RIASSUNTO
Abstract
SAGD (Steam Assisted Gravity Drainage) is an efficient and proven technology to recover vast reserves of Alberta's oil sands. Because of its thermal and compositional effects, numerical simulation of the SAGD process requires extensive computational run time, especially in a history matching framework. Therefore, it is beneficial to use an optimization technique that yields faster convergence and better match-quality solutions.
This paper presents a new population-based optimization technique, called differential evolution, in the assisted history matching process. Differential evolution belongs to the class of evolutionary algorithms in the continuous parameter space that has been used successfully in a large range of engineering optimization problems outside the oil industry. Differential evolution converges faster than many other global optimization methods. It requires fewer control variables, is robust and easy to use, and lends itself very well to parallel computing.
We applied the differential evolution technique to a SAGD case study to history match saturation and temperature profiles as well as cumulative oil and water production and cumulative SOR. The results show that it is an excellent optimization technique for obtaining multiple good history matched models, which allow the assessment of uncertainty for the forecast stage. The match-quality of the history matched models obtained with differential evolution has been compared to the results of the particle swarm optimization method that is widely used in history matching. The comparison shows that differential evolution offers much better match-quality solutions with much lower number of simulation runs.
Introduction
For the past 50 years, finding models that can reproduce the history of the reservoir is one of the topics where researchers within the petroleum engineering community have focused. Generally, an initial reservoir model does not match the historical data well enough to use it confidently for future forecasts (Ertekin et al., 2001 and Chen Z., 2007). History matching is defined as a process in which reservoir parameters are altered until it closely reproduces the past behavior of a reservoir. The objective is to update the reservoir model in order to have a confident tool to forecast the future.
Traditionally, it was performed manually by trial and error in which the engineer investigates the difference between a simulation model and historical data and changes one or some parameters at a time to improve the match quality. The first attempt was done by Kruger (1960) where he tried to match the areal permeability distribution of the reservoir. Other authors applied techniques such as variation analysis (Jacquard and Jain, 1965), least squares and linear programming (Coast et al., 1968), and gradient method (Slater and Durrer, 1970) to minimize the misfit between observed and simulated data. Chavent et al. (1973) performed history matching of a single-phase oil reservoir. Dougherty and Kheirkhah (1975) and Fasanino et al. (1986) considered a single-phase gas reservoir in their history matching.