A method for automatic history matching of a compositional reservoir simulator with multipoint flux approximation

2008 ◽  
Vol 12 (2) ◽  
pp. 209-225 ◽  
Author(s):  
Dmitry Eydinov ◽  
Sigurd Ivar Aanonsen ◽  
Jarle Haukås ◽  
Ivar Aavatsmark
SPE Journal ◽  
2007 ◽  
Vol 12 (02) ◽  
pp. 196-208 ◽  
Author(s):  
Guohua Gao ◽  
Gaoming Li ◽  
Albert Coburn Reynolds

Summary For large- scale history- matching problems, optimization algorithms which require only the gradient of the objective function and avoid explicit computation of the Hessian appear to be the best approach. Unfortunately, such algorithms have not been extensively used in practice because computation of the gradient of the objective function by the adjoint method requires explicit knowledge of the simulator numerics and expertise in simulation development. Here we apply the simultaneous perturbation stochastic approximation (SPSA) method to history match multiphase flow production data. SPSA, which has recently attracted considerable international attention in a variety of disciplines, can be easily combined with any reservoir simulator to do automatic history matching. The SPSA method uses stochastic simultaneous perturbation of all parameters to generate a down hill search direction at each iteration. The theoretical basis for this probabilistic perturbation is that the expectation of the search direction generated is the steepest descent direction. We present modifications for improvement in the convergence behavior of the SPSA algorithm for history matching and compare its performance to the steepest descent, gradual deformation and LBFGS algorithm. Although the convergence properties of the SPSA algorithm are not nearly as good as our most recent implementation of a quasi-Newton method (LBFGS), the SPSA algorithm is not simulator specific and it requires only a few hours of work to combine SPSA with any commercial reservoir simulator to do automatic history matching. To the best of our knowledge, this is the first introduction of SPSA into the history matching literature. Thus, we make considerable effort to put it in a proper context.


1980 ◽  
Vol 20 (06) ◽  
pp. 521-532 ◽  
Author(s):  
A.T. Watson ◽  
J.H. Seinfeld ◽  
G.R. Gavalas ◽  
P.T. Woo

Abstract An automatic history-matching algorithm based onan optimal control approach has been formulated forjoint estimation of spatially varying permeability andporosity and coefficients of relative permeabilityfunctions in two-phase reservoirs. The algorithm usespressure and production rate data simultaneously. The performance of the algorithm for thewaterflooding of one- and two-dimensional hypotheticalreservoirs is examined, and properties associatedwith the parameter estimation problem are discussed. Introduction There has been considerable interest in thedevelopment of automatic history-matchingalgorithms. Most of the published work to date onautomatic history matching has been devoted tosingle-phase reservoirs in which the unknownparameters to be estimated are often the reservoirporosity (or storage) and absolute permeability (ortransmissibility). In the single-phase problem, theobjective function usually consists of the deviationsbetween the predicted and measured reservoirpressures at the wells. Parameter estimation, orhistory matching, in multiphase reservoirs isfundamentally more difficult than in single-phasereservoirs. The multiphase equations are nonlinear, and in addition to the porosity and absolutepermeability, the relative permeabilities of each phasemay be unknown and subject to estimation. Measurements of the relative rates of flow of oil, water, and gas at the wells also may be available forthe objective function. The aspect of the reservoir history-matchingproblem that distinguishes it from other parameterestimation problems in science and engineering is thelarge dimensionality of both the system state and theunknown parameters. As a result of this largedimensionality, computational efficiency becomes aprime consideration in the implementation of anautomatic history-matching method. In all parameterestimation methods, a trade-off exists between theamount of computation performed per iteration andthe speed of convergence of the method. Animportant saving in computing time was realized insingle-phase automatic history matching through theintroduction of optimal control theory as a methodfor calculating the gradient of the objective functionwith respect to the unknown parameters. Thistechnique currently is limited to first-order gradientmethods. First-order gradient methods generallyconverge more slowly than those of higher order.Nevertheless, the amount of computation requiredper iteration is significantly less than that requiredfor higher-order optimization methods; thus, first-order methods are attractive for automatic historymatching. The optimal control algorithm forautomatic history matching has been shown toproduce excellent results when applied to field problems. Therefore, the first approach to thedevelopment of a general automatic history-matchingalgorithm for multiphase reservoirs wouldseem to proceed through the development of anoptimal control approach for calculating the gradientof the objective function with respect to theparameters for use in a first-order method. SPEJ P. 521^


2021 ◽  
Vol 73 (04) ◽  
pp. 60-61
Author(s):  
Chris Carpenter

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 199149, “Rate-Transient-Analysis-Assisted History Matching With a Combined Hydraulic Fracturing and Reservoir Simulator,” by Garrett Fowler, SPE, and Mark McClure, SPE, ResFrac, and Jeff Allen, Recoil Resources, prepared for the 2020 SPE Latin American and Caribbean Petroleum Engineering Conference, originally scheduled to be held in Bogota, Colombia, 17–19 March. The paper has not been peer reviewed. This paper presents a step-by-step work flow to facilitate history matching numerical simulation models of hydraulically fractured shale wells. Sensitivity analysis simulations are performed with a coupled hydraulic fracturing, geomechanics, and reservoir simulator. The results are used to develop what the authors term “motifs” that inform the history-matching process. Using intuition from these simulations, history matching can be expedited by changing matrix permeability, fracture conductivity, matrix-pressure-dependent permeability, boundary effects, and relative permeability. Introduction This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 199149, “Rate-Transient-Analysis-Assisted History Matching With a Combined Hydraulic Fracturing and Reservoir Simulator,” by Garrett Fowler, SPE, and Mark McClure, SPE, ResFrac, and Jeff Allen, Recoil Resources, prepared for the 2020 SPE Latin American and Caribbean Petroleum Engineering Conference, originally scheduled to be held in Bogota, Colombia, 17-19 March. The paper has not been peer reviewed. This paper presents a step-by-step work flow to facilitate history matching numerical simulation models of hydraulically fractured shale wells. Sensitivity analysis simulations are performed with a coupled hydraulic fracturing, geomechanics, and reservoir simulator. The results are used to develop what the authors term “motifs” that inform the history-matching process. Using intuition from these simulations, history matching can be expedited by changing matrix permeability, fracture conductivity, matrix-pressure-dependent permeability, boundary effects, and relative permeability. Introduction The concept of rate transient analysis (RTA) involves the use of rate and pressure trends of producing wells to estimate properties such as permeability and fracture surface area. While very useful, RTA is an analytical technique and has commensurate limitations. In the complete paper, different RTA motifs are generated using a simulator. Insights from these motif simulations are used to modify simulation parameters to expediate and inform the history- matching process. The simulation history-matching work flow presented includes the following steps: 1 - Set up a simulation model with geologic properties, wellbore and completion designs, and fracturing and production schedules 2 - Run an initial model 3 - Tune the fracture geometries (height and length) to heuristic data: microseismic, frac-hit data, distributed acoustic sensing, or other diagnostics 4 - Match instantaneous shut-in pressure (ISIP) and wellhead pressure (WHP) during injection 5 - Make RTA plots of the real and simulated production data 6 - Use the motifs presented in the paper to identify possible production mechanisms in the real data 7 - Adjust history-matching parameters in the simulation model based on the intuition gained from RTA of the real data 8 -Iterate Steps 5 through 7 to obtain a match in RTA trends 9 - Modify relative permeabilities as necessary to obtain correct oil, water, and gas proportions In this study, the authors used a commercial simulator that fully integrates hydraulic fracturing, wellbore, and reservoir simulation into a single modeling code. Matching Fracturing Data The complete paper focuses on matching production data, assisted by RTA, not specifically on the matching of fracturing data such as injection pressure and fracture geometry (Steps 3 and 4). Nevertheless, for completeness, these steps are very briefly summarized in this section. Effective fracture toughness is the most-important factor in determining fracture length. Field diagnostics suggest considerable variability in effective fracture toughness and fracture length. Typical half-lengths are between 500 and 2,000 ft. Laboratory-derived values of fracture toughness yield longer fractures (propagation of 2,000 ft or more from the wellbore). Significantly larger values of fracture toughness are needed to explain the shorter fracture length and higher net pressure values that are often observed. The authors use a scale- dependent fracture-toughness parameter to increase toughness as the fracture grows. This allows the simulator to match injection pressure data while simultaneously limiting fracture length. This scale-dependent toughness scaling parameter is the most-important parameter in determining fracture size.


2003 ◽  
Author(s):  
A.C. Reynolds ◽  
F. Zhang ◽  
J.A. Skjervheim

Sign in / Sign up

Export Citation Format

Share Document