In this paper we present a general formulation to solve the non-linear difference equations that arise in compositional reservoir simulation. The general approach here presented is based on Newton's method and provides a systematic approach to generate several formulations to solve the compositional problem, each possesing a different degree of implicitness and stability characteristics. The Fully-Implicit method is at the higher end of the implicitness spectrum while the IMPECS method, implicit in pressure-explicit in composition and saturation, is at the lower end.

We show that all methods may be obtained as particular cases of the fully-implicit method. Regarding the matrix problem, all methods have a similar matrix structure; the composition of the Jacobian matrix is however unique in each case, being in some instances amenable to reductions for optimal solution of the matrix problem. Based on this, a different approach to derive IMPECS type methods is proposed; in this case, the whole set of 2nc + 6 equations, that apply in each gridblock, is reduced to a single pressure equation through matrix reduction operations; this provides a more stable numerical scheme, compared to other published IMPECS methods, in which the subset of thermodynamic equilibrium equations is arbitrarily decoupled from the set of gridblock equations to perform such reduction.

We discuss how the general formulation here presented can be used to formulate and construct an adaptive-implicit compositional simulator. We also present results on the numerical performance of FI, IMPSEC and IMPECS methods on some test problems.

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