A Comparison of Two Different IMPSAT Models in Compositional Simulation
- Jarle Haukas (U. of Bergen) | Ivar Aavatsmark (U. of Bergen) | Magne Espedal (U. of Bergen) | Edel Reiso (Norsk Hydro E&P ASA)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- March 2007
- Document Type
- Journal Paper
- 145 - 151
- 2007. Society of Petroleum Engineers
- 5.5 Reservoir Simulation, 5.2 Reservoir Fluid Dynamics, 5.8.8 Gas-condensate reservoirs, 5.4.3 Gas Cycling, 5.2.1 Phase Behavior and PVT Measurements, 4.1.2 Separation and Treating
- 0 in the last 30 days
- 356 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
A new IMPSAT model, with explicit solution of variables that are isochoric (i.e., complementary to volumes), is compared to the conventional IMPSAT model, which determines phase mole fractions explicitly. The compared properties are performance of the nonlinear iteration and numerical stability.
The use of complementary variables in the new IMPSAT model makes the nonlinear system better conditioned. Consequently, fewer nonlinear iteration steps are required. The resulting speedup more than compensates for the added costs of introducing and using the isochoric variables.
The stability criterion associated with the new IMPSAT model is in many cases significantly less conservative than the conventional criterion. However, for cases in which there is little or no saturation change between the hydrocarbon phases (e.g., for retrograde gas condensate cases or single hydrocarbon phase cases), the difference between the criteria is insignificant.
The timestep sizes for which instabilities occur are practically the same for the two models, and no oscillations have been observed unless both the new and the conventional criterion are violated. Consequently, the stability properties are similar, and the new criterion seems to apply to both models.
Our conclusions are supported by numerical results.
An isothermal compositional model of Nc components involves the solution of Nc flow equations per gridblock (e.g., the mass balance equations):
where ?ni is the change in the amount of component i during timestep ?t, while fi and qi are the component interblock flow and source rates. In addition, phase equilibrium between the oil and gas phases (e.g., equalities of fugacities),
must be taken into account.
Because of the large number of equations and the complex thermodynamics, it is too demanding to determine all variables implicitly (i.e., simultaneously in all gridblocks). Instead, we use a partially explicit approach, where some variables are determined implicitly, while others are determined explicitly, gridblock by gridblock. The explicit solution relies on explicit treatment of variables (i.e., evaluating parts of the interblock flow with variables from the previous time level).
|File Size||453 KB||Number of Pages||7|
Aziz, K. and Settari, A. 1979. Petroleum Reservoir Simulation.London: Applied Science Publishers.
Branco, C.M. and Rodríguez, F. 1995. A Semi-Implicit Formulation forCompositional Reservoir Simulation. SPE Advanced Technology Series4 (1): 171-177.SPE-27053-PA.DOI:http://www.spe.org/elibrary/servlet/spepreview?id=27053-PA.
Cao, H. 2002. Development ofTechniques for General Purpose Simulators. PhD dissertation. Stanford,California: Stanford U.
Cao, H. and Aziz, K. 2002. Performance of IMPSAT and IMPSAT-AIMModels in Compositional Simulation. Paper SPE 77720 presented at the SPE Annual TechnicalConference and Exhibition, San Antonio, Texas, 29 September-2 October. DOI:http://www.spe.org/elibrary/servlet/spepreview?id=77720-MS.
Coats, K.H. 1999. A Note on Impes and Some Impes-BasedSimulation Models. Paper SPE49774 presented at the SPE Reservoir Simulation Symposium, Houston, 14-17February. DOI: http://www.spe.org/elibrary/servlet/spepreview?id=49774-MS.
Haukås, J. 2006. CompositionalReservoir Simulation With Emphasis on the IMPSAT Formulation. PhDdissertation. Bergen, Norway: U. of Bergen.
Haukås, J., Aavatsmark, I.,Espedal, M., and Reiso, E. In process. A Volume Balance Consistent IMPSATFormulation With Relaxed Stability Constraints. Submitted to ComputationalGeosciences.
Haukås, J., Aavatsmark, I.,Espedal, M., and Reiso, E. In process. Exact Volume Balance Versus Exact MassBalance in Compositional Reservoir Simulation. Submitted to ComputationalGeosciences.
Kenyon, D.E. and Behie, G.A.1987. Third SPE Comparative SolutionProject: Gas Cycling of Retrograde Condensate Reservoirs. JPT 39 (8): 981-997.SPE-12278-PA. DOI:http://www.spe.org/elibrary/servlet/spepreview?id=12278-PA.
Killough, J.E. and Kossack,C.A. 1987. Fifth ComparativeSolution Project: Evaluation of Miscible Flood Simulators. Paper SPE 16000presented at the SPE Symposium on Reservoir Simulation, San Antonio, Texas, 1-4February. DOI: http://www.spe.org/elibrary/servlet/spepreview?id=16000-MS.
Lohrenz, J., Bray, B.G., andClark, C.R. 1964. CalculatingViscosities of Reservoir Fluids From Their Compositions. JPT16 (10): 1171-1176; Trans., AIME, 231.SPE-915-PA.DOI:http://www.spe.org/elibrary/servlet/spepreview?id=915-PA.
Quandalle, P. and Savary, D. 1989. An Implicit in Pressure andSaturations Approach to Fully Compositional Simulation. Paper SPE 18423presented at the SPE Symposium on Reservoir Simulation, Houston, 6-8 February.DOI: http://www.spe.org/elibrary/servlet/spepreview?id=18423-MS.
Reid, R.C., Prausnitz, J.M., andPoling, B.E. 1987. The Properties of Gases and Liquids. New York:McGraw-Hill.
Watts, J. 1986. A CompositionalFormulation of the Pressure and Saturation Equations. SPERE 1(3): 243-252. SPE-12244-PA. DOI:http://www.spe.org/elibrary/servlet/spepreview?id=12244-PA.