A Mathematical Model of Repeated Steam Soaks of Thick Gravity Drainage Reservoirs
Authors: Seba R.D. , Perry G.E. 
Published: December 2007

Certain equations have been used to predict the performance and heat requirements of steam soaks applied to gravity drainage reservoirs. Good agreement has been obtained between calculated and observed performance.

Introduction
The steam soak process is the most widely applied and most successful thermal supplemental recovery process in use today. This process, which consists of injection of steam in various quantities into a well that is subsequently used as a producer, can be repeatedly applied to the same well. The treatment, if successful, will increase the production rate of the well for a given period. For this reason, the steam soak process should be considered primarily as an acceleration method rather than as a method for producing oil that could not be recovered by primary means. However, application of this process to reservoirs containing viscous crude may produce oil that otherwise would have zero present value or would be produced at such low rates by primary methods that it would not be profitable.
A major necessity for the successful application of the steam soak process is a source of natural energy. This source of energy may exist in one or more of the following forms: expansion of fluids, compaction, gravity drainage. This study was undertaken to determine the effect of gravity drainage on steam soak production and recovery and to develop a method for predicting production rates, ultimate recovery, and heat requirements when applying this process to a reservoir in which the primary driving mechanism is gravity drainage. (For additional discussion of some of the factors that affect recovery of viscous oils by the steam soak process, see Ref. 5.)

Model
The model developed for analyzing the performance of the steam soak process in gravity drainage reservoirs is a modified form of that developed by Matthews and Lefkovits. The model used in this study consists of two concentric cylindrical volumes of productive formation with cap and base rock of impermeable material. The inner cylinder, extending from the radius of the wellbore to some predetermined radius, is referred to as the hot zone; and the outer cylinder extending from the exterior boundary of the hot zone to the outer drainage boundary will be referred to as the partially heated zone. Fig. 1 is a schematic cross-section of the model, indicating its thermal properties. Horizontally the reservoir is divided into two regions, the upper region having a high gas saturation and residual liquid saturation, and the lower region containing a high liquid saturation. The boundary between these two regions is referred to as the free surface, which drops and changes shape as fluid is produced from the reservoir.
The model was used to analyze the steam soak process by applying the following assumptions:
The horizontal formation is composed of one ormore homogeneous noninterconnected layerscontaining incompressible fluids. Each layer is treatedseparately. The hot zone is heated by the initial soak and ismaintained at the steam temperature correspondingto atmospheric pressure by resoaking. The height of the free surface at the producingwell is at all times zero (producing well is pumpedoff).
JPT