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A Review of Modeling Thermal Displacement Processes in Porous Media

  • Review Article - Petroleum Engineering
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Abstract

The subject of heat transfer in oil reservoirs has gained huge attention, due to its diverse range of applications in petroleum reservoir management and thermal recovery for enhanced oil recovery. Thermal recovery methods entail the addition of heat energy into the reservoir through injection wells with the aim of reducing the in situ oil viscosity which is usually around several thousand centipoise cP (in S.I unit kg/m s) at reservoir conditions to very low values at steam temperatures. In addition, several other mechanisms are associated with thermal recovery methods. These include thermal expansion of oil, steam distillation, and relative permeability changes, which contribute to the ultimate recovery of the reservoir. In this article, a detailed review of non-isothermal modeling in an oil reservoir is presented. In addition, a few remarks regarding the momentum transport and the energy balance equations and its various modifications through the years are provided. Finally, a memory-based formulation is proposed to capture the alteration of rock and fluid properties with time as well as accounting for other phenomena not described by classic diffusion equations.

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Abbreviations

\(a_{\mathrm{sf}}\) :

Specific surface area (fluid to solid contact) (\(\hbox {m}^{2}\))

\(A\left( t \right) \) :

Cumulative heated area (\(\hbox {m}^{2}\))

\(c_\mathrm{F} \) :

Non-dimensional form-drag constant

\(c_\mathrm{p} \) :

Specific heat (J/kg K)

C :

Component

\(C_\mathrm{c} \) :

Coke concentration (gmol/\(\hbox {m}^{3}\))

\(d_\mathrm{p} \) :

Spherical particle diameter (m)

Da :

Darcy number, \(\kappa /{L^{2}}\), dimensionless

\(E_\mathrm{H} \) :

Heating efficiency, percentage

g :

Acceleration due to gravity (m/s\(^{2}\))

h :

Pay thickness (m)

\(h_{\mathrm{sf}} \) :

Fluid to solid heat transfer coefficient (W/m\(^{2}\) K)

H :

Aquifer height (m)

\(H_\mathrm{o} \) :

Heat injection rate (J/s)

k :

Thermal conductivity (W/m K)

K :

Permeability (\(\hbox {m}^{2}\))

P :

Pressure (Pa)

q :

Heat flux (W/m\(^{2}\))

Q(t):

Heat stored in the pay zone (J)

Ra :

Rayleigh number, dimensionless

\(Re_{dp}\) :

Reynolds number based on particle diameter, \(\rho u\frac{d_p }{\mu }\) dimensionless

\(Re_\kappa \) :

Reynolds number based on permeability, \(\rho \sqrt{\kappa }\frac{u}{\mu }\), dimensionless

r :

Radial distance (m)

R :

Thermal retardation factor

S :

Saturation, fraction

t :

Time (s)

T :

Temperature (K)

\({u}\) :

Velocity vector (m/s)

\(U_{hz} ( {x,y,z,t})\) :

Heat flux in the vertical direction (J/s)

v :

Heat velocity (m/s)

\(x_D \) :

Dimensionless distance

z :

Vertical distance (m)

\(\alpha \) :

Thermal diffusivity (\(\hbox {m}^{2}/\hbox {s}\))

\(\alpha _\mathrm{L} \) :

Longitudinal dispersivity (m)

\(\alpha _t \) :

Transverse dispersivity (m)

\({\alpha }'\) :

Overburden thermal diffusivity (\(\hbox {m}^{2}/\hbox {s}\))

\(\gamma \) :

Fractional-order derivative

\(\eta \) :

Pseudo-diffusivity (\(\hbox {m}^{3}\,\hbox {s}^{2-\gamma }/\hbox {kg}\))

\(\mu \) :

Dynamic viscosity (kg/m s)

\(\kappa \) :

Thermal dispersion tensor (W/m K)

\(\nu \) :

Kinematic viscosity (\(\hbox {m}^{2}/\hbox {s}\))

\(\rho \) :

Fluid density (\(\hbox {kg/m}^{3}\))

\(\sigma _r \) :

Mean square variance

\(\tau \) :

Dimensionless time

\(\phi \) :

Porosity, fraction

\({\varGamma }\) :

Standard gamma function

\({\varPhi }\) :

Fluid potential (Pa)

c:

Coke

e:

Effective

f:

Fluid

g:

Gas

o:

Oil

p:

Pore

r:

Reservoir

s:

Rock solid matrix

sf:

Solid-to-fluid interface

w:

Water

0:

Initial

1:

Reservoir

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Acknowledgments

The authors would like to acknowledge the support provided via King Abdulaziz City for Science and Technology (KACST), through the Science and Technology Unit at King Fahd University of Petroleum & Minerals (KFUPM), for funding this work through project No. 11-OIL1661-04, as part of the National Science, Technology and Innovation Plan (NSTIP).

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  1. Department of Petroleum Engineering, College of Petroleum Engineering and Geosciences, King Fahd University of Petroleum and Minerals, KFUPM Box 2020, Dhahran, 31261, Saudi Arabia

    Abiola David Obembe, Sidqi A. Abu-Khamsin & M. Enamul Hossain

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Obembe, A.D., Abu-Khamsin, S.A. & Hossain, M.E. A Review of Modeling Thermal Displacement Processes in Porous Media. Arab J Sci Eng 41, 4719–4741 (2016). https://doi.org/10.1007/s13369-016-2265-5

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  • DOI: https://doi.org/10.1007/s13369-016-2265-5

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