A Gravity Drainage Model for the Steam-Soak Process
Authors: Kuo C.H. , Shain S.A. , Phocas D.M. 
Published: December 2007

Abstract
This paper deals with production performance for the steam-soak process, as applied to a reservoir where oil is produced by gravity drainage. It is assumed that the steamflooded zone is maintained at a fixed constant temperature and that a portion of the injected heat is transported into the cool zone by radial conduction. On the basis of these assumptions a mathematical model of the production performance has been constructed. The continuity performance has been constructed. The continuity equation is solved by a finite difference method to obtain the distribution of The height of free-oil surface. Then the flow rate and the cumulative oil production are calculated production are calculatedThe results of this study indicate that a large portion of the oil adjacent to the hot zone flows portion of the oil adjacent to the hot zone flows radially toward the production well in the early life. This occurs despite the fact that the formation near the outer boundary remains fairly cold. A high ultimate recovery of oil is predicted for repeated soaks for the case of a thick reservoir containing very viscous oil.
The largest improvement in cumulative production from the steam-soak process over primary production is achieved when the hot-zone radius is less than or equal to one-quarter of the outer drainage radius. The further acceleration of oil production is very little for larger hot-zone radii.
The time required to achieve a certain cumulative production is found to be cut more than one-half by production is found to be cut more than one-half by halving the well spacing. The selection of a close well spacing is suggested by this result.

Introduction
The steam-soak process has been a successful method of recovering very viscous oil from an underground reservoir. It involves injection of steam into. an oil-bearing formation for a certain period of time. The well is then closed in for a period of time. The well is then closed in for a short time, after which it is opened for oil production. These steam-injection and oil-production production. These steam-injection and oil-production processes are repeated for a number of cycles until processes are repeated for a number of cycles until the economic limit is reached. Because of the relatively short history of the steam-soak recovery process, field experience alone does not provide process, field experience alone does not provide enough information for estimation of long-term effects. These effects will influence the design of a field steam-soak operation. Therefore, it is desirable to supplement field experience with model studies. For example, a theoretical analysis of steam stimulation has been given by Martin.
This paper deals with the production performance of a reservoir in which gravity drainage is the dominant production mechanism. In a previous study, Towson and Boberg predicted gravity drainage production rates utilizing the semisteady-state equation developed by Matthews and Lefkovits. Their predictions were based on the assumption that the zone not flooded by steam was maintained at the original formation temperature and the average temperature in the steamflooded zone varied with time as calculated from an energy balance. On the other hand, Seba and Perry assumed that the formation outside the steamflooded zone was heated to a uniform temperature while the temperature in the flooded region remained constant. They considered that, within the flooded zone, a rate equation obtained by Muskat for an infinite reservoir was applicable. Outside the flooded zone, the Matthews-Lefkovits equation was employed.
The influence of temperature, and thus viscosity, on the fluid flow at larger distances from the producing well is important when considering long-term effects. Therefore, a more appropriate temperature distribution than is used in the previously referenced studies is required when previously referenced studies is required when estimating future production rates. The present work aims at combining a temperature distribution, which varies continuously in the part of the reservoir that is being heated by conduction from the hot zone, with a model of the fluid flow. With the temperature distribution specified, the continuity equation will be solved by finite difference methods to obtain the height of the free-oil surface as a function of time and radial distance. The cumulative oil produced can then be predicted. predicted.
JPT
P. 119