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Numerical Investigation of Excess Capillary Pressure Created by Dry-Out and Replenishment Phenomenon in Geothermal Reservoirs

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Abstract

Accurate prediction of mass and heat exploitation potential of geothermal reservoirs is necessary for successful geothermal field development. In boiling zones of these reservoirs, the flow of steam and water is governed by complex physical phenomena involving mechanical interaction between two phases due to the dry-out and replenishment of water which makes an excess imbibition capillary pressure. So the capillary pressure can be a function of heat flux in addition to wettability and saturation. In this paper, based on the previous theoretical and experimental works, a modified capillary pressure function has been proposed that considers the effect of boiling and heat flux. This function is implemented in a local thermal non-equilibrium (LTNE) model to simulate the water and steam flow in porous media which is verified by experimental data. Finally, the model is used to investigate the effect of excess capillary pressure on the geothermal reservoir’s performance. The results represent a good agreement with the experimental data and show that the excess capillary pressure reduces the total mass and energy produced from the reservoir by about 5 percent. Then, a sensitivity study is conducted to see the effect of some critical parameters on the performance of a geothermal reservoir.

Highlights

  • Dry-out and replenishment phenomenon creates excess capillary pressure in porous media.

  • The replenishment effect imbibes the liquid into the corners of rock grains during the boiling.

  • The produced energy from a boiling reservoir can be at least 5 percent less than others due to replenishment.

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Abbreviations

ϕ :

Porosity

S :

Saturation

ρ :

Density (kg/m3)

C p :

Specific heat capacity (J/kg K)

U :

Velocity (m/s)

t :

Time (s)

q m :

Mass flow (kg/s)

h :

Specific enthalpy (J/kg)

U :

Internal energy (J/kg)

Q sf :

Internal heat exchange flow (J/m3 s)

Q E :

Volumetric heat source (J/m3 s)

T :

Temperature (K)

σ :

Interfacial tension (N/m)

J :

Capillary J-function

k r :

Relative permeability

µ :

Dynamic viscosity (kg/m s)

K :

Absolute permeability

k :

Heat conductivity (W/m K)

Nu:

Nusselt number

Re:

Reynolds number

Pr:

Prandtl number

d p :

Average pore diameter (m)

α sf :

Specific surface of the solid matrix (1/m)

h lv :

Latent heat (J/kg)

h sv :

Heat transfer coefficient of vapor (W/m2 K)

h sl :

Heat transfer coefficient of liquid (W/m2 K)

P :

Pressure (bar)

g :

Acceleration of gravity (m/s2)

s :

Solid (rock)

f :

Fluid

l :

Liquid

v :

Vapor

c :

Capillary pressure

sat:

Saturated

eff:

Effective

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Authors and Affiliations

  1. Department of Petroleum Engineering, Amirkabir University of Technology, Tehran, Iran

    Nasser Faraz & Ehsan Khamehchi

  2. Department of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran

    Hamid Naderan Tahan

Authors
  1. Nasser Faraz
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  2. Ehsan Khamehchi
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  3. Hamid Naderan Tahan
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Contributions

NF was involved in methodology, software, data curation, writing—original draft preparation, validation, visualization, investigation. EK and HNT helped in supervision.

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Correspondence to Ehsan Khamehchi.

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Faraz, N., Khamehchi, E. & Naderan Tahan, H. Numerical Investigation of Excess Capillary Pressure Created by Dry-Out and Replenishment Phenomenon in Geothermal Reservoirs. Transp Porous Med 139, 559–578 (2021). https://doi.org/10.1007/s11242-021-01679-y

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