A Semi-Analytical Model for Poro-Thermo-Elastic Stresses by Injection in a Finite-Height Layer

ABSTRACT The injection of fluids in geothermal energy, as well as in CCS, is accompanied by changes in stresses due to the reduced temperatures and elevated pressures. This can result in unwanted hydraulic fracturing and fault reactivation. We have developed a fast, semi-analytic tool to evaluate these changes and their consequences in terms of risk measures like fault reactivation probability, fracturing potential, and their spatial distribution. The tool has been designed for radially symmetric scenarios, which facilitated the use of an analytical approach. Pressure and temperature are calculated based on advection in the injection layers and diffusion in the bounding layers. The induced stresses are calculated based on these fields, using expressions for finite cylinders with elevated temperatures or pressures. Together with the virgin stress field, this provides input for the risk measures. With the semi-analytic approach, calculation times are limited and stochastic analyses are possible. We show how the shape of the disturbed zone in the injection layer and the amount of temperature and pressure diffusion into the bounding layers critically affect the stress field and the associated risk measures. We demonstrate how the tool can be applied to a geothermal injection well and to a CCS prospect, and how it helps in deciding what to target with data gathering. INTRODUCTION The transition to a sustainable energy economy poses multiple new challenges. Many of them are related to new ways of using the subsurface. As an example, the utilization of geothermal energy through an injection – production well doublet can only be safeguarded if the produced water is injected in the reservoir from where it was produced and does not leak away. For the storage of CO2 in CCS (Carbon Capture and Storage), it is also of prime importance that the carbon remains within the intended reservoir. Both applications thus require that the integrity of bounding layers is not breached. Induced seismicity can also be an unwanted result of injection operations. Several geothermal field trials have been suspended or terminated because of unwanted induced earthquakes (Grigoli et al., 2018; Vörös & Baisch, 2022; Zang et al., 2014). At the same time, fault reactivation is sometimes required to ensure adequate transmissivity, e.g. in Enhanced Geothermal Systems (Majer et al., 2007). The concept of soft stimulation was introduced as a means of optimization of these two requirements (Hofmann et al., 2019). For balanced injection into porous sandstone formations seismicity has not yet been observed. However, because the number of projects is still small and duration of operations is short, it is important to assess fault reactivation potential for these types of operations as well.