Estimation of Three-Phase Relative Permeabilities for a Water-Alternating-Gas Process by Use of an Improved Ensemble Randomized Maximum-Likelihood Algorithm

2016 ◽  
Vol 19 (04) ◽  
pp. 683-693 ◽  
Author(s):  
Zhaoqi Fan ◽  
Yin Zhang ◽  
Daoyong Yang
Keyword(s):  
Maximum Likelihood ◽  
History Matching ◽  
Step Length ◽  
Production Data ◽  
Damping Factor ◽  
Relative Permeabilities ◽  
Reservoir Simulations ◽  
Water Alternating Gas ◽  
Three Phase ◽  
Randomized Maximum Likelihood

Summary In this paper, a modified ensemble randomized maximum-likelihood (EnRML) algorithm has been developed to estimate three-phase relative permeabilities with consideration of the hysteresis effect by reproducing the actual production data. Ensemble-based history matching uses an ensemble of realizations to construct Monte Carlo approximations of the mean and covariance of the model variables, which can acquire the gradient information from the correlation provided by the ensemble. A power-law model is first used to represent the three-phase relative permeabilities, the coefficients of which can be automatically adjusted until production history is matched. A damping factor is introduced as an adjustment to the step length because a reduced step length is commonly required if an inverse problem is sufficiently nonlinear. A recursive approach for determining the damping factor has been developed to reduce the number of iterations and the computational load of the EnRML algorithm. The restart of reservoir simulations for reducing the cost of reservoir simulations is of significant importance for the EnRML algorithm where iterations are inevitable. By comparing a direct-restart method and an indirect-restart method for numerical simulations, we optimize the restart method used for a specific problem. Subsequently, we validate the proposed methodology by use of a synthetic water-alternating-gas (WAG) displacement experiment and then extend it to match laboratory experiments. The proposed technique has proved to efficiently determine the three-phase relative permeabilities for the WAG processes with consideration of the hysteresis effect, whereas history-matching results are gradually improved as more production data are taken into account. The synthetic scenarios demonstrate that the recursive approach saves 33.7% of the computational expense compared with the trial-and-error method when the maximum iteration is 14. Also, the consistency between the production data and model variables has been well-maintained during the updating processes by use of the direct-restart method, whereas the indirect-restart method fails to minimize the uncertainties associated with the model variables representing three-phase relative permeabilities.

A Robust Methodology To Simulate Water-Alternating-Gas Experiments at Different Scenarios Under Near-Miscible Conditions

SPE Journal ◽  
2017 ◽  
Vol 22 (05) ◽  
pp. 1506-1518 ◽  
Author(s):  
Pedram Mahzari ◽  
Mehran Sohrabi
Keyword(s):  
Porous Media ◽  
History Matching ◽  
Flow In Porous Media ◽  
Phase Flow ◽  
Two Phase ◽  
Matching Process ◽  
Water Alternating Gas ◽  
Three Phase ◽  
Three Phase Flow ◽  
Cycle Dependent

Summary Three-phase flow in porous media during water-alternating-gas (WAG) injections and the associated cycle-dependent hysteresis have been subject of studies experimentally and theoretically. In spite of attempts to develop models and simulation methods for WAG injections and three-phase flow, current lack of a solid approach to handle hysteresis effects in simulating WAG-injection scenarios has resulted in misinterpretations of simulation outcomes in laboratory and field scales. In this work, by use of our improved methodology, the first cycle of the WAG experiments (first waterflood and the subsequent gasflood) was history matched to estimate the two-phase krs (oil/water and gas/oil). For subsequent cycles, pertinent parameters of the WAG hysteresis model are included in the automatic-history-matching process to reproduce all WAG cycles together. The results indicate that history matching the whole WAG experiment would lead to a significantly improved simulation outcome, which highlights the importance of two elements in evaluating WAG experiments: inclusion of the full WAG experiments in history matching and use of a more-representative set of two-phase krs, which was originated from our new methodology to estimate two-phase krs from the first cycle of a WAG experiment. Because WAG-related parameters should be able to model any three-phase flow irrespective of WAG scenarios, in another exercise, the tuned parameters obtained from a WAG experiment (starting with water) were used in a similar coreflood test (WAG starting with gas) to assess predictive capability for simulating three-phase flow in porous media. After identifying shortcomings of existing models, an improved methodology was used to history match multiple coreflood experiments simultaneously to estimate parameters that can reasonably capture processes taking place in WAG at different scenarios—that is, starting with water or gas. The comprehensive simulation study performed here would shed some light on a consolidated methodology to estimate saturation functions that can simulate WAG injections at different scenarios.

Global-Search Distributed-Gauss-Newton Optimization Method and Its Integration With the Randomized-Maximum-Likelihood Method for Uncertainty Quantification of Reservoir Performance

SPE Journal ◽  
2018 ◽  
Vol 23 (05) ◽  
pp. 1496-1517 ◽  
Author(s):  
Chaohui Chen ◽  
Guohua Gao ◽  
Ruijian Li ◽  
Richard Cao ◽  
Tianhong Chen ◽  
...  
Keyword(s):  
History Matching ◽  
Optimization Method ◽  
Global Search ◽  
Real Field ◽  
Production Data ◽  
Finite Difference Approximations ◽  
Production Forecasting ◽  
Novel Method ◽  
Randomized Maximum Likelihood ◽  
Search Capability

Summary Although it is possible to apply traditional optimization algorithms together with the randomized-maximum-likelihood (RML) method to generate multiple conditional realizations, the computation cost is high. This paper presents a novel method to enhance the global-search capability of the distributed-Gauss-Newton (DGN) optimization method and integrates it with the RML method to generate multiple realizations conditioned to production data synchronously. RML generates samples from an approximate posterior by minimizing a large ensemble of perturbed objective functions in which the observed data and prior mean values of uncertain model parameters have been perturbed with Gaussian noise. Rather than performing these minimizations in isolation using large sets of simulations to evaluate the finite-difference approximations of the gradients used to optimize each perturbed realization, we use a concurrent implementation in which simulation results are shared among different minimization tasks whenever these results are helping to converge to the global minimum of a specific minimization task. To improve sharing of results, we relax the accuracy of the finite-difference approximations for the gradients with more widely spaced simulation results. To avoid trapping in local optima, a novel method to enhance the global-search capability of the DGN algorithm is developed and integrated seamlessly with the RML formulation. In this way, we can improve the quality of RML conditional realizations that sample the approximate posterior. The proposed work flow is first validated with a toy problem and then applied to a real-field unconventional asset. Numerical results indicate that the new method is very efficient compared with traditional methods. Hundreds of data-conditioned realizations can be generated in parallel within 20 to 40 iterations. The computational cost (central-processing-unit usage) is reduced significantly compared with the traditional RML approach. The real-field case studies involve a history-matching study to generate history-matched realizations with the proposed method and an uncertainty quantification of production forecasting using those conditioned models. All conditioned models generate production forecasts that are consistent with real-production data in both the history-matching period and the blind-test period. Therefore, the new approach can enhance the confidence level of the estimated-ultimate-recovery (EUR) assessment using production-forecasting results generated from all conditional realizations, resulting in significant business impact.

An Improved Three-Phase Relative Permeability and Hysteresis Model for the Simulation of a Water-Alternating-Gas Injection

SPE Journal ◽  
2013 ◽  
Vol 18 (05) ◽  
pp. 841-850 ◽  
Author(s):  
H.. Shahverdi ◽  
M.. Sohrabi
Keyword(s):  
Relative Permeability ◽  
Oil Recovery ◽  
Gas Injection ◽  
Phase Flow ◽  
Relative Permeabilities ◽  
Water Alternating Gas ◽  
Three Phase ◽  
Three Phase Flow ◽  
Oil Water ◽  
Wag Injection

Summary Water-alternating-gas (WAG) injection in waterflooded reservoirs can increase oil recovery and extend the life of these reservoirs. Reliable reservoir simulations are needed to predict the performance of WAG injection before field implementation. This requires accurate sets of relative permeability (kr) and capillary pressure (Pc) functions for each fluid phase, in a three-phase-flow regime. The WAG process also involves another major complication, hysteresis, which is caused by flow reversal happening during WAG injection. Hysteresis is one of the most important phenomena manipulating the performance of WAG injection, and hence, it has to be carefully accounted for. In this study, we have benefited from the results of a series of coreflood experiments that we have been performing since 1997 as a part of the Characterization of Three-Phase Flow and WAG Injection JIP (joint industry project) at Heriot-Watt University. In particular, we focus on a WAG experiment carried out on a water-wet core to obtain three-phase relative permeability values for oil, water, and gas. The relative permeabilities exhibit significant and irreversible hysteresis for oil, water, and gas. The observed hysteresis, which is a result of the cyclic injection of water and gas during WAG injection, is not predicted by the existing hysteresis models. We present a new three-phase relative permeability model coupled with hysteresis effects for the modeling of the observed cycle-dependent relative permeabilities taking place during WAG injection. The approach has been successfully tested and verified with measured three-phase relative permeability values obtained from a WAG experiment. In line with our laboratory observations, the new model predicts the reduction of the gas relative permeability during consecutive water-and-gas-injection cycles as well as the increase in oil relative permeability happening in consecutive water-injection cycles.

Experiences With Streamline-Based Three-Phase History Matching

2009 ◽  
Vol 12 (04) ◽  
pp. 528-541 ◽  
Author(s):  
Adedayo Oyerinde ◽  
Akhil Datta-Gupta ◽  
William J. Milliken
Keyword(s):  
History Matching ◽  
Field Application ◽  
Production Data ◽  
Time Inversion ◽  
Two Phase ◽  
Major Drawback ◽  
Three Phase ◽  
Production History ◽  
Water Cut ◽  
Matching Techniques

Summary Streamline-based assisted and automatic history matching techniques have shown great potential in reconciling high resolution geologic models to production data. However, a major drawback of these approaches has been incompressibility or slight compressibility assumptions that have limited applications to two-phase water/oil displacements only. Recent generalization of streamline models to compressible flow has greatly expanded the scope and applicability of streamline-based history matching, in particular for three-phase flow. In our previous work, we calibrated geologic models to production data by matching the water cut (WCT) and gas/oil ratio (GOR) using the generalized travel-time inversion (GTTI) technique. For field applications, however, the highly nonmonotonic profile of the GOR data often presents a challenge to this technique. In this work we present a transformation of the field production data that makes it more amenable to GTTI. Further, we generalize the approach to incorporate bottomhole flowing pressure during three-phase history matching. We examine the practical feasibility of the method using a field-scale synthetic example (SPE-9 comparative study) and a field application. The field case is a highly faulted, west-African reservoir with an underlying aquifer. The reservoir is produced under depletion with three producers, and over thirty years of production history. The simulation model has several pressure/volume/temperature (PVT) and special core analysis (SCAL) regions and more than 100,000 cells. The GTTI is shown to be robust because of its quasilinear properties as demonstrated by the WCT and GOR match for a period of 30 years of production history.

Automatic History Matching in a Bayesian Framework, Example Applications

2005 ◽  
Vol 8 (03) ◽  
pp. 214-223 ◽  
Author(s):  
Fengjun Zhang ◽  
Jan-Arild Skjervheim ◽  
Albert C. Reynolds ◽  
Dean S. Oliver
Keyword(s):  
Objective Function ◽  
History Matching ◽  
Maximum Likelihood Method ◽  
Likelihood Method ◽  
Production Data ◽  
A Posteriori ◽  
Automatic History Matching ◽  
Flow Problems ◽  
Static Data ◽  
Randomized Maximum Likelihood

Summary The Bayesian framework allows one to integrate production and static data into an a posteriori probability density function (pdf) for reservoir variables(model parameters). The problem of generating realizations of the reservoir variables for the assessment of uncertainty in reservoir description or predicted reservoir performance then becomes a problem of sampling this a posteriori pdf to obtain a suite of realizations. Generation of a realization by the randomized-maximum-likelihood method requires the minimization of an objective function that includes production-data misfit terms and a model misfit term that arises from a prior model constructed from static data. Minimization of this objective function with an optimization algorithm is equivalent to the automatic history matching of production data, with a prior model constructed from static data providing regularization. Because of the computational cost of computing sensitivity coefficients and the need to solve matrix problems involving the covariance matrix for the prior model, this approach has not been applied to problems in which the number of data and the number of reservoir-model parameters are both large and the forward problem is solved by a conventional finite-difference simulator. In this work, we illustrate that computational efficiency problems can be overcome by using a scaled limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm to minimize the objective function and by using approximate computational stencils to approximate the multiplication of a vector by the prior covariance matrix or its inverse. Implementation of the LBFGS method requires only the gradient of the objective function, which can be obtained from a single solution of the adjoint problem; individual sensitivity coefficients are not needed. We apply the overall process to two examples. The first is a true field example in which a realization of log permeabilities at26,019 gridblocks is generated by the automatic history matching of pressure data, and the second is a pseudo field example that provides a very rough approximation to a North Sea reservoir in which a realization of log permeabilities at 9,750 gridblocks is computed by the automatic history matching of gas/oil ratio (GOR) and pressure data. Introduction The Bayes theorem provides a general framework for updating a pdf as new data or information on the model becomes available. The Bayesian setting offers a distinct advantage. If one can generate a suite of realizations that represent a correct sampling of the a posteriori pdf, then the suite of samples provides an assessment of the uncertainty in reservoir variables. Moreover, by predicting future reservoir performance under proposed operating conditions for each realization, one can characterize the uncertainty in future performance predictions by constructing statistics for the set of outcomes. Liu and Oliver have recently presented a comparison of methods for sampling the a posteriori pdf. Their results indicate that the randomized-maximum-likelihood method is adequate for evaluating uncertainty with a relatively limited number of samples. In this work, we consider the case in which a prior geostatistical model constructed from static data is available and is represented by a multivariate Gaussian pdf. Then, the a posteriori pdf conditional to production data is such that calculation of the maximum a posteriori estimate or generation of a realization by the randomized-maximum-likelihood method is equivalent to the minimization of an appropriate objective function. History-matching problems of interest to us involve a few thousand to tens of thousands of reservoir variables and a few hundred to a few thousand production data. Thus, an optimization algorithm suitable for large-scale problems is needed. Our belief is that nongradient-based algorithms such as simulated annealing and the genetic algorithm are not competitive with gradient-based algorithms in terms of computational efficiency. Classical gradient-based algorithms such as the Gauss-Newton and Levenberg-Marquardt typically converge fairly quickly and have been applied successfully to automatic history matching for both single-phase- and multiphase-flow problems. No multiphase-flow example considered in these papers involved more than 1,500reservoir variables. For single-phase-flow problems, He et al. and Reynolds et al. have generated realizations of models involving up to 12,500 reservoir variables by automatic history matching of pressure data. However, they used a procedure based on their generalization of the method of Carter et al. to calculate sensitivity coefficients; this method assumes that the partial-differential equation solved by reservoir simulation is linear and does not apply for multiphase-flow problems.

History Matching of Three-Phase Flow Production Data

SPE Journal ◽  
2003 ◽  
Vol 8 (04) ◽  
pp. 328-340 ◽  
Author(s):  
Ruijian Li ◽  
A.C. Reynolds ◽  
D.S. Oliver
Keyword(s):  
History Matching ◽  
Production Data ◽  
Phase Flow ◽  
Three Phase ◽  
Three Phase Flow
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