Estimating the Permeability–Depth Relation of Slate Formation for Geothermal Project

Slate formation is one of the potential geothermal sites in Taiwan. However, the fluid flow capability of slate formations has not been well investigated internationally. This study proposes a procedure to evaluate the permeability–depth relationship in slate formations. We used slate samples from the Hungyeh Formation in Taiwan to measure the permeability ( $$k$$ ) of intact slate and the hydraulic aperture ( $$e$$ ) of natural/artificial tensile fractures along the foliation, under confining pressures up to 60 MPa (~ 3500 m depth). Stress-dependent models of permeability and hydraulic aperture were developed using a power law and an exponential function, respectively. The equivalent vertical permeability ( $${k}_{v,eq}$$ ) of slate formation with fractures is calculated using Snow’s model, which considers the aperture ( $$e$$ ) and spacing ( $$s$$ ) of vertical fractures subparallel to the foliation. The matrix permeability (< 0.001 mD) decreases with increasing depth. The $${k}_{v,eq}$$ of the slate formation, contributed by fractures along the vertical foliation (assuming $$s$$ = 1.0 m), is several tens of times greater than the intact slate permeability. Within the target depth range of 1500–1700 m, and assuming $$s$$ = 0.2 m generated by hydraulic fracturing (HF), the mean $${k}_{v,eq}$$ ranges from 3.0 $$\times$$ 10–2 to 2.3 $$\times$$ 10–2 mD under an injection pressure of 10 MPa. To enhance energy generation efficiency in slate formations, improving HF design to create denser fractures and identify fracture zones, is suggested. The proposed approach is a simple and feasible way to evaluate the permeability–depth relation of reservoirs for geothermal projects before the detailed site investigation program.