Geostatistical Simulations of Geothermal Reservoirs: Two- and Multiple-point Statistic Models

Abstract

Reservoir engineers and geoscientists working on subsurface process are commonly faced with a lack of information related with geological structures, rock properties and sometimes a lack of comprehension of the underlying process and the physics that govern it, hence subsurface models are built from limited information with its own resolution and quality. In the light of these facts is that data uncertainty appears as one of the major obstacles in subsurface reservoir modelling, analysis and forecasting. The uncertainty of a numerical simulation of a natural reservoir will depend on the uncertainties associated with different reservoir parameters related to subsurface rock properties, their spatial distribution and state variables. This uncertainty is also directly linked with the availability of data and its spatial coverage, so a maximum benefit from data must be considered for any model under development. Stochastic simulation has become a popular methodology in areas such as groundwater and hydrocarbon reservoir modelling for simulating unknowable reservoir properties and geometries, and quantifying reservoir heterogeneity. However, these techniques are not being commonly used in geothermal reservoir modelling. Additionally, stochastic approaches have an extensive risk analysis capability. In this sense, geostatistical based-models are a robust methodology to include available data into simulations in a stochastic framework, and also allow an easier link between simulations and geological knowledge. Variogram based-models, like kriging or sequential gaussian simulations, are based on two-point statistical models which don’t necessarily allow a satisfactory reproduction of complex, curvilinear geological features. Multiple-point statistics (MPS) models are a novel technique of simulation which is based on patterns composed of several points, so a better reproduction of complex geometries may be achieved. Another key characteristic of MPS models is the absence of any variographic analysis since all the conditional probabilities are extracted from a Training Image (TI). A TI basically is a repository of the spatial patterns and their likelihood of occurrence in the model. This work presents some of the theoretical aspects of MPS simulations compared to classical two-point models and presents some results for the simulation of a synthetic geothermal reservoir. The set of realizations generated in the previous step are used as input parameters for setting up a numerical flow model.