The paper proposes a new formulation of the problem of three-phase non-isothermal flow of immiscible fluids based on the introduction of a change of variables by which the gradients of the capillary pressure functions are excluded from the equations for the pressure and temperature. It is known [1] that these gradients increase unboundedly when saturations approach corresponding residual values. For the numerical solution of the problem, an implicit difference scheme is obtained with integro-interpolation method is developed. The properties of approximation and stability of the difference scheme are studied, a theorem on the convergence of the difference problem solution to the solution of the differential problem is proved. The adequacy of the proposed model is verified on the example of a non-isothermal problem of oil displacement by means of injection of steam. The results of computational experiments with varying input parameters and empirical relationships are presented, features of the solution of the difference problem are analysed.
REFERENCES
1. Chavent G. A fully equivalent global pressure formulation for three-phase compressible flow. CoRR, Vol. abs/0901.1464, 2009, 19 p.