Effects of Criterion Values on Estimation of the Radius of Drainage and Stabilization Time

Abstract After a well starts flowing, a larger and larger portion of the reservoir contributes to production. At any given time, the radius of the portion of the reservoir that demonstrates a pressure gradient and contributes to production of fluid is the radius of drainage (ROD). The time required for the entire reservoir just to be able to contribute production is the stabilization time. Estimating the ROD and stabilization time is very important in well test design and production optimization. It has been a great challenge to estimate accurately the ROD and stabilization time because of inherent uncertainties with respect to the rock and fluid properties. This study examines the effects of criterion values on the estimated values of the ROD and stabilization time. As expected, estimated values of the ROD and stabilization time vary considerably, depending on the suggested criteria. The primary objective of this study is to recognize and appreciate the importance of criterion values for defining the ROD and stabilization time. Generalized correlations have been proposed that allow one to determine the ROD and stabilization time as a function of the criterion values. The relationship between a pressure criterion and the corresponding rate criterion has been examined also. Introduction The concepts of ROD and stabilization time are commonly used in reservoir engineering and in well test analysis. Estimating the ROD is very important on many counts. A well-test analysis provides important reservoir information based on the area sampled within the ROD. It is important to know the extent of the reservoir that is being sampled when determining the parameters like permeability and storage capacity from a well-test analysis. In other words, the well test analysis provides the global values of the reservoir parameters that are valid over the radius of investigation.1 Thus, the obtained reservoir information is good for the region within the ROD. In addition, knowing the ROD helps optimize the locations of new wells to be drilled in a field. It is very difficult to identify the well-test run time without an estimate of the ROD and stabilization time. The ROD concept has both quantitative and qualitative importance in well-test design and analysis. This distance is dependent on the way the pressure response propagates through the reservoir. It is also related to formation rock and fluid properties and elapsed time. Thus, the ROD concept presents a guide for well test design. This concept can be used also to estimate the time required to test to the desired depth in the formation. However, estimating any ROD has been dependent on the assumed level of the criterion for pressure or flow rate. As a result, there can be substantial variations in the estimated magnitude of the ROD. Depending on the criterion parameters and their values, a number of definitions have been proposed for the ROD and stabilization-time equations. Daungkaew et al.2 have provided a comprehensive account of these efforts.3–16