Conditional Simulation of the Geometry of Fluvio-Deltaic Reservoirs

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^

Dealing with spatial heterogeneity

“…The concept of disjunctive Kriging was introduced by Matheron as early as 1973 (Matheron 1973(Matheron , 1976, but not commonly used; Journel (1983), Journel and Isaaks (1984), Journel and Alabert (1990) and Journel and Gomez-Hernandez (1993) developed the Indicator Kriging approach, where an indicator can take (at any given point in space) the value zero or one, depending on whether the point is inside or outside a given facies. Matheron and the Heresim Group at the French Institute of Petroleum developed the Gaussian Threshold model, where a continuous Gaussian random function in space generates a given facies if the function value at a point in space falls between two successive prescribed thresholds (Matheron et al 1987(Matheron et al , 1988see also Rivoirard 1994;Chiles and Delfiner 1999;Armstrong et al 2003, for a review of such stochastic models). With the new method, "objects" are also produced as in the Boolean one, but these objects are defined by applying a threshold value to the result of a continuous Geostatistical simulation.…”

An integrated approach to discretized 3D modeling of geomechanical properties for unconventional mature field appraisal in the western Canadian sedimentary basin

“…Truncated Gaussian simulation (TGS) (Matheron et al 1987) and Plurigaussian simulation (PGS) (Galli et al 1994) technique are two popular methods of reservoir modeling workflow for simulating lithotype and facies of sedimentary rocks. TGS technique is best suitable for reservoirs where the lithotypes occur in a sequential order and it helps in defining the geometry and internal architecture of the reservoir rocks (Armstrong et al 2003).…”

Direct Conditioning of Fine-Scale Facies Models to Dynamic Data by Combining Gradual Deformation and Numerical Upscaling Techniques

“…This method consists in truncating a continuous Gaussian simulation with multiple thresholds to represent the distribution of (litho-)facies in a heterogeneous reservoir [5] . It has been proven to be highly flexible for representing a wide range of geological patterns and shapes .…”