Drawdown Behavior Of A Well With Storage And Skin Effect Communicating With Layers Of Different Radii And Other Characteristics
Authors: Tariq Syed M. , Ramey Henry J. 
Published: December 2007

Abstract
Although a number of studies on the pressure behavior of layered systems have been undertaken during the past two decades, the state of knowledge is not complete for well test analysis. The problem lies in the evaluation of complex mathematical expressions that describe the analytical solution of such systems, and in the large number of possible solutions. Numerical evaluations often are inefficient and painstaking and have tended to limit the scope of previous studies of layered systems. previous studies of layered systems. In this study, a numerical inversion method was used to evaluate the analytical solution of the layered system problem in Laplace space. The methods was found to be efficient and provided a convenient means for generating dimensionless pressure versus dimensionless time data for large numbers of layered system cases. Computer software was developed which can be used to generate PD vs tD data.
Drawdown data for a number of cases including wellbore storage, skin effect, and differences in thicknesses, skin effects and radii among the layers was generated. The maximum number of layers considered was ten.
New conclusions were reached concerning the behavior of multi-layer systems. The most important of these is that false wellbore storage effects may appear in cases involving high permeability contrast and a small, highly permeable layer. Also, it was found that two semi-log permeable layer. Also, it was found that two semi-log straight lines may exist for two-layer reservoirs. The slopes of these semi-log straight lines correspond to the permeability-thickness of the system as a whole, and to permeability-thickness of the system as a whole, and to that of the larger radius layer, respectively. Finally, and perhaps most important, it was found that layered system data can be analyzed under certain circumstances to yield information about the permeability ratio and the radii of the layers.

Introduction
The methods of analyzing pressure transient behavior of wells have often assumed that a reservoir consist of a single layer, constant in thickness, isotropic, having uniform porosity, permeability, pore size distribution, and rock-fluid properties pore size distribution, and rock-fluid properties throughout. The actual occurrence of such an ideal reservoir would be miraculous. Due to the complexity of the environment in which sediments were deposited, and as a result of subsequent physical and chemical changes, many types of heterogeneities are present in all reservoirs, although not necessarily obvious in the reservoir behavior. A common type of heterogeneity is the presence of impermeable laminations within sand bodies separating the sand into two or more layers of differing physical characteristics in the producing formation. The pressure drawdown behavior of such reservoir is the subject matter of this study.
No reservoir rock is perfectly homogeneous. All reservoir rocks are inherently heterogeneous because of the complexity of the geologic processes involved in their evolution. The geologic processes of sedimentation, solution, glaciation, erosion, etc., all tend to produce reservoir rocks that are non-uniform, although the reservoir rock may appear homogeneous, if the non-uniformities have a normal distribution or if viewed on a large scale. In order to analyze well test data properly, it is necessary to consider the common heterogeneities, and the resulting interpretation problems. problems. In recent years, the subject of well-test interpretation in heterogeneous systems has received considerable attention. Many large oil reservoirs are fractured systems, for example. Model studies of the pressure behavior of wells near faults, wells near pressure behavior of wells near faults, wells near fluid-fluid contacts, wells in naturally-fractured, and hydraulically-fractured reservoirs, and wells in layered, communicating and non-communications systems, have been performed during the last two decades.
One of the most common types of heterogeneous systems, and one which is also the subject matter of this study, is the reservoir composed of a number of segregated layers, each with different intensive and extensive physical properties.