The Practical Aspects of Interlayer Crossflow
Authors: Russell D.G. , Prats M. 
Published: December 2007

Abstract
As a result of knowledge gained from recent theoretical work, the production and/or pressure response of wells in layered oil or gas reservoirs can be interpreted to determine whether communication exists between the layers. If crossflow between layers can occur, the pressure and production behavior of a well can be represented or interpreted by use of homogeneous reservoir theory. A well in a layered reservoir with cross flow behaves as a well in a homogeneous, single-layer reservoir which possesses the same dimensions and pore volume as the cross flow system and a "kh" product (permeability-thickness product) equal to the total "kh" of the cross flow system. The occurrence of cross flow can be confirmed by the "homogeneous-like" appearance of the pressure and/or production decline data and by the absence of "layer effects" which appear when cross flow does not occur. These layer effects in reservoirs without crossflow are characterized by sharply rising sections on the late-time portion of pressure build-up curves and by continuously changing production decline rates. Interlayer crossflow in oil or gas reservoirs can have a significant effect on exploitation economics. If cross flow can occur, the result is a shorter operating life and a higher primary ultimate recovery. Cross flow may obviate the need for perforating and treating long sections of low-permeability rock.

Introduction
The development of improved methods for predicting recoveries and interpreting the natural performance from heterogeneous reservoirs is of vital interest to reservoir and production engineers, and currently occupies a prominent position in petroleum production research. Over the past few years, with the advent of improved well-completion techniques such as hydraulic fracturing, the industry-wide trend has been toward exploitation of increasingly tighter and more heterogeneous reservoir rocks. To predict the production performance of this type of reservoir, the engineer must first characterize and define the nature and extent of the heterogeneities. By analysis of reservoir and well production and pressure data, it frequently is possible to identify the nature and extent of heterogeneities in the field. This paper is concerned with the practical aspects of the performance of one basic type of heterogeneous reservoir-the layered reservoir with interlayer crossflow, shown schematically in Fig. 1.The extent of production from a tight layer into an adjacent and connected layer of higher permeability and, subsequently, into a production well has been the subject of speculation for many years. During the past two years this high level of interest has culminated in the publication of several significant theoretical papers on the performance of reservoirs with interlayer crossflow. Jacquard presented a rigorous analysis of the performance of a well which produces at constant rate from a two-layer crossflow system. No numerical results from evaluation of the very complex mathematical solutions were presented. Katz and Tek analyzed mathematically the constant-terminal-pressure case with crossflow and obtained numerical results principally applicable to aquifer performance. Russell and Prats, in a recently published paper, also considered the constant- pressure case but presented numerical results and simplified performance formulas for well analysis. Vacher and Cazabat and Pelissier and Seguier have obtained numerical results for the constant-rate case. Maksimov has also indicated a solution of the crossflow problem. Pendergrass and Berry have recently presented an analysis of the effect of multilayer permeability variations on the production rate response of crossflow systems. Thus, in a comparatively short period of time, sufficient theory has evolved to enable reservoir and production engineers to allow for interlayer crossflow in performance calculations.
JPT
P. 589^