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Geofluids

Volume 2017, Article ID 4653278, 15 pages

https://doi.org/10.1155/2017/4653278

## On the Role of Thermal Stresses during Hydraulic Stimulation of Geothermal Reservoirs

Center for Hydrogeology and Geothermics (CHYN), Laboratory of Geothermics and Geodynamics, University of Neuchâtel, Neuchâtel, Switzerland

Correspondence should be addressed to Gunnar Jansen; hc.eninu@nesnaj.rannug

Received 30 March 2017; Accepted 18 May 2017; Published 28 June 2017

Academic Editor: Weon Shik Han

Copyright © 2017 Gunnar Jansen and Stephen A. Miller. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Massive quantities of fluid are injected into the subsurface during the creation of an engineered geothermal system (EGS) to induce shear fracture for enhanced reservoir permeability. In this numerical thermoelasticity study, we analyze the effect of cold fluid injection on the reservoir and the resulting thermal stress change on potential shear failure in the reservoir. We developed an efficient methodology for the coupled simulation of fluid flow, heat transport, and thermoelastic stress changes in a fractured reservoir. We performed a series of numerical experiments to investigate the effects of fracture and matrix permeability and fracture orientation on thermal stress changes and failure potential. Finally, we analyzed thermal stress propagation in a hypothetical reservoir for the spatial and temporal evolution of possible thermohydraulic induced shear failure. We observe a strong influence of the hydraulic reservoir properties on thermal stress propagation. Further, we find that thermal stress change can lead to induced shear failure on nonoptimally oriented fractures. Our results suggest that thermal stress changes should be taken into account in all models for long-term fluid injections in fractured reservoirs.

#### 1. Introduction

One of the primary driving mechanisms for permeability creation in engineered geothermal systems (also known as enhanced geothermal systems), or EGS, involves shear failure induced by fluid injection at high pressures. In environments with low differential stress, tensile fractures may develop if the injection pressure exceeds the minimal principal stress (e.g., fracking). The injection of cold water into a reservoir at substantially higher temperature also induces thermal stress changes that contribute to the overall evolution of the local stress and failure potential. This rapid cooling of the reservoir can lead to thermal cracking and thus further enhance permeability [1–4], but thermal fracturing, fracture propagation, or fracture reactivation may also contribute to premature cold water breakthrough into producing wells.

The basis for EGS is usually geothermal plays of the “hot dry rock” type where the available water in the porous medium is considered negligible. These conditions are found primarily in metamorphic or igneous terrains with low permeability and porosity containing fractures and faults that provide the major pathways for fluid flow. In geothermal energy systems, the fracture’s surfaces serve as the main heat exchanger. Clearly, preexisting, critically stressed, and optimally oriented fractures provide the most favorable conditions for enhancing permeability of EGS [5, 6].

In this paper, we focus on the role of thermal stresses during cold fluid injection and stimulation of an EGS site. Of special interest, here is the interplay of hydraulic and thermally induced stresses. The processes involved in permeability creation during hydraulic stimulation act on different timescales. While the poromechanical coupling is active throughout the injection, its dominance over thermomechanical effects depends on the state of the injection. Thermomechanical coupling plays a particularly important role during prolonged periods of injection (weeks to years) because the variation of injectivity with injection water temperatures can be attributed to thermal stress [7].

A major concern in EGS is induced seismicity at levels above that tolerated by the local population, in either frequency or magnitude. Usually induced seismic events are attributed to the change in effective stress due to the change in fluid pressure [8–10]. However, thermal stress also significantly contributes to induced seismicity in petroleum and geothermal fields [7, 11, 12]. Stark [12] found that, in the Geysers geothermal field in northern California, USA, half of the measured earthquakes appear associated with cold water injection.

In this paper, we present the theoretical basis for thermal stresses, evaluate the temperature distribution during injection in a borehole, and determine a modeling framework for evaluating the influences of thermal stress generation and propagation in a hypothetical reservoir. We describe the numerical method and present results of numerical experiments focusing on the influence of thermal stress on permeability, fracture orientation, and failure potential. We discuss the results in terms of thermal influence on induced seismicity and reservoir characteristics.

#### 2. Theory

Here we present the mathematical basis for the formulation of thermal stresses. In addition, the temperature profile in an injection well is considered because this has a significant impact on the initial conditions of the numerical simulations.

##### 2.1. Mathematical Description of Thermal Stress

A body will change its shape and/or volume when exposed to a temperature change . This change is called* thermal strain* and can be expressed aswhere is the coefficient of linear thermal expansion in 1/K. In most materials, is positive and on the order of . In isotropic materials, the thermal strain acts only on the normal strains with the same magnitude. If the body’s deformation is restricted, as it would be the case for a small volume inside a rock mass, the strain results in thermal stress.where is the elastic stiffness tensor of the material. If we restrict ourselves to isotropic conditions, the thermal strain has only normal components with equal magnitude in which case we can simplify the previous expression towhere is Young’s modulus (Pa) and Poisson’s ratio (—). It is important to note that (3) is only nonzero for the three normal stresses . It is immediately obvious that larger temperature differences will result in higher thermal stress changes. Additionally, the thermal stress is positive (relative compression) if the temperature difference is positive (), and if the temperature difference is negative, the thermal stress is negative (relative tension). The magnitude of thermal stress can change widely depending on the material. Assuming a constant thermal expansion coefficient and fixed temperature difference of , the resulting thermal stress for an elastic sandstone ( = ~20 GPa) is smaller than the resulting thermal stress in a typical granite ( = ~50 GPa). The granite would undergo a stress change of 1 MPa in this case compared to a 0.4 MPa stress change in the sandstone.

Thermal expansion coefficients are well-constrained by experiments and show only minor influences of temperature and pressure on the thermal expansion coefficients [13, 14]. Cooper and Simmons [15] attributed some of the change in the thermal expansion coefficient to the formation of microcracks by differential expansion of mineral grains. Considering the small magnitude in the change of the thermal expansion coefficient compared with the order of magnitude expected in temperature and pressure change, it is a valid assumption that the thermal expansion coefficient is constant.

In the following, we assume that the thermal stress is independent of the fluid pressure and the in situ stress state of the rock. Thus, the resulting stress can be obtained by superposition of the effective stress () and the thermal stress. Changes in the in situ stress of the rock are negligible on the timescales of interest for hydraulic stimulation. Considering only stress changes resulting from pore pressure and thermal expansion, we can formulate the total stress change asClearly, other stress contributions as slip-induced stresses and stresses induced by chemical reaction have to be considered in a general case. However, for reasons of simplicity, we restrict ourselves to only pore pressure and thermally induced stress changes.

##### 2.2. Induced Shear Failure Potential

Induced shear failure potential is estimated by a Mohr-Coulomb failure condition. We restrict ourselves to a cohesion-less material with a friction coefficient of . A fracture segment is able to slip and is thus categorized as “potential slip” if the following condition is met:The effective normal stress is defined aswhere is the normal stress, is the fluid pressure, and the thermal stress as introduced in the previous section. The effective normal stress and shear stress acting on a fracture segment arewhere and are the maximum and minimum principal stresses acting in the far field and is the angle between and the fracture segment measured from the normal to the plane.

The poroelastic deformation of the fractured reservoir during the injection as well as the deformation due to fracture slip is not included in the present model. Consequently, this simple model does not predict magnitudes or estimation of the amount of slip but rather identifies when a frictional failure condition is met, similar to other approaches in modeling EGS [9, 10].

##### 2.3. Heat Distribution in a Geothermal Well

The temperature inside an injection well is not constant with depth. The injected water is heated by the rock mass surrounding the borehole while moving downwards through the borehole. Although the heat distribution in geothermal boreholes can be measured, in many cases it is still useful to describe it mathematically. Such calculations can be used in numerical simulations and aid the drilling crews during their operation. In most cases, description of well bore heat transmission is based on a well bore heat balance equation. Most of the literature is based on the initial work of Ramey [16] in which they derived the temperature distribution in a well used for hot fluid injection. The work was later enhanced by the rate of heat loss from the well to the formation by Ramey [17]. Recent work from Hagoort [18] reevaluated Ramey’s classical work and found that it is an excellent approximation.

Following Satman and Tureyen [19], the temperature in an injection well into which a single-phase fluid is injected is given byHere, is the distance downwards from surface in meters, is the geothermal gradient in , is the surface temperature in , and is the temperature in of the injected fluid. is a variable defined aswhere is the mass flow rate in ks/s, the heat capacity of the fluid (assumed constant), and the thermal conductivity of the formation (also assumed constant with depth). The dimensionless function describes the transient heat transfer to the formation. There are a number of different formulations for function available. Kutun et al. [20] provide a simple formulation:which is based on a best curve fit of the data provided by Ramey [16] and Ramey [17, 21]. According to Satman and Tureyen [19], it is accurate within 1% for the relevant timescales. In (10), is a dimensionless time defined bywhere is the mean thermal diffusivity of the formation in and the well radius in meters.

A detailed review on the methods to describe well bore heat distributions, prevalent assumptions, and different formulations for the transient heat transfer function can be found in Satman and Tureyen [19].

##### 2.4. Heat Distribution in a Geothermal Well

Based on (8) to (11), the general characteristics of fluid injection in the well are presented and examined in detail. The model parameters are given in Table 1. Figure 1 shows the temperature distribution with depth of well bore temperature during prolonged fluid injection. The profiles are plotted for different injection times: 1 d, 10 d, 30 d, and 365 d. The geothermal gradient shown as a dashed line represents also the static (long term) temperature distribution in the well bore. It is clearly visible that it is not a static profile but contains a dynamic evolution with time. During the first days of injection, the temperature profile changes most rapidly. After about 10 days of continuous injection, the rates of the temperature profile change decrease. After 365 days of continuous injection, the bottom hole temperature has decreased from after 1 day of injection to in the case of an injection rate of . When the injection rate is lower at , the temperature decreases from initially after 1 day of injection to after one year. This demonstrates the highly dynamic temperature distribution during injection with respect to time and injection rates.