A semi-analytical model for heat and mass transfer in geothermal reservoirs to estimate fracture surface-are-to-volume ratios and thermal breakthrough using thermally-decaying and diffusing tracers
- Los Alamos National Laboratory
A semi-analytical model was developed to conduct rapid scoping calculations of responses of thermally degrading and diffusing tracers in multi-well tracer tests in enhanced geothermal systems (EGS). The model is based on an existing Laplace transform inversion model for solute transport in dual-porosity media. The heat- and mass-transfer calculations are decoupled and conducted sequentially, taking advantage of the fact that heat transfer between fractures and the rock matrix is much more rapid than mass transfer and therefore mass transfer will effectively occur in a locally isothermal system (although the system will be nonisothermal along fracture flow pathways, which is accounted for by discretizing the flow pathways into multiple segments that have different temperature histories). The model takes advantage of the analogies between heat and mass transfer, solving the same governing equations with k{sub m}/({rho}C{sub p}){sub w} being substituted for {phi}D{sub m} in the equation for fracture transport and k{sub m}/({rho}C{sub p}){sub m} being subsituted for D{sub m} in the equation for matrix transport; where k = thermal conductivity (cal/cm-s-K), {rho} = density (g/cm{sup 3}), C{sub p} = heat capacity (at constant pressure) (cal/g-K), {phi} = matrix porosity, and D = tracer diffusion coefficient (cm{sup 2}/s), with the subscripts w and m referring to water and matrix, respectively. A significant advantage of the model is that it executes in a fraction of second on a single-CPU personal computer, making it very amenable for parameter estimation algorithms that involve repeated runs to find global minima. The combined thermal-mass transport model was used to evaluate the ability to estimate when thermal breakthrough would occur in a multi-well EGS configuration using thermally degrading tracers. Calculations were conducted to evaluate the range of values of Arrhenius parameters, A and E{sub {alpha}} (pre-exponential factor, 1/s, and activation energy, cal/mol) required to obtain interpretable responses of thermally-degrading tracers that decay according to the rate constant k{sub d} = Ae{sup -E{sub {alpha}}/RT}, where k{sub d} = decay rate constant (1/s), R = ideal gas constant (1.987 cal/mol-K), and T = absolute temperature (K). It is shown that there are relatively narrow ranges of A and E{sub {alpha}} that will result in readily interpretable tracer responses for any given combination of ambient reservoir temperature and working fluid residence time in a reservoir. The combined model was also used to simulate the responses of conservative tracers with different diffusion coefficients as a way of estimating fracture surface-area-to-volume ratios (SA/V) in multi-well EGS systems. This method takes advantage of the fact that the differences in breakthrough curves of tracers with different matrix diffusion coefficients are a function of SA/V. The model accounts for differences in diffusion coefficients as a function of temperature so that tracer responses obtained at different times can be used to obtain consistent estimates of SA/V as the reservoir cools down. Some single-well applications of this approach are simulated with a numerical model to demonstrate the potential to evaluate the effectiveness of EGS stimulations before a second well is drilled.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- AC52-06NA25396
- OSTI ID:
- 1043466
- Report Number(s):
- LA-UR-10-08174; LA-UR-10-8174; TRN: US201214%%22
- Resource Relation:
- Conference: Fall 2010 American Geophysical Union Meeting ; December 13, 2010 ; San Francisco, CA
- Country of Publication:
- United States
- Language:
- English
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