Transient-Pressure Behaviour of Compartmentalized Reservoirs
Authors: Rahman N.M. Anisur , Ambastha A.K. 
Published: December 2007

Abstract
Compartmentalized reservoirs are usually analyzed using the models that are based on the material balance technique. These models have neglected the effects of internal resistance to flow, contrasts of rock and fluid properties and shape of the reservoir. However, this study concentrates on the effects of rock and fluid properties using an analytical solution for transient pressure of compartmentalized reservoirs. It is also shown that the reservoir parameters including those related to the geologic structure of a compartmentalized system can be estimated using transient-pressure data. Considering its ability to demonstrate more features than the pressure responses, the pressure-derivative analysis is also considered for drawdown responses. A compartmentalized system of a small compartment in communication with a big one is considered which is one of the very important aspects of reservoir compartmentalization. Time criteria are developed for the end of the infinite-acting radial flow period and the start of the steady-state flow period.

Introduction
A compartmentalized reservoir is considered to be made up of a number of hydraulically-communicating compartments or regions. This hydraulic communication between adjoining compartments may be poor due to the presence of faults or low-permeability barriers. Compartmentalization of reservoirs is evident in both oil and gas reservoirs. Understanding the pressure behaviour of compartmentalized reservoirs is very important to assess the long-term production performance. Therefore, it is required to identify the reservoir compartmentalization if there is any. In the case of detection of an unexpected compartmentalization in a reservoir during production, sometimes it becomes essential to drill more wells and facilities which could force re-evaluation of the whole development project based on economics. An unexpected detection of the presence of any compartment with a high gas-oil ratio might cause oil production rates to be constrained due to the limited capacity of the gas-handling facilities located it surface. Therefore, it is a good idea to have as much information about the compartmentalization of a reservoir as possible to avoid any unpleasant surprises in future. A number of compartmentalized reservoirs have been discovered in different regions around the world. These include Texas Gulf coast, North sea and South Australia. A parameter in relation to the inter-compartment fluid communication has been termed as barrier transmissibility in Ref. 3. Assigning low values of barrier transmissibility has been the means in Refs. 3 and 4 to simulate the poor communication of fluid between these compartments. This parameter of barrier transmissibility allows a restricted amount of fluid that can cross the interface boundary depending on the difference of average pressures of the adjoining compartments. But in this study, the poor communication of fluid between two adjoining compartments is considered as due to the presence of a thin skin at the interface between the compartments following the ideas in Refs. 5 and 6. This means that the resistance to flow of fluid at an interface is expressed in terms of skin factor which is an inverse but more comprehensive approach in comparison to the use of barrier transmissibility. Moreover, this way any inconsistencies in the definition of barrier transmissibility, as dealt with in material balance techniques, are eliminated. Ref. 4 has presented the material balance equations for different compartmentalized systems based on the assumption that the pressure over each compartment is uniform. This work has also assumed that the resistance to flow of fluid has been lumped into the barrier transmissibility. However, in Ref. 7, it has been observed that the tank models work reasonably well for gas reservoirs having permeability in the range of moderate to high (greater than 5 md). It has also been concluded that these tank models are not appropriate for formation permeability being less than 5 md. Hence, it is obvious that the criterion of using such tank models will become much more restrictive for oil reservoirs.
In Ref. 8, it is suggested that the interpretation of transient pressure by the use of analytical models leads to a simplified description of the geological heterogeneities around the well. P. 519^