An analytical model to estimate the cumulative steam/oil ratio of SAGD or other steam-based bitumen recovery processes is presented. Model predictions are compared with both numerical and field cases. Cyclic steam processes are interpreted as unsteady-state SAGD recovery, which can be operated at effective temperatures about half that for SAGD.
Attempts are sometimes made to correlate the cumulative steam/oil ratio (CSOR) performance of current SAGD projects against single reservoir variables, whether pay thickness, operating pressure, oil saturation, etc. In fact, all of these and more reservoir variables come into play; but the SOR is not just a property of the rocks and the process, but also of time. Due to ongoing reservoir heat loss, production or facility delays also have an impact on the field CSOR.
This paper presents a simple analytical model to predict the CSOR for steam-based recovery of bitumen from highpermeability reservoirs. The model is useful for screening and evaluation purposes, as well as the analysis of the economic effects of various production variables, including shut-ins or impairment.
The founding assumptions are that
1. depletion is gravity driven, and therefore the geometry of the depleted zone (steam chamber) more or less follows from the production well geometry; and
2. produced oil is from the steam zone, and the steam zone has been uniformly reduced to residual oil saturation (pace Butler's SAGD model1, this is equivalent to saying that drainage within the chamber is much more rapid than the rate of chamber expansion).
The present model can be viewed as a simplification and generalization of one published by Reis.2 The main simplification is the use of an empirical constant, which accounts for heat stored below the chamber as a factor of the overburden transient losses.
As in Reis' model, the CSOR is predicted as a function of time, rather than recovery factor. Some external estimate of the recovery vs. time is therefore required in order to transform CSOR to a function of recovery. This estimate may be based on an analytical model such as Butler's,1 Reis', 2,3 field experience, or any other source.
A major extension of the present model is the application to cyclic steaming operations, by use of a time-average effective temperature for the steam zone. Calculation of the effective temperature for some cyclic field cases suggests that it corresponds, on the saturated steam curve, to a pressure close to that of the end of the production cycle. The same is probably also true of a SAGD project that is blown down near the end of its life, and reflects the ability of blowdown or cycles to utilize heat already stored in the chamber.
The claimed scope of this model is "steam-based recovery of bitumen from high permeability reservoirs". This phrase is carefully chosen to encapsulate conditions under which oil recovery is predominately due to gravity drainage, and to not exclude possible application to non-SAGD processes, in particular CSS.
Gravity dominance as used here means that either liquids are moving substantially downwards, or else steam is moving upwards, or both.