Modelling and Simulation of Heterogeneous and Anisotropic Formations using Advanced Fractal Reservoir Models

Energy and carbon-efficient exploitation, management, and remediation of subsurface aquifers, gas and oil resources, CO₂-disposal sites, and energy storage reservoirs all require high quality modelling and simulation. The heterogeneity and anisotropy of such subsurface formations has always been a challenge to modellers, with the best current technology not being able to deal with variations at scales of less than about 30-50 m. Most formations exhibit heterogeneities and anisotropy which result in variations of the petrophysical properties controlling fluid flow down to millimetre scale and below. These variations are apparent in well-logs and core material, but cannot be characterised in the inter-well volume which makes up the great majority of the formation.

This paper describes a new fractal approach to the modelling and simulation of heterogeneous and anisotropic aquifers and reservoirs. This approach includes data at all scales such that it can represent the heterogeneity of the reservoir correctly at each scale.

Advanced Fractal Reservoir Models (AFRMs) in 3D can be produced using our code. These AFRMs can be used to model fluid flow in formations generically to understand the effects of an imposed degree of heterogeneity and anisotropy, or can be conditioned to match the characteristics of real aquifers and reservoirs. This paper will show how 3D AFRMs can be created such that they represent critical petrophysical parameters, as well as how fractal 3D porosity and permeability maps, synthetic poro-perm cross-plots, water saturation maps and relative permeability curves can all be calculated. It will also show how quantitative controlled variation of heterogeneity and anisotropy of generic models affects fluid flow. We also show how AFRMs can be conditioned to represent real reservoirs, and how they provide a much better simulated fluid flow than the current best technology.

Results of generic modelling and simulation with AFRMs show how total hydrocarbon production, hydrocarbon production rate, water cut and the time to water breakthrough all depend strongly on heterogeneity, and also depend upon anisotropy. Modelling with different degrees and directions of anisotropy shows how critical hydrocarbon production data depends on the direction of the anisotropy, and how that changes over the lifetime of the reservoir.

Advanced fractal reservoir models are of greatest utility if they can be conditioned to represent individual reservoirs. We have developed a method for matching AFRMs to aquifer and reservoir data across a wide range of scales that exceeds the range of scales currently used in such modelling. We show a hydrocarbon production case study which compares the hydrocarbon production characteristics of such an approach to a conventional krigging approach. The comparison shows that modelling of hydrocarbon production is appreciably improved when AFRMs are used, especially if heterogeneity and anisotropy are high. In this study AFRMs in moderate to high heterogeneity reservoirs always provided results within 5% of the reference case, while the conventional approach resulted in massive systematic underestimations of production rate by over 70%.