Journal of Canadian Petroleum Technology
Volume 48,
Number 1,
January 2009,
pp. 14-18
Abstract
Western Canada has large reserves of heavy crude oil and bitumen. The
Steam-Assisted Gravity Drainage (SAGD) process that couples a steam-based in
situ recovery method with horizontal well technology, has emerged as an
economic and efficient way to produce the shallow heavy oil reservoirs in
Western Canada. Numerical reservoir simulation is used to predict reservoir
performance. However, prior to the prediction phase, integration of production
data into the reservoir model by means of history matching is the key stage in
the numerical simulation workflow. Research and development of efficient
history matching techniques for the SAGD process is important.
An automated technique to assist in the history matching phase of the SAGD
process is implemented and tested. The developed technique is based on a global
optimization method known as Simultaneous Perturbation Stochastic Approximation
(SPSA). This technique is easy to implement, robust with respect to non-optimal
solutions, can be easily parallelized and has shown an excellent performance
for the solution of complex optimization problems in different fields of
science and engineering. The reservoir parameters are estimated at reservoir
scale by solving an inverse problem. At each iteration, selected reservoir
parameters are adjusted. Then, a commercial thermal reservoir simulator is used
to evaluate the impact of these new parameters on the field production data.
Finally, after comparing the simulated production curves to the field data, a
decision is made to keep or reject the altered parameters tested. This research
is preliminary. Although the results are not ready for commercial
implementation, the ideas and results presented here should prove interesting
and fuel development in this important subject area.
A Matlab(1) code, coupled with a reservoir simulator, is implemented
to use the SPSA technique to study the optimization of a SAGD process. A
synthetic case that considers average reservoir and fluid properties present in
Alberta heavy oil reservoirs is presented to highlight the advantages and
disadvantages of the technique.
Introduction
The Simultaneous Perturbation Stochastic Approximation (SPSA) methodology(2)
has been implemented in optimization problems in a variety of fields with
excellent performance. This paper considers production data integration in
reservoir modelling for Steam-Assisted Gravity Drainage (SAGD) processes by
automatic history matching with SPSA.
Automatic history matching problems are optimization problems that must find
the minimum of an objective function. The efficient determination of the
gradient of the objective function is one of the most important aspects of the
overall efficiency of an optimization methodology. For some cases, it is easy
to obtain the gradient of the objective function and the application of
'gradient-based' methods for the solution of the optimization problem is the
natural choice in these circumstances. However, for many practical problems, it
is time-consuming and expensive or simply impossible to estimate the gradient
of the objective function. The notion of 'gradient-free' methods is introduced
to overcome this problem. As a method in this category, SPSA provides a
powerful technique for automatic history matching.
In this work, the objective function related to a synthetic SAGD case is
defined for automatic history matching.
© 2009. Petroleum Society of Canada (now Society of Petroleum Engineers)
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History
- Original manuscript received:
26 March 2006
- Meeting paper published:
13 March 2006
- Revised manuscript received:
30 September 2008
- Manuscript approved:
1 December 2008
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