The application of the Constrained Interpolation Profile (CIP) scheme is extended from single-phase to two-phase one-dimensional hydrothermal reservoir simulations. This extension not only applies the CIP scheme to the advection term of a conservation equation for each phase as in single-phase problems but also evaluates its applicability using a dimensionless parameter called ‘applicability index.’ The applicability index indicates the relative absolute difference between the advancing velocities of the distribution of specific enthalpy due to flow and phase transition front. If the applicability index is exactly or nearly zero, the CIP scheme is applicable because the difference is insignificant. On the other hand, if the value of the applicability index becomes greater than zero, the CIP scheme is inapplicable because the difference becomes significant. The application of the CIP scheme in the inapplicable condition results in numerical failures, such as the degradation of convergence in Newton-Raphson iteration and oscillating distribution of liquid saturation. The conventional first-order upstream difference scheme is adopted when the CIP scheme is inapplicable. Two contrasting examples demonstrate the applicability of the CIP scheme. The first example injects hot fluid into the initially single-phase reservoir with relatively low permeability. The second example injects cold water into the initially two-phase reservoir with relatively high permeability. In the former example, the CIP scheme is inapplicable in the entire two-phase region expanding from the source. On the other hand, in the latter example, the CIP scheme is applicable in the phase transition zone where liquid saturation is changing with the sweeping of the single-phase region expanding from the source. The numerical failures were overcome as demonstrated in the comparison with a trial run adopting the CIP scheme regardless of the applicability index.

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