Abstract
This work is concerned with the mathematical modelling of nonisothermal water injection problems using analytical techniques. The solutions derived incorporate the effects of temperature and saturation gradients and give the pressure, saturations and temperature as functions of distance and time in a one dimensional radial reservoir. A two-step procedure is used to derive the solutions to the moving boundary injection problem. Assnming the fluids to he incompressible, we obtain a non-strictly hyperbolic system for saturation and temperature (Riemann problem). This problem is solved by using the method of characteristics together with the appropriate shock-admissibility criteria. With the knowledge of the saturation and temperature distributions, and hence the mohilities and diffusivities, from step one, the second order pressure diffusivity equation is solved assuming slightly compressible fluids. Both a similarity and a. quasi-stationary method is used to solve the resulting moviug boundary problem. The falloff solution is derived both by solving the complete initial-boundary value problem with the injection solution as the initial condition and by superposing solutions to the stationary variable coefficients problem. It is demonstrated that the saturation and temperature gradients have significant effects on the pressure data for both the injection and falloff periods.
Published Version
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