Efficient application of reduced variable transformation and conditional stability testing in reservoir simulation flash calculations

#The present invention relates generally to computer enabled reservoir simulation of fluid flow in subterranean reservoirs and more particularly, to compositional reservoir simulation.

#Conceptually a compositional reservoir simulator for simulating flow in a subterranean hydrocarbon-bearing reservoir can be viewed as modeling a series of connected mixing tanks of fluids (cells) at given pressure, temperature and compositions. As time evolves (as the simulator is taking time-steps toward some final time at which results are sought), conditions in the tanks change as a result of fluid movement, wells and other external factors. Flash calculations are necessary to establish, for each new set of pressure, temperature and overall fluid composition, the number of fluid phases, their amounts and compositions. This calculation fundamentally involves finding the minimum of a thermodynamic state function (the Gibbs Free Energy (GFE), and as such is iterative in nature and frequently difficult to converge and computationally expensive, particularly when detailed fluid models are used, i.e., when there are many hydrocarbon components present. There is therefore great interest in devising algorithms which are computationally efficient yet robust and accurate.

#For the purpose of discussion, the activity performed in “flash” calculation shall be subdivided into stability testing, which attempts to reveal instability of a given phase at the current conditions; and split calculations, which aims at determining the equilibrium phases and compositions for an assumed phase configuration.

#These and other objects, features and advantages of the present invention will become better understood with regard to the following description, pending claims and accompanying drawings where:

#FIG. 1 is a pressure-temperature diagram delineating several regions in the phase-plane to illustrate concepts central to a conditional stability test approach;

#FIG. 2 is a flow-chart illustrating the combined usage of conditional stability test logic for the overall flash update, and reduced variable algorithms for iterative solution of the stability and phase-split problems at a particular time-step of a compositional reservoir simulator;

#The following nomenclature shall be used with the equations that follow:

#Symbols D = Tangent Plane Distance (TPD) G = Gibbs Free Energy function (GFE) c = Number of hydrocarbon components m = Number of non-zero Eigen values M = Number of reduced parameters. Equalsm+1 P = Pressure Q = Reduced variables (M-vector) of entriesQα Q = Reduction coefficients matrix of sizeMc of entriesqij R = Universal Gas Constant T = Temperature x = Liquid phase composition (mole fractions) y = Vapor phase composition (mole fractions) Y = Unnormalized moles of trial phase z = Feed (total) composition (mole fractions) Subscripts i, j = Component index α = Reduced variable index L = Liquid V = Vapor Superscripts F = Feed phase T = Trial phase Greek symbols φi = Fugacity coefficient δij = Binary interaction coefficients (BIC)

#The teachings of Firoozabadi, A. and Pan, H., Fast and Robust Algorithm for Compositional Modeling Part I—Stability Analysis, SPE 63083 and Firoozabadi, A. and Pan, H., Fast and Robust Algorithm for Compositional Modeling: Part II—Two-Phase Flash, SPE 7160, are hereby incorporated by reference in their entireties. Similarly, the contents of U.S. patent application, 2006/0036418 to Pita et al., Highly-Parallel, Implicit Compositional Reservoir Simulator for Multi-Million-Cell Models, is incorporated by reference in its entirety. Further, the contents of Claus P. Rasmussen, Kristian Krejbjerg, Michael L. Michelsen and Kersti E. Bjurstrom, Increasing the Computational Speed of Flash Calculations with Applications for Compositional, Transient Simulations, Society of Petroleum Engineers, SPE 84181, February 2006 SPE Reservoir Evaluation & Engineering, are incorporated reference. Finally, the teachings contained within Michael L. Michelsen, The isothermal flash problem, Part I. Stability, Fluid Phase Equilbria, 9 (1982) 1-19 Michael L. Michelsen, The Isothermal Flash Problem, Part II, Phase-split Calculation, Fluid Phase Equilibria, 9 (1982) 21-40 are also incorporated by reference in their entireties.