A Simple Analytical Model For Heat Flow In Fractures - Application To Steam
Enhanced Remediation Conducted In Fractured Rock
K.S. Novakowski1, K.M. Stephenson2, E.L. Davis3, S. Carroll3, G. Heron4, andK. Udell5
1 Queen's University, Dept. of Civil Engineering, Kingston, ON, CANADA K7L 3N6
2 Golder Associates Ltd., Ottawa, ON, CANADA K2C 2B5
3R.S. Kerr Environmental Research Center, Ada, OK, USA 74821-1198
4 Steamtech Environmental Services, Inc., Bakersfield, CA, USA 93308
5University of California, Dept. of Mechanical Engineering, Berkeley, CA, USA
Remediation of fractured rock sites contaminated by non-aqueous phase liquids has long
been recognized as the most difficult undertaking of any site clean-up. Recent pilot
studies conducted at the Edwards Air Force Base in California and the former Loring Air
Force Base in Maine have provided valuable field data that can support the evaluation of
Steam Enhanced Remediation (SER) for this setting. To aid in the interpretation of field
temperature measurements collected during and after steam injection, a semi-analytical
model was developed which can simulate radial convection and conduction of heat in a
discrete fracture. The governing equations are formulated under the assumptions that the
steam condensate boundary is stationary, that the rock is sparsely fractured, and that the
aperture of the fractures are known. The boundary value problem was solved using the
Laplace transform method and numerically inverted using the DeHoog algorithm.
Generic simulations conducted using a range of steam injection pressures, fracture
apertures, and thermal conductivities of the matrix show that the aperture size and the
properties of the matrix act as the principal features governing the transport of heat in this
setting. Comparison of the generic simulations to the temperature migration observed
during the SER pilot study conducted at Loring shows general agreement. In this case, it
was determined that the principal limiting factor in the propagation of heat was fracture
aperture size. Smaller fracture apertures common to the Loring limestone bedrock led to
limitations in the ability to inject steam. Consequently the steam condensed near the
borehole and much of the heat was lost to the matrix. Based on these results, alternate
scenarios are proposed for future pilot studies of SER in bedrock.
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