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Experimental and numerical study of flow and thermal transport in fractured rock

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Abstract

An experimental and numerical study was carried out to investigate matrix-fracture thermal transport in fractured rock. Two different synthetically fractured core plugs were used during the flow-through experiments while core plugs’ outer surface was maintained at two different constant temperatures. To investigate the matrix-fracture thermal transport, cold water was injected through the single fracture core plugs at different flow rates. A film type heat flux sensor was used in the fractured core plug to measure the fracture temperature and heat flux over the matrix-fracture interface. Experimental results showed that fracture temperature decreases with increasing flow rate while heat flux increases. At high flow rates, temperature difference over matrix-fracture interface increases due to large volume of water contacting the fracture at a given time. Water temperature decreased more in the case of fracture surrounded by rock matrix with low volumetric heat capacity and thermal conductivity. A numerical model calibrated using experimental values of the fracture temperature was developed to estimate thermal properties of rock matrix and to identify their importance on the matrix-fracture thermal transport. Using the calibrated numerical model, it has been shown that temperature in the fracture and fracture surface temperature are different contrary to previous studies assuming the same values for these two temperatures. Local and transient convective heat transfer coefficients were introduced with respect to local values of temperature difference and transient values of heat flux along matrix- fracture interface enabling accurate representation of matrix-fracture thermal transport.

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Abbreviations

\(\phi\) :

porosity [dimensionless]

ρi :

density of component i [kg/m3]

np :

total number of phase [dimensionless]

cij :

fraction of component i in phase j [dimensionless]

uj :

Darcy velocity of phase j [m/s]

Ri :

total source/sink term for the component i [kg/m3·s]

k:

intrinsic permeability [mD]

krj :

relative permeability of phase j [dimensionless]

μj :

viscosity of phase j [cp]

pi :

is pressure of phase j [atm]

γj :

specific weight of phase j [kg/m2·s2]

d:

is vertical depth [m]

ρR :

density of reservoir rock [kg/m3]

Csp,R :

heat capacity of rock [J/K]

ρj :

density of phase j [kg/m3]

Csp,j :

heat capacity of phase j at constant volume [J/K]

Cp,j :

heat capacity of phase j at constant pressure [J/K]

κ:

thermal conductivity [J/m∙d∙K]

Qgain :

heat gain rate [J/d]

qH :

enthalpy source term [J/d]

h:

Convective heat transfer coefficient (J/min cm2°C)

q:

Heat flux (J/min cm2)

Tf :

Temperature of flowing fluid in fracture (°C)

Ts :

Temperature of solid surface (°C)

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Authors and Affiliations

  1. Department of Petroleum and Natural Gas Engineering, Middle East Technical University, Ankara, Turkey

    Yashar Tavakkoli Osgouei & Serhat Akin

  2. Department of Petroleum and Natural Gas Engineering, Near East University, Mersin 10, Nicosia, Turkey

    Yashar Tavakkoli Osgouei

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  1. Yashar Tavakkoli Osgouei
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  2. Serhat Akin
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Correspondence to Serhat Akin.

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Tavakkoli Osgouei, Y., Akin, S. Experimental and numerical study of flow and thermal transport in fractured rock. Heat Mass Transfer 57, 1053–1068 (2021). https://doi.org/10.1007/s00231-020-03001-w

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