Semi-analytical solutions for nonisothermal fluid injection including heat loss from the reservoir: Part 1. Saturation and temperature

• New semi-analytical solutions for nonisothermal two-phase flow with heat loss from the reservoir have been developed.
• Examples are solved for the linear and radial flow regimes.
• It is possible to predict a-priori whether the thermal shock velocity will be a function of time in the displacements.
• Solutions are benchmarked against existing analytical solutions and a research reservoir simulator.

This work introduces the derivation and solution of the conservation laws for nonisothermal immiscible two-phase flow in one dimension (1D) with heat loss to surrounding strata. Purely advective flow is assumed so that the method of characteristics can be applied to the fluid flow and thermal equations with an arbitrary relative permeability model. The formulation allows for a wide class of time-dependent models for heat loss into surrounding strata. One-dimensional linear and radial displacements are considered. Thermal losses to the under- and over-burden are modelled using a heat-loss coefficient derived from the classic Lauwerier model. In order to demonstrate the two kinds of solution that may occur, examples are shown for cold methane injection into an aquifer and cold water injection into a natural gas reservoir. Finally the new analytical solutions are compared with two literature models which assume piston-like displacement, and numerical reservoir simulations. The solutions from the proposed model match the thermal profile from the reservoir simulation much better than either of the literature models in the examples considered.