A multiphase implicit numerical model applied to the closed chamber test.

摘要

The work is a fundamental reformulation of the problem of well-testing. First the pipeline multiphase flow equations and an implicit four-point finite difference scheme are developed and validated. Analytical solutions for single phase flow obtained by heaviside calculus permit design of the numerical scheme so that induced numerical dissipation should not mask the physical. Time weighting factors {dollar}theta{dollar}, greater than 1/2 and less than.55, proved the needed stability and required accuracy. Larger values of {dollar}theta{dollar} can be used for short duration tests. Additional transients caused by series connection in multidiameter pipeline are investigated and results compared with the method of characteristics. The system of equations is cast in the divergent form so that computation of wavefronts is straightforward.; The phase properties are obtained via a generalized flash routine for the modified Peng-Robinson equation of state that uses SSM with an option to switch to the more stable ASSM or MVNR if poor convergence is detected.; The axisymmetric equations for single phase porous media flow are solved by the four-point finite difference scheme. The two-dimensional parabolic equation for porous media flow is solved by Galerkin's method and results by both methods compare well with results given by a modified Bessel's equation.; Secondly, a Lagrangean form of the mathematical model is applied to the closed-chamber test (CCT for short). The initial conditions include an initial mud column, over 4000 psi pressure discontinuity at the well, conditions not heretofore investigated. The physical process described are momentum, body and dissipative forces. Skin and sand failure as function of time are modeled, together with possible non-potential flow in the immediate vicinity of the well. Gas compression is considered isothermal. The results obtained by the implicit hydrodynamic model are in good agreement with two actual field tests from offshore Gulf coast. Sensitivity analyses permit deduction of transmissibility. As a design tool, this model predicts bottom hole flow rate. Buildup, slug test and DST are special cases of this model. The method lends itself naturally as an interpretation tool and permits analysis of all data.