Small-scale heterogeneities have a significant effect on the behaviour of fluid flow through a reservoir, since capillary forces trap the non-wetting phase in the high-permeable parts of a water-wet porous medium. An upscaling procedure must therefore be able to account for reservoir structure as well as for relative permeabilities and capillary pressures on the lamina scale.
For the geological model we propose a five-scale hierarchy with crossbed and subfacies as key elements: i.e. lamina scale ? flow cell scale ? flow unit scale ? facies scale ? reservoir scale. The reservoir model is a simplified version of the geological model with the flow cell and flow unit as building blocks. As an example we take a model of a meandering river with three types of flow units, viz. channel, pointbar, and floodplain. Each of these consists of one type of flow cell, i.e. trough crossbedding, longitudinal bedding and horizontal bedding, respectively (Fig. 2).
We propose a four-step procedure (Fig. 1):
Assignment of flow cells and flow units;
Calculation of capillary pressures and relative permeabilities of laminae;
Steady state flow simulation on flow cells;
Assignment of the ensuing effective phase permeabilities and capillary pressures to the flow units. The macro reservoir has the flow units as building blocks.
We use lamina permeabilities either from our strongly improved probe-permeameter or from a database. We calculate lamina scale capillary pressures and relative permeabilities using Brooks-Corey and Leverett-J function. Upscaling is realized using flow simulation: A microsimulation is performed on each flow cell for a number of water/oil injection ratios. The ensuing upscaled relative permeabilities are anisotropic and flow-rate dependent. They are used as the constitutive relations for the flow units, which is the next superior level to the crossbed.
This model and its properties are incorporated into the simulation of the full reservoir described in the SPE ninth comparative study on black oil simulators in heterogeneous reservoirs. We will ignore the rate dependence and use a constant anisotropy factor in each flow unit. The result shows that small-scale heterogeneities characteristic of the various flow cells must be specifically taken into account. Our procedure provides a method to accomplish this. The method is easy to implement.
Reservoirs are heterogeneous at all scales. Lack of data and limitation in computer power, dictates that we need to simplify to obtain a manageable reservoir model. In this simplification process two disciplines are involved, one is essentially geological and deals with the construction of a detailed reservoir model; the other is to assign appropriately averaged permeabilities and constitutive relations to the grid blocks used in the reservoir simulation.
Lack of data precludes the construction of a completely deterministic reservoir model. Deterministic models are also unnecessarily complex, because many structures are repetitive55. Stochastic models can represent variability and correlation, but require quantification of the statistical properties9,14,21 e.g. variograms. These statistics, even when they are based on geological data, are often not directly related to a geological model of the deposits and often disregard the fine scale detail2,4,21,51. Genetically based models can be an alternative if the relation between sedimentary environment and resulting structure is well known. The model procedure is to split the geological structure into units and subunits etc. This first of all requires a full description of these flow (sub)units. Subsequently we need a simplification of their internal heterogeneity and reconstitute the reservoir in terms of the simplified units. For reasons of lack of data natural variation is often disregarded38, but can be easily incorporated.