🌋Geothermal Systems Engineering Unit 9 – Geothermal Reservoir Modeling & Simulation

Key Concepts and Terminology

• Geothermal reservoir a subsurface volume of hot permeable and porous rocks saturated with hot water or steam that can be exploited for geothermal energy production
• Porosity the fraction of the rock volume occupied by voids or pores, typically expressed as a percentage
• Permeability the ability of a porous medium to allow fluids to pass through it, measured in units of darcy (D) or millidarcy (mD)
  • Permeability depends on factors such as pore size, pore connectivity, and fracture networks
• Hydraulic conductivity a measure of the ease with which a fluid can move through a porous medium under a hydraulic gradient, expressed in units of length per time (m/s or ft/day)
• Geothermal gradient the rate of increase in temperature with depth in the Earth's crust, typically around 25-30°C/km
• Geothermal system includes the heat source, reservoir, cap rock, and fluid circulation pathways
• Fluid enthalpy the total heat content of a fluid, expressed in units of energy per mass (kJ/kg or Btu/lb)

Geothermal Reservoir Characteristics

• Geothermal reservoirs are typically found in areas with high heat flow, such as near tectonic plate boundaries, volcanic regions, or deep sedimentary basins
• Reservoir rocks must have sufficient porosity and permeability to allow fluid circulation and heat extraction
  • Common reservoir rocks include sandstones, limestones, and fractured volcanic or metamorphic rocks
• Geothermal fluids can be liquid-dominated (hot water) or vapor-dominated (steam), depending on the temperature and pressure conditions
• Reservoir temperature ranges from low-enthalpy (< 150°C) to high-enthalpy (> 150°C) systems
• Reservoir depth can vary from shallow (< 1 km) to deep (> 3 km) depending on the geological setting
• Geothermal reservoirs often have a cap rock, an impermeable layer that prevents the escape of hot fluids and maintains the reservoir pressure
• Fracture networks and fault zones can significantly enhance the permeability and fluid flow in the reservoir

Governing Equations and Physics

• Fluid flow in geothermal reservoirs is governed by Darcy's law, which relates the fluid velocity to the pressure gradient, permeability, and fluid viscosity: $v = -\frac{k}{\mu}\nabla P$
• Heat transfer in geothermal reservoirs occurs through conduction, convection, and radiation
  • Conductive heat transfer is described by Fourier's law: $q = -k\nabla T$
  • Convective heat transfer is driven by fluid motion and is described by the advection-diffusion equation: $\rho c_p \frac{\partial T}{\partial t} + \rho c_p v \cdot \nabla T = \nabla \cdot (k\nabla T)$
• Mass conservation equation ensures that the mass of fluid entering and leaving the reservoir is balanced: $\frac{\partial (\phi \rho)}{\partial t} + \nabla \cdot (\rho v) = Q$
• Energy conservation equation accounts for the balance of heat energy in the reservoir: $\frac{\partial (\phi \rho U + (1-\phi)\rho_r c_r T)}{\partial t} + \nabla \cdot (\rho H v) = \nabla \cdot (k\nabla T) + Q_H$
• Equation of state relates the fluid density to pressure and temperature, often using the steam tables for water and steam

Data Collection and Analysis

• Geological data includes lithology, stratigraphy, and structural features obtained from surface mapping, well logs, and core samples
• Geophysical data provides information on subsurface properties and structures, such as:
  • Seismic surveys (reflection and refraction) to image reservoir geometry and faults
  • Gravity and magnetic surveys to delineate density and magnetic anomalies related to geothermal systems
  • Electrical resistivity surveys to identify conductive zones associated with hot fluids
• Well logging data includes temperature, pressure, flow rate, and fluid composition measurements from exploration and production wells
• Tracer tests involve injecting chemical tracers into the reservoir and monitoring their arrival at production wells to characterize fluid flow paths and velocities
• Pressure transient tests (e.g., well interference tests) are used to estimate reservoir properties such as permeability, porosity, and boundary conditions
• Geochemical data analysis of fluid samples helps to determine the origin, age, and evolution of geothermal fluids, as well as to assess scaling and corrosion potential

Modeling Techniques and Software

• Conceptual models are simplified representations of the geothermal system, incorporating key geological, hydrological, and thermal features
• Numerical models discretize the reservoir into grid blocks or elements and solve the governing equations using finite difference or finite element methods
  • Common numerical modeling software includes TOUGH2, FEFLOW, COMSOL Multiphysics, and ECLIPSE
• Stochastic modeling techniques (e.g., Monte Carlo simulation) are used to account for uncertainties in reservoir properties and to generate multiple realizations of the reservoir
• Coupled models integrate different physical processes, such as fluid flow, heat transfer, and geomechanics, to provide a more comprehensive representation of the geothermal system
• Upscaling techniques are employed to transfer properties from fine-scale models (e.g., fracture networks) to coarser-scale models (e.g., reservoir-scale) while preserving the essential flow and transport behavior
• Inverse modeling (history matching) is used to calibrate the model by adjusting reservoir properties to match observed data, such as well pressures and temperatures
• Sensitivity analysis is performed to identify the most influential parameters on the model output and to guide data collection efforts

Simulation Processes and Methods

• Steady-state simulations represent the equilibrium conditions of the reservoir, neglecting time-dependent changes
• Transient simulations capture the time-dependent behavior of the reservoir, such as pressure and temperature changes during production or injection
• Single-phase simulations consider only one fluid phase (e.g., liquid water or steam), assuming no phase changes occur in the reservoir
• Multiphase simulations account for the presence and interaction of multiple fluid phases (e.g., liquid water and steam), which is essential for modeling high-enthalpy geothermal systems
• Reactive transport simulations couple fluid flow and heat transfer with geochemical reactions, such as mineral dissolution and precipitation, to predict scaling and corrosion issues
• Wellbore flow simulations model the fluid flow and heat transfer within the production and injection wells, considering factors such as pressure drop, heat loss, and phase changes
• Fracture flow simulations explicitly represent the flow and transport in discrete fracture networks, which can significantly influence the behavior of fractured geothermal reservoirs

Interpretation of Results

• Pressure and temperature distributions provide insights into the reservoir's energy potential and the effects of production and injection on the system
• Fluid flow patterns and velocities help to identify high-permeability zones, preferential flow paths, and potential short-circuiting between wells
• Produced fluid enthalpy and mass flow rates are key indicators of the reservoir's productivity and sustainability over time
• Reservoir lifetime and recovery factor estimates are used to assess the long-term viability of the geothermal project and to guide management strategies
• Thermal breakthrough time predictions indicate when cooler injected fluids may reach the production wells, potentially impacting the system's efficiency
• Pressure depletion and subsidence forecasts are essential for assessing the geomechanical impacts of geothermal production on the reservoir and surrounding formations
• Uncertainty quantification and risk assessment help to communicate the reliability of the simulation results and to guide decision-making processes

Real-World Applications and Case Studies

• The Geysers geothermal field in California, USA, is the world's largest geothermal power production site, with a capacity of over 1,500 MW
  • Numerical modeling has been used to optimize injection strategies and to predict the long-term performance of the reservoir under different production scenarios
• The Larderello geothermal field in Tuscany, Italy, has been in operation since the early 1900s and currently produces about 10% of the world's geothermal electricity
  • Reservoir modeling has helped to understand the complex fluid flow and heat transfer processes in this vapor-dominated system
• The Reykjanes geothermal field in Iceland is a high-enthalpy system located on the Mid-Atlantic Ridge, with a power plant capacity of 100 MW
  • Coupled hydro-thermal-mechanical modeling has been applied to investigate the effects of fluid injection on reservoir productivity and seismicity
• The Salton Sea geothermal field in California, USA, is a high-temperature, liquid-dominated system with a high salinity and mineral content
  • Reactive transport modeling has been used to predict scaling and corrosion issues and to design appropriate fluid treatment strategies
• The Wairakei geothermal field in New Zealand, one of the world's oldest and largest geothermal power production sites, has a capacity of over 350 MW
  • Numerical modeling has been employed to optimize the balance between production and injection, ensuring the sustainable use of the resource