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: (1) 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; (2) When the ratio of the dimensionless radius of the two zones is less than ten, the naturally fractured reservoir behaves like a homogeneous system; (3) 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; and (4) the 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.
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