Interpretation of Post-Deep-Acidizing Pressure Tests in a Naturally Fractured Reservoir
Authors: Bensalem Omar , Tiab Djebbar 
Published: December 2007

Abstract
Acidizing wells after completion or even after some period of production is a standard practice in naturally fractured reservoirs. Such a practice allows easier and faster removal of mud materials from the fractures intersecting the well. In some reservoirs, acidizing is performed deep into the formation for the purpose of enlarging the width of fissures and enhancing their interconnectivity. This results in a composite system with two zones, each having different characteristics, including storage capacity ratio, interporosity flow coefficient, and permeability. Composite systems may also result from fluid injection. High injection of fluids causes larger opening of fractures near the wellbore (due to higher pore pressure), which results in an increase of fracture permeability around the well.
A model for a composite naturally fractured system has been developed by assuming pseudo-steady state fluid transfer from matrix to fractures, and taking into consideration the effects of: wellbore storage, near-wellbore formation damage and skin at the interface of the two zones. The inner zone is considered to be finite, but the outer zone can be bounded or infinite. The loglog plots of the pressure and pressure derivative as a function of the storage capacity and permeability ratios of the two zones provide unique characteristics, which were used to derive equations for calculating various parameters of the two zones, e.g. radius of the inner zone, mechanical skin, and skin at the interface.
From the interpretation of the loglog plots of the pressure and pressure derivative data, using Tiab's Direct Synthesis (TDS) technique, we have found that:the contribution of the matrix to the flow can occur in the inner zone or the outer zone, depending on the product of the interporosity flow factor and radius of the inner zone;When the ratio of the dimensionless radius of the two zones is less than ten, the naturally fractured reservoir behaves like a homogeneous system;For storage capacity and permeability ratios greater than unity, the pressure derivative curve has a hump, which may appear before or after the trough; the coordinates of this maximum point may be used to calculate the permeability of the outer zone in the absence of the second radial flow line; andthe presence of a thin skin zone at the interface influences the starting time of the radial flow line of the outer zone.
Several numerical examples are included in the paper.

Introduction
Naturally fractured reservoirs have been studied intensively during the last 30 years in geological and engineering fields. Transient pressure analysis has received particular attention. In naturally fractured reservoirs, the unique pressure behavior due to the double porosity medium and their interaction has lead to the development of a variety of sophisticated models. These models differ from each other in a way the matrix/fracture fluid transfer is handled. The aim of these models is to evaluate the special flow characteristic and provide useful information from interpretation of pressure data.
One of the earliest models was developed by Pollard to quantify skin resistance from pressure buildups and used to evaluate acid treatment in fractured limestone. Not only the skin, but also the fracture and matrix pore volume could be determined from the graphical analysis. The pressure differential in the well was assumed to be in response to three distinct flow regions connected in series. The first region is the damaged or improved region in the fracture near the well (skin region). The second region considers the pressure loss due to the flow resistance within the fractures, and the last one is the pressure response between the matrix and the fracture system.
The flux between the matrix and fractures and between fractures and wellbore was assumed to be under pseudosteady state condition.
Warren and Root 19 modified Barenblatt et al.'s solution to account for fracture compressibility. They present a comprehensive and applicable solution to the double porosity, naturally fractured problem.