Pressure Transient Behavior and Inflow Performance of Multiple Wells in Closed Systems
Authors: Umnuayponwiwat S. , Ozkan E. , Raghavan R. 
Published: December 2007

Abstract
This paper presents an investigation of transient pressure behavior of multiple wells in closed rectangular systems. Combinations of vertical and horizontal wells with rate variations and buildup periods are considered. Pressure transients caused by the rate changes or shut-ins are discussed in terms of their effect on inflow performances. It is shown that even in homogeneous and isotropic reservoirs, the maximum interference may not be between the closest wells. Well interference effects on buildup tests are also scrutinized. The meaning and importance of local vs. overall average pressures are discussed. An example is presented to demonstrate the estimation of the local drainage area from a horizontal-well buildup test in a multi-well system.

Introduction
The conventional theories of transient pressure analysis and inflow performance consider a single well with fixed drainage boundaries.1–11 These boundaries may be the physical boundaries of the reservoir or the fixed flow boundaries that are a result of stabilized flow conditions (pseudo-steady or steady flow). In many realistic multi-well production systems, however, wells are not completely isolated from each other by fixed boundaries; that is, they interfere with each other's performance because of transient flow conditions resulting from the changes in the production conditions of the wells (rate changes, shut-in periods, etc.). Nowadays, multi-well production systems may be a mixture of vertical, fractured, and horizontal wells. In such systems, complex interactions take place among the wells during production and shut-in periods. Therefore, there has always been an effort to better understand the behavior and performance of wells in multi-well production systems and an interest in the extension of the conventional theory to the analysis of the responses of such systems.12–18
In general, two issues pertain to the pressure transient behavior and inflow performance of multiple wells in closed systems:the effect of pressure transients due to the changes in the production rates andanalysis of buildup responses and estimation of the wells' drainage areas.
The former of these issues has been conveniently ignored in the evaluation of inflow performances of vertical wells because of their relatively short durations.16,17 Similarly, by assuming pseudo-steady state in the entire reservoir prior to shut-in, the solution to well interference problem in buildup analysis has been simplified to the division of the total reservoir area to drainage volumes proportional to the wells' production rates. The latter of the issues noted above has been discussed in Refs. 1 and 12–15. The existence and duration of the radial/pseudo-radial flow straight line were investigated in Refs. 11 and 14. Estimation of the drainage area was the focus of Refs. 1, 9, 10, and 12–14. All of these studies assumed pseudo-steady flow in the reservoir prior to shut-in and none was concerned with horizontal wells.
In this work, our objective is to improve our understanding of the transient pressure responses and inflow performances of multiple wells. We particularly investigate the effect of transient flow periods on the estimation of inflow performances and the analysis of buildup responses of horizontal wells. We use the analytical model discussed in Ref. 18. We first demonstrate and discuss the well interference effects on the pressure behavior and productivity of multiple wells. Then, we discuss the analysis of buildup responses. The importance of local vs. overall average reservoir pressure is also underlined in the discussion of the buildup responses. Finally, we demonstrate the application of the techniques discussed in Refs. 12 and 14 to estimate the drainage area of a horizontal well in a multi-well system.