For thermal recovery processes, the use of well test analysis to determine the swept volume is an important concern. Well tests conducted on wells undergoing a thermal recovery process have been typically idealized using a two- or three-region composite reservoir model. However, simulated thermal falloff tests have shown that mobility and storativity may be continuously changing in the swept region. For these reservoirs, a two- or three-region composite model may not be appropriate, while a multi-region composite model is suitable. A multi-region, composite reservoir analytical model has been developed to study the effects of various trends of mobility and storativity variations, within the swept region, on well tests for reservoirs undergoing a thermal recovery process. Pressure transient responses from this multi-region composite reservoir model show that on a log-log graph, the intermediate-time semi-log pressure derivative data falling on a straight line, whose slope is less than unity, is due to continuously changing mobility or storativity. The preceding behavior has been observed on several simulated thermal well tests. However, no theoretical explanation for this phenomenon has been advanced prior to this study.
In recent years, the behavior of composite reservoirs has attracted much attention and many studies have appeared on this subject. A composite reservoir is made up of two or more regions. Rock and fluid properties are different in each region. The origin of composite systems may be natural or artificial. Examples of naturally created multi-zone composite systems include a reservoir with different permeability zones, an oil reservoir in communication with an aquifer, and an oil well with a finite-thickness skin zone surrounding the wellbore. Enhanced oil recovery projects, such as CO2 miscible flooding, polymer flooding, in-situ combustion and steam injection, are examples of artificially created conditions, wherein the reservoir can be viewed as a multi-region system with different rock and/or fluid properties.
Fig. 1 schematically illustrates the reservoir model considered in this study. This model represents a radial multi-region composite reservoir in which there are interfaces or discontinuities between each region. In Fig. 1, the distances Ri are the different positions where a discontinuity or front can be recognized. Discontinuities are the locations where rock and/or fluid properties have a significant variation.
In general, reservoirs with contrasts in physical properties have been analyzed using analytical or numerical composite reservoir models. The pressure behavior of composite reservoirs has been considered extensively in many studies. All of these studies can be classified in three large groups: two-region composite, three-region composite and multi-region 8 (more than three regions) composite reservoir models. Based on a two-region model, Eggenschwiler et al. developed the pseudosteady state method to compute the swept volume using a Cartesian graph of the intermediate-time pressure versus time data after the end of the infinite-acting radial flow corresponding to the inner region mobility. They argued that a short-time pseudosteady state flow would occur for large mobility and/or storativity contrasts between the inner and the outer regions for a typical thermal recovery situation. During the pseudosteady state period, the semi-log pressure derivative versus time data would exhibit a unit slope line on a log-log graph.