Closed-Form Solution of Radial Transport of Tracers in Porous Media Influenced by Linear Drift

Akanji, Lateef; Falade, G.K.

doi:10.3390/en12010029

Cited by 5 publications

(10 citation statements)

References 30 publications

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“…Figure 1 shows a schematic representation of a chemical tracer injection/extraction test in a porous media system. The drift effect fully manifested due to the microscopic variation of the fluid flow field at a later time during the extraction stage (Figure 1f) [16]. However, a continuing challenge in mathematical and computational modelling is how to capture these mechanisms accurately and to handle them to relevant scales properly [17].…”

Section: Pore-scale Radial Diffusion Models With Driftmentioning

confidence: 99%

“…Despite the numerous studies of flow and transport of tracers through geological porous media, our understanding still faces a significant challenge. One of the challenges is the observation of drift phenomena at a Darcy or field scale [5,16]. The signatures of drift phenomena affect tracer concentration distribution at field scale as reported in the literature [22].…”

Section: Pore-scale Radial Diffusion Models With Driftmentioning

confidence: 99%

“…Al Mukahal et al, 2017 provide a description of long-time Taylor-Aris dispersion of solute by using multiple scales to arrive at the expression of effective diffusivity. However, problems associated with Taylor dispersion in a capillary tube are momentous, i.e possibility of micro-macro duality and their interrelationship among scales manifest [16].…”

Section: Introductionmentioning

confidence: 99%

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Investigation of Drift Phenomena at the Pore Scale during Flow and Transport in Porous Media

et al. 2021

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This paper reports an analytical study conducted to investigate the behaviour of tracers undergoing creeping flow between two parallel plates in porous media. A new coupled model for the characterisation of fluid flow and transport of tracers at pore scale is formulated. Precisely, a weak-form solution of radial transport of tracers under convection–diffusion-dominated flow is established using hypergeometric functions. The velocity field associated with the radial transport is informed by the solution of the Stokes equations. Channel thickness as a function of velocities, maximum Reynolds number of each thickness as a function of maximum velocities and concentration profile for different drift and dispersion coefficients are computed and analysed. Analysis of the simulation results reveals that the dispersion coefficient appears to be a significant factor controlling the concentration distribution of the tracer at pore scale. Further analysis shows that the drift coefficient appears to influence tracer concentration distribution but only after a prolonged period. This indicates that even at pore scale, tracer drift characteristics can provide useful information about the flow and transport properties of individual pores in porous media.

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Section: Pore-scale Radial Diffusion Models With Driftmentioning

confidence: 99%

Section: Pore-scale Radial Diffusion Models With Driftmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Investigation of Drift Phenomena at the Pore Scale during Flow and Transport in Porous Media

et al. 2021

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“…Because there is no analytical inversion solution of ξ wD (s), it is difficult to discuss the accuracy of the Laplace transform by comparing the analytical inversion solution with the numerical inversion solution [43]. In order to validate the proposed model and show how this model was used in practice, the drawdown test data of a vertical fractured well with four fracture wings were collected from the published literature [44].…”

Section: Model Validation and Applicationmentioning

confidence: 99%

Transient-Flow Modeling of Vertical Fractured Wells with Multiple Hydraulic Fractures in Stress-Sensitive Gas Reservoirs

Guo

Sun

Peng³

et al. 2019

Applied Sciences

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Massive hydraulic fracturing of vertical wells has been extensively employed in the development of low-permeability gas reservoirs. The existence of multiple hydraulic fractures along a vertical well makes the pressure profile around the vertical well complex. This paper studies the pressure dependence of permeability to develop a seepage model of vertical fractured wells with multiple hydraulic fractures. Both transformed pseudo-pressure and perturbation techniques have been employed to linearize the proposed model. The superposition principle and a hybrid analytical-numerical method were used to obtain the bottom-hole pseudo-pressure solution. Type curves for pseudo-pressure are presented and identified. The effects of the relevant parameters (such as dimensionless permeability modulus, fracture conductivity coefficient, hydraulic-fracture length, angle between the two adjacent hydraulic fractures, the difference of the hydraulic-fracture lengths, and hydraulic-fracture number) on the type curve and the error caused by neglecting the stress sensitivity are discussed in detail. The proposed work can enrich the understanding of the influence of the stress sensitivity on the performance of a vertical fractured well with multiple hydraulic fractures and can be used to more accurately interpret and forecast the transient pressure.

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“…(2) and (3) appear as source/sink terms in the advection-dispersion equation (2), describing the transport of SI chemical in the bulk fluid. Quite often, with regard to field applications, model equations are written in spherical or cylindrical polar coordinates, which are particularly suitable for describing a near-wellbore geometry (see, for instance, Akanji and Falade 2019). However, in this paper, we will simplify the three-dimensional Cartesian equations (2)-(3) into a one-dimensional form appropriate for the analysis of core-flood experiments (Sect.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions for a 1D Scale Inhibitor Transport Model with Coupled Adsorption and Precipitation

Stamatiou

Sorbie

2020

Transp Porous Med

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In a previous publication (Sorbie and Stamatiou in Transp Porous Media 123:271-287, 2018), we presented a one-dimensional analytical solution for scale inhibitor transport and retention in a porous medium through a kinetic precipitation mechanism. In this process, a chemical complex of the scale inhibitor precipitates within the porous matrix and it then re-dissolves through a kinetic solubilisation process. Considering the re-dissolution of this precipitate in a one-dimensional linear system such as a reservoir layer or indeed in a laboratory core/pack flood, the flowing aqueous phase gradually dissolves the precipitate which is then eluted from the system. The most novel aspect of this previous analytical solution arose from the fact that, at a certain point in time (or pore volume throughput), the precipitate in the system was locally fully re-dissolved, forming an internal moving boundary between where no precipitate remained (closer to the system inlet) and where a precipitate was present (further into the system up to the outlet). In the current paper, we extend this work by presenting analytical solutions for the case where precipitation/dissolution occurs simultaneously with an adsorption/desorption interaction between the scale inhibitor and the rock surface, described by the nonlinear Langmuir isotherm. When examining this more complex problem in the flow scenario where the local precipitate is completely dissolved, several interesting analytical solution structures are obtained as a result of the internal moving boundary. Which of these structures occurs is rigorously categorised according to the solubility, the initial levels of precipitate and adsorbate, as well as the shape of the Langmuir isotherm. After the mathematical development of the analytical solutions, they are applied to some example problems which are compared with numerical solutions. Finally, a number of different generic features in the scale inhibitor effluent concentration profile are predicted and discussed with regard to practical field applications.

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Closed-Form Solution of Radial Transport of Tracers in Porous Media Influenced by Linear Drift

Cited by 5 publications

References 30 publications

Investigation of Drift Phenomena at the Pore Scale during Flow and Transport in Porous Media

Investigation of Drift Phenomena at the Pore Scale during Flow and Transport in Porous Media

Transient-Flow Modeling of Vertical Fractured Wells with Multiple Hydraulic Fractures in Stress-Sensitive Gas Reservoirs

Analytical Solutions for a 1D Scale Inhibitor Transport Model with Coupled Adsorption and Precipitation

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