A three-dimensional coupled thermo-hydro-mechanical numerical model with partially bridging multi-stage contact fractures in horizontal-well enhanced geothermal system

The problem

Enhanced geothermal systems (EGS) aim to produce heat from hot rock whose permeability is too low for water to flow through it naturally. Water is injected down one well, absorbs heat from the rock, and returns up a second well. To be viable, an EGS has to circulate water through a large volume of rock while avoiding thermal short circuits, fast pathways that return cold water to the production well early. However, technical and financial challenges remain before EGS can be widely deployed.

In the usual design, a horizontal well is stimulated in several stages, and each hydraulic fracture grows until it meets the second well (Han et al., 2020; Li et al., 2016; Shiozawa and McClure, 2014). We call these fractures fully bridging. Some injected water enters the rock between fractures, absorbs heat, and exits into the production well (Asai et al., 2018). However, this design is usually associated with early thermal breakthrough.

What we did

We proposed partially bridging fractures. Half of the fractures grow from the injection well and half from the production well, alternating along the wells, and each stops short of the other well. Water entering an injection fracture has to cross the rock between fractures, the stimulated reservoir volume (SRV), to reach a production fracture.

To test the design, we built a three-dimensional thermo-hydro-mechanical (THM) model in COMSOL Multiphysics, a finite element simulator. Each fracture is two contacting surfaces that can separate when cooling and fluid pressure remove the normal stress across them (Salimzadeh et al., 2018). Fracture permeability rises as the fracture opens. The modelled rock lies at 4.5 to 5.5 km depth, initially at 300 °C and 40 MPa. Injected water enters at 20 °C.

We compared designs by the temperature of the produced water at equal mass produced. This is because any design can delay cooling by circulating less water. We also computed the volume of rock in which stresses during operation exceed the Mohr–Coulomb failure criterion. We used this failed volume as a measure of secondary stimulation.

What we found

Over 20 years of production in our model, the partially bridging design delivered hotter water than the fully bridging design for the same mass produced. The model fractures start out 20 times more permeable than the SRV. In the fully bridging design, most of the water therefore stayed in the fractures. In the partially bridging design, cold water reached the production fractures only after crossing the SRV. However, the partially bridging design produced less water, because the SRV is less permeable than fractures that connect the wells.

Cooling makes the rock contract. This lowers the horizontal stress in the rock. Because our model rock starts at the failure limit, this stress drop causes it to fail. In the partially bridging design, cold water travelled further into the SRV. At a point midway between two fractures, modelled failure began after 12.5 years with partially bridging fractures and after 14.5 years with fully bridging fractures. The failed volume was larger for the partially bridging design at all times. We suggest this design would promote more secondary stimulation, through shear failure, during production.

For the partially bridging design at a fixed injection pressure of 45 MPa, 5 MPa above the initial reservoir pressure of 40 MPa, the injection rate fell over time. For the same total volume, failure came sooner and over a larger volume at fixed pressure than at fixed rate. This is because more water was injected early. These results imply that careful thought should be given to choosing a realistic injection scheme when models are used to predict EGS performance.

A single modelled fracture opened by about 3.5 mm. Midway between the wells, failure came about 1.8 years earlier than for a fracture that could not open and so kept its initial permeability. This is because the more permeable fracture let cold water reach further into the rock.

However, opening also relieves stress. To isolate this effect, we reran the four-fracture, partially bridging model with fractures that cannot open but keep the same permeability. In these simulations, leaving opening out of the model overestimated the failed volume by 10 to 20%. In a deeper EGS with higher stresses, where fractures might never open, we expect the error to be smaller.

Stresses from cooling (thermoelastic) had the largest effect on stress changes in the SRV. Failed volumes were much smaller when we removed them. Stresses from fluid pressure (poroelastic) had a minor effect and appeared to delay failure.

Limitations

Fracture growth is not entirely controllable, particularly where existing fractures alter the stress field or provide preferred paths for fracture growth (McClure and Horne, 2014). A fracture that grew through to the second well would need some form of plugging. We assumed that all rock started at the failure limit, with no stress relief from earlier stimulation. This assumption may not be valid at every site. Our results come from five sets of simulations, with parameters taken largely from earlier studies. They sample a small part of the range of possible reservoirs. More failure could raise permeability, but we caution that thermal channelling could reduce the efficiency of the heat sweep if fast pathways began to dominate (Rongved et al., 2021).

Optimising injection temperature and pressure, well and fracture spacing, and fracture number for specific field sites, alongside an analysis of economic and environmental factors, should help establish whether partially bridging designs are feasible.

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.

A hydraulic fracture is a crack opened in rock by injecting fluid at high pressure.

Fully bridging fractures connect the injection well directly to the production well.

Partially bridging fractures grow from one well and stop short of the other.

The stimulated reservoir volume (SRV) is the rock between the fractures, made more permeable than the surrounding rock by stimulation.

A thermal short circuit is a fast flow path that returns cold injected water to the production well early.

Thermal breakthrough is the arrival of cooler water at the production well, after which the production temperature falls.

The heat sweep is the flow of injected water through the rock that extracts its heat.

A thermo-hydro-mechanical (THM) model couples heat transfer, fluid flow, and rock deformation.

A finite element simulator solves the governing equations on a mesh of small elements.

A megapascal (MPa) is a unit of pressure.

The normal stress on a fracture presses its walls together.

The Mohr–Coulomb criterion states that rock fails when its shear stress exceeds its frictional strength. Frictional strength rises with normal stress.

Secondary stimulation is failure of rock, and possible permeability gain, caused by injection during production, after the initial stimulation.

Thermoelastic stresses arise from contraction or expansion of rock as it cools or heats.

Poroelastic stresses arise from changes in fluid pressure in the pores of rock.

Thermal channelling is the concentration of flow into a few fast paths that cool first.