Advanced Fractal Modelling of Heterogeneous and Anisotropic Reservoirs

The hydrocarbon industry is currently transitioning from a world where hydrocarbon reservoirs were large and homogeneous to one where reservoirs are often small, heterogeneous, anisotropic, as well as having other challenges. Heterogeneous and anisotropic reservoirs are extremely difficult to model and simulate. The reason lies in our lack of knowledge of the inter-well volume where much of the variability of the reservoir occurs. Conventional approaches use interpolation between wells that is influenced by 3D seismic information. As the resolution of that seismic information is about 50 m, no information can be included in the reservoir model below that scale.

In this paper we describe the creation and validation of advanced fractal reservoir models (AFRMs) which use fractal mathematics to represent heterogeneous and anisotropic variation in reservoirs at all scales from the scale of the model cell to that of the whole reservoir. These deterministic models take into consideration variability in the reservoir at all scales.

Generic modelling of AFRMs shows how reservoir heterogeneity can reduce hydrocarbon and water production by as much as 69%, an effect that would not be seen if conventional reservoir modelling had been carried out. Furthermore, anisotropy has an additional effect on both oil and water cumulative production and production rate as well as the time to water breakthrough and water cut. The effect of anisotropy has been shown by generic modelling of AFRMs to be significant in early and middle production and becomes less important in late production. Generic modelling has also confirmed that placement of wells (both injectors and producers) in high permeability rock provides the best production in heterogeneous reservoirs.

Recent work has allowed AFRMs to be conditioned to real reservoirs, making their application of wider use. In this paper we compare the performance of conditioned AFRMs to more conventional reservoir models by comparing them against a reference ideal reservoir. This shows that the conventional approach performs well for homogeneous reservoirs but breaks down badly for heterogeneous reservoirs, while the conditioned AFRMs accurately portray the reservoir from fluid production point of view irrespective of its heterogeneity.