| Summary: | The accurate description of fluid flow through porous media allows an engineer to properly analyze past
behavior and predict future reservoir performance. In particular, appropriate mathematical models which
describe fluid flow through porous media can be applied to well test and production data analysis. Such
applications result in estimating important reservoir properties such as formation permeability, skin-factor,
reservoir size, etc.
"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. Whether in terms of limited applicability (say a specific pressure range), or due to the relative
complexity (e.g., iterative character of the solution), each of the existing approximate solutions does have
disadvantages. The purpose of this work is to provide a solution mechanism for the case of timedependent
real gas flow which contains as few "limitations" as possible.
In this work, we provide an approach which combines the so-called average pressure approximation, a
convolution for the right-hand-side non-linearity, and the Laplace transformation (original concept was put
forth by Mireles and Blasingame). 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 solution
schemes 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.
Our work shows that while the validity of this approach does have its own assumptions (in particular,
referencing the right-hand-side non-linearity to average reservoir pressure (similar to Mireles and
Blasingame)), these assumptions are proved to be much less restrictive than those required by existing
methods of solution for this problem. We believe that the accuracy of the proposed solution makes ituniversally applicable for gas reservoir engineering. This suggestion is based on the fact that no
pseudotime formulation is used. We note that there are pseudotime implementations for this problem, but
we also note that pseudotime requires a priori knowledge of the pressure distribution in the reservoir or
iteration on gas-in-place. Our new approach has no such restrictions.
In order to determine limits of validity of the proposed approach (i.e., the limitations imposed by the
underlining assumptions), we discuss the nature of the average pressure approximation (which is the basis
for this work). And, in order to prove the universal applicability of this approach, we have also applied
this methodology to resolve the time-dependent inner boundary condition for real gas flow in reservoirs.
|
|---|
