# Two-dimensional numerical modelling of strategies to avoid thermal stress induced flow channeling in fractured geothermal reservoirs - **Authors:** Mats Rongved; Andreas Bauer; David Dempsey; Rune M. Holt - **Journal:** Geothermics, vol. 90, pp. 101978 (2021) - **Publisher:** Elsevier BV - **DOI (version of record):** [https://doi.org/10.1016/j.geothermics.2020.101978](https://doi.org/10.1016/j.geothermics.2020.101978) - **This page:** https://ddempsey.github.io/papers/2021-rongved-two-dimensional-numerical-modelling-strategies/ - **Open PDF:** [https://ddempsey.github.io/papers/2021-rongved-two-dimensional-numerical-modelling-strategies/rongved2021-two-dimensional-numerical.pdf](https://ddempsey.github.io/papers/2021-rongved-two-dimensional-numerical-modelling-strategies/rongved2021-two-dimensional-numerical.pdf) (Accepted manuscript (peer-reviewed, author's version)) - **Full text (Markdown):** [https://ddempsey.github.io/papers/2021-rongved-two-dimensional-numerical-modelling-strategies/fulltext.md](https://ddempsey.github.io/papers/2021-rongved-two-dimensional-numerical-modelling-strategies/fulltext.md) - **Notice:** Accepted manuscript. © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/. The version of record is available at https://doi.org/10.1016/j.geothermics.2020.101978 - **Explainer:** all explainers on this site are AI-generated. - **BibTeX:** https://ddempsey.github.io/papers/2021-rongved-two-dimensional-numerical-modelling-strategies/citation.bib - **Topics:** Induced seismicity & faults; Geothermal systems - **Keywords:** Geothermal gradient; Petroleum engineering; Mechanics; Flow (mathematics); Thermal; Volumetric flow rate; Fracture (geology); Geology ## In brief Cooling by injected water can concentrate flow into one fracture. In our two-dimensional model of two parallel fractures, flow stayed even or evened out with wider, more alike fractures or a higher injection rate. A high starting rate, or injecting through each fracture in turn, made even flow more likely. - In our model, flow between two fractures splits by the ratio of their apertures. A narrower fracture with a larger relative aperture gain can regain flow. - With an initial fracture permeability of 5 × 10^-10 m², flow stayed close to even. At 10^-11 m², one fracture took most of the flow within about two days. - At 1.5 × 10^-10 m², a tenfold lower injection rate gave uneven flow. A tenfold higher rate gave uneven flow at first, then even flow. - In our model, a high injection rate for the first 30 days, or injection through each fracture in turn for 100 days each, gave close to even flow. - Resolving temperature beside the fracture on a finer grid changed the modelled timing of thermal breakthrough. ## The problem Enhanced geothermal systems (EGS) produce heat from hot, low-permeability rock by circulating water through fractures between injection and production wells. Because rock conducts heat poorly, evenly spread flow delays thermal breakthrough, the arrival of cooled water at the production well. However, Grant (2016) found that in earlier EGS projects, flow was generally confined to a small part of the stimulated volume. As rock around a fracture cools, the compressive stress on the fracture falls and its aperture, the width of the opening, increases (Ghassemi et al., 2008). The fracture that takes the most water tends to cool fastest. This suggests a feedback in which it widens fastest and takes an increasing share of the flow. Guo et al. (2016) concluded that this uneven flow, or flow channelling, was inevitable in a single fracture. We asked whether it is inevitable between fractures, and whether well operations could reduce it. ## What we did We used a two-dimensional thermo-hydro-mechanical (THM) model. MDEM, a hybrid finite-discrete element code, computes rock stress, fracture opening and permeability. TOUGH2, a reservoir simulator (Pruess et al., 1999), computes fluid flow and heat transport. To resolve the steep temperature gradient beside a fracture, we divided each fractured element into 16 sub-grid elements for flow and heat. We checked heat conduction and thermal stress against analytical solutions (Carslaw and Jaeger, 1959; Perkins et al., 1984). The model reservoir is granite at 150 °C, with wells 90 m apart. One or two parallel fractures connect them, 40 m apart in the two-fracture cases. Water at 2 °C is injected at 10^-5 to 10^-3 m²/s, a rate per metre of reservoir height in a two-dimensional model, or 0.01 to 1 litre per second per metre (our conversion). Two-fracture initial permeabilities range from 10^-11 to 5 × 10^-10 m², equivalent to apertures of 11 to 77 micrometres, or about a hundredth to a tenth of a millimetre (our conversion). Both fractures start the same, but irregularities in the mesh give one slightly more flow. We use these irregularities to approximate natural variability. ## What we found The sub-grid changed the modelled timing of thermal breakthrough. Without it, heat stored in the coarse fracture elements kept the production temperature high until those elements had cooled. It then fell abruptly. With the sub-grid, it began to fall almost immediately. Under the same pressure gradient, flow through a fracture scales with the cube of its aperture. The split of flow between two fractures therefore depends on the ratio of their apertures. The aperture gain from cooling does not depend on the initial aperture, except through the initial split of flow. So a narrower fracture can gain more in relative terms and regain flow, even while the wider fracture opens by more. In the widget, fractures of 20 and 10 micrometres that open by 10 and 8 micrometres shift the wider fracture's share of flow from 89% to 82% (our illustration of the paper's Eq. 11).
At the highest two-fracture initial permeability (5 × 10^-10 m²), flow was close to even from the start, whereas at 1.5 × 10^-10 m² it was uneven at first and then evened out. At 10^-11 m², one fracture took most of the flow after about two days. Production temperature also dropped sooner than in the two higher-permeability cases. We take this to indicate lower energy production. We reran the 1.5 × 10^-10 m² case at tenfold lower and higher rates. At the lower rate, almost all the flow went through one fracture early in the run, whereas at the higher rate flow was uneven at first and then evened out. In our model, aperture gain is not linear in rate. A rate change has little effect at low rates, where the flow is too small to cool the rock appreciably, and at high rates, where the fracture is already cold. A higher rate can therefore give a narrower fracture between these limits a larger percentage gain than the wider one. However, higher rates normally mean higher pumping costs. To limit that cost, we ran a separate two-fracture case at 10^-3 m²/s for the first 30 days only, then at a lower rate. Both fractures had cooled by similar amounts by 30 days, and flow stayed even after the rate was lowered. Because production temperature fell quickly during the high-rate phase, we suggest keeping that phase short. We also directed all the flow through each fracture in turn for 100 days each, before opening both. Close to even flow followed, whereas flow stayed uneven with injection through both fractures from the start at the same rate and initial permeability (10^-11 m²). Our results indicate that sequential injection could increase heat recovery. However, we did not optimise the 100-day stage length. ## Limitations We excluded chemical effects because we expect them to be minor in the crystalline rock typical of EGS. The model also omits fracture growth during production, and a field reservoir would need a three-dimensional model. With two parallel fractures in an idealised reservoir, we are cautious in extrapolating to a complex network. We suggest that as fractures are added, uniform permeability becomes less likely and flow channelling more likely. In a natural network, we expect some low-permeability paths not to receive enough flow to cool and open. Wellhead interventions before normal production could still increase the number of fractures that contribute. Our next step is to test sequential injection in a more complex network between two wells. ## Glossary An **enhanced geothermal system (EGS)** produces heat from hot rock whose permeability has been increased by stimulation. **Permeability** measures how easily fluid flows through rock or a fracture. A fracture's **aperture** is the width of its opening. A **micrometre** is a thousandth of a millimetre. **Thermal breakthrough** is the arrival of cooled water at the production well, after which the production temperature falls. **Flow channelling**, or uneven flow, is the concentration of flow into a small part of a fracture network. A **thermo-hydro-mechanical (THM)** model couples heat transfer, fluid flow, and rock deformation. A **finite-discrete element** code treats intact rock as a continuous mesh and represents failed elements as discrete blocks. A **sub-grid** divides one model element into smaller elements to resolve steep gradients. **Sequential injection** directs all the injected water through each fracture in turn before normal production. ## Cite Rongved, Mats, Bauer, Andreas, Dempsey, David, Holt, Rune M. (2021). Two-dimensional numerical modelling of strategies to avoid thermal stress induced flow channeling in fractured geothermal reservoirs. Geothermics, 90, 101978. https://doi.org/10.1016/j.geothermics.2020.101978 ```bibtex @article{rongved2021two, title = {Two-dimensional numerical modelling of strategies to avoid thermal stress induced flow channeling in fractured geothermal reservoirs}, author = {Rongved, Mats and Bauer, Andreas and Dempsey, David and Holt, Rune M.}, journal = {Geothermics}, year = {2021}, volume = {90}, pages = {101978}, publisher = {Elsevier BV}, doi = {10.1016/j.geothermics.2020.101978}, url = {https://ddempsey.github.io/papers/2021-rongved-two-dimensional-numerical-modelling-strategies/} } ```