Application of Type-curve Analysis In Interpreting Pressure Data From a Stratified Reservoir
Authors: Falade G.K. 
Published: March 2010

Abstract
One of the more recent innovations in well test analysis is the use of type-curve matching for interpreting storage-controlled short-time bottom-hole pressure data. More recently, the use of type-curve matching has been extended to cover areas of interpretation for both short-time and long-time pressure data particularly fracture-influenced pressure data.
This paper investigates yet another application of type-curve matching in the interpretation of both short- and long-time pressure data in stratified reservoir systems. Results indicate that changes in skin and storage factors due to rebalancing of stratification-induced differential pressure depletion could be detected and evaluated by type-curve matching.

Introduction
Analysis of bottom-hole pressure data (build-up or drawdown) is more frequently based on the semi-log straight-line concept arising from the long-time approximation of the line source solution as proposed by Horner. The line source solution in its pure form is accurate with homogeneous, isotropic reservoirs, or reservoirs with randomly distributed in homogeneities. It does not give an account of those well-bore pressure-sensitive phenomena such as skin and storage factors, or the formation-controlled pressure effects such as fractures and stratification due to layering. However, recent advances in well testing have succeeded in modifying interpretation techniques based on the line source solution to cater to the analysis of such problems as skin factor, storage or annulus unloading(l), fracture-controlled flow(2), down-hole reverse now or casing leakage(3), etc. In all of these, the versatility of type curve matching, based on the basic line source solution, is the central focus. The same versatility has, however, not found widespread application in the analysis of down-hole pressure data from stratified reservoirs.
The objective of this paper is to highlight the applicability of the log-log type-curve matching technique for the analysis of pressure data from stratified reservoirs.

Pressure Characteristics of Stratified Formations
Several authors have studied various aspects of the pressure dynamics of stratified formations(4,5,6); however, only a few have looked at the problem from the viewpoint of well test analysis. The most important factor in the pressure dynamics of a two-layered stratified reservoir is the concept of differential depletion. Both Lefkovits et al.(7) and Cobb et al(8) used this concept in the qualitative interpretation of the double pressure build-Up usually associated with stratified reservoirs.
Figure 1 is a typical pressure build-up profile for a two-layered reservoir showing the characteristic double build-up. For the purposes of analysis, one can section this pressure profile into two regions ABC and CDE. Region ABC is analogous to what would be expected from a single-layered reservoir which is initially infinite-acting, but eventually building up to static pressure. Region CDE, which represents the second pressure build-Up stage, arises as a result of repressurization due to internal flow from the less permeable layer to the more permeable and hence more depleted, zone. The region CD will persist for as long as the internal now continues. The region E results when the two zones have reached a uniform average pressure.