A New Analytical Cyclic Steam Stimulation Model Including Formation Fracturing
Authors: Tamim M. , Ali S.M. Farouq 
Published: March 2010

Abstract
Cyclic steam stimulation (CSS) is the commercial oil recovery process of choice for the Cold Lake oil sands. Much of CSS is performed under fracture pressures, and as a result, performance predictions are difficult. This paper presents a new mathematical model, involving analytical techniques, for CSS performance prediction. The model is based upon a fracture heating computation, coupled with fluid flow-both during steam injection and oil and water production. Thus two-phase flow is accounted for. Two situations, involving different flow geometries, bracketing actual flow in the field are considered. These consist of fracture flow, and flow in an elliptical geometry with a circular well in the centre. The model is used to simulate previously reported results. The model can serve as a valuable adjunct to numerical simulation or physical modelling.

Introduction
For reservoirs with medium to high viscosity oil, thermal methods of enhanced oil recovery are very effective. Among all the methods, cyclic steam stimulation (CSS) is used most widely. It is successfully applied in California where many reservoirs contain high viscosity crude oil. Success with this method has also been reported in Cold Lake, Alberta and Venezuela. For improved economies and high cycle production rates, it has become routine to employ CSS for moderate to heavy oil reservoirs prior to a steamflood.
A number of analytical models(1–9) have been proposed in the literature, but most of these models are not applicable to CSS in Cold Lake and other heavy oil reservoirs in Alberta, where formation parting takes place. McGee et al.(10) and Arthur et al.(11) considered the fracturing phenomenon during the injection period. This was ignored by others who considered only radial flow whereas the fluid flow from a fractured well is elliptic. Elliptic flow geometry has been investigated in different fields of petroleum engineering: hydraulic fracturing, water-flooding, well testing, etc. The two extreme views regarding flow during production involve the opening and closure of the fracture. Arthur et al.(10) assumed flow into a fracture during production. They introduced anisotropy in the rectangular co-ordinate to handle the opening and closure of the fracture but their flow equation was based on elliptic co-ordinate system.
To understand the actual flow in the field, both cases have to be investigated. This paper examines flow into a completely closed fracture which involves a circular well at the centre of an elliptic flow geometry. An exact as well as an approximate solution of this problem is investigated. Based on the results of these studies, a new analytical model is proposed, which uses a simple linear gravity drainage flow equation. It also includes the effect of horizontal conductive heat transfer from the inner hot zone to the outer warm zone during soak and production periods. Effects of several flow reduction factors are also accounted for. The calculation method is simplified and can easily be programmed into a desktop or portable computer for quick evaluation of CSS operations and sensitivity analysis.

Model Development
This study examines CSS performances under fractured as well as unfractured wellbore conditions.