Two-Phase Multicomponent Diffusion and Convection for Reservoir Initialization
- Hadi Nasrabadi (Imperial College) | Kassem Ghorayeb (Schlumberger S.A.) | Abbas Firoozabadi (Reservoir Engr. Research Inst.)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- October 2006
- Document Type
- Journal Paper
- 530 - 542
- 2006. Society of Petroleum Engineers
- 5.3.2 Multiphase Flow, 5.5 Reservoir Simulation, 5.2.2 Fluid Modeling, Equations of State, 5.8.8 Gas-condensate reservoirs, 5.9.2 Geothermal Resources, 4.3.4 Scale, 4.1.2 Separation and Treating, 5.2.1 Phase Behavior and PVT Measurements, 5.2 Reservoir Fluid Dynamics, 3.3.6 Integrated Modeling, 4.1.5 Processing Equipment, 5.1 Reservoir Characterisation
- 6 in the last 30 days
- 839 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
We present formulation and numerical solution of two-phase multicomponent diffusion and natural convection in porous media. Thermal diffusion, pressure diffusion, and molecular diffusion are included in the diffusion expression from thermodynamics of irreversible processes.
The formulation and the numerical solution are used to perform initialization in a 2D cross section. We use both homogeneous and layered media without and with anisotropy in our calculations. Numerical examples for a binary mixture of C1/C3 and a multicomponent reservoir fluid are presented. Results show a strong effect of natural convection in species distribution. Results also show that there are at least two main rotating cells at steady state: one in the gas cap, and one in the oil column.
Proper initialization is an important aspect of reliable reservoir simulations. The use of the Gibbs segregation condition generally cannot provide reliable initialization in hydrocarbon reservoirs. This is caused, in part, by the effect of thermal diffusion (caused by the geothermal temperature gradient), which cannot be neglected in some cases; thermal diffusion might be the main phenomenon affecting compositional variation in hydrocarbon reservoirs, especially for near-critical gas/condensate reservoirs (Ghorayeb et al. 2003).
Generally, temperature increases with increasing burial depth because heat flows from the Earth's interior toward the surface. The temperature profile, or geothermal gradient, is related to the thermal conductivity of a body of rock and the heat flux.
Thermal conductivity is not necessarily uniform because it depends on the mineralogical composition of the rock, the porosity, and the presence of water or gas. Therefore, differences in thermal conductivity between adjacent lithologies can result in a horizontal temperature gradient. Horizontal temperature gradients in some offshore fields can be observed because of a constant water temperature (approximately 4°C) in different depths in the seabed floor.
The horizontal temperature gradient causes natural convection that might have a significant effect on species distribution (Firoozabadi 1999). The combined effects of diffusion (pressure, thermal, and molecular) and natural convection on compositional variation in multicomponent mixtures in porous media have been investigated for single-phase systems (Riley and Firoozabadi 1998; Ghorayeb and Firoozabadi 2000a).The results from these references show the importance of natural convection, which, in some cases, overrides diffusion and results in a uniform composition. Natural convection also can result in increased horizontal compositional variation, an effect similar to that in a thermogravitational column (Ghorayeb and Firoozabadi 2001; Nasrabadi et al. 2006).
The combined effect of convection and diffusion on species separation has been the subject of many experimental studies. Separation in a thermogravitational column with both effects has been measured widely (Schott 1973; Costeseque 1982; El Mataaoui 1986). The thermogravitational column consists of two isothermal vertical plates with different temperatures separated by a narrow space. The space can be either without a porous medium or filled with a porous medium. The thermal diffusion, in a binary mixture, causes one component to segregate to the hot plate and the other to the cold plate. Because of the density gradient caused by temperature and concentration gradients, convection flow occurs and creates a concentration difference between the top and bottom of the column. Analytical and numerical models have been presented to analyze the experimental results (Lorenz and Emery 1959; Jamet et al. 1992; Nasrabadi et al. 2006). The experimental and theoretical studies show that the composition difference between the top and bottom of the column increases with permeability until an optimum permeability is reached. Then, the composition difference declines as permeability increases. The process in a thermogravitational column shows the significance of the convection from a horizontal temperature gradient.
|File Size||4 MB||Number of Pages||13|
Acs, G., Doleschall, S., and Farkas, E.1985. General PurposeCompositional Model. SPEJ 25(4): 543-553. SPE-10515-PA.DOI: 10.2118/10515-PA.
Brigham, W.E., Reed P.W., and Dew, J.N.1961. Experiments on Mixing During Miscible Displacement in Porous Media. SPEJ1 (1): 1-8; Trans., AIME, 222. SPE-1430-G. DOI:10.2118/1430-G.
Costeseque, P. 1982. Sur la migrationselective des isotopes et des elements par thermodiffusion dans les solutions.Applications de l'effet thermogravi-tationnel en milieu poreux; observationsexperimentales et consequences geochimiques. PhD dissertation, U. PaulSabatier, Toulouse, France.
El Maataoui, M. 1986. Consequences de laThermodiffusion en Milieu Poreux sur l'Hydrolyse des Solutions de ChloruresFerriques et sur les Migrations d'Hydrocarbures dans les Melanges den-Alcanes et dans Un Petrole Brut: Implications Geochimiques. PhDdissertation, U. Paul Sabatier, Toulouse, France.
Firoozabadi, A. 1999. Thermodynamicsof Hydrocarbon Reservoirs. New York City: McGraw-Hill.
Firoozabadi, A., Ghorayeb, K., andShukla, K. 2000. Theoretical model of thermal diffusion factors inmulticomponent mixtures. AIChE J. 46 (5): 892. DOI: http://dx.doi.org/10.1002/aic.690460504.
Ghorayeb, K., Anraku, T., andFiroozabadi, A. 2003. Interpretation of the Unusual FluidDistribution in the Yufutsu Fractured Gas-Condensate Field. SPEJ8(2): 114-123. SPE-84953-PA. DOI: 10.2118/84953-PA.
Ghorayeb, K. and Firoozabadi, A. 2000a.Modeling Multicomponent Diffusionand Convection in Porous Media. SPEJ5(2):158-171. SPE-62168-PA. DOI: 10.2118/62168-PA.
Ghorayeb, K. and Firoozabadi, A. 2000b.Molecular, pressure, and thermal diffusion in non-ideal multicomponentmixtures. AIChE J. 46 (5): 88. DOI: http://dx.doi.org/10.1002/aic.690460503.
Ghorayeb, K. and Firoozabadi, A. 2001.Features of convection and diffusion in porous media for binary systems. J.Cdn. Pet. Tech. (February) 21.
Høier, L. and Whitson, C.H. 2001. Compositional Grading—Theory andPractice. SPEREE4 (6): 525-535. SPE-74714-PA. DOI:10.2118/74714-PA.
Hoteit, H. and Firoozabadi, A. 2006.Simple phase stability-testing algorithm in the reduction method. AIChEJ. 52 (8): 2909. DOI: http://dx.doi.org/10.1002/aic.10908.
Hoteit, H., Santiso, E., and Firoozabadi,A. 2006. An Efficient and Robust Algorithm for Gas-Liquid Critical Point ofMulticomponent Petroleum Fluids. Fluid Phase Equilibria 241(1-2): 186. DOI: http://dx.doi.org/10.1016/j.fluid.2005.12.019.
Jamet, Ph., Fargue, D., Costesque, P.,and Cernes, A. 1992. The thermogravitational effect in porous media: a modelingapproach. Transport in Porous Media 9 (3): 223. DOI: http://dx.doi.org/10.1007/BF00611968.
Kendall, R.P., Morrell, G.O., Peaceman,D.W., Silliman, W.J., and Watts, J.W. 1983. Development of a Multiple ApplicationReservoir Simulator for Use on a Vector Computer. Paper SPE 11483 presentedat the SPE Middle East Oil Technical Conference and Exhibition, Manama,Bahrain, 14-17 March. DOI: 10.2118/11483-MS.
Lee, S.T. and Chaverra, M. 1998. Modeling and Interpretation ofCondensate Banking for the Near Critical Cupiagua Field. Paper SPE 49265prepared for presentation at the SPE Annual Technical Conference andExhibition, New Orleans, 27-30 September. DOI: 10.2118/49265-MS.
Lohrenz, J., Bray, B.G., and Clark, C.R.1964. Calculating Viscosities ofReservoir Fluids From Their Compositions. JPT 16(10):1171-1176; Trans., AIME, 231. SPE-915-PA. DOI:10.2118/915-PA.
Lorenz, M. and Emery, A.H. 1959. Thepacked thermal diffusion column. Chem. Eng. Sci. 11 (1):16. DOI: http://dx.doi.org/10.1016/0009-2509(59)80069-5.
Michelsen, M. 1982. The Isothermal FlashProblem: Part I. Stability Analysis. Fluid Phase Equilibria9 (1): 1-20. DOI: http://dx.doi.org/10.1016/0378-3812(82)85001-2.
Michelsen, M.L. and Mollerup, J.M. 2004.Thermodynamic Models: Fundamentals & Computational Aspects. Holte,Denmark: Tie-Line Publications.
Nasrabadi, H., Hoteit, H., andFiroozabadi, A. 2006. An Analysis of Species Separation in ThermogravitationalColumn Filled with Porous Media. Transport in Porous Media (toappear).
Pedersen, K.S. and Lindeloff, N. 2003. Simulation of Compositional Gradientsin Hydrocarbon Reservoirs Under the Influence of a Temperature Gradient.Paper SPE 84364 presented at the SPE Annual Technical Conference andExhibition, Denver, 5-8 October. DOI: 10.2118/84364-MS.
Peng, D.Y. and Robinson, D.B. 1976. A newtwo-constant equation of state. Ind. Eng. Chem. Fund. 15(1): 59. DOI: http://dx.doi.org/10.1021/i160057a011.
Perkins, T.K. and Johnston, O.C. 1963. A Review of Diffusion and Dispersion inPorous Media. SPEJ 3 (1): 70-84; Trans., AIME,228. SPE-480-PA. DOI: 10.2118/480-PA.
Pirson, S.J. 1958. Oil ReservoirEngineering. New York City: McGraw-Hill.
Riley, M.F. and Firoozabadi, A. 1998.Compositional variation in hydrocarbon with natural convection and diffusion.AIChE J. 44 (2): 452. DOI: http://dx.doi.org/10.1002/aic.690440221.
Schott, J. 1973. Contribution a letude dela thermodiffusion dans les milieux poreux. Application aux possibilities deconcentration naturelles. PhD dissertation, U. Paul Sabatier, Toulouse,France.
Shukla, K. and Firoozabadi, A. 1998. Anew model of thermal diffusion coefficients in binary hydrocarbon mixtures.Ind. Eng.Chem. Res. 37 (8): 3331. DOI: http://dx.doi.org/10.1021/ie970896p.
Watts, J.W. 1986. A Compositional Formulation of thePressure and Saturation Equations. SPERE 1 (3):243-252. SPE-12244-PA. DOI: 10.2118/12244-PA.
Young, L.C. and Stephenson, R.E. 1983. A Generalized Compositional Approachfor Reservoir Simulation. SPEJ 23 (5): 727-742.SPE-10516-PA. DOI: 10.2118/10516-PA.