The Role of Geology in Stochastic Reservoir Modelling: The Future Trends

Stochastic simulation is a popular approach for the quantification of reservoir heterogeneity. From the geological viewpoints, however, the role of reservoir geology in stochastic models is diminishing in recent years. This paper reviews the major characteristics of the stochastic models, and geological knowledge is identified as the major missing element in the current practices of the simulation techniques. A detailed discussion of the meaning and usefulness of geological knowledge is given. We have also provided a list of future research directions showing how we can make use of conceptual geological models to bridge the gap between reservoir geology and stochastic simulation practices. Introduction Reservoir characterisation plays a crucial role in reservoir management practices. It is an important joint between geology, geophysics and reservoir simulation. It aims to integrate information from various sources and generate numerical models from sparsely distributed reservoir properties, such as lithofacies, porosity, permeability and fluid saturations. Without a realistic geological framework incorporated into the reservoir study, no reservoir model can be used reliably as a predictive tool. Philosophical Issues in Reservoir Modelling. Obtaining realistic reservoir models requires fast and flexible processes to handle reservoir data which are, unfortunately, often incomplete. Because of the incompleteness of the available data, reservoir modelling becomes a very challenging problem as the establishment of truth is impossible (although the reservoir is of a deterministic nature in reality). This means that verification and validation of any reservoir models also becomes impossible. Many studies have used history matching as a tool to “verify” the accuracy of the reservoir models. This, in fact, is a result of committing a logical fallacy of “affirming the consequent” because there exists more than one numerical model which can produce the same outputs. This situation is referred to by scientists as nonuniqueness. Therefore, if a reservoir model fails to match the observed data (e.g. production data), then we know that the model is faulty in some way, but the reverse is never the case. This means that we may need to rely on other criteria in order to define a better model. Hence, reservoir characterisation studies are, in fact, not purely scientific works, but depend heavily on subjective modelling decisions. Data Integration. In order to reduce the subjectivity involved, the current practice is to incorporate as many inputs (e.g. well data, seismic attributes, well tests and production data) as possible into the modelling algorithms. The only advantage of data integration is to reduce the uncertainty of the model, but may not necessarilly produce a more “accurate” model because the truth is never available for verification. In order to integrate data from various sources into the reservoir models, geologists have experienced many difficulties, as it is difficult and nearly impossible for them to process these data quantitatively and to provide high resolution 3D models. With the rapid development of modern computer technology, stochastic simulation becomes a popular approach for simulating unknowable reservoir properties and quantifying reservoir heterogeneity with extensive risk analysis capability. Despite the usefulness of stochastic models, there is still much evidence that the predicted performance is below expectation. This is an indication of our failure to understand the process involved and to recognise the uncertainty inherent in the definition of important reservoir characteristics. There are many possibilities for poor predictions, and all of them are more or less associated with the input parameters to the simulation algorithms. We can certainly improve the predictions if we are able to identify the problem inputs and model their uncertainty appropriately. SPE 54307 The Role of Geology in Stochastic Reservoir Modelling: The Future Trends D. Tamhane, SPE, L. Wang and P.M. Wong, SPE, University of New South Wales, Sydney, Australia. 2 D. Tamhane, L. Wang and P. M. Wong SPE 54307 Model Uncertainty. According to Zimmermann, “certainty” implies that a person [model] has quantitatively and qualitatively the appropriate information to describe, prescribe or predict deterministically and numerically a system, its behaviour or other phenomena. The situations which are not described by this definition shall be called “uncertain.” The causes of uncertainty mainly include lack of information, abundance of information (complexity), conflicting evidence, ambiguity, engineering measurement, and subjective belief. From our experience, the major uncertainty in reservoir modelling is the subjective geological interpretation of the field. This strongly relates to the understanding of the reservoir geology. However, the commonly identified problem inputs in stochastic models are hardly related to reservoir geology. Hence, there is a great need to re-examine the characteristics of the conceptual geological models, which are known to be fully charged with valuable geological knowledge. Objective. The objective of this paper is to firstly revisit the current practices of stochastic simulation. This is followed by a discussion of the conceptual geological models. Lastly, we will provide a list of future research directions, showing how we can make use of geological knowledge in stochastic simulation for improved predictions. Stochastic Simulation Stochastic simulation is a very fast and flexible approach to generate reservoir models. The use of Monte Carlo methods is extremely convenient to simulate unknowable events. Many are able to generate multiple conditional realisations for local uncertainty analysis. With the increasing interest of stochastic modelling in reservoir characterisation, many stochastic models have been developed in the past several years. They can be classified into two broad types: pixel-based models and object-based models. In this section, we will briefly discuss the characteristics of these models. Pixel-based Models. Most of the pixel-based stochastic methods are based on kriging or cokriging in a sequential manner. Examples are sequential Gaussian simulation, sequential indicator simulation and truncated Gaussian simulation. They are all able to obtain estimates of the necessary conditional distributions by using simple kriging or ordinary kriging. In order to incorporate soft data (e.g. seismic impedance), cokriging technique can be used during the sequential simulation processes. They can directly analyse the quantitative data and utilise them for prediction purpose via the use of direct-variograms or cross-variograms. Apart from the sequential simulation algorithms, simulated annealing is also flexible to incorporate more data types into the model by adding new components to the objective function. Object-based Models. Object-based models present a promising concept to integrate stochastic geological objects. They treat each geological body (e.g. a sand body) as an object, and parameterise the body by constructing a series of probability distributions according to the known data, Then, they generate different bodies for the geological model by Monte Carlo sampling from the distributions of the parameters. During the process, geologists can also put specific sedimentary body with certain parameters into the model and match their geological knowledge. The most popular model is the marked point processes. The small-scale features are simulated mostly by the use of simulated annealing. The Major Difficulty. From the geological viewpoints, the role of reservoir geology in stochastic models is diminishing and is increasingly replaced by two-point statistics (e.g. variograms) used in pixel-based models that are far too simple to parameterise complex geology, and are often unrepresentative when the data are sparse, limited and biased. The object-based models present a more geologically intuitive concept, but it requires many parameters that are difficult to interpret geologically and does not consider information derived from sedimentary processes. From our experience, geological knowledge is extremely important and often represents the major uncertainty component in reservoir characterisation. Unfortunately, this is not what the current practices of stochastic simulation are trying to model. There also exists a general misunderstanding of what “geological knowledge” really means. The next section will give a detailed discussion of conceptual geological models and clarify the meaning of geological knowledge. Conceptual Geological Models Conceptual models have placed a central role in reservoir modelling for many decades, even before the birth of modern computers. Despite the boom of stochastic simulation in recent years, there are still many so-called “conservative geologists” who do not appreciate the value of stochastic simulation, partly because of the complex mathematics involved, but mostly because of the lack of geological soundness in the simulated models. We forecast that the merging of conceptual models and stochastic simulation will become an important breakthrough in reservoir characterisation. Construction of conceptual models is in fact a highly nonlinear and complex process, which is difficult to be described by precise mathematics. It involves a good understanding of physical and chemical reactions in earth sciences, and depends heavily on the knowledge of the geologist(s) involved. The next section will expound the meaning of geological knowledge. Geological Knowledge. The meaning of “knowledge” is abstractive and difficult to be quantified. It is a result of learning and understanding of a certain subject. In the formalism of knowledge, there is a set of facts contained in the knowledge. When the subject wants to speak about its knowledge, it can only use its concepts. In geolog