The Impact of Variable Formation Thickness on Pressure Transient Behavior and Well Test Permeability in Fluvial Meander Loop Reservoirs
Authors: Zheng Shiyi , Corbett Patrick , Stewart George 
Published: December 2007

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Abstract
Routine well test interpretation is based on a prototype analytical model which assumes that both the reservoir geometry (thickness; boundary conditions etc.) and property/heterogeneity (porosity/permeability/flow capacity) are symmetric about the well bore or are treated mathematically as symmetric (by using image wells and superposition). The information from seismic, logging and core description/analysis will help in the selection of different models. Transient well test interpretation yields the transmissibility of the reservoir which can be used to determine the average permeability in the block across the total thickness, that is usually assumed to be constant. For the constant production rate, the rate of pressure decline in the formation is inversely proportional to the reservoir permeability, k, and to the net pay thickness, h. The following two situations have to be borne in mind while analyzing the core and well test interpreted permeability. (1) In a reservoir having constant formation thickness, when only part of the total thickness is contributing to flow, a greater or smaller thickness input for classical interpretation will lead to under or over estimate reservoir permeability. (2) When the formation thickness varies with the position, the interpreted permeability is largely dependent on where the formation was intersected. This is especially true when the well penetrates a sand body which has a non-tabular geometry. An example is an asymmetric channel sandstone that can be laterally deposited by a meandering river (fluvial meander loop reservoir embedded in an impermeable matrix).
Mis-interpreting the reservoir permeability can result in an erroneous calculation of reservoir productivity index which depends on kh. This paper reports the numerical simulation results with respect to the second case which has been proved diagnosable by the pressure derivative method. Within a meander loop reservoir, the well test interpreted permeability is mainly dependent on the following two factors: Intersection Ratio Ri which is defined as the ratio of well bore intersected thickness to the maximum thickness (Total Thickness) and Pinch-out Ratio Rp defined as the ratio of the minimum reservoir sandbody thickness to the maximum thickness. Clearly, 0 &lt; Rp 1. The results of study have also shown that, no matter where the well is located in a reservoir having variable thickness, none of these cases will yield the correct kh and hence k by traditional well test interpretation. With 0.1 Rp 0.5, when well intersected at Maximum thickness, the interpretation will yield the best permeability estimation while well intersected at the Average Formation Thickness (arithmetic average of minimum and maximum thickness), the interpretation will give a less reliable estimation of the reservoir permeability with an error of about 4%,

Introduction
In the recent several decades, reservoirs having the shape of a circle; square; rectangle; triangle and wedge etc. have been studied. In order to use the radial inflow equation to describe the reservoirs having different shapes from a circle, a correction factor called Dietz shape factor is added to the model for each specific case. Here the "shape" of the reservoir is the reservoir geometry in a plan view and all the layers from the top to the bottom covering the formation thickness are assumed to be the same. The formation thickness is decided mainly from logging. Since the logs only measured the piece of formation penetrated by well bore, the formation thickness away from the well-bore is extrapolated.
In the experience of interpreting well tests, it was found that in nine cases out of ten, the interpreted permeability (calculated from kh) was rarely consistent with the permeability measured from the core/probe average.
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