Cosimulations of Lithofacies and Associated Reservoir Properties Using Well and Seismic Data
Authors: Fichtl P. , Fournier F. , Royer J.-J. 
Published: December 2007

Abstract
Subsurface models of reservoir properties like porosity or permeability are often related to lithological parameters describing the reservoir in terms of flow units. Otherwise, seismic data provide valuable information regarding the lateral variation of lithology not given by the sparse well control. An integrated geostatistical method is proposed here to generate a reservoir model in terms of physical properties by the control of lithofacies and seismic information. The method is divided in two steps, including a sequential indicator cosimulation of lithofacies where the seismic constraint is introduced, followed by the reservoir property simulation based on three different simulation approaches. A case study based on synthetic but realistic models is used to validate the method and to underline the best approach for the reservoir property simulation.

Introduction
Integration of data of different sources and nature leads to more accurate reservoir models, useful for controlling fluid flow and assessing final uncertainties. In this frame, stochastic simulation techniques have become popular as a mean of generating detailed subsurface models by integrating different types of data, including seismic information. In reservoir stochastic models, two aspects are identified as important for flow studies. The first aspect is the architecture of the flow units, described in terms of different lithofacies, and the second aspect is the spatial distribution of rocks and fluid properties (porosities, permeabilities, saturations, …) within each flow unit.
From a practical point of view, the important difference between modelling lithofacies versus reservoir properties is that the lithofacies is a categorical variable, whereas the reservoir properties are continuous variables. This different nature of variables leads to use a combination of various stochastic methods. For example, a boolean technique may be used to create a model of lithofacies within a reservoir, whereas a sequential gaussian simulation is used to fill each lithofacies with porosities or permeabilities. It is also possible to combine deterministic and stochastic methods. For example, Cox et al. used a deterministic approach to create plausible images of lithofacies. These images are then used for calculating indicator variograms for a sequential indicator simulation procedure in which reservoir properties are generated.
However, boolean simulation or deterministic techniques for modelling flow units do often not account for seismic information which is much easily introduced with sequential simulation techniques. Seismic information is indeed useful for better controlling the distribution of heterogeneities in the interwell spaces and thus for reducing the uncertainties on the reservoir model. Here, we propose a two-step method composed of a sequential indicator cosimulation allowing direct incorporation of seismic constraint for generating lithofacies distribution, relying on cokriging, and of a continuous variable technique to simulate the associated reservoir properties. Three different approaches based on sequential gaussian (co)simulations or P-field simulations are used in this second step of the algorithm for generating the reservoir properties constrained by the previously simulated lithofacies The method generates alternative and equiprobable models of lithofacies and associated reservoir properties consistent with well and seismic data.
First we introduce our cosimulation techniques with the different approaches. P. 381^