to 30 was investigated and used to develop and verify the characterization procedures presented in the subsequent section.

C7+ Characterization of Heavy Oil Mixture

To perform phase equilibrium calculations on a reservoir oil mixture using a cubic equation of state as for example the volume corrected equation of Soave (Soave (1972) and Peneloux et al. (1982))

. (3)

the plus fraction must be split into carbon number fractions, equation of state parameters (Tc, Pc and ) must be determined for each carbon number fraction, and the C7+ components must be lumped into a manageable number of pseudo-components.

In this work the plus fraction is split into carbon number fractions using Equation (2) and the C7+ fractions are lumped into 12 pseudo-components of approximately equal weight. This follows the work of Pedersen et al. (1992). The heaviest hydrocarbon fraction handled is C200.

The following property correlations are applied

( )( )( )2cbVcV

TabV

RTP+++

=

NN zBAC ln+=

3

...... (4)

(5)

....... (6)

where Tc is critical temperature in K, Pc critical pressure in atm, is the liquid density in g/cm3 and M the molecular weight. The parameter m is a 2nd order polynomial in the acentric factor, which polynomial for the Soave equation takes the form

......... (7)

Two sets of coefficients (I and II) were estimated based on the available heavy oil PVT data. The two sets were estimated with two different objectives in mind: Set I was estimated to avoid liquid-liquid splits, whereas set II was estimated to create liquid-liquid splits in certain situations (discussed in the following). These coefficients are shown in Table 5. Table 6 shows two alternative characterizations for the fluid in Table 3, one using each set of coefficients in Table 5. The binary interaction parameters are shown in Table 7. Figure 10 shows plots of the Soave a-parameters of the C7+ components for a temperature of 52 C determined by each of the two sets of coefficients in Equations (4)-(6). For the carbon number fractions with molecular weights above 1,000 the a-parameters determined using set II are substantially higher than those determined using set I. The a-parameter is for a given component a measure of the attractive forces acting between the molecules of that type of component. It is analyzed in the following, how the difference in assumed intermolecular attractions influences PVT simulation results for the oil in Table 6 and other heavy oils.

The Peneloux volume shift parameter was assumed to be linear in temperature as suggested by Pedersen et al. (2004)

.................... (8)

The coefficient c0 is determined from the liquid densities of the C7+ components at 288.15 K and the coefficient c1 is determined to comply with the ASTM 1250-80 correlation for the variation of the density of a stable oil with temperature. The temperature T in Equation (8) is in Kelvin.

PVT Simulation Results Figures 4-6 show simulated differential liberation Bo-factors,

gas/oil ratios and oil densities for the oil mixture in Table 3 using the property correlations in Equations (4)-(6) and each of the two sets of coefficients in Table 5. The saturation point is simulated to be 8-10 bar too low, which is the major reason for the deviations between the experimental and simulated results in Figures 4-6. The deviations could easily be eliminated by a parameter tuning. Even though the C7+ properties deviate considerably between the two fluid descriptions as may be seen from Table 6, the simulation results are quite similar. Figure 11 shows plots of the phase envelopes for the mixture in Table 3 using each of the fluid descriptions. At 52 C, which was the temperature in the differential liberation experiment, the

simulated saturation pressure is almost the same, but at higher temperatures the two phase envelopes differ substantially. Using coefficient set II a large 3-phase area is seen for temperatures between 400 and 600 C and the simulated dew point line is at a much higher temperature than what is seen using coefficient set I. Temperatures above 400 C will not occur during oil production and one may wonder whether the difference between the two sets of coefficients is at all important.

Figure 7 shows simulation results for a swelling experiment on the oil mixture in Table 1 using CO2 as injection gas. Using coefficient set I the simulated saturation points of the swelled mixtures are somewhat too low, while the agreement is much better for coefficient set II. Simulated phase envelopes are shown in Figure 12 for the swelled mixture with the highest CO2 concentration (1.85 mole CO2 per mole original oil). With either characterization the phase envelope bends off at some (low) temperature and from that point on it increases almost vertically. Below that temperature it is not possible to keep the fluid single-phase, no matter how much the pressure is increased. With coefficient set I the bend comes at a somewhat lower temperature than with coefficient set II. The lower degree of miscibility simulated using coefficient set II rather than coefficient set I is probably the main reason for the better match of the swelling data using the former set of coefficients.

Figure 8 shows simulation results for another swelling experiment on the oil mixture in Table 1. The injection gas has the composition shown in Table 4 and is rich in ethane. Again the simulated saturation points of the swelled mixtures are too low if coefficient set I is used, while the agreement is much better for coefficient set II. Figure 13 shows the simulated phase envelope for the swelled mixture using coefficient set II for the highest gas concentration (2.31 mole injection gas per mole original oil). The figure reveals that the bubble point at the swelling temperature of 74 C is at the phase boundary between a 3 phase (VLLE) area and a 2-phase liquid-liquid (LLE) area. The phase boundary at the outer phase envelope for a temperature around 74 C in other words marks the transition from a liquid-liquid region to a single-phase liquid region. A phase envelope for the swelled mixture characterized using coefficient set I does not show any liquid-liquid split. As was the case when CO2 was used as injection gas, it seems that the higher component miscibility simulated using coefficient set I prevents it from simulating the right phase behavior when gas is injected into a heavy oil.

Figure 14 shows simulated saturation pressures for the oil mixture in Table 2 recombined with C1 and mixed with an equimolar mixture of C1, C2, C3 and nC4. The saturation pressures agree fairly well with those measured, but as opposed to the measurements no 3-phase zone is seen in the simulations.

Figure 15 shows the phase diagram of the same mixtures simulated using coefficients set II in Table 5. The experimental bubble point pressures are simulated reasonably well, but what is more interesting, a liquid-liquid split is seen when the concentration of injection gas is above 33 weight %. This is consistent with the experimental observations, although the simulated area with a liquid-liquid split does not extend quite as far in pressure as is seen experimentally.

McMcMccTc 4321 ln +++=

243

215ln

Md

MdddP dc +++=

( ) MeeMeem 4321 ln +++=

20.1761.5740.480m +=

)288.15(Tccc 1i0ii +=

4

Discussion Based on the simulation results one might be tempted to

conclude that the optimum set of property correlations would be Equations (4) (6) with coefficient set II in Table 5. All the simulations conducted with this set of coefficients show a good match of experimental PVT data. Using the same correlations with coefficient set I, saturation points and conventional PVT data with no gas injection are matched well, but with this set of coefficients the correlations lack the ability to simulate the phase behavior at conditions with a liquid-liquid split. In most cases that results in too low saturation pressures being simulated for mixtures of a heavy oil and an injection gas.

This conclusion is however not as obvious as it may seem at first hand. Using coefficient set II there is a strong attraction between the heavier molecules (illustrated by the plot of the a-parameter in Figure 10). When gas is injected into a fluid with strong attractive forces acting between the heavier molecules, it may be thermodynamically favorable for the heavier molecules to split out as a separate liquid phase. As is exemplified above this is consistent with experimental data, but it may nevertheless cause numerical problems in compositional reservoir simulations because the reservoir simulators are not set up to handle more than one liquid hydrocarbon phase at a time. At conditions where the model says that two liquid phases are present, the reservoir simulator will at best predict a phase split that does not give a true picture of the phase behavior, but it may also completely fail to find a solution.

To avoid numerical problems in compositional reservoir simulations, coefficient set I in Table 5 may be a better starting point. As is exemplified in Figures 4-6 it has about the same predictive capabilities when it comes to regular PVT data with no gas injection involved. Figure 14 illustrates that it may also under influence of gas injection perform very well with respect to bubble point pressures.

Figures 7 and 8 show examples where the saturation pressures simulated using coefficient set I are too low for swelled mixtures. It may be worth pointing out that all the simulation results shown so far are without any parameter tuning. Figure 16 shows the swelling curve saturation points simulated for the mixture in Table 1 with the injection gas in Table 4 and the binary interaction parameter kij for C2-C7+ changed from 0.00 to 0.04. After this modification the experimental swelling curve is matched almost perfectly. Non-zero binary interaction coefficients are known to sometimes give raise to false liquid-liquid splits. Figure 17 shows the simulated phase envelope (with C2-C7+ kijs of 0.04) for the swelled mixture of the highest gas concentration (2.31 mole injection gas per mole original oil). A VLLE area is seen, but at a somewhat lower temperature than the reservoir temperature (74 C), for which reason this (false) liquid-liquid split is not likely to cause numerical problems in compositional reservoir simulations carried out for reservoir conditions.

Conclusion Classical cubic equations of state are applicable to simulate

the phase behavior of heavy reservoir oil mixtures. They are even capable of predicting the liquid-liquid splits often seen as a result of gas injection in heavy oil reservoir fields. Compositional reservoir simulators generally cannot handle more than one liquid phase and may therefore be unable to give a true picture of the phase behavior of heavy oil reservoir fluids

in fields with gas injection. When characterizing a fluid for a compositional reservoir simulation study, simulated liquid-liquid split at reservoir conditions may be avoided starting out with a fluid characterization that only gives a slight increase in a-parameter with increasing carbon number. Using this strategy, simulated saturation pressures are often too low for swelled mixtures. They may afterwards be corrected by using non-zero binary interaction parameters between the main constituent of the injection gas and the C7+ fraction. For fluids splitting into two liquid phases at reservoir conditions this will not give a fully correct picture, but approximately the right saturation points and gas/liquid ratios. The true phase behavior involving VLLE regions can be achieved by selection a fluid characterization where the a-parameter increases more steeply with increasing carbon number.

Acknowledgement The authors want to thank ConocoPhillips and Statoil for

kindly making experimental data available for this study.

NOMENCLATURE A = Constant in Equation (2) API = API gravity a = Parameter a in Soave equation B = Constant in Equation (2) b = Parameter a in Soave equation CN = Carbon number c = Peneloux volume correction parameter c1-c4 = Coefficients defined in Equation (4) and

tabulated in Table 5 d1-d4 = Coefficients defined in Equation (5) and

tabulated in Table 5 e1-e4 = Coefficients defined in Equation (6) and

tabulated in Table 5 M = Molecular weight m = 2nd order polynomial in defined in

Equation (7) P = Pressure SG = Specific gravity T = Temperature V = Molar volume z = Mole % = Acentric factor = Liquid density in g/cm3

REFERENCES 1. LINDELOFF, N., PEDERSEN, K.S., RNNINGSEN,

H.P. and MILTER, J., The Corresponding States Viscosity Model Applied to Heavy Oil Systems; Journal of Canadian Petroleum Technology 43, 2004, pp. 47-53.

2. PEDERSEN, K. S., THOMASSEN, P. and FREDENSLUND, AA., SRK-EOS Calculation for Crude Oils; Fluid Phase Equilibria 14, 1983, pp. 209-218.

3. PEDERSEN, K. S., THOMASSEN, P. and FREDENSLUND, AA., Thermodynamics of Petroleum Mixtures Containing Heavy Hydrocarbons. 1. Phase Envelope Calculations by Use of the Soave-Redlich-Kwong Equation of State; Ind. Eng. Chem. Process Des. Dev. 23, 1984, pp. 163-170.

4. PEDERSEN, K. S., BLILIE, A. L. and MEISINGSET, K.K., PVT Calculations on Petroleum Reservoir

5

FluidsUsing Measured and Estimated Compositional Data for the Plus Fraction; I&EC Research 31, 1992, pp. 1378-1384.

5. PEDERSEN, K. S., MILTER, J. and SRENSEN, H., Cubic Equations of State Applied to HT/HP and Highly Aromatic Fluids; SPE Journal 9, 2004, pp. 186-192.

6. PENELOUX, A., RAUZY, E. and FREZE, R., A Consistent Correction for Redlich-Kwong-Soave Volumes; Fluid Phase Equilibria 8, 1982, pp. 7-23.

7. SOAVE, G., Equilibrium Constants from a Modified Redlich-Kwong Equation of State; Chem. Eng. Sci. 27, 1972, pp. 1197-1203.

6

Tables and Figures

Component Mole% Molecular Weight (g/mol)

Density at 1.01 bar, 15 oC (g/cm3)

N2 0.49 CO2 0.31 C1 44.01 C2 3.84 C3 1.12 iC4 0.61 nC4 0.72 iC5 0.69 nC5 0.35 C6 1.04 C7 2.87 96 0.738 C8 4.08 107 0.765 C9 3.51 121 0.781 C10 3.26 134 0.792 C11 2.51 147 0.796 C12 2.24 161 0.810 C13 2.18 175 0.825 C14 2.07 190 0.836 C15 2.03 206 0.842 C16 1.67 222 0.849 C17 1.38 237 0.845 C18 1.36 251 0.848 C19 1.19 263 0.858 C20 1.02 275 0.863 C21 0.89 291 0.868 C22 0.78 305 0.873 C23 0.72 318 0.877 C24 0.64 331 0.881 C25 0.56 345 0.885 C26 0.53 359 0.889 C27 0.48 374 0.893 C28 0.46 388 0.897 C29 0.45 402 0.900 C30+ 9.96 449.1 0.989

Table 1 Molar composition of heavy reservoir fluid with an API gravity of 28. The reservoir temperature is 74 C and the saturation pressure at this temperature is 227.2 bar.

7



nC5 1.07 C6 0.47 C7 1.22 96 0.7908 C8 3.44 107 0.8197 C9 4.42 121 0.8369 C10 5.21 134 0.8486 C11 6.07 147 0.8529 C12 4.99 161 0.8679 C13 5.63 175 0.8840 C14 4.68 190 0.8958 C15 4.62 206 0.9022 C16 5.44 222 0.9097 C17 3.08 237 0.9054 C18 3.94 251 0.9087 C19 2.91 263 0.9194 C20 2.75 275 0.9247 C21 2.53 291 0.9301 C22 3.13 305 0.9354 C23 1.43 318 0.9397 C24 2.01 331 0.9440 C25 1.87 345 0.9483 C26 1.80 359 0.9526 C27 1.19 374 0.9569 C28 1.18 388 0.9612 C29 1.73 402 0.9644 C30 1.07 416 0.9676 C31 0.99 430 0.9719 C32 0.90 444 0.9751 C33 1.23 458 0.9783 C34 0.75 472 0.9815 C35 0.71 486 0.9847 C36 0.33 500 0.9879 C37 0.64 514 0.9901 C38 0.60 528 0.9933 C39 0.56 542 0.9965 C40 0.39 556 0.9987 C41+ 15.03 761 1.0019

Table 2 Molar composition of oil from flash of heavy reservoir oil to standard conditions (15 C and 1.01 bar). The oil has an API gravity of 18.

8



CO2 1.44 C1 18.72 C2 0.14 C3 0.03 iC4 0.01 nC4 0.01 iC5 0.01 nC5 0.27 C6 0.41 C7 0.13 96 0.722 C8 0.32 107 0.745 C9 0.45 121 0.764 C10 0.90 134 0.778 C11 1.45 147 0.789 C12 1.97 161 0.800 C13 2.50 175 0.811 C14 2.57 190 0.822 C15 2.86 206 0.832 C16 2.91 222 0.839 C17 2.96 237 0.870 C18 2.99 251 0.852 C19 3.07 263 0.857 C20 2.72 275 0.862 C21 1.96 345 0.885 C22 1.77 359 0.889 C23 1.68 374 0.893 C24 1.82 388 0.896 C25 1.96 345 0.885 C26 1.77 359 0.889 C27 1.68 374 0.893 C28 1.82 388 0.896 C29 1.64 402 0.899 C30 1.63 416 0.902 C31 1.36 430 0.906 C32 1.33 444 0.909 C33 1.12 458 0.912 C34 1.19 472 0.914 C35 1.00 486 0.917 C36+ 25.17 1038.1 1.104

Table 3 Molar composition of heavy reservoir fluid with an API gravity of 10. The reservoir temperature is 52 C and the saturation pressure at this temperature is 71.5 bar.

9

Mole% N2 0.02 CO2 14.04 C1 17.17 C2 59.88 C3 4.01 iC4 1.41 nC4 1.51 iC5 1.95 nC5 0.01 Table 4 Molar composition of injection gas used in swelling experiment on oil in Table 1. The swelling results are plotted in Figure 8.

Coefficient Set I Sub-index/ Coefficient

1 2 3 4 5

c 1948.17 -173.805 0.327780 -2449.00 - d 11.5465 -9.12042 0.830005 354.507 0.25 e -1.54778 -0.233701 5.53193

-1.4840310-2 - Coefficient Set II

Sub-index/ Coefficient

1 2 3 4 5

c 830.631 17.5228 4.5591110-2 -11348.4 - d 1.28155 1.26838 167.106 -8101.64 0.25 e -0.238380 6.1014710-2 1.32349 -6.5206710-3 -

Table 5 Coefficients in the correlations in Equations (4) (6) for use with the SRK equation.

Characterization I Characterization II

Mole %

Tc (C)

Pc (bar)

c0 cm3/mol

c1 cm3/(mol K)

Tc (C)

Pc (bar)

c0 cm3/mol

c1 cm3/(mol K)

CO2 1.44 31.1 73.76 0.225 3.0 0.01 31.1 73.76 0.225 3.0 0.01 C1 18.72 -82.6 46.00 0.008 0.6 0.00 -82.6 46.00 0.008 0.6 0.00 C2 0.14 32.3 48.84 0.098 2.6 0.00 32.3 48.84 0.098 2.6 0.00 C3 0.03 96.7 42.46 0.152 5.1 0.00 96.7 42.46 0.152 5.1 0.00 iC4 0.01 135.0 36.48 0.176 7.3 0.00 135.0 36.48 0.176 7.3 0.00 nC4 0.01 152.1 38.00 0.193 7.9 0.00 152.1 38.00 0.193 7.9 0.00 iC5 0.01 187.3 33.84 0.227 10.9 0.00 187.3 33.84 0.227 10.9 0.00 nC5 0.27 196.5 33.74 0.251 12.2 0.00 196.5 33.74 0.251 12.2 0.00 C6 0.41 234.3 29.69 0.296 18.0 0.00 234.3 29.69 0.296 18.0 0.00 C7 0.13 292.7 28.15 0.382 33.6 0.01 346.1 24.52 0.508 69.8 -0.01 C8 0.32 326.4 27.94 0.404 31.4 -0.01 378.3 22.76 0.576 83.0 -0.02 C9 0.45 357.2 27.21 0.423 28.3 -0.03 401.1 21.41 0.625 88.8 -0.03 C10-C19 24.18 472.1 22.37 0.498 9.1 -0.10 485.2 17.30 0.790 85.4 -0.09 C20-C25 14.17 530.2 19.61 0.535 -36.6 -0.17 526.0 15.63 0.845 36.8 -0.16 C26-C32 11.23 568.4 18.21 0.560 -89.9 -0.22 562.1 14.64 0.879 -11.8 -0.22 C33-C46 9.15 621.3 17.16 0.599 -169.7 -0.28 638.8 13.24 0.972 -49.4 -0.28 C47-C61 5.89 705.3 16.52 0.666 -288.4 -0.34 797.7 11.10 1.202 -20.5 -0.34 C62-C79 4.81 774.6 16.23 0.720 -421.7 -0.39 945.8 9.70 1.396 18.6 -0.39 C80-C101 3.69 841.4 16.08 0.769 -586.1 -0.45 1104.6 8.59 1.582 70.1 -0.45 C102-C132 2.83 911.6 16.04 0.817 -791.9 -0.51 1289.7 7.64 1.780 151.2 -0.51 C133-C200 2.11 1007.8 16.09 0.876 -1143.2 -0.60 1577.7 6.62 2.032 297.7 -0.60

Table 6 Two alternative characterizations of fluid composition in Table 3. The property correlations in Equations (4)-(6) are used with each set of coefficients (I and II) in Table 5. The binary interaction coefficients are shown in Table 7.

10

N2 CO2 CO2

-0.032 C1 0.028 0.120 C2 0.041 0.120 C3 0.076 0.120 iC4 0.094 0.120 nC4 0.070 0.120 iC5 0.087 0.120 nC5 0.088 0.120 C6 0.080 0.120 C7+ 0.080 0.100

Table 7 Non-zero binary interaction coefficients for mixture in Table 6.

5 10 15 20 25 30Carbon number

0.1

1

10

Mo

le %

Figure 1 C7+ component mole %s for fluid in Table 1 plotted against carbon number. The mole %s are shown as circles and the dashed line is a best-fit line according to Equation (2).

5 10 15 20 25 30 35 40Carbon number

0.1

1

10

Mo

le %

Figure 2 C7+ component mole %s for fluid in Table 2 plotted against carbon number. The mole %s are shown as circles and the dashed line is a best-fit line according to Equation (2).

11

5 10 15 20 25 30 35Carbon number

0.1

1

10

Mo

le %

Figure 3 C7+ component mole% for fluid in Table 3 plotted against carbon number. The mole %s are shown as circles and the dashed line is a best-fit line according to Equation (2).

0 10 20 30 40 50 60 70 80Pressure (bar)

1.02

1.03

1.04

1.05

Bo (m

3 /Sm

3 )

ExperimentalChar IChar II

Figure 4 Measured and simulated Bo factors for differential liberation experiment on oil mixture in Table 3. The experiment was carried out at a temperature of 52 C.

0 10 20 30 40 50 60 70 80Pressure (bar)

0

4

8

12

16

20

Rs

(Sm

3 /Sm

3 )


Figure 5 Measured and simulated gas/oil ratios (Rs) for differential liberation experiment on oil mixture in Table 3. The experiment was carried out at a temperature of 52 C.

12

0 10 20 30 40 50 60 70 80Pressure (bar)

0.94

0.95

0.96

0.97

0.98

0.99

1.00

Oil

densi

ty (g/

cm3 )


Figure 6 Measured and simulated oil densities for differential liberation experiment on oil mixture in Table 3. The experiment was carried out at a temperature of 52 C.

0 40 80 120 160 200Mole% CO2 Added

200

300

400

500

Pre

ssu

re (ba

r)

ExpChar IChar II

Figure 7 Measured and simulated saturation pressures for swelling experiment on the oil mixture in Table 1. CO2 was used as injection gas and the experiment was carried out at a temperature of 74 C.

0 50 100 150 200 250Mole% Gas Added

220

230

240

250

260

270

Pres

sure

(ba

r)

ExpChar IChar II

Figure 8 Measured and simulated saturation pressures for swelling experiment on the oil mixture in Table 1. The composition of the injection gas is shown in Table 4. The experiment was carried out at a temperature of 74 C.

13

10 20 30 40 50Weight % Solvent

40

80

120

160

200

Pres

sure

(ba

r)

L L+L

V+L+LV+L

Figure 9 Measured phase diagram for the oil mixture in Table 2. It has initially been recombined with C1 to a gas/oil ratio of 29.7 Sm3/m3 and an equimolar mixture of C1, C2, C3 and nC4 and added the resulting mixture. The phase study was conducted at a temperature of 24 C. V stands for vapor and L for liquid.

0 500 1000 1500 2000 2500Molecular weight

0

40

80

120

160

a-pa

ram

eter

(m

6 ba

r/mol

e2 )

Char IChar II

Figure 10 SRK a-parameters for C7+ components in the characterized oil mixture in Table 6. Two different sets of coefficients (I and II in Table 5) have been used in the property correlations in Equations (4) (6). The a-parameters are for a temperature of 52 C.

0 200 400 600 800 1000 1200 1400Temperature (oC)

0

50

100

150

200

250

Pres

sure

(ba

r)

Char IChar II3-Phase areaCritical point

VLE

VLE

VLLE

VL

Figure 11 Simulated phase envelopes for the oil mixture in Table 3 using the SRK-equation of state and the fluid characterizations in Table 6.

14

0 200 400 600 800Temperature (oC)

0

400

800

1200

1600

Pres

sure

(ba

r)

Char IChar IICritical point

VLELLE

Figure 12 Simulated phase envelopes for the oil mixture in Table 1 mixed with CO2 in molar ratio 1:1.85. Char I and Char II refer to the two coefficient sets in Table 5.

-200 0 200 400 600 800Temperature (oC)

0

200

400

600

Pres

sure

(ba

r)

Phase envelope3-Phase area

VLLE

VLE

LLE

Figure 13 Simulated phase envelopes for the oil mixture in Table 1 mixed with gas in Table 4 in ratio 1:2.31. Coefficient set II in Table 5 was used when characterizing the fluid composition.


40

80

120

160

200

Pres

sure

(ba

r)

ExperimentalSimulated Char I

Figure 14 Measured and simulated saturation points for the oil mixture in Table 2, which has initially been recombined with C1 to a gas/oil ratio of 29.7 Sm3/m3 and then mixed with an equimolar mixture of C1, C2, C3 and nC4 at a temperature of 24 C. The simulation results are for coefficient set I in Table 5.

15


40

80

120

160

200Pr

essu

re (ba

r)ExperimentalSimulated Char II

Figure 15 Measured and simulated phase diagram for the oil mixture in Table 2, which has initially been recombined with C1 to a gas/oil ratio of 29.7 Sm3/m3 and then mixed with an equimolar mixture of C1, C2, C3 and nC4 at a temperature of 24 C. The simulation results are for coefficient set II in Table 5.

0 50 100 150 200 250Mole% Gas Added

220

230

240

250

260

270

Pres

sure

(ba

r)

ExpChar I with kij for C2

Figure 16 Measured and simulated saturation pressures for swelling experiment on oil mixture in Table 1. The composition of the injection gas is shown in Table 4. The experiment was carried out at a temperature of 74 C. Coefficient set I in Table 5 is used. A kij of 0.04 was assumed for C2-C7+.

-100 0 100 200 300 400 500Temperature (oC)

0

100

200

300

400

Pres

sure

(ba

r)

Phase envelope3-Phase areaCritical point

Figure 17 Simulated phase envelopes for the oil mixture in Table 1 mixed with gas in Table 4 in ratio 1:2.31. Coefficient set I in Table 5 was used when characterizing the fluid composition. A kij of 0.04 was assumed for C2-C7+.

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