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A Novel Workflow to Model Permeability Impairment through Particle Movement and Deposition in Porous Media

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Abstract

This article presents a practical transfer function type solution to a complex problem in which variations in a number of parameters can be taken into account. A new mathematical model, which is based on mass balance transfer function of particles movement/retention in porous media, has been derived. It is used to predict permeability reduction as a function of time. The linear forms as well as the radial forms of the model are described. Although the differential equations derived are similar to the general form of diffusion–convection equations, the marked difference is the suitability of the model, for being applied for variation of parameters, such as particle concentration in the fluid, injection rate, density of solid particles, against the depth and time of invasion. This transfer function has been solved, and the results of the simulation run agree reasonably well with the experimental damage data obtained in laboratory. Owing to its simplicity, this model is more practical to describe permeability reduction for the flow of suspended particles in porous media.

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Abbreviations

A :

Area (m2)

C :

Mass solid concentration (ppm)

C d :

Constant

K :

Permeability (m2)

L :

Length (m)

M :

Model parameter (s−1)

m :

Mass of suspension particle (kg)

p :

Pressure (N/m2)

q :

Volumetric flow rate (m3/s)

t :

Time (s)

V :

Volume (m3)

n :

Number of elements

\({\phi }\) :

Porosity

λ :

Trapping efficiency

λ c :

Filtration coefficient

λ 0 :

Initial filtration coefficient

σ v :

The volume of particles deposited per unit volume of the bed

ν :

Approach velocity

μ 1 :

Viscosity of the carrier liquid (kg/m s)

ρ :

Fluid density (kg/m3)

τ :

Time constant

o:

Core inlet, stagnant or initial

b:

Bulk

i :

Initial or inlet

in:

Inlet

out:

Outlet

j :

Order of elements

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Authors and Affiliations

  1. Petroleum and Natural Gas Engineering, West Virginia University, Morgantown, WV, 26505, USA

    Amirmasoud Kalantari Dahaghi & Vida Gholami

  2. University of Surrey, Surrey, UK

    Jamshid Moghadasi

Authors
  1. Amirmasoud Kalantari Dahaghi
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  2. Vida Gholami
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  3. Jamshid Moghadasi
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Correspondence to Amirmasoud Kalantari Dahaghi.

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Dahaghi, A.K., Gholami, V. & Moghadasi, J. A Novel Workflow to Model Permeability Impairment through Particle Movement and Deposition in Porous Media. Transp Porous Med 86, 867–879 (2011). https://doi.org/10.1007/s11242-010-9658-9

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  • DOI: https://doi.org/10.1007/s11242-010-9658-9

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