Geothermal reservoir modeling in a coupled thermo-hydro-mechanical-chemical approach: A review
Introduction
Thermal energy stored in the earth's crust is known as geothermal energy. Geothermal heat originates within the earth by the decay of natural radioactive isotopes (uranium, thorium, potassium) trapped in magma during formation of the earth. Heat flows towards the surface by rising of the magmas and buoyantly circulating water. The energy usually heats the rock and fluids inside fractures and pores within the rock. However, heat flow and geothermal gradient are not uniform; regional and local variations are always there. The estimated average heat flow from the earth is 82 MW/cm2 and the total global output is over 4 × 1013 W (Uyeda, 1988).
Nowadays, geothermal energy has become a significant source of energy for heating/cooling of buildings and for electricity generation in several countries (New Zealand, Turkey, France, Germany, Norway, Iceland, Japan, Indonesia, USA, etc.). The worldwide installed capacity has exceeded 12GW, and annual energy production is around 70,000 GWh shown in Fig. 1 (Bertani, 2016). The application and utilization of georesource largely depend on resource temperature. For example, low temperature (30–90 °C) geothermal resources at shallow depths are utilized for direct applications such as heating/cooling of buildings, paper drying, chemical processing, fish farming, agriculture greenhouses, oil recovery from tar sands and water desalination (Stauffer et al., 2013; Noorollahi et al., 2017; Luo et al., 2015; Bundschuh et al., 2015; Gude, 2016; Focaccia et al., 2016; Goosen et al., 2010; Missimer et al., 2013; Holbein et al., 2016; Omer, 2008). At present, 82 countries utilize the low-temperature geothermal water for direct applications with an installed thermal power capacity of 70,885 MW and a thermal energy use of 164,635 GWh/year (Fig. 2) (Lund and Boyd, 2016). Fig. 3, Fig. 4 show the direct utilization of geothermal energy (MWt) and installed capacity of geothermal energy (MW) of top 10 countries. The moderate temperature geothermal resources in the range of 90 °C to 150 °C are useful for both direct use and electricity generation. Around 70% of the geothermal resource worldwide has a temperature <150 °C. Due to its low temperature, the thermal efficiency of plant is usually low (6–12%) (Zarrouk and Moon, 2014) and uneconomical for electricity production. For generation of electricity, the temperature of geothermal resources should be nearly 150 °C or more. The high-temperature geothermal resources are mostly located in active volcanic areas and adjoining the tectonic plate boundaries where active geothermal activity commonly happens in the form of hot springs, fumaroles, steam vents, and geysers. Beside these locations, high energy containing reservoir with a desirable temperature for electricity generation could also be possible if the rock is rich in radioactive minerals. Hot dry rock (HDR) or high heat producing granites can be a good source as these reservoirs store enormous amounts of heat energy. Such reservoirs are usually located at 3–10 km below the earth's surface. It is estimated that at a depth of 10 km across the world, HDR reservoir energy contains 1.3x1027J of energy which is 100–1000 times more than the quantity of fossil energy (Lu, 2018). However, HDR reservoirs are almost dry and impermeable in the natural state. The permeability enhancement of the reservoirs is required before actual production, by different techniques such as thermal, chemical or hydraulic stimulation. The hydro-fracturing method of reservoir enhancement is the most common method for the geothermal industry. In hydro-fracturing, fluid is injected into the reservoir rock at a pressure above the minimum in-situ principal stress at a given depth. This creates a fracture and opens up the pre-existing interlocking joints or new fractures. Once the reservoir permeability has been artificially enhanced, fluid can be circulated through the fractures/cracks. The fracture surface area acts as a heat exchanger between the host rock and the injected fluid. The engineered HDR is known as the enhanced geothermal system (EGS). In an EGS reservoir, three physical reservoir measurements are important for better exploitation of the resources. These are impedance, recovery factor and tracer-swept volume test (Grant, 2016).
This paper provides a state of art review of the various physical and chemical processes inside the geothermal reservoir that take place during fluid injection and heat extraction process. The review work has covered the numerical modeling approaches and development of various tools during last four decades. This paper also highlights the capability of various numerical tools to handle coupled processes. Based on the past studies, the paper is organized in four groups based on the coupled processes: thermo-hydro i.e. decoupled the mechanical and chemical effects, thermo-hydro-chemical i.e. decoupled the mechanical effect, thermo-hydro-mechanical i.e. decoupled the chemical effect, and fully coupled thermo-hydro-mechanical-chemical effects. The importance of these coupled processes and their influence on energy production or heat extraction are also highlighted.
Section snippets
Numerical modeling of geothermal reservoir
Numerical modeling of a geothermal reservoir is important for long-term understanding of the interaction of injected fluids with existing reservoir fluids and with the reservoir rocks. Relatively cold water injection into the reservoir disturbs the chemical, thermal and mechanical equilibrium of reservoir which modifies the porosity/permeability and other transport properties of the reservoir. The porosity/permeability the stress field changes largely depend on dissolution/precipitation
Geothermal heat extraction modeling
Porosity/permeability distribution, and presence of faults and fractures play an important role in fluid flow in a geothermal reservoir. The processes within the reservoir during relatively cold water injection are: convection (at the solid-fluid interface by the motion of fluid), advection (transport of heat as well as reactants products by bulk motions of fluids), heat conduction in the low permeable rock matrix, molecular diffusion, hydrodynamic dispersion and thermo-poro-elastic deformation
Governing equations of coupled THMC processes in geothermal reservoir
The governing equations for modeling a geothermal system include mass, momentum, energy, species transport, stress and displacement equations. Geothermal reservoirs can either be a porous medium or have permeable fractures inside a low permeable rock matrix. In case of latter, the modeling of various physical and chemical processes in fracture and rock matrix requires solving the partial differential equations separately but coupled at the fracture rock interfaces. The governing equations for
Thermo-hydro modeling
Hydro-thermal flow occurs when cold water is injected into the reservoir and hot water is pumped out from the reservoir after receiving the heat energy. In a thermo-hydro coupling, the effect of deformation (porosity/permeability evolution due to fluid pressure and chemical reaction are decoupled with deformation) is neglected but the temperature and pressure dependent fluids properties such as viscosity, density, heat transfer coefficient etc. are the main dominating variables that decide the
Thermo-hydro-chemical modeling
The injection of cold water into geothermal reservoirs enhances the water-rock reactions which initiates the dissolution/precipitation processes, alter the pore-geometry of the reservoir, and, as a consequence, their hydraulic and transport properties, such as porosity/permeability. A number of studies have focused on the evolution of the porosity/permeability by geochemical effects during heat extraction (Jing et al., 2002, Rabemanana et al. (2003), Kiryukhin et al., 2004, Bächler and Kohl,
Thermo-hydro-mechanical modeling
During heat extraction from a geothermal reservoir, the matrix and fracture/joints deform due to cooling and fluid overpressure. Cooling causes contraction while fluid overpressure results in the expansion of reservoir matrix. The spatial variation of thermal stress and pore pressure due to injection and production during operation can cause a non-uniform evolution of reservoir porosity/permeability. This creates a spatially varying reservoir transmissivity and may generate channelized flow
Thermo-hydro-mechanical-chemical modeling
The studies on coupled TH, THM and THC do not capture the complete evolution of permeability/porosity during geothermal heat extraction. In a real scenario, the porosity/permeability evolution is combined with effects of THMC processes. The coupling among the various processes is shown in Fig. 14. There are limited studies on modeling of fully coupled thermo-hydro-mechanical-chemical effects on geothermal reservoir evolution. Taron and Elsworth (2009) proposed a fully coupled THMC model in a
Conclusion and future directions
Long-term permeability change during geothermal heat extraction is influenced by complex interactions among fluid flow, reaction rates, mineralogy, thermo-mechanical properties of reservoir, residence time of fluid, joint stiffness and heterogeneity. However, detailed quantitative understanding remains to be developed for a field-scale geothermal system having a long-term sustainable operation. Based on previous numerical studies, it may be summarized that coupling among different physical
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