Automatic History Matching by use of Response Surfaces and Experimental Design

1994 ◽  
Author(s):  
Alfhild L. Eide ◽  
Lars Holden ◽  
Edel Reiso ◽  
Sigurd I. Aanonsen
Keyword(s):  
Experimental Design ◽  
History Matching ◽  
Response Surfaces ◽  
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＾

Capturing the Reservoir Uncertainty through Probabilistic Dynamic Modelling and Prediction: A Case Study of Multi-Layered Waterflood Reservoir with 90 Years Production History and 293 Wells

2021 ◽  
Author(s):  
E. Noviyanto
Keyword(s):  
Experimental Design ◽  
History Matching ◽  
Pearson Correlation ◽  
Probabilistic Method ◽  
Dynamic Modelling ◽  
Development Planning ◽  
Base Case ◽  
Objective Functions ◽  
Parameter Uncertainties ◽  
Pareto Chart

This paper presents a probabilistic modeling and prediction workflow to capture the range of uncertainties and its application in a field with many wells and long history. A static model consisting of 19 layers and 293 wells was imported as the base model. Several reservoir properties such as relative permeability, PVT, aquifer, and initial condition were analyzed to obtain the range of uncertainties. The probabilistic history matching was done using Assisted History Matching (AHM) tools and divided into experimental design and optimization phases. The inputted parameters and their range sensitive to objective functions, e.g., oil rate/total difference, could be determined using a Pareto chart based on Pearson Correlation during experimental design. The optimization phase carried over the most sensitive parameters. It utilized Particle Swarm Optimization (PSO) algorithm to iterate the process and find the equiprobable models with minimum objective functions. After filtering a set of models created by AHM tools by the total oil production, field/well oil objective functions, the last three years' performance, and clustering using the k-means algorithm, there are 11 models left. These models were then analyzed to understand the final risk and parameter uncertainties, e.g., mobile oil or sweep efficiency. Three models representing P10, P50, and P90 were picked and used as the base models for developing waterflood scenario designs. Several scenarios were done, such as base case, perfect pattern case, and existing well case. The oil incremental is in the range of 1.60 – 2.01 MMSTB for the Base Case, 7.57 – 9.14 MMSTB for the Perfect Pattern Case, and 6.01 – 7.75 MMSTB for the Existing Well Case. This paper introduces the application of the probabilistic method for history matching and prediction. This method can engage the uncertainty of the dynamic model on the forecasted production profiles. In the end, this information could improve the quality of management decision-making in field development planning.

Probabilistic Dynamic Modelling and Prediction Workflows: Application to Multi-Layered Waterflood Reservoir with 90 Years Production History and 293 Wells

2021 ◽  
Author(s):  
Ecko Noviyanto ◽  
Deded Abdul Rohman ◽  
Theoza Nopranda ◽  
Rudini Simanjorang ◽  
Kosdar Gideon Haro ◽  
...  
Keyword(s):  
Experimental Design ◽  
History Matching ◽  
Pearson Correlation ◽  
Probabilistic Method ◽  
Dynamic Modelling ◽  
Development Planning ◽  
Base Case ◽  
Objective Functions ◽  
Parameter Uncertainties ◽  
Pareto Chart

Abstract This paper presents a probabilistic modeling and prediction workflow to capture the range of uncertainties and its application in a field with many wells and long history. A static model consisting of 19 layers and 293 wells was imported as the base model. Several reservoir properties such as relative permeability, PVT, aquifer, and initial condition were analyzed to obtain the range of uncertainties. The probabilistic history matching was done using Assisted History Matching (AHM) tools and divided into experimental design and optimization. The inputted parameters and their range sensitive to objective functions, e.g., oil rate/total difference, could be determined using a Pareto chart based on Pearson Correlation during experimental design. The optimization phase carried over the most sensitive parameters and utilized Particle Swarm Optimization (PSO) algorithm to iterate the process and find the equiprobable models with minimum objective functions. After filtering a set of models created by AHM tools by the total oil production, field/well oil objective functions, the last three years' performance, and clustering using the k-means algorithm, there are 11 models left. These models were then analyzed to understand the absolute risk and parameter uncertainties, e.g., mobile oil or sweep efficiency. Three models representing P10, P50, and P90 were picked and used as the base models for developing waterflood scenario designs. Several scenarios were done, such as base case, perfect pattern case, and existing well case. The oil incremental is in the range of 1.60 – 2.01 MMSTB for the Base Case, 7.57 – 9.14 MMSTB for the Perfect Pattern Case, and 6.01 – 7.75 MMSTB for the Existing Well Case. This paper introduces the application of the probabilistic method for history matching and prediction. This method can engage the uncertainty of the dynamic model on the forecasted production profiles. In the end, this information could improve the quality of management decision-making in field development planning.

An Automatic History Matching Example

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

The Chemical Vapor Deposition of Dispersed Phase Composites in the B-Si-C-H-Cl-Ar System

1994 ◽  
Vol 363 ◽  
Author(s):  
T. S. Moss ◽  
W. J. Lackey ◽  
G. B. Freeman
Keyword(s):  
Experimental Design ◽  
Vapor Deposition ◽  
Multivariate Regression ◽  
Chemical Vapor ◽  
Deposition Process ◽  
Response Surfaces ◽  
Dispersed Phase ◽  
Designed Experiment ◽  
Cell Volumes ◽  
Central Composite

AbstractThe CVD of the coatings in the B-Si-C-H-C1-Ar system was accomplished using a statistically designed experiment. The experimental design used five factor half-fraction factorial with a central composite design that was both rotatable and orthogonal. Deposits were thick and dense and were composed of B13C2 and β-SiC with compositions ranging from 0 to 100%. Response surfaces were generated using multivariate regression for unit cell volumes of B13C2 and β-SiC, %B13C2/%SiC in the coating, and the Si to B ratio in the deposit. These equations could then be used to examine the significant variables in the reaction, as well as for tailoring and optimizing the deposition process.

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