An Automatic History-Matching Workflow for Unconventional Reservoirs Coupling MCMC and Non-Intrusive EDFM Methods

2018 ◽  
Author(s):  
Wei Yu ◽  
Sutthaporn Tripoppoom ◽  
Kamy Sepehrnoori ◽  
Jijun Miao
Keyword(s):  
History Matching ◽  
Unconventional Reservoirs ◽  
Automatic History Matching

History Matching in Two-Phase Petroleum Reservoirs

1980 ◽  
Vol 20 (06) ◽  
pp. 521-532 ◽  
Author(s):  
A.T. Watson ◽  
J.H. Seinfeld ◽  
G.R. Gavalas ◽  
P.T. Woo
Keyword(s):  
Optimal Control ◽  
Parameter Estimation ◽  
Objective Function ◽  
History Matching ◽  
Computing Time ◽  
Absolute Permeability ◽  
Two Phase ◽  
Automatic History Matching ◽  
Control Approach ◽  
First Order

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＾

An Automatic History Matching Example

2003 ◽  
Author(s):  
A.C. Reynolds ◽  
F. Zhang ◽  
J.A. Skjervheim
Keyword(s):  
History Matching ◽  
Automatic History Matching

Comparison of Sensitivity Coefficient Calculation Methods in Automatic History Matching (includes associated paper 10873 )

1981 ◽  
Vol 21 (05) ◽  
pp. 551-557 ◽  
Author(s):  
Ali H. Dogru ◽  
John H. Seinfeld
Keyword(s):  
History Matching ◽  
Direct Method ◽  
Optimization Methods ◽  
Sensitivity Coefficient ◽  
Additional Time ◽  
Automatic History Matching ◽  
Matching Algorithm ◽  
Iterative Optimization ◽  
Incremental Change ◽  
Two Factors

Abstract The efficiency of automatic history matchingalgorithms depends on two factors: the computationtime needed per iteration and the number of iterations needed for convergence. In most historymatching algorithms, the most time-consumingaspect is the calculation of the sensitivitycoefficientsthe derivatives of the reservoir variables(pressure and saturation) with respect to the reservoirproperties (permeabilities and porosity). This paper presents an analysis of two methodsthe direct andthe variationalfor calculating sensitivitycoefficients, with particular emphasis on thecomputational requirements of the methods.If the simulator consists of a set of N ordinary differential equations for the grid-block variables(e.g., pressures)and there are M parameters forwhich the sensitivity coefficients are desired, the ratioof the computational efforts of the direct to thevariational method is N(M + 1)R = .N(N + 1) + M Thus, for M less than N the direct method is moreeconomical, whereas as M increases, a point isreached at which the variational method is preferred. Introduction There has been considerable interest in thedevelopment of automatic history matching algorithms.Although automatic history matching can offer significant advantages over trial-and-errorapproaches, its adoption has been somewhatlower than might have been anticipated when thefirst significant papers on the subject appeared. Oneobvious reason for the persistence of thetrial-and-error approach is that it does not requireadditional code development beyond that already involvedin the basic simulator, whereas automatic routinesrequire the appendixing of an iterative optimization routine to the basic simulator. Nevertheless, theinvestment of additional time in code developmentfor the history matching algorithm may be returned many fold during the actual history matchingexercise. In spite of the inherent advantages ofautomatic history matching, however, the automatic adjustment of the number of reservoir parameterstypically unknown even in a moderately sizedsimulation can require excessive amounts ofcomputation time. Therefore, it is of utmost importancethat an automatic history matching algorithm be asefficient as possible. Setting aside for the moment the issue of code complexity, the efficiency of analgorithm depends on two factors, the computationtime needed per iteration and the number ofiterations needed for convergence (whereconvergence is usually defined in terms of reaching acertain level of incremental change in either theparameters themselves or the objective function). Formost iterative optimization methods, the speed ofconvergence increases with the complexity of thealgorithm. SPEJ P. 551^

History Matching and Rate Forecasting in Unconventional Oil Reservoirs With an Approximate Analytical Solution to the Double-Porosity Model

2015 ◽  
Vol 19 (01) ◽  
pp. 070-082 ◽  
Author(s):  
B. A. Ogunyomi ◽  
T. W. Patzek ◽  
L. W. Lake ◽  
C. S. Kabir
Keyword(s):  
Analytical Solution ◽  
History Matching ◽  
Horizontal Wells ◽  
Double Porosity ◽  
Unconventional Reservoirs ◽  
Production Data ◽  
Time Space ◽  
Double Porosity Model ◽  
Fractured Horizontal Wells ◽  
Porosity Model

Summary Production data from most fractured horizontal wells in gas and liquid-rich unconventional reservoirs plot as straight lines with a one-half slope on a log-log plot of rate vs. time. This production signature (half-slope) is identical to that expected from a 1D linear flow from reservoir matrix to the fracture face, when production occurs at constant bottomhole pressure. In addition, microseismic data obtained around these fractured wells suggest that an area of enhanced permeability is developed around the horizontal well, and outside this region is an undisturbed part of the reservoir with low permeability. On the basis of these observations, geoscientists have, in general, adopted the conceptual double-porosity model in modeling production from fractured horizontal wells in unconventional reservoirs. The analytical solution to this mathematical model exists in Laplace space, but it cannot be inverted back to real-time space without use of a numerical inversion algorithm. We present a new approximate analytical solution to the double-porosity model in real-time space and its use in modeling and forecasting production from unconventional oil reservoirs. The first step in developing the approximate solution was to convert the systems of partial-differential equations (PDEs) for the double-porosity model into a system of ordinary-differential equations (ODEs). After which, we developed a function that gives the relationship between the average pressures in the high- and the low-permeability regions. With this relationship, the system of ODEs was solved and used to obtain a rate/time function that one can use to predict oil production from unconventional reservoirs. The approximate solution was validated with numerical reservoir simulation. We then performed a sensitivity analysis on the model parameters to understand how the model behaves. After the model was validated and tested, we applied it to field-production data by partially history matching and forecasting the expected ultimate recovery (EUR). The rate/time function fits production data and also yields realistic estimates of ultimate oil recovery. We also investigated the existence of any correlation between the model-derived parameters and available reservoir and well-completion parameters.

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