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Hydro-mechanical aspects of the sand production problem

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Abstract

This paper examines the hydro-mechanical aspect of the sand production problem and sets the basic frame of the corresponding mathematical modelling. Accordingly, piping and surface erosion effects are studied on the basis of mass balance and particle transport considerations as well as Darcy's law. The results show that surface erosion is accompanied by high changes of porosity and permeability close to the free surface. Quantities which can be measured in experiment, like the amount of produced solids or fluid discharge, can be used in an inverse way to determine the constitutive parameters of the problem.

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Abbreviations

dV :

Volume element

dV s :

Volume of solids pt

dV v :

Volume of voids

dV ff :

Volume of fluid phase

dV fs :

Volume of fluidized-particles

\(d\mathop V\limits^--\) :

Volume of mixture

dM s :

Mass of solids

dM ff :

Mass of fluid phase

d M fs :

Mass of fluidized-particles

\(d\mathop M\limits^--\) :

Mass of mixture

ϱs:

Density of solids

ϱf:

Density of fluid

ϱff:

Density of fluid phase

ϱfs:

Density of fluidized-particles

\(\bar \rho\) :

Density of mixture

ν ff i :

Velocity of fluid

ν fs i :

Velocity of fluidized-particles

ν s i :

Velocity of solids

\(\bar \upsilon _i\) :

Velocity of mixture

q ff :

Volume-discharge of fluid

q fs :

Volume-discharge of fluidized-particles

\(\bar q_i\) :

Volume-discharge of mixture

m ff :

Mass-discharge of fluid

m fs :

Mass-discharge of fluidized-particles

\(\mathop m\limits^-- _i\) :

Mass-discharge of mixture

\(\dot m\) er :

Rate of mass-eroded

\(\dot m\) dep :

Rate of mass-deposited

\(\dot m\) :

Mass generation term

dS i :

Surface element

\(d\mathop S\limits^-- _i\) :

Pore-surface element

D IJ :

Tensor of mechanical dispersion

x i :

Location

t :

Time

ϕ :

Porosity

c :

Transport concentration

c cr :

Critical value ofc

p :

Fluid-pressure

k :

Permeability coefficient

μ k :

Kinematic viscosity

λ:

Spatial frequency of erosion starter points

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Authors and Affiliations

  1. Department of Engineering Sciences, National Technical University of Athens, GR-157 73, Zographou, Greece

    I. Vardoulakis & M. Stavropoulou

  2. Schlumberger Cambridge Research, High Cross, Madingley Road, CB3 0EL, Cambridge, UK

    P. Papanastasiou

Authors
  1. I. Vardoulakis
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  2. M. Stavropoulou
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  3. P. Papanastasiou
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Vardoulakis, I., Stavropoulou, M. & Papanastasiou, P. Hydro-mechanical aspects of the sand production problem. Transp Porous Med 22, 225–244 (1996). https://doi.org/10.1007/BF01143517

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  • DOI: https://doi.org/10.1007/BF01143517

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