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ORIGINAL RESEARcH ARTicLE
DOI: https://doi.org/10.18599/grs.2018.4.336-343
Simulation of composition changes in reservoirs with large hydrocarbon columns and temperature gradient
A.V Yashin1-2*, I.M. Indrupskiy1,2, O.A. Lobanova1
1Oil and Gas Research Institute of the Russian Academy of Sciences, Moscow, Russian Federation 2Gubkin Russian State University ofOil and Gas (National Research University), Moscow, Russian Federation
Abstract. This paper compares three methods for calculation of initial composition variation with depth in hydrocarbon reservoirs: considering thermal diffusion, considering temperature gradient without thermal diffusion effects; and by gravity forces only. Newton method-based numerical algorithm was implemented for solution of thermodynamic equations to evaluate pressure and hydrocarbon composition. Test calculations are performed for main gas-condensate reservoir of Vuktylskoye field with a gas column of 1350 m.
The results obtained with the numerical algorithm indicate that gravity segregation impact is the strongest for all the cases considered. Concentration decreases with depth for low molecular weight components and increases for high molecular weight components. The higher molecular weight of the component, the stronger variation of its concentration with depth. Initial reservoir pressure also changes accordingly.
However, thermal diffusion also has a significant influence on variation of hydrocarbon composition with depth and initial reservoir pressure. For the test case considered, thermal diffusion magnifies the impact of gravity and results in strongly nonlinear dependencies of component concentrations on depth. When thermal gradient is taken into account without thermal diffusion effects, the results are only slightly different from those with the isothermal gravity segregation calculations.
None of the calculation methods were successful in matching estimates of initial composition variation with depth obtained from well exploitation data. Physical mechanisms governing variation of composition within the main reservoir of the Vuktylskoye field require additional investigation. Despite the long history of the reservoir development, this problem was previously studied based only on field development data.
Keywords: hydrocarbon mixture, geothermal gradient, thermal diffusion, component composition, initial composition, gas condensate reservoir, Vuktylskoye field
Recommended citation: Yashin A.V., Indrupskiy I.M., Lobanova O.A. (2018). Simulation of composition changes in reservoirs with large hydrocarbon columns and temperature gradient. Georesursy = Georesources, 20(4), Part 1, pp. 336-343. DOI: https://doi.org/10.18599/grs.2018A336-343
Introduction
Hydrocarbon reservoirs with large oil or gas columns are characterized by significant changes in reservoir pressure and temperature with depth. As a result, the initial composition of the reservoir fluid also changes significantly with depth.
The distribution of components in depth in massive hydrocarbon reservoirs is greatly influenced by gravitational forces. Initial composition of the fluid in such reservoirs is formed in such a way that the concentration of light components decreases in the direction from the top to the bottom, while concentration of heavy components increases on the contrary. Accordingly, the content of
*Corresponding author: Anton V. Yashin E-mail: antn-yashin@yandex.ru
© 2018 The Authors. Published by Georesursy LLC This is an open access article under the CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/)
condensate in the reservoir gas increases and the solution-gas content in oil decreases.
In 1954, A.Y. Namiot made calculations for mixtures modeling oils of different composition (Namiot, 1954). It was concluded that gravity forces have a significant impact on the composition of oils containing significant amounts of heavy hydrocarbons and dissolved gas. In case of reservoirs consisting mainly of light hydrocarbons, the composition varies slightly with depth. Subsequently, the mathematical apparatus for calculating changes in multicomponent mixtures composition under the influence of gravity has been widely developed and applied (Whitson, Belery, 1994; Brusilovskii, 2002).
The method of calculating gravitational distribution of pressure and composition by reservoir depth is based on the assumption of the system thermodynamic equilibrium in the gravity field. This state of the system can be achieved at a constant system temperature throughout the entire volume.
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For most formations, the temperature increases substantially with depth. Usually, the natural vertical temperature gradient (geothermal gradient) is 0.02-0.03°C/m. In such conditions, thermodynamic equilibrium is not achieved, so there should be vertical heat and mass transfer within the hydrocarbon-saturated part of reservoir.
Many authors have shown a significant influence of the thermal diffusion effect on the distribution of component composition (Pedersen, Hjermstad, 2006; Belery, Da Silva, 1990; Whitson, Belery, 1994; etc.). However, unlike the effect of gravity, there is no generally accepted opinion about the nature of this effect as well as there is no correct mechanism for its consideration for hydrocarbon reservoirs, and therefore a number of conclusions in the above-mentioned works are contradictory. Therefore, there are no established approaches for taking into account the temperature factor influence on the change in the initial composition with depth when calculating reserves and designing the development of specific reservoirs. In addition, the methodology of the corresponding options in the PVT-modeling packages (Schlumberger PVTi, Roxar PVTx, etc.) are poorly documented.
One interesting example in terms of assessing the temperature factor influence is the Vuktylskoye oil-and gas-condensate field. For the initial conditions in the main gas-condensate reservoir, the difference in pressures within the gas column was 4.3 MPa and in temperatures - 25.65°C. The depth of the reservoir varies in the range from 2000 m to 3350 m. However, despite the 50-year history of the field development, until now the change in the initial composition with depth has been studied mainly on the basis of the actual well data analysis. As for mathematical modeling, there remains the problem of setting thermodynamically consistent input data for performing calculations with a reservoir simulation model.
In this paper, using the example of the Vuktylskoye field, the authors estimate thermal diffusion effect on the component composition distribution in a gas-condensate reservoir with a large gas column. The results of mathematical modeling are compared with actual field data.
calculation of changes in component composition with depth in isothermal conditions
In isothermal equilibrium conditions, fugacity values of >th component of the mixture at depths h1 and h2 are interrelated by the following equality (Brusilovskii, 2002):
RTlnfi(p,y)\h2 = RTlnfi(p,y~)\hl + Aii5(7ii - h2y,
i = l,2,...,N, (1)
where f and M. are the fugacity and molecular weight of the j-th component, respectively, p is the reservoir pressure, Tis the reservoir temperature, y is the vector of molar fractions (concentrations) for components in the gas-condensate mixture, g is the gravity acceleration, R is the universal gas constant, N is the number of components of the mixture.
Let's denote:
xl)i = RTlnfi(p,y)\hl + MigQir - h2y,
i = l,2,...,N, (2)
The relation (1) corresponds to the balance between the changes in chemical and gravitational potentials for each component of the mixture between two depth under conditions of thermodynamic equilibrium in the field of gravity. For molar concentrations of the components, the normalization condition is also satisfied:
n
¿>1. (3)
£=1
If the mixture's component composition y1(h1),..., yN(h1) and pressure p(h1) at the level h1 are known, the composition and pressure at the level h2 are determined by solving the following set of N+1 non-linear algebraic equations:
' RTlnf^Qiily^hi), - .yjvCia)] = 0
RTlnfN[p(Ti2),yi(h2).....yN(h2)} -x/jn = 0
n
2>2)-l = 0 (4)
¿=i
where p(h2) ,y(h2) ,...,yN(h2) are the pressure and component composition (mole fractions of the components) of the mixture at h, respectively.
The Newton method is used to effectively solve the system (4). This method has a high convergence rate in the presence of a good initial approximation, which is achieved by adjusting the depth step in the calculation (Brusilovskii, 2002).
Solution by the Newton's method
From the last equation of system (4) one can express:
n
yi = !-2>2) (5)
1=2
and reduce its order by one. The base (iterative) unknowns are p, yz,---yN.
After transformations, the system of equations for calculating the component composition and pressure of the mixture at a depth of h2 is reduced to solving the following system of N transcendental equations:
®i(.P>y2,-.Vn) = RTlnfilvQiJ.y^hJ, ...,yN(h2)] -
-ipi = 0,i = l,...,N (6)
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Successive approximation of the variables is performed by solving at each step the system of equations JS=Fobtained by linearizing the equations of system (6). The matrix J and the vectors S, F have the following form:
N N
] =
9®! 9®! 9<t>! dp dy2 " dyN
9G>jv 90jv 9<t>jv
dp dy2 " dyN,
S =
(ptn+1 _ pm\ ym+l _ym
F =
-0™
vm+1 \SN
■yf)
(7)
where m = 0,1,2,... is the iteration number.
The components of the matrix J are calculated as follows:
3$; dlnfi
—- =-— i- 1 N;
a a I L —I"'
op dp d$>i _ dlnfj dlnft dyj dyj dyt
(8)
,i = l.....N,j = 2.....N. (9)
The apparatus of cubic equations of state is used for calculation of fugacities and their derivatives (Brusilovskii, 2002).
Within the approximate approach, it is possible to take into account temperature changes with depth in the system (4). For this, hydrocarbon column is divided into a number of small intervals and the temperature is considered constant within each interval. The difference in temperatures between the intervals should be taken into account when calculating fugacities; however, thermodynamic equilibrium conditions (1) are considered approximately valid. However, such a calculation neglects the heat transfer and the accompanying mass transfer of components caused by thermal diffusion.
Equation of state
The following Peng-Robinson cubic equation of state was applied to calculate the fugacities in this work:
Z3-(l- B)Z2 + (A- 3B2)Z - (AB — B2— B3) = 0.
(10)
For a given equation of state, the fugacities are calculated by the following formula:
Inf = In(ytp) + ^ (Z - 1) - ln(Z - B) +
2A/2B '
In
7=1
Z + (l + V2)g
Z + (l-V2)ß.
where
p v
Z = —, RT
(11)
(12)
i=1 7=1 N
B^ViBi, i=1
Aij = (l — kij) JAiAJ,
At =
Q-iV R2T2 -
B = — 1 RT -
(/?rc.)2
a£ = 0.45724 v lJ a ,
bi = 0.07780
Va
RTci Pci '
a = (1 + m * (l -_ T
Tr — rp >
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20) (21)
m = 0.03796 + 1.485 0.1644 * wf +
+ 0.01667 * wf (Wi > 0.4) , (22)
m = 0.37464 + 1.54226 * w£ -
- 0.26992 * w?(wt < 0.4) , (23)
where Z is the compressibility factor; p is the reservoir pressure; T is the reservoir temperature; R is the universal gas constant; T is the reduced temperature; Tci is the critical temperature of the component; pci is critical component pressure; wi is acentric factor; yi is the mole concentration of the component in the mixture.
Thermal diffusion
The temperature gradient makes a significant contribution to the change in the composition of the hydrocarbon mixture. Taking into account the vertical temperature gradient leads, as a rule, to a stronger dependence of the initial composition on the depth than can be explained only by gravitational forces.
The effect of thermal diffusion on the distribution of the reservoir components is described using nonequilibrium thermodynamical models. Different approaches to considering the effect of thermal diffusion have been proposed by such authors as Belery and Da Silva (Belery, Da Silva, 1990), Haase (Haase, 1990), Kempers (Kempers, 1989), Whitson (Whitson, Belery, 1994), etc.
Pedersen and Lindeloff (Pedersen, Lindeloff, 2003) proposed the following relationships to calculate the compositional change with depth in reservoirs under the influence of gravity and thermal diffusion:
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RTilnfifaWh, = RTiWi(p,y)K + Mtgihi - h2)
H H,\AT
(24)
where Ht is the absolute partial molar enthalpy of i-th component, H is the absolute molar enthalpy of the mixture, M is the average molecular weight of the mixture, AT is the temperature difference between the depths h2 and hv Tx is the temperature at the depth hp T2 is the temperature at the depth h2. Relation (24) corresponds to the nonequilibrium stationary state of the system in a gravitational and geothermal field.
The authors (Pedersen, Lindeloff, 2003) suggested that the change in component composition under stationary conditions and influence of the temperature gradient is determined by the specific enthalpy of each component. Components with a higher enthalpy than the average for the mixture tend to a warmer zone. Under typical reservoir conditions, high molecular weight components will have a higher specific enthalpy than low molecular weight ones. This corresponds to actual observations showing that the change in component composition with depth in reservoirs with a positive vertical temperature gradient is higher than can be explained only by the gravitational effect.
The partial molar enthalpy of Z-th component in a mixture at temperature T can be represented by the following expression:
K(.T) = + (Hl9(T) - + X
(25)
where Hl9(T} u H^9 is the partial molar enthalpy of Z-th component in the ideal-gas state at temperatures T and 273.15 K, respectively, Ht - is the partial residual molar enthalpy:
dlncpi
Ht = —RTZ
dT
(26)
where 9 is the fugacity coefficient of the Z-th component.
Enthalpy of the Z-th component in an ideal-gas state at a temperature of 273.15 K can be determined by the following formula:
/i^9 (273.15/0 , ,
1 -- = -134.2 + 8.367 * Mu (27)
R
and at temperature T, it can be determined from the following thermodynamic relation:
rT
ClPdi dT, (28)
'273.15K '
where the heat capacity of an ideal gas is determined by the correlation with temperature:
H)9(T) - H)9(213.1SK) = [
Clpdi = CUT + c2iiT2 + C3jT3 + cAiiT\
(29)
where the coefficients C ,-C.
M 4,i
are tabulated for Cj-C5
components of the mixture (Reid, Prausnitz, Poling, 1987). For C6+ components, the coefficients are calculated using Kesler-Lee empirical formulas (Kesler, Lee, 1976).
Vuktylskoye field
Based on the described model, calculation were performed for changes in the initial composition with depth for the main gas-condensate reservoir of the Vuktylskoye field with a large gas column (Tables 1-3). Fig. 1 shows the changes in the initial component composition of the gas-condensate mixture with the reservoir depth according to the data of (Dolgushin, 2007). The plots shown were obtained from actual data analysis of wells completed in the reservoir at various depths. Fig. 2 shows the change in the initial reservoir pressure and temperature over the depth of the reservoir. It is interesting to compare the dependences of the initial composition and pressure on the depth according to Fig. 1-2 and obtained by mathematical modeling. The latter are necessary as initial conditions for forecast simulations on a multicomponent 3D reservoir flow model.
Constant temperature Interval temperatures Thermal diffusion
N2 5.45201 5.46618 6.09901
2 0.03593 0.03571 0.03625
Cl 79.22680 79.31150 80.15020
C2 7.76406 7.72844 7.28671
C3 2.82648 2.80510 2.57673
iC4 0.33319 0.33012 0.30394
nC4 0.58375 0.57766 0.51958
iC6 0.10752 0.10618 0.09520
nC6 0.09297 0.09175 0.08075
C6+(1) 1.25377 1.23458 0.91920
C6+(2) 1.68256 1.68550 1.51376
C6+(3) 0.55714 0.54645 0.37851
C6+(4) 0.07829 0.07547 0.03763
C6+(5) 0.00534 0.00513 0.00244
C6+(6) 0.00021 0.00020 0.00011
P 33.04260 32.93150 33.02160
Table 1. Calculated component composition (molar fractions of the components in the mixture) at a depth of2000 m
Constant Interval Thermal
temperature temperatures diffusion
N2 5.28145 5.28555 5.62076
2 0.03791 0.03784 0.03805
Cl 77.43990 77.46610 78.24030
C2 8.13089 8.12082 7.86716
C3 3.11116 3.10486 2.95724
iC4 0.38162 0.38069 0.36201
nC4 0.67508 0.67320 0.63203
i C5 0.12954 0.12912 0.12066
nC5 0.11273 0.11233 0.10392
C6+(1) 1.58503 1.57859 1.33152
C6+(2) 2.09588 2.09788 1.94260
C6+(3) 0.84917 0.84494 0.67343
C6+(4) 0.15536 0.15387 0.10148
C6+(5) 0.01359 0.01345 0.00838
C6+(6) 0.00075 0.00074 0.00047
P 34.50070 34.47140 34.50690
Table 2. Calculated component composition (molar fractions of the components in the mixture) at a depth of2500 m
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Constant temperature Interval temperatures Thermal diffusion
n2 4.68992 4.69193 4.18694
2 0.04139 0.04135 0.04100
Cl 71.89110 71.90820 68.45650
C2 8.93229 8.92625 9.25570
C3 3.81971 3.81585 4.12125
iC4 0.50947 0.50890 0.56036
nC4 0.92533 0.92411 1.03742
i C5 0.19383 0.19354 0.22240
nC5 0.17162 0.17134 0.19968
C6+(i) 2.64608 2.64113 3.38334
C6+(2) 3.24845 3.25410 3.75229
C6+(3) 2.11299 2.10898 3.10978
C6+(4) 0.69862 0.69576 1.37629
C6+(5) 0.10599 0.10547 0.25513
C6+(6) 0.01317 0.01305 0.04189
P 37.34190 37.32690 37.38680
15 20 25 30 35 40 45 50 55 60 65 70
Table 3. Calculated component composition (molar fractions of the components in the mixture) at a depth of3350 m
E l"
260 280
pf, kgf/m
Fig. 2. Dependence ofthe initial values ofreservoir pressure (1) and temperature (2) on the depth for the Vuktylskoye field (Dolgushin, 2007)
Well 26 Well 28
nC4, mol.%
0,9 -i
2394,7 2532,5 2641,0
2300 2500 2700
0 0,48 ¿0,45 ¿0,45
«0 41 ^ 0,42 i T ■
90,86 !
' 0 Ô 0,66
I 7 14 -fr 7,3
06,14 _
! 05,85 - -------"¿5,01 !
4,770 —Ä----¿TO" —CH;48-;- 0 4,85
3100,5 3200,5 3100 3300
H, m
Fig. 1. Changes in the content of CT C2 C3, iC4, nC4 C+, N5 reservoir gas components within the vertical reservoir section for the initial conditions of the Vuktylskoye field (Dolgushin, 2007)
The model of the gas-condensate mixture was adopted according to the latest development design document (Supplement to the field development plan ..., 2014) and is represented by hydrocarbon components (methane, ethane, propane, butane, pentane and six fractions), as well as nitrogen and carbon dioxide (Table 4). At a depth of 3000 m, the initial composition of the mixture is known, the temperature of the reservoir is 334 K, the reservoir pressure is 36.1 MPa. Geothermal gradient equals to 0.019°C/m. Physical properties of hydrocarbon fractions are presented in Table 5. The goal is to recalculate the pressure and composition from the initial depth of 3000 m to a depth of 2000 m (upper level of the reservoir), 2500 m and 3350 m (gas-liquid contact).
Components Mole fraction, % Molar mass, kg/kmol P, MPa , K dT, -m
N2 5.01 28.01
2 0.04 44.01
C1 74.85 16.04
C2 8.56 30.07
C3 3.47 44.1
iC4 0.45 58.12
nC4 0.8 58.12
ÍC5 0.16 72.15 36.1 334 0.019
nC5 0.14 72.15
C6+(i) 2.08 85.02
Cß+(2) 2.67 110.46
C6+(3) 1.38 157.95
C6+(4) 0.35 231.22
C6+(5) 0.0404 338.18
C6+(6) 0.0034 500
Table 4. Model of gas condensate mixture and input data at a depth of3000 m (Supplement to the field development plan ... , 2014)
t, 0c
0
500
300
C, mol.%
Well 11
Well 8
Well 12
Well 21
73
C, mol.%
C„ mol.%
c
3,5
3,1
3,34
3,0
2,5
2,0
iC,, mol.%
0,6
0,3
0,8
0,/
0,6
C , mol.%
N„ mol.%
2900
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Fraction Density, g/cm3 Critical temperat., Tc, K Critical pressure Pc, MPa Acentric factor Molar concentration of the comp onent in the mixture z M, g/mol Boiling temperature, Tb, K
6+(1) 0.664 504.9 3.060 0.2923 0.02082 85.0188 339.126
6+(2) 0.708 570.4 2.505 -0.2581 0.02668 110.457 399.174
6+(3) 0.750 646.6 1.941 0.3433 0.01381 157.954 474.645
6+(4) 0.787 732.4 1.382 0.8143 0.003451 231.218 569.612
6+(5) 0.821 818.6 0.946 1.0015 4.04 10-4 338.184 673.787
6+(6) 0.854 904.8 0.645 1.2589 3.36 10-5 500 783.105
7,0
2000 • Dolgushin C2
2500
Constant temperature
Fig. 5. Change in ethane content with depth
Table 5. Physical properties offractions (Supplement to the field development plan ..., 2014)
The calculations were carried out using the following three methods:
1) Gravity method - the equation (1),
2) Taking into account the interval temperature change, but without thermal diffusion,
3) Taking into account thermal diffusion - the equation (24).
calculation results
Fig. 3-10 show some calculation results. The depth changes of pressure and initial concentrations of gas-condensate mixture individual components are given for the main reservoir of the Vuktylskoye field. Fig. 9 corresponds to the group of C5+ hydrocarbons, i.e. the sum of pentanes and all C6+ fractions.
The concentration of light components (nitrogen and methane) decreases with depth (Fig. 3-4), while the concentration of heavier hydrocarbons starting with ethane increases with depth (Fig. 5-9). The higher the molecular weight of the component, the more its content increases with depth. Initial reservoir pressure changes consistently (Fig. 10). These features are associated with the influence of the gravitational field and are predominant in all variants of calculations.
7 6 5
3000
• Interval temperatures -H
Depth, m ■ Thermal diffusion
2000 • Dolgushin C3
2500
Constant temperature
3000
•Interval temperatures —i
Depth, m - Thermal diffusion
Fig. 6. Change in propane content with depth
2000 • Dolgushin iC4
2500
Constant temperature
3000
• Interval temperatures —
Depth, m ■ Thermal diffusion
Fig. 7. Change in iso-butane content with depth
2000 • Dolgushin N2
2500
Constant temperature
3000
•Interval temperatures —
Depth, m • Thermal diffusion
Fig. 3. Change in nitrogen content with depth
80 78
* 76
2000
• Dolgushin N2
2500
Constant temperature
3000
•Interval temperatures -
Depth, m - Thermal diffusion
Fig. 8. Change in normal-butane content with depth
2000 • Dolgushin C1
2500
Constant temperature
3000
•Interval temperatures —i
Depth, m - Thermal diffusion
Fig. 4. Change in methane content with depth
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4
2
1
0
2OOO I Dolgushin C5+
2500
Constant temperature
3000
• Interval temperatures -
Depth, m Thermal diffusion
Fig. 9. Change in content of group of components C++ with depth
2000 • P(Dolgushin)
2500
Constant temperature
- Interval temperatures
Depth, m Thermal diffusion
Figg. 10. Change in initial reservoir pressure with depth
From Fig. 3-10, it can be seen that when taking into account the temperature variation, the obtained composition distribution with depth is only slightly different from the isothermal case. This result confirms the conclusions of the work (Whitson, Belery, 1994).
Also from Fig. 3-10, it follows that the effect of thermal diffusion is essential and enhances the gravitational field influence for the described hydrocarbon system. A similar result was obtained in (Pedersen, Hjermstad, 2006) for another reservoir, where it was shown to match the actual data. The same method to account for thermal diffusion was used. However, this conclusion should not be absolutized, since a number of other authors indicate that thermal diffusion can reduce the influence of the gravitational field. In any case, it is characteristic that the composition changes with depth taking into account thermal diffusion become essentially nonlinear.
From Fig. 3-6, it can be seen that the data calculated by the gravitational method of the composition distribution and the interval-wise temperature consideration do not agree well with the actual data presented by N.V. Dolgushin (Dolgushin, 2007). Accounting for the effect of thermal diffusion also does not give a satisfactory approximation, and for a number of components it makes bigger the observed deviation.
Thus, the physical mechanisms causing the initial distribution of the component composition with depth for the Vuktylskoye field require further analysis. In particular, it is advisable to take into account the possible effect of the residual liquid hydrocarbon phase, the effect of the adopted component model
of the mixture and to try other models for describing thermal diffusion.
On the other hand, it should be taken into account that information on the distribution of the composition according to well data (Dolgushin, 2007) is also not the result of direct measurements. It is obtained by analyzing and averaging the well performance data with significant (hundreds of meters) production intervals in a heterogeneous reservoir. It is also important that N.V. Dolgushin made some assumptions regarding the possibility of relying on data on the well production composition at certain dates as an estimate of the initial distribution.
conclusions
The paper considers mathematical modeling of changes in the initial component composition of hydrocarbon mixtures with depth in massive reservoirs under the influence of natural physical fields (gravitational and geothermal).
Numerical algorithms have been implemented to calculate the distribution of hydrocarbon mixture components over depth in the gravitational field under isothermal conditions, or taking into account interval temperature variation and thermal diffusion.
The results of comparative calculations for the main gas-condensate reservoir mixture of the Vuktylskoye field showed that thermal diffusion has a significant effect on the distribution of components, as well as the initial reservoir pressure. In the case under consideration, thermal diffusion magnifies the influence of the gravitational field and leads to pronounced non-linear dependencies for the components concentrations.
Satisfactory agreement of the calculations results with the component composition distribution according to well operation data was not achieved for any of the algorithms. The physical mechanisms determining the distribution of the initial composition within the reservoir volume of the Vuktylskoye field require further analysis.
References
Belery P., Da Silva F.V. (1990). Gravity and thermal diffusion in hydrocarbon reservoirs. Paper presented at the Third Chalk Research Program, June 11-12, Copenhagen, Denmark.
Brusilovskii A.I. (2002) Fazovye prirashcheniya pri razrabotke mestorozhdenii nefti i gaza [Phase transitions in the development of oil and gas fields]. Moscow: Graal Publ., 575 p. (In Russ.)
Dolgushin N.V. (2007) Metodologiya izucheniya gazokondensatnoi kharakteristiki neftegazokondensatnykh mestorozhdenii s vysokim soderzhaniem kondensata i bol'shim etazhom gazonosnosti [Methodology for studying gas-condensate characteristics of oil and gas-condensate fields with a high content of condensate and a large gas columns]. Diss. doktora tekhnicheskikh nauk [Dr. tech. sci. diss.]. Ukhta: SEVERNIPIGAZ, 400 p. (In Russ.)
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6
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Haase R. (1990). Thermodynamics of irreversible processes. New York: Dover.
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Kesler M.G., Lee B.I. (1976). Improve prediction of enthalpy of fractions. Hydrocarbon processing 55, pp. 153-158.
Namiot A.Yu. (1954) Razlichie svoistv nefti v predelakh neftenosnoi zalezhi. Issledovaniya v oblasti fiziki plasta [Differences in the properties of oil within an oil deposit. Studies in the reservoir physics]. Tr. VNII, 3, pp. 41-60. (In Russ.)
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About the Authors
Anton V. Yashin - Engineer, MSc student
Gubkin Russian State University of Oil and Gas (National Research University)
Oil and Gas Research Institute of the Russian Academy of Sciences
3, Gubkin st., Moscow, 119333, Russian Federation
Ilya M. Indrupskiy - DSc (Engineering), Professor, Head of Laboratory
Gubkin Russian State University of Oil and Gas (National Research University)
Oil and Gas Research Institute of the Russian Academy of Sciences
3, Gubkin st., Moscow, 119333, Russian Federation
Olga A. Lobanova - PhD (Engineering), Researcher
Oil and Gas Research Institute of the Russian Academy of Sciences
3, Gubkin st., Moscow, 119333, Russian Federation
Manuscript received 29 March 2018; Accepted 27 September 2018; Published 30 November 2018
SCIENTIFIC AND TECHNICAL JOURNAL MV
GEDRESURSY EE
