# Well-Doublets: A First-Order Assessment of Geothermal SedHeat Systems
## 3 Geomechanical Conditions
In general, in the low permeability host rock, higher pressures reduce the frictional strength (Equation (3)) of a slip plane by decreasing the effective normal stress (\(\sigma_{\mathrm{ij}}=S_{\mathrm{ij}}-P\delta_{\mathrm{ij}}\)), facilitating yield. In a Mohr stress diagram (Figure 5a) using total stresses, a pressure increase shifts the yield envelope (black line) into the Mohr circle (the stress state), and yield is said to have occurred when stresses lie outside the criterion limit. Because stiff, brittle earth materials store elastic strain energy but are strain-weakening, a sudden stress drop (weakening) accompanies shear slip, and a very small fraction of the released strain energy is evidenced as strain waves (seismic waves). Although the fluid-injection fracture-slip-induced deformation is not high, generally far less than a centimeter, \(\Delta\sigma_{\mathrm{ij}}\) may also trigger and reactivate nearby faults that are near critical stress conditions, causing felt seismicity and casing shear problems [53]. Injection-induced earthquakes are usually small with moment magnitude < 0. However, there are cases where large magnitude (>1) injection-induced seismicity has been recorded [54]. Two groups of field parameters can impact the magnitude and rate of injection-induced seismicity: controllable operational parameters that include fluid injection pressure, rate, temperature, and volume [54]. Uncontrollable subsurface parameters include the initial state of stress and pore pressure, size and density of pre-existing faults/fractures, fault/fracture orientation and shear strength, and other geomechanics parameters [55]. Figure 5 shows the effect of the pressure increase on the fault reactivation in the deep doublet geothermal Gross Schonebeck project in the North German Basin, where fluid-injection-induced seismicity is recorded [56]. The stress state at the injection depth of 4035 m is a normal faulting regime with S\({}_{\mathrm{v}}\) = 100 MPa, S\({}_{\mathrm{Hmax}}\) = 98 MPa, S\({}_{\mathrm{hmin}}\) = 55 MPa, and P\({}_{\mathrm{p}}\) = 43 MPa [56]. Faults striking in the S\({}_{\mathrm{Hmax}}\) direction with dip angles of 45-75\({}^{\circ}\) are critically stressed; increasing pore pressure by less than 7 MPa increases the risk of induced seismicity on two fault sets: the NW-SE set (rectangle), and the E-W set (Mohr circle). Shear slip of natural fractures in strong rocks is usually a dilatant process, so the rock mass permeability is enhanced in certain directions, which in turn will alter the fluid flow patterns, and probably increase the permeability anisotropy in a rock mass. The second mechanism, poroelasticity, governs fluid pressure change effects on in-situ states of stress and rock mass deformation [52; 57]. Geothermal SedHeat wells are drilled into porous, permeable reservoirs, and \(\Delta\)P causes volume changes that lead to stress changes, altering porosity and permeability. [PERSON] and [PERSON] [58] demonstrated that stress/pore pressure changes in a normal faulting regime as follows  
\[\frac{\Delta S_{\mathrm{hmin}}}{\Delta\mathrm{P}}=\alpha\frac{1-2\upsilon}{1- \upsilon} \tag{4}\]  
Figure 5: (**a**) 3D Mohr circles showing stress condition and slip tendency due to fluid injection in the deep geothermal reservoir Gross Schönbeck in the North German Basin. The red line is the Coulomb failure criterion when pore pressure has been elevated by 7 MPa, and (**b**) The lower hemisphere stereonet plot illustrates the slip-tendency (ratio of resolved shear to normal stress) and stress direction. where \(\alpha\) is Biot's poroelastic coefficient, for this relationship, it is assumed that vertical stress remains constant. In this study, we evaluated the pore pressure stress coupling at different tectonic stress settings employing 3D geomechanics modeling.