We have constructed new approximate analytical solutions for injection and falloff pressure response which include thermal effects that arise when flooding a reservoir with water having a temperature considerably below of that of the reservoir. We have developed an optimization code based on the Levenberg-Marquardt algorithm and coupled it with our new approximate analytical solutions to obtain a procedure for data analysis where our approximate analytical solutions are used as the forward model in the non-linear regression. We demonstrate that we can generate estimates of absolute permeabilities, the well skin factor, the length of the well and relative preme-abilities by matching data to analytical solutions by minimization of a weighted least squares objective function. The relative permeability curves are constructed assuming a power law parametrization. In the horizontal well case, we show that the absolute permeabilities in the three principal directions can be resolved separately provided the duration of the test is sufficiently long.
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