DEVELOPMENT OF AN ASSISTED HISTORY MATCHING AND UNCERTAINTY QUANTIFICATION TOOL BASED ON GAUSSIAN PROCESSES PROXY MODELS AND VARIOGRAM BASED SENSITIVITY ANALYSIS

Restricted (Penn State Only)
Author:
Rana, Sachin
Graduate Program:
Energy and Mineral Engineering
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
November 30, 2017
Committee Members:
  • Turgay Ertekin, Dissertation Advisor
  • Turgay Ertekin, Committee Chair
  • Gregory R King, Committee Member
  • Hamid Emami-Meybodi, Committee Member
  • Jing Yang, Outside Member
Keywords:
  • Assisted History Matching
  • Gaussian Processes
  • Sensitivity Analysis
  • Uncertainty Quantification
  • Bayesian Optimization
Abstract:
History matching is an inverse solution process in which uncertain parameters of the numerical reservoir model are tuned in an effort to minimize the mismatch between simulated production and observed production data. History matching problem can be solved as an optimization or data assimilation problem. In this research, the history matching problem is solved from the optimization point of view. Currently, many commercial history matching tools use evolutionary strategy optimization algorithms such as differential evolution, particle swarm optimization etc. to find solutions of history matching. However, these algorithms usually require a large number of numerical simulation runs in order to converge to acceptable solutions. If each numerical simulation takes an extensive time to complete, these algorithms become inefficient. In this research, a new assisted history matching tool named as GP-VARS is presented that can provide multiple solutions of history matching fewer numerical simulations. GP-VARS uses Gaussian process (GP) based proxy models to provide fast approximate forward solutions which are used in Bayesian optimization to find history match solutions in an iterative manner. An application of VARS based sensitivity analysis is applied on forward GP model to calculate the sensitivity index for uncertain reservoir parameters. The results of sensitivity analysis are used to regulate the lower and upper bounds of different reservoir parameters in order to achieve faster convergence. A second GP model is used to provide an inverse solution which also provides temporary history match solutions. Since the history matching problem has non-unique solutions, the uncertainty in reservoir parameters is quantified using Markov Chain Monte Carlo (MCMC ) sampling from the trained forward GP model. The collected MCMC samples are then passed to a third GP model that is trained to predict the EUR values for any combination of reservoir parameters. The GP-VARS methodology is applied to three different heterogeneous reservoir case studies including a benchmark PUNQ-S3 reservoir located in north sea and the M4.1 reservoir located in Gulf of Mexico. The results show that history matching can be performed in approximately four times less number of numerical simulation runs as compared to the state of the art differential evolution algorithm. In addition, it was found that the P50 estimates of EUR are in close agreement with truth values in the presented case studies.