Conditional Simulation of the Geometry of Fluvio-Deltaic Reservoirs

Abstract

Abstract Quantitative methods taking into account the sedimentological characteristics will answer the needs of reservoir engineers. We propose here a geostatistical method for the conditional modelling of the facies of a sedimentary fluvio-deltaic series. This model was elaborated jointly by I.F.P. and the Paris School of Mines, with the aim of modelling reservoir heterogeneities. From the sedimentological study contained in the paper by C. Ravenne et al., we present several simulations, conditioned by "drill-core" taken from the outcrop. The block permeabilities are then calculated from the values given to the facies. Introduction Reservoir engineers have, for a long time, been asking what type of models could be entered into reservoir simulators. The geological models that are normally used are essentially qualitative and so it is difficult to numerize them, except by correlating the drillholes facies, which is not always self evident. This often leads to models with too many constraints for simulating reservoirs. Their dynamic behaviour worsens considerably going from very continuous layers of sandstone to disseminated lenses. (Fig. 1). This raises the question of how to characterize the geometry of the sandstone given the drillhole data, the geologist's interpretation and also other measurements (e.g. seismic recordings), and how to model the reservoir levels to suit this shape. As well as this, the models must match the lithology along the drillholes. In this article, we present a method for conditionally modelling the lithology which is designed for sedimentary processes. This approach was tested using the geological section of a cliff-face in Yorkshire (England) which shows a fluvio-deltaic environment similar to some of the levels in the Brent formation in the North Sea. A detailed description of the geology of the cliff-face studied and of the approach used in this project have been presented by Ravenne et al. Here we shall only consider the problem of modelling random sets by using a probabilistic method for representing the spatial distribution of the facies (sandstone, shaly sandstone, shale) in a heterogeneous reservoir. Before presenting the method, we review the main procedures for modelling random sets, that are used in the petroleum industry. REVIEW OF THE EXISTING METHODS Boolean Sets A simple way is to consider a heterogeneous medium as consisting of sandstone lenses in a shale matrix (or vice versa). Boolean sets (Matheron, Serra, Jeulin) are a mathematical way for modelling this type of deposit, that has been used for many years in other fields (Fig. 2). This method consists of putting lenses of a predetermined shape (e.g. ellipses or rectangles) at random points in the domain under study (i.e. the points are statistically uniformly distributed in space). Lenses are not correlated. The advantage of this approach is that it is easy to use in 2D or 3D spaces. It only depends on a few parameters: the number of seed points per unit space (called density), the shape of the lenses (fixed or variable), their size and orientation. The model is very flexible. The parameters can be modified locally in order to reproduce the real phenomenon more accurately. Clearly the more complicated the model is, the more parameters there are to fit but this can be overcome by fitting them by trial and error. P. 591^