The Gravity Drainage of Steam-heated Heavy Oil to Parallel Horizontal Wells
Authors: Butler R.M. , Stephens D.J. 
Published: March 2010

Introduction
In a previous paper, an equation was derived which predicts the rate of drainage of heavy oil around an expanding steam chamber which is above a horizontal production well. The theory was developed for a reservoir of finite height, but infinite extent. In the present paper, the theory is extended to the more practical confined arrangement in which drainage is to a series of parallel wells. Theoretical expressions are derived for the rate of drainage as a function of the main significant variables.
The paper also describes scaled experiments carried out using a reservoir model with a transparent side. A series of photographs of this model show the development of the steam chamber with time. The results from the model are compared with the theoretical predictions.

INTRODUCTION
In a previous paper (Ref. 1), a novel approach to the production of heavy oils was described in which steam was injected continuously into a growing steam chamber which formed above a horizontal production well. In this process, the steam injection rate is controlled so as to maintain the steam pressure within the chamber approximately constant. Steam flows to the edge of the chamber and condenses. This heats the oil which drains from around the walls of the chamber to the production well below. This paper extends the theory developed earlier.
A main requirement in the mathematical analysis was that a simple solution was sought. The analysis started from a consideration of a small part of a freely moving interface. Heal was assumed to penetrate beyond the interface by thermal conduction using a constant thermal diffusivity for the reservoir. The interface was assumed to be at steam temperature and the temperature distribution beyond the interface was assumed to be the steady-state distribution corresponding to the instantaneous rate of advance of the interface. The viscosity of the oil was calculated as a function of temperature and then of distance and the total drainage flow was obtained using Darcy"s equation and the gravity driving force. Allowance was made for the fact that the interface was inclined and curved. The differential equations were then integrated over the height of the reservoir and the simple equation (1) which resulted expressed the total rate of drainage.
(Equation in Full Paper)
In this paper, the theory is extended and modified in two directions:The calculated interface curves are modified so that they remain attached to the production well. This makes allowance for the head required to move oil from the interface horizontally to the well. This is discussed below under the heading TANDRAIN.The theory is modified to allow for the confining effect of adjacent wells. In the previous theory, the interface was allowed to spread horizontally to infinity; in the present treatment, it spreads only to a vertical no-flow boundary located half way to the next adjacent well.

TANDRAIN
The interface curves which are generated by the original theory rise rapidly and then become asymptotic to the top of the reservoir.