A Mathematical Model of Reservoir Response During the Cyclic Injection of Steam
Authors: Mueller T.D. 
Published: December 2007

Abstract
A mathematical model of reservoir behavior during one cycle of the intermittent steam injection process is presented in this paper. A cycle of the process is considered to be composed of three stages: injection, condensation and production. The model concentrates on behavior during the production stage. The influence of several parameters on production improvement is described, using the results obtained with a numerical equivalent of the model. Reservoir system parameters considered are thickness, reservoir thermal conductivity, oil viscosity, solution gas-oil ratio and the change in oil effective permeability with temperature. Operating parameters investigated are heat injection rate, steam temperature and cumulative injection time.
In the face of considerable uncertainty, the model appears to give a fair prediction of the behavior observed during an actual test. This makes the model a useful means of selecting projects. It is shown that the model may also be utilized to select an optimum set of operating conditions for a particular project. Results of this study show the extent to which production improvement depends on each of the parameters investigated and give an indication of the range of system conditions within which the process would be effective.

INTRODUCTION
In recent years the intermittent steam injection or steam soak process of oil recovery has become a popular method of improving recovery in reservoirs bearing high-viscosity hydrocarbons. Production improvement due to the process results from heating the reservoir near the wellbore. The process is applied on an individual well basis and is executed in a series of cycles, each consisting of three stages: injection, condensation (the soaking period) and production.
During the injection stage, high-pressure steam is injected into the reservoir surrounding the wellbore. This study assumes that injection is carried out over the entire vertical section of the reservoir rock that can be exposed to fluid injection. The condition of steam entering the reservoir is considered to fall within the following limits:steam pressures less than 1,000 psig,steam temperatures between 300 and 700F andsteam quality less than 90 percent. The last restriction is due to equipment limitations. Normally, injection is maintained for less than 3 weeks.
After termination of injection, the condensation stage begins. The well is shut in for several days, supposedly to make certain that the injected steam condenses. This condensation would insure the retention of injected heat. The production stage is initiated when the well is opened again. Reservoir response during this stage determines the effectiveness of the process (response is defined as the oil production rates, the water production rates and the wellbore temperatures observed during the entire production stage). The immediate response of the reservoir is sometimes quite good. Sets of case histories by Long1 and by Owens and Suter2 give some typical figures for response. Duration of the production stage is equal to the time needed for the oil production rate to decline to some predetermined value. This usually requires 4 to 6 months. Termination of the production stage coincides with the start of the next cycle. The process is continued, cycle by cycle, until it becomes unprofitable to continue.