Inverse Modeling in Gas Reservoirs

Abstract

ABSTRACT The distribution of permeability or transmissibility is of interest to the engineers for several reasons. These reasons may be related to design, operation, development or understanding of reservoir performance. In order to determine the distribution of the permeability, in general, several sources of information are available. These include: Transient tests in individual wells which give estimates of local permeability in the surrounding matrix,Longer term interference tests which relate to the influence of permeabilities around several observation wells,Geological information about the formation which involves statistically significant representation hereby referred to as ‘geostatistics’,And, finally, observations made during the operation of the field. The first three items above relate to reservoir description while the fourth relates to reservoir performance. The paper describes a procedure developed for determining the distribution of permeability by an inverse modeling technique. The procedure combines the data from various sources of information listed above in a manner which compatibly reconciles local observations with spatially structured reservoir properties, and recorded pressure history. It was implemented through a computer program cal led MAGHY (Modèle d'Ajustement de Grandeurs HYdrauliques). It applies to reservoirs or aquifers subject to the flow of slightly compressible liquids (oil or brine), or compressible gases in single phase, in two dimensions. Two examples are included as application of the procedure. One involves an aquifer study where the flow field was in single phase liquid. The other presents validation of the procedure through a hypothetical case where a pre-determined permeability distribution was converged upon through the use of computer program implementing the inverse modeling technique. It was based on single phase gas flow.