Fractals in Reservoir Engineering

Hardy, H. H.; Beier, Richard A.

doi:10.1142/2574

Cited by 92 publications

(48 citation statements)

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“…When we consider an oil well as a fractal, it is important to choose which of its properties can be useful for elaborating a mathematical model [20,21,26,27]. …”

Section: Background Of the Approach Of Models Of Diffusion On Fractalmentioning

confidence: 99%

Application of Fractional Calculus to Oil Industry

Martínez-Salgado¹,

Rosas-Sampayo²,

AnthonyTorres-Hernández³

et al. 2017

Fractal Analysis - Applications in Physics, Engineering and Technology

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In this chapter, we present a discussion about the practical application of the fractal properties of the medium in the mathematical model through the use of fractional partial derivatives. We present one of the known models for the flow in saturated media and its generalization in fractional order derivatives. In the middle section, we present one of the main arguments that motivate the use of fractional derivatives in the porous media models, this is the Professor Nigmatullin's work. The final part describes the process for obtaining the coupled system of three equations for the monophase flow with triple porosity and triple permeability, briefly mentioning the method used for the first solutions of the system.

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“…When we consider an oil well as a fractal, it is important to choose which of its properties can be useful for elaborating a mathematical model [20,21,26,27]. …”

Section: Background Of the Approach Of Models Of Diffusion On Fractalmentioning

confidence: 99%

Application of Fractional Calculus to Oil Industry

Martínez-Salgado¹,

Rosas-Sampayo²,

AnthonyTorres-Hernández³

et al. 2017

Fractal Analysis - Applications in Physics, Engineering and Technology

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“…The numerically found raw semivariogram is approximated by one of the following simple mathematical models (where σ 2 is the sill, a is the range, the separation distance, called lag, and ε 2 is the nugget): Spherical; Exponential; Gaussian; Pure nugget and Power Law models. Modern texts (Korvin, 1992;Hardy and Beier, 1994) use power law semivariogram models to describe fractal HC reservoirs. In this case…”

Section: Spatial Interpolation Of Irregularly Sampled Data (Kriging)mentioning

confidence: 99%

Mapping soil fractal dimension in agricultural fields with GPR

Oleschko¹,

Korvin

Muñoz³

et al. 2008

Nonlin. Processes Geophys.

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Abstract. We documented that the mapping of the fractal dimension of the backscattered Ground Penetrating Radar traces (Fractal Dimension Mapping, FDM) accomplished over heterogeneous agricultural fields gives statistically sound combined information about the spatial distribution of Andosol' dielectric permittivity, volumetric and gravimetric water content, bulk density, and mechanical resistance under seven different management systems. The roughness of the recorded traces was measured in terms of a single number H , the Hurst exponent, which integrates the competitive effects of volumetric water content, pore topology and mechanical resistance in space and time. We showed the suitability to combine the GPR traces fractal analysis with routine geostatistics (kriging) in order to map the spatial variation of soil properties by nondestructive techniques and to quantify precisely the differences under contrasting tillage systems. Three experimental plots with zero tillage and 33, 66 and 100% of crop residues imprinted the highest roughness to GPR wiggle traces (mean H R/S =0.15), significantly different to Andosol under conventional tillage (H R/S =0.47).

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“…The pioneering work of Hewett (1986) in using fractal interpolation functions (fractional Brownian motion and fractional Gaussian noise) has been applied to many reservoirs since (e.g. Hardy & Beier 1994). However, such modelling has lacked a detailed geoscientific basis, and is, therefore, probably incomplete, for example in anisotropy or relationship to other known structural features.…”

Section: Current Standard Practice In Characterization Of Geology Andmentioning

confidence: 99%

The NERC Micro to Macro Programme: implications for fluid resource management

Heffer

2005

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Abstract:The Micro to Macro (I~2M) Programme has been focused on developing understanding of subsurface fluid flows within geological heterogeneities spanning wide ranges of spatial and temporal scales. This paper highlights the opportunities for industries to incorporate recent observations and emerging theories in this field towards improved fluid resource management. The background to, and objectives of, the 1~2M Programme are reviewed. Selected results from the projects in the programme are discussed and, where possible, compared with evidence from industrial field data. Some conclusions and recommendations for future practice in reservoir characterization are made. For example, there is currently very little recognition of modern theories that point to the likelihood of prevailing criticality in the mechanical state of the Earth's crust and its implication for coherent large-scale collective behaviour emerging from small-scale interactions. Also associated with criticality are long-range spatial correlations and the likelihood that flow properties change during the life of commercial developments: such changes, for example, to absolute permeability, should be looked for and analysed for spatial and temporal patterns. Allied with these features is the importance of coupled processes, principally geomechanics, fluid flow, heat flow and chemistry. Knowing that local faults and fractures play a strong role in fluid flow mechanisms in a potentially time-varying, rather than just a static, fashion, gives even more motivation for acquiring detailed information on micro-and macro-structure over a range of scales.Industries whose resources lie in the subsurface base most of their planning and investment decisions on models of their sites that require numerical description of the geology. Such modelling has often turned out to be inadequate. The commercial consequences of poor geological modelling can be particularly severe where fluid flow is involved because fluid flow is governed by the spatial arrangement of extremes in the range of permeabilities. The Micro to Macro (p~2M) Programme has been focused on developing understanding of the relationships between measured and modelled subsurface fluid flows, spanning the range of spatial and temporal scales relevant to fluid resource management. The programme was motivated by observations and emerging theories of how geological heterogeneities vary across these ranges in scales, and the consequences for extrapolating fluid behaviour both in time and space; the aim was to provide a clearer physical understanding on which to base more effective geofluid management and to allow better integration of data for reservoir characterization and improved models for fluid flow. The scope of the project involved workers with backgrounds in hydrocarbon, water, radioactive waste, mining, and geothermal industries and a major objective was to foster communication between disciplines and communities to mutual benefit.In order to place the aims and achievements of the ~2M Programme into...

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Fractals in Reservoir Engineering

Cited by 92 publications

References 0 publications

Application of Fractional Calculus to Oil Industry

Application of Fractional Calculus to Oil Industry

Mapping soil fractal dimension in agricultural fields with GPR

The NERC Micro to Macro Programme: implications for fluid resource management

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