Unconventional Fractal Modelling and Simulation of Heterogeneous and Anisotropic Reservoirs
Authors: Glover Paul , Yaghoobpour Mehdi , Lorinczi Piroska , Wei Wei , Bo Li , Sinan Saddam 
Published: February 2023

One strategy for reducing global greenhouse gas emissions as the world progresses towards net zero is to extract more hydrocarbons from existing resources. Conventional modelling and simulation of heterogeneous and anisotropic reservoirs consistently and significantly underestimates production, sometimes by as much as 70%.We now understand that many reservoir properties are fractal, such as porosity, grain size and permeability. While water saturation and capillary pressure have distributions which arise from fractally-distributed microstructural properties. Recent work has resulted in the development of the fractal theory of Archie&#8217;s laws, providing fractal dimensions underlying both the cementation and saturation exponents that is consistent with the n-phase Archie&#8217;s law theory.The significant underestimation of production by conventional reservoir models can be overcome by the use of advanced fractal reservoir models (AFRMs) which take account of the fractal distribution of key petrophysical properties such as porosity, grain size, cementation exponent, permeability, water saturation and capillary pressure. These models employ existing and interpolated data across an extended range of scales and take account of variability less than the 50 m seismic resolution limit. AFRMs provide production profiles that are much closer to actual production profiles.This presentation describes briefly the AFRM approach to the modelling and simulation of heterogeneous and anisotropic reservoirs, showing how AFRMs can be generated easily to match an imposed degree of heterogeneity and anisotropy, or can be conditioned to represent the heterogeneity and anisotropy of the target reservoirs. We describe how AFRMs can be generated and normalised to represent key petrophysical parameters, how AFRM models can be used to calculate permeability, synthetic poroperm cross-plots, water saturation maps and relative permeability curves, and how AFRMs which have been conditioned to represent real reservoirs provide a much better simulated production parameters than the current best technology.Generic AFRM modelling and simulation show that total production, production rate, water cut and the time to water breakthrough all depend strongly on heterogeneity and anisotropy. Counter to expectation, optimal production is obtained from placing both injectors and producers in the most permeable areas of heterogeneous reservoirs. Furthermore, modelling with different degrees and directions of anisotropy shows how hydrocarbon production depends critically on anisotropy direction, which changes over the lifetime of the reservoir.AFRMs are ultimately only useful if they can be conditioned to real reservoirs. We have developed a method of fractal interpolation to match AFRMs to reservoir data across a wide scale range. Results comparing the hydrocarbon production characteristics of such an approach to a conventional krigging approach show a remarkable improvement in the modelling of hydrocarbon production when AFRMs are used; with AFRMs in moderate and high heterogeneity reservoirs returning values always within 5% of the reference case, while the conventional approach often resulted in systematic underestimations of production rate by over 70%.Although more work needs to be done on this new approach to reservoir modelling, initial results indicate that it has the potential for improving the accuracy of modelling and simulation in heterogeneous and anisotropic reservoirs by an order of magnitude or more.