Uncertainty Management Book

Chapter 1: Uncertainty Management in Reservoir Engineering

Almost all activities in real life entail different kinds of uncertainty. From daily decisions to complicated problems, such as petroleum reservoir characterization, suffer from uncertainties. Uncertainty can have different roots, including incomplete observation of the system, incomplete modeling of the system because of our limited knowledge and understanding of the underlying mechanisms and rules of the system, intrinsic uncertainty in the system, and inaccurate measurement of the system’s parameters. The first step to deal with uncertainty is to recognize its root and type. This chapter introduces different types of uncertainty in reservoir engineering, challenges induced by uncertainty, and common ways to treat them. Two general approaches to handle the uncertainty are described, named forward uncertainty management and inverse uncertainty management. Forward uncertainty management tries to propagate the uncertainty from inputs to the output(s) to make robust decisions regarding the problem understudy. On the other hand, inverse uncertainty management deals with calibrating model parameters to reduce the range of uncertainty.

 

Chapter 2: Geological Uncertainty Quantification

Our knowledge from underground reservoirs is not complete and is limited to some sparse core and log data, seismic data, geological interpretations, etc. This limited knowledge leads to a significant extend of uncertainty that is common in reservoir modeling and characterization. This kind of uncertainty is known as the geological uncertainty since the uncertainty is present in geological parameters, such as permeability, porosity, fluid contacts, reservoir compartmentalization, fault transmissibility, existence, type, and characteristics of aquifer, etc. Accordingly, geological uncertainty can have different scales including the macro- and micro-scale geological uncertainties. This chapter introduces the geological uncertainty, geological uncertainty scales, geological prior information, structural and stratigraphic uncertainties, geological parametrization, use of seismic and petrophysical data in uncertainty quantification, exploring the range of scenarios, geological realizations, and the geostatistical methods to generate geological realizations. The main geostatistical techniques for generating the realizations of the uncertain parameters, including the kriging-based, object-based, and multiple-point geostatistical methods, are introduced, and their applications, advantages and disadvantages are presented.

 

Chapter 3: Reducing the Geological Uncertainty by History Matching

Whenever there are observed dynamic data obtained from the reservoir understudy, we can reduce the geological uncertainty by conditioning the prior geological realizations to the observed data (Oliver and Chen in Computational Geosciences. 15:185–221, 2010; Ghoniem et al. in Applied Mathematical Modelling. 8:282–287, 1984; Heidari et al. in Computers and Geosciences. 55:84–95, 2013;Zhang and Oliver in SPE Journal. 16:307–317, 2011). This kind of uncertainty management is an inverse uncertainty management/quantification, which is mainly based on Bayesian approaches as described in Sect. 1.5.2. Inverse uncertainty management is technically known as model updating, model conditioning, model adjusting, model calibration, parameter estimation, data assimilation, history matching, automated history matching, or computer-assisted history matching. No matter what you call this process, it helps to have better and more reliable estimations of the true model. This chapter provides the details of history matching, different data types and their scale that are used in history matching, use of seismic, static, and production data in history matching, challenges encountered during history matching, history matching methods, and different approaches to reservoir management under geological uncertainty. Open-loop and closed-loop reservoir management are described and their pros and cons are discussed. Also, the most commonly used ensemble-based methods, ensemble-smoother methods, and stochastic optimization algorithms used for history matching are described.

 

Chapter 4: Dimensionality Reduction Methods Used in History Matching

As discussed in Sect. 3.4, one of the challenges in history matching is the high dimensionality (large number of model parameters) of the reservoir model realizations that raises two challenges: 1- more data assimilation iterations are required to get a satisfactory match, 2- preserving the geologic realism becomes harder as there are an infinite number of solutions that can match the actual production data. These challenges are more prominent when dealing with spatially distributed properties such as the permeability distribution. Thereby, dimensionality reduction (also known as parametrization) methods are required to reduce the number of adjustable parameters while keeping the most salient ones. In the following, some of the dimensionality reduction methods used in the course of history matching are explained. These methods include the conventional methods, such as the pilot points, gradual deformation, principal component analysis, and higher-order singular value decomposition, and deep learning methods, including the autoencoders, variational autoencoders, and convolutional variational autoencoders. Also, a brief introduction to machine learning and deep learning is provided.

 

Chapter 5: Field Development Optimization Under Geological Uncertainty

Decision making about field development plans has to consider the inherent uncertainties of sub-surface hydrocarbon reservoirs; therefore, the decisions would be stable under different geological scenarios. As described in Sect. 1.5.1, the aim of this kind of uncertainty management is to propagate the uncertainty from inputs to the outputs. Therefore, instead of a single deterministic output, the output will be probabilistic from which some statistical measures, such as the expected value, standard deviation, etc. can be calculated to account for the uncertainty. Therefore, the final decision regarding the field development plan can be taken according to the statistical measures. This kind of uncertainty management is also known as the robust field development optimization as explained in the following. In addition, different risk measures, different approaches to selecting an ensemble of representative geological realizations to be used in robust optimization, decreasing the computational cost of the optimization under geological uncertainty by constrained optimization, and challenges related to these activities are described in this chapter.

 

Chapter 6: History Matching and Robust Optimization Using Proxies

As mentioned earlier, one of the challenges in history matching and field development optimization under geological uncertainty is the high computational cost of the process. The majority of the computational burden is associated with numerous reservoir simulations required to calculate the misfit/objective function over a large number of realizations. In addition to reducing the number of geological scenarios, another way to reduce the computational cost associated with history matching (HM) and robust optimization (RO) under geological uncertainty is to use proxy models. Proxy models are simpler models than the full-physics reservoir simulation with ignorable computational costs compared to reservoir simulation. These models can substitute the reservoir simulator to speed up the computation of the misfit/objective function. This chapter is dedicated to introducing proxy models used in history matching and robust field development optimization. Different kinds of proxy models; such as physics-based, non-physics-based, and hybrid proxies; pros and cons of using proxy models; and some example applications of proxy models are introduced.