"Real gas" flow problems (i.e., problems where the gas properties are specifically taken as implicit functions of pressure, temperature, and composition) are particularly challenging because the diffusivity equation for the "real gas" flow case is strongly non-linear. Whereas different methods exist which allow us to approximate the solution of the real gas diffusivity equation, all of these approximate methods have limitations (including numerical models).
The purpose of this work is to provide a direct solution mechanism for the case of time-dependent real gas flow which uses an approach that combines the so-called average pressure approximation (a convolution for the right-hand-side nonlinearity) and the Laplace transformation. For reference, Mireles and Blasingame used a similar scheme to solve the real gas flow problem conditioned by the constant rate inner boundary condition.
In this work we provide a direct solution scheme to solve the constant pressure inner boundary condition problem. Our new semi-analytical solution was developed and implemented in the form of a direct (non-iterative) numerical procedure and successfully verified against numerical simulation.