Scale-up and stochastic modelling

Hence in order to utilise such geomodels for evaluation of specific field developments and for production forecasting, it is necessary to scale up these detailed geomodels to a full field reservoir simulation scale. It is the object of this project to establish general produres which as physical correct as possible may scale-up detailed models to a reservoir simulation scale with particular consideration to field dominated by capillary forces such as the Danish. A geostatistical model of a section of a typical chalk reservoir has been constructed which describle a layered sequence of the oil saturated upper Maastrichtian zone. The geomodel consist of 320,000 cells and covers a range of 80x80x10 meters. The geomodel has been scaled up to full field reservoir simulation scale, by assuming each geomodel to make up a single large grid block. The geomodel has been subjected to different heights over the free water level in the reservoir, which give rise to different saturations of oil and water as a function of this height and the porosity variation. It is important to estiblish these saturation accurately, since they determine the amount oil in the reservoir. It were determined from this investigation that the water saturation can be calculated on a coarse scale from the mean porosity of the fine scale model, whereas this does not apply for the residual oil saturations. They can generally not be found on the coarse scale without a detailed calculation of the residual oil saturation on the fine scale. Pressure maintenance by aquifer influx or water injection makes it very important also to consider scale-up of two phase behavior. This scale-up must take into account both the influence from fine scale variations in the detailed model and also the fact that physical description of a progressing waterfront in a single coarse grid cell must correspond closely, in time, to the movement of the front in the associated fine cells. Three new methods has been developed and investigated, all based on fine scale simulation on a cross section of the geomodel. The first method is derived from the classical Kyte and Berry method, but inserted into a renormalisation scheme as suggested by King and his co-workers. The second method assumes piston style behaiour and a coupled viscosity is introduced into the basic Darcy's equations. The final method is a modification of the JBN method traditionally applied in analysing results from core flooding experiments, which emerged as the most successful and therefore also the recommended method. In addition to compensate for the coarser description of the two phase flow this method also provide contributions entirely due to variations in the fine scale geology