New reservoirs are increasingly more heterogeneous and more anisotropic. Unfortunately, conventional reservoir modelling has a resolution of only about 50 m, which means it cannot be used to model heterogeneous and anisotropic reservoirs effectively when such reservoirs exhibit significant inter-well variability at scales less than 50 m. This paper describes a new fractal approach to the modelling and simulation of heterogeneous and anisotropic reservoirs. This approach includes data at all scales such that it can represent the heterogeneity of the reservoir correctly at each scale. Three-dimensional Advanced Fractal Reservoir Models (AFRMs) can be generated easily with the appropriate code. This paper will show: (i) how 3D AFRMs can be generated and normalised to represent key petrophysical parameters, (ii) how these models can be used to calculate permeability, synthetic poro-perm cross-plots, water saturation maps and relative permeability curves, (iii) the effect of altering controlled heterogeneity and anisotropy of generic models on fluid production parameters, and (iv) how AFRMs which have been conditioned to represent real reservoirs provide a much better simulated production parameters 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 both on heterogeneity and anisotropy. The results also show that in heterogeneous reservoirs, the best production data is obtained from placing both injectors and producers in the most permeable areas of the reservoir – a result which is at variance with common practice. 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. We have developed a method of fractal interpolation to condition AFRMs to real reservoirs across a wide scale range. Comparison of the hydrocarbon production characteristics of such an approach to a conventional krigging shows 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%.
Effective and optimal hydrocarbon production from heterogeneous and anisotropic reservoirs is a developing challenge in the hydrocarbon industry. While experience leads us to intuitive decisions for the production of these heterogeneous and anisotropic reservoirs, there is a lack of information concerning how hydrocarbon and water production rate and cumulative production as well as water cut and water breakthrough time depend on quantitative measures of heterogeneity and anisotropy. In this work, we have used Generic Advanced Fractal Reservoir Models (GAFRMs) to model reservoirs with controlled heterogeneity and vertical and/or horizontal anisotropy, following the approach of Al-Zainaldin et al. (Transp Porous Media 116(1):181-212, 2017). This Generic approach uses fractal mathematics which captures the spatial variability of real reservoirs at all scales. The results clearly show that some anisotropy in hydrocarbon production and water cut can occur in an isotropic heterogeneous reservoir and is caused by the chance placing of wells in high-quality reservoir rock or vice versa. However, when horizontal anisotropy is introduced into the porosity, cementation exponent and grain size (and hence also into the permeability, capillary pressure, water saturation) in the reservoir model, all measures of early stage and middle stage hydrocarbon and water production become anisotropic, with isotropic flow returning towards the end of the reservoir's lifetime. Specifically, hydrocarbon production rate and cumulative production are increased in the direction of anisotropy, as is water cut, while the time to water breakthrough is reduced. We found no such relationship when varying vertical anisotropy because we were using vertical wells but expect there to be an effect if horizontal wells were used.
<p>Energy and carbon-efficient exploitation, management, and remediation of subsurface aquifers, gas and oil resources, CO<sub>2</sub>-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.</p><p>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.</p><p>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.</p><p>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.</p><p>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%.</p>
<p>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%.</p><p>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 <em>n</em>-phase Archie&#8217;s law theory.</p><p>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.</p><p>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.</p><p>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.</p><p>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%.</p><p>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.</p>
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