An analytical composite model using non-linear least square regression technique for estimation of real parameters of naturally fractured reservoirs, utilizing well test data is presented. The problem of alteration of fracture properties due to acidizing or damage called by drilling fluid is taken into account by introducing two concentric media of different fractures. In this work correlations amongst fracture permeability and porosity, ω, λ, skin factor and matrix block size together with field examples are also presented.
The double porosity models presented by Barenblatt et all and many others2–4 treat naturally fractured reservoirs by superimposing two continua, One for the fracture system and another for the porous matrix. The flow of fluid in the fracture system toward the wellbore is assumed to be radial. This holds only for infinisimal matrix block dimensions. For real cases where the matrix blocks are of finite dimensions, several fee~ the flow in the fractures near the wellbore is linear. It has been shown5 that the pressure drop in the fractures with linear flow is less than the pressure drop caused by a radial system with a bulk permeability identical to that of the fractures. This is why the analysis of well test data obtained from naturally fractured reservoirs usually show negative skins by semilog analysis.
The flow behavior of a two dimensional fracture network with nonporous identical parallelepiped matrix blocks under steady state conditions5 has shown that the negative skin is proportional to the logarithmic of the matrix block size and the flow system starts exhibiting radial flow behavior from a radial distance of one matrix block from the wellbore.
Drilling and workover operations may alter the width of the fractures around the wellbore resulting in two damaged and undamaged zones. The damage zone may be assumed circular and the fractures in this zone of uniform thickness. In order to study the behaviour of the flow system with the above mentioned features a composite model consisting of three regions is considered.
Composite systems have been the subject of considerable attention in the petroleum literature. In general, the composite model consists of a well completed in the centre of a circular inner region with fluid and rock properties different from those in an outer region. This approach has been used to study interference between oil fields in a common aquifer of different permeabilities6. A two region composite model has been used to study the behavior of wells intersected by fractures extending over a limited area7, It also has been used to study the behavior of wells intersected by infinite conductivity vertical fracture in dual porosity reservoirs8.
In this work a general flow equation for a composite system consisting of three (inner, intermediate and outer) regions is presented to describe the near wellbore linear flow and the outer radial flow in the two damaged and undamaged regions.