On the multiscale characterization of effective hydraulic conductivity in random heterogeneous media: A historical survey and some new perspectives

Colecchio, Iván; Boschan, Alejandro; Otero, Alejandro D.; Nœtinger, B.

doi:10.1016/j.advwatres.2020.103594

Cited by 32 publications

(38 citation statements)

References 76 publications

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“…They derived the head variance and the autocorrelation between the head near the source and at arbitrary distances. In the work by Colecchio et al (2020) , scale-independent analytical results for the variance of the effective hydraulic conductivity were obtained by means of an energy dissipation formulation. The analysis was performed under steady conditions considering two-dimensional domains for lognormal and binary media, considering an ample range of coarsening scales and heterogeneities.…”

Section: Current Methods For Computing Effective Parameters In Porous Mediamentioning

confidence: 99%

Editorial: Recent developments in upscaling and characterization of flow and transport in porous media

Lasseux

Valdés‐Parada

Wood

2021

Advances in Water Resources

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Le et al. (2020) studied the flow and transport problem of CO 2 -enhanced coalbed methane recovery also by means of the homogenization technique. They considered a multiscale model that incorporated two levels of porosity that correspond to nanopores and the cleat network. This work includes a set of numerical simulations showing that the cleat permeability decreases significantly near the injection well because of the high injection pressure. In addition, Sharmin et al. (2020) considered two-phase (or unsaturated) incompressible flow in a thin, but long, single pore (a thin strip) with a stratified distribution of the two phases and derived an effective model starting from the Navier-Stokes equations. The upscaled model was obtained using the asymptotic homogenization method. It encompasses different regimes associated to the values of the capillary number and viscosity ratio. It also accounts for surface tension variations (Marangoni effects) which may result from the transport of a solute in one of the two phases. The upscaled model was compared to direct numerical simulations of the 2D pore-scale model. Finally, Airiau and Bottaro (2020) used the adjoint homogenization method to shed new light on the derivation of upscaled models for steady and creeping flow of a shear-thinning fluid in homogeneous porous media. These authors derived a Darcy-like model, where the components of the effective permeability tensor were obtained from the solution of an associated boundary-value problem in a periodic unit cell. Due to the dependence of the viscosity on the pore-scale flow, a coupled solution approach was used that translated into a strong anisotropy of the permeability tensor, even in isotropic geometries.Not all the works corresponding to this research topic used the homogenization method to carry out their analysis. For example, Cotta et al. (2020) studied flow and transport in fractured porous media using the generalized integral transform technique to derive analytical and numerical-analytical solutions. A salient feature of this work is the treatment of multiporosity cases, by means of a single integral transformation process. This approach is illustrated with two examples in fractured media and unsaturated soils. In addition, Angot et al. ( 2020) used an asymptotic analysis to study single-phase inertial flow in the fluidporous boundary. They show that the total inertial work exerted by the fluid over the solid is always positive. Non-equilibrium modeling for transport in homogeneous and heterogeneous porous mediaThis research subject comprises stochastic modeling and upscaling of transport processes. Engdahl and Bolster (2020) proposed to use a

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Section: Current Methods For Computing Effective Parameters In Porous Mediamentioning

confidence: 99%

Editorial: Recent developments in upscaling and characterization of flow and transport in porous media

Lasseux

Valdés‐Parada

Wood

2021

Advances in Water Resources

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“…No simple general analytical expression exists in the general case for D ≥ 3, even if a great deal of research was devoted to develop such analytical expressions using additional hypothesis. SP techniques such as field theoretical methods [47,48,53,60,63] were employed to find some robust approximations. Many authors attempted to justify the so called Landau-Lifschitz-Matheron (LLM) [14,56] formula that reads:…”

Section: Averaging Darcy's Lawmentioning

confidence: 99%

Statistical physics and applied geosciences: some results and perspectives

Nœtinger¹

2021

Comptes Rendus. Physique

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“…The power value of p numbers depends on the spatial distribution of permeability. In 2D, it corresponds to the geometric average that was found to be exact in 2D for lognormal media by Matheron (1967), who derived it using an elegant duality argument specific to 2 dimensions [32].…”

Section: Well Testing In Heterogeneous Reservoirmentioning

confidence: 99%

Analysis of well testing results for single phase flow in reservoirs with percolation structure

Shahrian

Masihi

2021

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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Constructing an accurate geological model of the reservoir is a preliminary to make any reliable prediction of a reservoir’s performance. Afterward, one needs to simulate the flow to predict the reservoir’s dynamic behaviour. This process usually is associated with high computational costs. Therefore, alternative methods such as the percolation approach for rapid estimation of reservoir efficiency are quite desirable. This study tries to address the Well Testing (WT) interpretation of heterogeneous reservoirs, constructed from two extreme permeabilities, 0 and K. In particular, we simulated a drawdown test on typical site percolation mediums, occupied to fraction “p” at a constant rate Q/h, to compute the well-known pressure derivative (dP/dlnt). This derivative provides us with “apparent” permeability values, a significant property to move forward with flow prediction. It is good to mention that the hypothetical wellbore locates in the middle of the reservoir with assumed conditions. Commercial software utilized to perform flow simulations and well test analysis. Next, the pressure recorded against time at different realizations and values of p. With that information provided, the permeability of the medium is obtained. Finally, the permeability change of this reservoir is compared to the permeability alteration of a homogeneous one and following that, its dependency on the model parameters has been analysed. The result shows a power-law relation between average permeability (considering all realizations) and the occupancy probability “p”. This conclusion helps to improve the analysis of well testing for heterogeneous reservoirs with percolation structures.

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On the multiscale characterization of effective hydraulic conductivity in random heterogeneous media: A historical survey and some new perspectives

Cited by 32 publications

References 76 publications

Editorial: Recent developments in upscaling and characterization of flow and transport in porous media

Editorial: Recent developments in upscaling and characterization of flow and transport in porous media

Statistical physics and applied geosciences: some results and perspectives

Analysis of well testing results for single phase flow in reservoirs with percolation structure

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