| Title | Approximate Solutions to Fracture-Matrix Heat Transfer for Numerical and Analytical Modeling of Enhanced Geothermal Systems |
|---|---|
| Authors | Quanlin ZHOU, Curtis M. OLDENBURG, Jens T. BIRKHOLZER, and Jonny RUTQVIST |
| Year | 2017 |
| Conference | Stanford Geothermal Workshop |
| Keywords | heat transfer, fractures, matrix, diffusion, injection, analytical solutions, enhanced geothermal systems |
| Abstract | Dual-continuum models, such as dual-porosity and dual-permeability models, have often been employed to simulate heat transfer induced by fluid injection and production in geothermal systems, despite the known shortcomings of first-order approximations that may significantly underestimate fracture-matrix heat transfer, leading to earlier and larger thermal drawdown at production wells. For accurate modeling of enhanced geothermal systems (EGS), cooling-induced fracturing that occurs in EGS reservoirs demands high-resolution non-isothermal modeling. To avoid the effects of first-order approximations, we have developed unified-form approximate solutions to fracture-matrix heat transfer based on existing analytical solutions with infinite exponential series (Zhou et al., 2017). Our newly developed approximate solutions combine the early- and late-time solutions that are continuous at a dimensionless switchover time, td0. The early-time solutions are based on three-term polynomial functions in terms of square root of dimensionless time, with the first coefficient dependent on dimensionless area-to-volume ratio. The last two coefficients solely depend on the aspect ratios for anisotropic rectangular blocks, while they are determined analytically for isotropic blocks of various shapes. For the late-time solutions, only the leading exponential term is needed for isotropic blocks, while a few additional exponential terms are needed for highly anisotropic rectangular blocks. The developed solutions are used to demonstrate the effects of anisotropy, multiple rates, and early- and late-time heat transfer in idealized geothermal systems. These solution can be easily extended to modeling reservoir-scale heat transfer with any shape and size of rock matrix blocks, with the aid of time-convolution. |