A new methodology for Bayesian history matching using parallel interacting Markov chain Monte Carlo

This paper presents an innovative application of a new class of parallel interacting Markov chains Monte Carlo to solve the Bayesian history matching (BHM) problem. BHM consists of sampling a posterior distribution given by the Bayesian theorem. Markov chain Monte Carlo (MCMC) is well suited for sampling, in principle, any type of distribution; however the number of iteration required by the traditional single-chain MCMC can be prohibitive in BHM applications. Furthermore, history matching is typically a highly nonlinear inverse problem, which leads in very complex posterior distributions, characterized by many separated modes. Therefore, single chain can be trapped into a local mode. Parallel interacting chains is an interesting way to overcome this problem, as shown in this paper. In addition, we presented new approaches to define starting points for the parallel chains. For validation purposes, the proposed methodology is firstly applied in a simple but challenging cross section reservoir model with many modes in the posterior distribution. Afterwards, the application to a realistic case integrated to geostatistical modelling is also presented. The results showed that the combination of parallel interacting chain with the capabilities of distributed computing commonly available nowadays is very promising to solve the BHM problem.     

Assisted History Matching Using Streamline Simulation

The quantity and quality of the information obtained from modern reservoir characterization techniques is still not sufficient to perfectly represent the reservoir. Therefore, reservoir models must be calibrated in order to provide a more reliable production forecast. This process is called production history matching. History matching is one of the most time-consuming tasks of a reservoir study due to the complexity of the process, multiple acceptable solutions, and demand for specialist knowledge. Many times this task is still based on a trial and error procedure, which is normally very inefficient because it involves a large number of cycles. This paper shows that it is possible to integrate the experience of the professionals involved in the process with some automatic techniques to accelerate the process and to obtain better solutions. This process is called Assisted History Matching. The use of streamline simulation as a complementary technique is applied to allow a better understanding of fluid flow behavior on the reservoir, mapping heterogeneities location, and then choosing adequate geological parameters, such as permeability and porosity, according to the identified flow patterns. Reservoir parameters are modified along blocks mapped by the streamlines. Automatic procedures are then applied along with parallel computing to find the best combination of the selected parameters. The methodology was applied to a complex real field where satisfactory results were obtained.     

A framework to integrate history matching and geostatistical modeling using genetic algorithm and direct search methods

History matching is an inverse problem where the reservoir model is modified in order to reproduce field observed data. Traditional history matching processes are executed separately from the geological and geostatistical modeling stage due to the complexity of each area. Changes made directly on the reservoir properties generally yield inconsistent geological models. This work presents a framework to integrate geostatistical modeling and history matching process, where geostatistical images are treated as matching parameters. The traditional optimization methods normally applied in history matching generally use gradient information. The treatment of geostatistical images as matching parameters is difficult for these methods due to the strong non-linearities in the solution space. Therefore, another objective of this work is to investigate the application of two optimization methods: genetic algorithm and direct search method in the proposed framework. In order to accelerate the optimization process, two additional techniques are used: upscaling and distributed computing. Results are presented showing the viability of the genetic algorithm in the type of problem addressed in this work and also that direct search method can be used with some restriction. Finally, the benefits of distributed computing and the consistence of the upscaling process are shown.     

A New Methodology for Assisted History Matching Using Independent Objective Functions

Abstract

History matching is a complex inverse problem for which the degree of difficulty and the computational effort (in terms of number of simulations) increase with the increasing of the number of matching parameters. This article presents a new methodology for assisted history matching based on independent objective functions that decrease the number of simulations. The proposed approach consists of the optimization of several objective functions related to each region of the reservoir to be matched, such as a well or a group of wells. Optimization processes, one for each objective function, are started simultaneously, modifying the same data file, yielding a more efficient process, allowing speedup and preserving the quality of the results. The methodology was successfully applied to an offshore field. The results show that the quality of results is practically the same when compared to the conventional procedures, i.e., matching of the wells individually or combining several wells. The advantage is a significant reduction on the number of simulations, preserving the quality of the results.     

Risk Assessment of Petroleum Fields—Use of Numerical Simulation and Proxy Models

Abstract

The development of petroleum fields is a complex task due to the high influence of uncertainties on E&P projects. During the appraisal and development phases, uncertainties related to geologic and fluid models play an important role, especially in offshore heavy oil fields due to the low economic return, limited flexibility, and importance of reservoir modeling. The flexibility is limited because of the necessity to design the production facilities based on a low amount of information. The reservoir modeling process is important because risk of field development projects is normally caused by a high uncertainty on the recovery factor. Due to the necessity of a more robust evaluation of recovery factor, risk assessment methodologies normally are integrated with reservoir simulation, which is the best available tool to predict reservoir performance. However, higher precision on prediction of reservoir behavior is normally associated with fine simulation grid and high computation effort. In this article, some alternatives are presented to improve the efficiency of risk assessment, considering precision and computation effort. Among these alternatives are (1) use of coarse models, (2) use of coarse models modified to reproduce fine grid results, (3) simplifications on the risk assessment procedure, and (4) use of proxy models based on statistical (experimental) design and response surface methodology. A general discussion, including each alternative, use of upscaling techniques, reduction of grid size, number of attributes, use of parallel computing, and use of proxy models are made based on previous publications and results of a case study.

The methodology applied to quantify risk involves a sensitivity analysis in order to reduce the number of critical attributes and simulation of reservoir models obtained through the combination of these attributes. Afterward, a statistic treatment is used to evaluate the risk involved in the process. Based on a case study, it is shown that the use of faster simulation models and proxies can speed up risk assessment, but a few steps must be performed to guarantee the quality of the results.     

Value assessment for reservoir recovery optimization

This paper analyzes the managerial flexibility embedded in oil and gas exploration and production. The analysis includes the economic impact of using different production techniques on the valuation of oil reserves. Two methodologies are used to evaluate the simulation of engineering techniques: (i) the real option approach; and (ii) the discounted cash flow (DCF) method. Given the external variables (e.g., oil price, interest rate), this paper evaluates the best engineering technique for oil recovery by using a valuation approach. We conclude that by appropriately combining different production techniques, the value of oil reserves can increase under the real option approach and can be higher than the value assessed under the DCF method. Since oil recovery includes many managerial choices, we argue that the real option approach is more appropriate than the DCF method. The paper concludes that concession time and dividend yield are the most sensitive parameters for the valuation of oil reserves.     

Use of Neuro-Simulation techniques as proxies to reservoir simulator: Application in production history matching

The Well Placement Optimization, Field Development Scheduling, History Matching with Multiple Models, Global Optimization of Oil Production Systems are procedures related to Reservoir Engineering realized generally with base in a very large number of reservoir simulations which can yield slow developments and large computational effort. To minimize this problem some techniques such as Spline, Neural Networks, Kriging and Experimental Design, have been presented in the literature to be used as proxies to reservoir simulator. Due to the importance of the decisions related to the development and management of petroleum fields, the development of proxies with high accuracy can be a decisive aspect in a project. The successful applications of Neural Networks in several research fields suggest the investigation of appropriated architectures to be used as proxies to reservoir simulator. In this article novel proxies to reservoir simulator which are based on Neuro-Simulation techniques are introduced that present a high accuracy to reservoir simulator. Five different architectures of Neural Networks were studied and applied in two case studies related to history matching. The results obtained showed the large potential of application of the techniques introduced.     

A new optimization framework using genetic algorithm and artificial neural network to reduce uncertainties in petroleum reservoir models

In this article, a new optimization framework to reduce uncertainties in petroleum reservoir attributes using artificial intelligence techniques (neural network and genetic algorithm) is proposed. Instead of using the deterministic values of the reservoir properties, as in a conventional process, the parameters of the probability density function of each uncertain attribute are set as design variables in an optimization process using a genetic algorithm. The objective function (OF) is based on the misfit of a set of models, sampled from the probability density function, and a symmetry factor (which represents the distribution of curves around the history) is used as weight in the OF. Artificial neural networks are trained to represent the production curves of each well and the proxy models generated are used to evaluate the OF in the optimization process. The proposed method was applied to a reservoir with 16 uncertain attributes and promising results were obtained.