Reservoir Model Uncertainty Quantification Through Computer-Assisted History Matching

Abstract

Quantification of uncertainty in production forecasting is an important aspect of reservoir simulation studies. The uncertainty in the forecasting stems from the uncertainties of various model-input parameters, such as permeability, porosity, relative permeability endpoints, etc. Traditionally, the outcome of history matching is a set of parameter values that result in a good match of the historical production data. Clearly, the history matching process will be even more valuable if the uncertainties of these model-input parameters can be quantified in the process. In this paper, we present a systematic history matching approach to condition a reservoir model to production data and quantify the uncertainties of history matching parameters in terms of probability density functions. The new approach utilizes experimental design and multi-objective global optimization techniques. More specifically, for a given list of uncertain parameters, the history matching process is treated as a combinatorial optimization problem to find the best combination of these parameters to achieve the minimum history match error. The combinatorial optimization problem is solved by applying a hybrid metaheuristic method that combines evolutionary algorithms, Tabu search, and experimental design techniques. In the optimization process, reservoir models containing different combinations of parameter values are automatically generated to cover a wide range of possibilities based on the principles of experimental design and Tabu search. The search space of the optimization problem is gradually reduced by adopting the natural selection mechanism to discard parameter values that do not fit field data. Finally, the posterior probability density functions of the uncertain parameters are estimated by applying Bayesian theory. The proposed methodology is demonstrated in a real field case study of a complex oil field, which has 12 production wells and 10 years of production history. Some of the wells in the reservoir are found to be difficult to match using the traditional manual history matching approach. After applying the new approach, all the well histories are successfully matched. More importantly, the posterior probability density functions of uncertain parameters are estimated in the history matching process. The results can be further used to quantify the uncertainty in the production forecasting of follow-up recovery processes. Introduction Traditionally, history matching is done manually by varying a few reservoir parameters until a satisfactory match is obtained. It is often the most tedious and time-consuming task in a reservoir simulation study project. Limited by the time frame available, the manual trial-and-error approach usually leads only to a single matched model and provides very little information on the uncertainties of the model. History matching is by nature a very complex non-linear and ill-posed inverse problem. Like most inverse problems, it is characterized by the non-uniqueness of the solution, which means that different combinations of model parameter values may yield similar acceptable matches of the reservoir historical data. In order to achieve a better understanding of the uncertainties of the reservoir, it is necessary to obtain as many multiple good matches as possible in the history matching process1–3.

Recent Developments in Closed-Loop Approaches for Real-Time Mining and Petroleum Extraction

“…reservoir simulation runs), they are restricted to the assimilation of a limited number of parameters. Often, the computational burden is reduced with the aid of 'surrogate' or 'proxy' models, in the form of response surfaces that require a large number of upfront 'training' simulations but can subsequently be evaluated very many times and very quickly during the history matching procedure (Omre and Lødøen, 2004;Cullick et al 2006;Yang et al 2007;Alpak et al 2009). We note that machine learning techniques are sometimes also used to predict production performance more directly from past well performance, i.e., in a black-box or gray-box fashion without the use of reservoir flow models ).…”

Simulation of Bacterial Souring Control in an Alberta Heavy-Oil Reservoir

“…This software uses a combinatorial optimization algorithm based on Experimental Design, Tabu search, and an Evolutionary (Genetic) Algorithm to find the best combination of parameter values that reproduces the observed data (2,3) . The parameters eventually chosen for the history match were the gas and water relative permeabilities (actually block endpoint rescaling of residual saturations and relative permeability maximums) in the well blocks of the individual producers, one set for each producer.…”

“…The field operator initiated a field-wide nitrate treatment (injected nitrate water concentration profiles of 2.4 mM HNO 3 ) in May 2007, and hence the activation of reaction (2). Figure 12 shows the areally-reduced level of H 2 S predicted by the model with nitrate treatment, and should be contrasted with the untreated prediction, Figure 11.…”

“…This is consistent with the equations presented above. Namely, injection of HNO 3 results in cycling of H 2 S as long as a carbon source for NRSOB activity remains via reaction (3). There are two methods of toluene removal, both of which depend on the concentration of toluene in the water phase.…”

Retaining geological realism in dynamic modelling: a channelized turbidite reservoir example from West Africa

“…Stochastic global search techniques are simulator-independent, relatively more straightforward to implement and tend to avoid local optima. Several stochastic search algorithms -genetic algorithms (Erbas & Christie 2007), simulated annealing (Ouenes et al 1993), tabu search (Yang et al 2007), neighbourhood algorithm (Sambridge 1999;Stephen et al 2006), modified Markov-chain Monte Carlo algorithms (Maučec et al 2007;Alpak et al 2009) and agent based optimization techniques, such as particle swarm optimization (Mohamed et al 2009) -have been applied to historymatching problems. Christie et al (2006) used neural networks in combination with the neighbourhood algorithm for history matching.…”