One area that has always generated a significant portion of the papers that appear in SPEJ is the area of automatic history matching. This month’s issue is no exception, although it is apparent that the approaches to automatic history matching have been continuously evolving. In the 1970s, SPEJ published a number of classic papers on automatic history matching, including the papers by Chavent, Dupuy, and Lemonnier (1975); Gavalas, Shah, and Seinfeld (1976); and Chen, Gavalas, Seinfeld, and Wasserman (1974). Many of the ideas developed in these papers form the basis for current research in the area of history matching. On the other hand, history matching has seen a variety of approaches over the years, some of which, like the control theory and Bayesian approaches of Seinfeld and Chavent, have stayed with us. Other methods enjoy a brief flurry of activity, and then disappear from sight when their limitations become apparent.
This issue contains three papers that could be classified as being in the area of automatic history matching. None of them follow closely the path set in the early 1970s, but two are directly related. The third, which uses ideas from percolation theory, follows a much different path.
The ensemble Kalman filter (EnKF) is an approach that has attracted considerable attention recently, as evidenced by the recent average of one EnKF paper per issue in SPEJ. Much of the early development of the method was in the fields of meteorology (weather prediction) and oceanography. Although there are similarities between weather prediction and forecasting of oil and water production in that both require large models, with large amounts of data available, the differences are also substantial. Most of the parameters in weather prediction models are known, and only the state of the system (e.g., temperature, water content, wind velocity, and pressure) is unknown. A typical history-matching problem in petroleum engineering contains many thousands of unknown reservoir parameters (permeability, porosity, anisotropy, and initial OWC) as well as a large number of unknown state variables (pressures, saturations, and concentrations). If the parameters and initial conditions are known, the state variables can be computed, but the EnKF takes an approach that is fundamentally different from typical history matching: both the parameters and the state variables are updated as data are assimilated.
Wen and Chen identify several practical issues with the application of the EnKF for updating of reservoir models. When a state variable such as saturation is updated using the Kalman filter, it is possible that the updated value may be nonphysical; that is, it may be greater than one or less than zero. While this might potentially be corrected simply by truncating the values to their physical limits, this would result in values of saturation that are inconsistent with the flow parameters. The authors propose an iterative approach in which the updated state variables are computed from the updated parameters. A second problem is that large ensembles of realizations are sometimes required to get good results from ensemble-based methods such as the EnKF. Wen and Chen propose a method for generating the initial ensemble that incorporates information on the variability of the forecast. By doing so, it attempts to reduce the redundancy in the ensemble and the time required to obtain results.
Gao, Li, and Reynolds report results of a study of a different approach to history matching that, like EnKF, does not require the computation of the gradient of a data mismatch objective function using the adjoint method. The simultaneous perturbation stochastic approximation (SPSA) uses a simultaneous perturbation of all variables to generate a downhill search direction that can be used in an iterative search procedure. The authors show that the expectation of the stochastic gradient computed using this approach is the true gradient. Several versions of the SPSA algorithm are compared with results from the gradual deformation method, steepest descent, and a quasi-Newton method for history matching. They conclude that SPSA is not competitive with an efficient quasi-Newton history-matching code based on the adjoint, but that it might be useful if an adjoint code is not available.
Masihi, King, and Nurafza present a percolation based method for estimating connectivity of fracture systems in a reservoir. The greatest application of this method will be in those cases in which the reservoir matrix is relatively impermeable and the flow is controlled by the fracture network. Knowledge of connectivity is closely connected to knowledge of dynamic behavior in this case.
In addition to the three papers described here, this issue contains eight others that contribute to SPEJ’s stated mission of publishing “fundamental research papers on all aspects of engineering for oil and gas exploration and production.” I know that you will find something of value here.
Three new Review Chairs join us with the June issue. Hussein Hoteit is a senior reservoir engineer at ConocoPhillips. He has worked on topics including EOR in naturally fractured reservoirs, including molecular diffusion effects, phase behavior calculation, wax deposition in oil pipelines with thermal effect and EOS, and reactive transport in porous media. Larry Lake is the Moncrief Centennial Endowed Chair in Petroleum Engineering at the University of Texas at Austin. He is a specialist in reservoir engineering with research interests in enhanced oil recovery, reservoir characterization, geochemistry, and flow in permeable media. Yucel Akkutlu is currently an assistant professor at the University of Alberta. His research interests include theoretical description of fluid flow and heat/mass transport and reaction in heterogeneous porous media.