Geomechanical Integrity of Offshore Oil Reservoir During EOR-CO₂ Process: A Case Study

Abstract

The aim of this work was to investigate the evolution of the mechanical integrity of the selected offshore oil reservoir during its life cycle. The geomechanical stability of the reservoir formation, including the caprock and base rock, was investigated from the exploitation phase through waterflooding production to the final phase of enhanced oil recovery (EOR) with CO₂ injection. In this study, non-isothermal flow simulations were performed during the process of cold water and CO₂ injection into the oil reservoir as part of the secondary EOR method. The analysis of in situ stress was performed to improve quality of the geomechanical model. The continuous changes in elastic and thermal properties were taken into account. The stress–strain tensor was calculated to efficiently describe and analyze the geomechanical phenomena occurring in the reservoir as well as in the caprock and base rock. The integrity of the reservoir formation was then analyzed in detail with regard to potential reactivation or failure associated with plastic deformation. The consideration of poroelastic and thermoelastic effects made it possible to verify the development method of the selected oil reservoir with regard to water and CO₂ injection. The numerical method that was applied to describe the evolution of an offshore oil reservoir in the context of evaluating the geomechanical state has demonstrated its usefulness and effectiveness. Thermally induced stresses have been found to play a dominant role over poroelastic stresses in securing the geomechanical stability of the reservoir and the caprock during oil recovery enhanced by water and CO₂ injection. It was found that the injection of cold water or CO₂ in a supercritical state mostly affected horizontal stress components, and the change in vertical stress was negligible. The transition from the initial strike-slip regime to the normal faulting due to formation cooling was closely related to the observed failure zones in hybrid and tensile modes. It has been estimated that changes in the geomechanical state of the oil reservoir can increase the formation permeability by sixteen times (fracture reactivation) to as much as thirty-five times (tensile failure). Despite these events, the integrity of the overburden was maintained in the simulations, demonstrating the safety of enhanced oil recovery with CO₂ injection (EOR-CO₂) in the selected offshore oil reservoir.

1. Introduction

One of the most important issues in the field of industry and energy in Europe at the moment is the reduction in the CO₂ footprint. The most effective way to reduce the CO₂ that is released during industrial processes and energy production is to store carbon in subsurface structures [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. Sequestration can take place in water-saturated structures (aquifers) or in depleted hydrocarbon reservoirs (crude oil and natural gas). Due to the relatively lower costs associated with existing infrastructure and known storage capacities, depleted hydrocarbon reservoirs are increasingly being considered as sites for future storage of large amounts of carbon dioxide [23,24,25,26,27,28,29,30,31,32,33]. In improved oil recovery (IOR)/enhanced oil recovery (EOR) production methods, cold water or CO₂ is injected into the reservoir formation to displace additional oil. When the temperature of the injected fluid is much lower than that of the surrounding reservoir rock, poroelastic and thermoelastic phenomena are triggered in the geological structure [22,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48]. These processes contribute to changing the in situ stress tensor to varying degrees throughout the reservoir structure [49,50,51,52,53,54]. During water and/or CO₂ injection, conditions favorable to critically stressed discontinuities can occur more rapidly, as can new failure. Such changes in rock integrity may help to accelerate the unsealing of the geologic structure by opening escape pathways for CO₂ [2,3,4,5,6,7,8,9,10,11,24,25,26,27,28,29,30,31,32,33,35,36,37,38,39,49,50,51,55,56,57,58,59,60]. The proposed work will analyze the geomechanical stability of an offshore oil reservoir and determine the impact of geomechanics on IOR/EOR processes involving water and CO₂ injection.

Studies of poroelastic stresses associated with thermal effects have been described quite extensively in the scientific literature over the past two decades. Oil and gas companies have recently engaged in research on the injection of water and CO₂ into oil reservoirs, including waterflooding, EOR-CO₂, or carbon capture sequestration (CCS), which are supported by modeling and numerical simulations. The coupling of reservoir and geomechanical simulations is crucial for solving problems related to wellbore stability, hydraulic fracturing, and injection- or production-induced deformations on the seafloor. This approach is mandatory when the coupling is strong, and therefore, the changes in porosity and permeability cannot be explained by the compressibility of the rock alone [34]. In subsurface structures, the process of EOR-CO₂ can trigger a series of coupled physical and chemical processes that lead to changes in the in situ stress field and rock deformation [1,23]. These changes, generally caused by reservoir overpressure and temperature drop near the injection wells, have led to the following processes: uplift of the seafloor, induced microseismicity, reactivation of faults and fractures in the reservoir, and reactivation of fractures in the overburden, leading to the development of CO₂ leakage paths [35,55,56,57,58]. In addition, an increase in permeability due to thermal unloading is usually observed in the vicinity of wells into which cold fluids are injected [23]. The results of some previous studies were highly dependent on the assumptions made and the numerical method chosen, where only the pressure was coupled iteratively [2,24,25,26,27,36,59], or by evaluating single-fluid flows [3]. Jabbari and his team [28] have shown that the interactions between reservoir flow and geomechanics can help to model the stresses and strains affecting the EOR-CO₂ process in tight reservoirs. The efficiency of EOR-CO₂, especially CO₂- water alternating gas (WAG) and CO₂- simultaneous water alternating gas (SWAG), has been mentioned as an economic method of CO₂ utilization in the context of implementing other technologies, including enhanced gas recovery (EGR), enhanced water recovery (EWR), and enhanced geothermal systems (EGS) [29,30,31]. According to Chinese experience, reservoir simulation technology can be successfully applied to carbon capture, utilization, and storage (CCUS) and CO₂-EOR projects in heterogeneous reservoirs with relatively low permeability [4]. It has been found that the petrophysical and geomechanical heterogeneity of the overburden increases the volume of CO₂ leakage and leads to the largest vertical displacements [5]. However, when two-way coupled simulations are considered, both pressure and temperature effects lead to a reduction in fracture stability [1,6,34,37]. The coupled thermo-hydro-mechanical (THM) simulations also aimed to analyze the potential of the geothermal reservoirs. It was found that thermal drawdown increases the long-term permeability of fractured geothermal reservoirs [49,50,51]. In case of deep saline aquifers, it is worth considering pressure and temperature variations to mitigate geomechanical problems during CO₂ injection [7]. Vilarrasa et al. [8] point out that the non-isothermal effect plays a key role in the whole CCS project, including CO₂ transport. Among the thermal effects, they distinguish the Joule–Thomson cooling effect, endothermic water evaporation, and exothermic CO₂ dissolution, which lead to coupled thermo-hydro-mechanical-chemical processes. Accordingly, the injection process can be economically optimized if the injection conditions are similar to those of CO₂ transport. However, coupled THM simulations of steam-assisted gravity drainage (SAGD) processes can be very time-consuming if permeability variations due to stress changes are taken into account [38]. An important postulate has already been formulated regarding the importance of geomechanics for the decision-making process in all phases of hydrocarbon exploration and exploitation [35,39]. It has already been suggested that induced seismicity should be minimized in order to achieve the successful implementation of geoenergy projects [9]. It has been recommended to monitor overpressure [10] and thermal drawdown [11] to prevent potential reservoir failure that could lead to leakage of stored CO₂ into the caprock and eventually into the atmosphere. Other researchers [32] point out the need to consider miscibility and geomechanics in the uncertainty analysis of simulation results in order to increase oil productivity from hydraulically fractured wells by CO₂ injection. The unique approach of the storage-based CO₂-EOR method, which utilizes dimethyl ether (DME) to enhance the solubility of CO₂ in oil and achieve a net-zero CO₂ emission agenda, has been recommended previously [33]. Ye et al. conducted a numerical study on the geomechanical behavior of CO₂-EOR and CO₂ sequestration to investigate the phenomena of surface uplift and subsidence [60]. Recently, Qiao et al. [40] developed a custom finite element method (FEM) code to overcome the challenges of coupled geomechanical simulations of giant naturally fractured reservoirs. Some researchers point out that it is necessary to use 1D geomechanical earth models (MEM) to build reliable 3D-MEMs at the reservoir scale before conducting simulation studies for CCUS and CO₂-EOR [12,35,41,42,43].

During the literature review on the scientific problem described in this paper, it was noticed that coupled hydro-thermo-mechanical (THM) simulations have a relatively poor representation in solving problems in the oil and gas industry with full-field geomechanical models [1,9,23,28,35,37,38,49,50,51,55,56,57]. Thermally induced stresses have a key impact on the geomechanical stability of realistic hydrocarbon structures, as well as on the geological risks associated with depletion/re-pressurization operations [6,20,34,37]. Therefore, other cited research examples are relevant to the topic but have certain shortcomings that this article seeks to address. These include following: reservoir simulations coupled with geomechanics, but considering only pressure changes, which leads to the underestimation of stability loss issues [2,3,5,10,12,13,14,15,16,17,18,19,20,24,25,26,27,32,35,36,40,44,52,53,54,55,58,59,60,61,62], including coupled simulations on simple geometry artificial meshes (insightful basic research, but not a case study) [2,5,15,32,40,60], high-uncertainty three-dimensional (3D) geomechanical models due to lack of data to calibrate mechanical earth models at wells (1-D MEMs), the requirement for an additional commercial or open-source geomechanical simulators, and even the high computational demand [6,10,13,14,15,16,17,18,19,20,25,26,27,36,44,61,62]. Both Eclipse and Petrel are widely used in the oil and gas industry. Eclipse reservoir simulator is appreciated for its robustness, numerical precision, and efficiency in predicting pressure, temperature, and fluid saturation distributions. To address this problem, the author proposed an approximate solution that is simpler than other works for the geomechanical state and its interaction with the reservoir simulator. The numerical method presented in the article allows for the assessment of the geomechanical state within the framework of the adopted assumptions, using closed-form equations, which makes the solution very efficient and adaptable and extends the capabilities of the Eclipse platform. In general, the described approach relies on two computational procedures: first, the reservoir property distributions are solved numerically in Eclipse, and second, the geomechanical state is approximated analytically in the Petrel environment. In this case, Eclipse’s capabilities were extended to include geomechanical state assessment by incorporating user-defined Petrel workflows. The use of this approach eliminated the need to use a geomechanical simulator (e.g., Visage) and significantly increased the time efficiency of the reservoir simulation. This solution has not been previously mentioned in the literature.

Geological Setting

The author selected one of the offshore oil fields in the Baltic Sea to study geomechanical integrity during the EOR-CO₂ process. That specific subsurface structure represents an ideal target for geomechanical stability analysis (using a non-isothermal approach) within the framework of exemplary but realistic prediction operational strategies. From a tectonic point of view, the structure is located in the Baltic Syneclise, an extensive monocline filled with sediments from the bay-shaped subsidence of the basement of the ancient Precambrian platform, which opens to the southwest. The analyzed oil field is characterized by a relatively simple geological structure, in which the geological strata have a slight dip. The structure of the reservoir was formed in the shape of an anticline as a result of the deformation of a monoclinal sedimentary complex caused by faulting. The conditions of sedimentation within the southern margin of the Baltic region, during the Middle Cambrian (shallow epicontinental basin), had a significant influence on the facies variability of the reservoir horizon.

The Middle Cambrian facies are characterized by the predominance of sandstone and mixed sandstone–mudstone material. In the reservoir series, five facies associations were identified, including coastal sandstones, regressive sandstone heteroliths, transgressive sandstone heteroliths, mudstones, and mudstone heteroliths. The deposited material was repeatedly washed out and redeposited, resulting in the formation of quartz sandstone layers of the Paradoxides paradoxissimus horizon. The quartz sandstones are considerably thick, relatively monomineralic, and strongly rounded and sorted. In the area of the neighboring offshore oil field, this sandstone series forms the best reservoir horizon with a porosity of almost 20% and a relatively high permeability. The reservoir formation is cut off from the east by a regional fault zone.

From above, the reservoir rock is sealed by an Ordovician clay–carbonate complex several tens of meters thick that transitions upwards into Silurian clay sediments, which form a regional seal. The lower part of the Ordovician complex represents caprock region of the reservoir model. The reservoir interval is also sealed by the underlaying Eccaparadoxides oelandicus horizon, consisting of clay–sand sediments, which are developed as mudstones and mudstones with (irregular) intercalations of clayey sandstones. They represent the base rock region of the reservoir model, as well as the lower boundary of the reservoir zone is the oil–water contact. In the central and southern parts, the lower boundary is assumed to be the elevation of the oil–water contact.

2. Method

In order to fulfill the task set in the topic of the study, the author created a hydro-thermal (flow) reservoir model of the selected geological structure. The lateral section of the flow model was optimized to take into account the boundary conditions for the cross-flows of the fluids. The reservoir zone model was extended vertically to include the underlying strata and the overburden, and these two zones formed the seal of the oil reservoir. The geomechanical state calculations were performed directly on the flow model grid. The wells were added to the flow model, including those injecting cold water and carbon dioxide in supercritical state (scCO₂) into the hot rock formation. The most realistic operating conditions of the oil reservoir were assumed, taking into account the history of oil production and injection scenarios, so that the geomechanical state reflected the actual conditions of the reservoir.

2.1. Physical Model

Physico-mathematical modeling of offshore oil reservoirs requires defining the interactions between produced/injected fluids and the deforming reservoir rock. These processes trigger a geomechanical response that induces changes in transport properties (porosity and permeability). In general, the numerical model refers to the fundamental equations of thermo-poroelasticity, which can be divided into the following subcategories: constitutive equations of mechanical equilibrium (changes in total stress and changes in fluid content), fluid flow equation (Darcy’s law), heat transfer equation through the rock matrix (Fourier’s law), and the diffusion equation [52]. The continuity equation of incompressible fluid transport is commonly known as Darcy’s law. The single-fluid flow relationship, taking into account the Darcy velocities in the radial ($v_r$), circumferential ($v_{\theta }$) and vertical ($w$) directions [52], can be expressed as follows:

$${\displaystyle \frac{𝜕{\rho }_w}{𝜕t}}+{\displaystyle \frac{𝜕\left({\rho }_{w}r{v}_r\right)}{r𝜕r}}+{\displaystyle \frac{𝜕\left({\rho }_{w}r{v}_{\theta }\right)}{r𝜕\theta }}+{\displaystyle \frac{𝜕\left({\rho }_{w}w\right)}{𝜕z}}=0.$$

(1)

The diffusion equation of pressure is a derivative of pore pressure change through time, as well as the expansion of porous rock and hydro-thermal expansion [53], as presented below:

$${\displaystyle \frac{k}{\mu }}{\nabla }^{2}P={\displaystyle \frac{1}{M}}{\displaystyle \frac{𝜕P}{𝜕t}}+\alpha {\displaystyle \frac{𝜕{\epsilon }_{kk}}{𝜕t}}-{\beta }_m{\displaystyle \frac{𝜕T}{𝜕t}},$$

(2)

where $M={\displaystyle \frac{2G\left(v_u-v\right)}{{\alpha }^2\left(1-2v\right)\left(1-2v_u\right)}},{\beta }_m=\alpha {\beta }_T+\varphi \left({{\beta }_f-\beta }_T\right)$.

The governing equation of the heat conduction and total energy conservation is known as Fourier’s law [45]. The diffusion of temperature is a function of total heat capacity of the rock–fluid system (${\left({\rho }_c\right)}_t$) and a derivative of temperature change through time ($𝜕T/𝜕t$), as follows:

$${\left({\rho }_c\right)}_t{\displaystyle \frac{𝜕T}{𝜕t}}-{\displaystyle \frac{1}{r}}{\displaystyle \frac{𝜕}{𝜕r}}\left(k_{t}r{\displaystyle \frac{𝜕T}{𝜕r}}\right)-{\displaystyle \frac{1}{r^2}}{\displaystyle \frac{𝜕}{𝜕\theta }}\left(k_{t}r{\displaystyle \frac{𝜕T}{𝜕\theta }}\right)-{\displaystyle \frac{𝜕}{𝜕z}}\left(k_t{\displaystyle \frac{𝜕T}{𝜕z}}\right)-q_{t}r=0.$$

(3)

The mechanical equilibrium is a function of total stress tensor (${\sigma }_{i,j,j}$) and body forces ($f_i$) [52], as shown below:

$${\sigma }_{i,j,j}+f_i=0.$$

(4)

The change in total stress ($\Delta {\sigma }_{ij}$) can be rewritten by incorporating elastic properties (G, K, v) and changes in diagonal components of strain ($\Delta {\epsilon }_{ij}$), volumetric strain ($\Delta {\epsilon }_{kk}$), and also changes in poroelastic (${\Delta \sigma }^P$) and thermoelastic component ($\Delta {\sigma }^T$) of stress along the diagonal directions [53]:

$${\Delta \sigma }_{ij}={2G\Delta \epsilon }_{ij}+{\displaystyle \frac{2Gv}{1-2v}}{\Delta \epsilon }_{kk}{\delta }_{ij}-{\Delta \sigma }^P{\delta }_{ij}+\Delta {\sigma }^T{\delta }_{ij},$$

(5)

where ${\Delta \sigma }^P=\alpha \left(S_{w}P+S_{o}P+S_{{CO}_2}P\right),{\Delta \sigma }^T={\displaystyle \frac{{\beta }_T·E·\Delta T}{1-2v}}$.

If we assume that the bulk forces resulting from the flow of a non-isothermal fluid through isotropic porous media with small deformation are neglected, the total stress changes are then influenced by variations in pore pressure (ΔP) and temperature (ΔT) only. The THM simulations consider proportional heat transfer through porous media to specific fluid content. The variation in fluid content in three-phase flow per unit of volume of porous rock (${\zeta }_{i=1,2,3}$) is a summation of volumetric stress (${\sigma }_{kk}$), poroelastic response, and thermal expansion, as shown below:

$${\zeta }_{i=1,2,3}={{\displaystyle \frac{\alpha }{3K}}\sigma }_{kk}+\sum _{n=1}^3{c}_{n}P-S_i\varphi \left({{\beta }_f-\beta }_T\right)\Delta T,$$

(6)

where $K={\displaystyle \frac{2G(1+v)}{3(1-2v)}},B={\displaystyle \frac{3(v_u-v)}{\alpha \left(1-2v\right)\left(1-2v_u\right)}}.$

2.2. THM Coupled Simulations

The numerical model presented in this article is conducted by performing two types of calculations that are solved separately: hydro-thermal flows in the commercial Eclipse^TM simulator (finite-difference equations) and geomechanical state calculations in user-defined Petrel^TM workflows, and both are coupled in the Petrel^TM interface. The coupled THM model is a product of integrating equations of linear elasticity for isotropic material (Hook’s law), fluid flow through porous media by seepage (Darcy’s law), and heat transfer by conduction (Fourier’s law). As mentioned earlier, the body forces were neglected due to the fact that, in reality, a reservoir is bounded by a large volume of low-compressibility rock from all directions, and rock–fluid systems produce very low strains. It was also considered in this paper that the reservoir model was initially in a state of stress–strain equilibrium, and that upcoming changes in the geomechanical state (${\Delta \sigma }_{ij},{\Delta \epsilon }_{ij},{{\Delta \sigma }_{kk},\Delta \epsilon }_{kk}$) were influenced by changes in pressure (ΔP) and temperature (ΔT). The geomechanical state assessment presented in this work is based on the Eclipse^TM simulator results (pressure and temperature changes between time intervals) and is calculated using approximating equations in a closed-form to determine changes in diagonal components of both stress and strain tensors, as follows (also found in

Table A5. Average geomechanical properties of the integrated model.

Property	Reservoir	Caprock	Base Rock	Unit
Young’s modulus, $\mathrm{E}$	46.7	64.7	58.4	GPa
Bulk modulus, $K$	33.7	52.2	46.7	GPa
Poisson’s ratio, $v$	0.27	0.29	0.29	-
Compressive strength, ${\mathrm{q}}_{UCS}$	67.3	82.6	82.8	MPa
Tensile strength, ${\mathrm{T}}_0$	−7.6	−9.3	−9.4	MPa
Cohesion, $\mathrm{c}$	11.4	12.0/5.0 *	12.0	MPa
Biot coefficient, $\mathsf{\alpha }$	0.72	0.54	0.54	-
Friction angle, ${\mathsf{\phi }}_{AIF}$	52.0	49.5	57.7	°
Dilation angle, $\mathsf{\phi }\mathrm{’}$	33.3	36.9	36.9	°
Failure criterion	C-M, vM	C-M, vM	C-M, vM	-

Legend: C-M—Coulumb–Mohr failure criterion, vM —von Mises failure criterion, *—cohesional fractures in caprock carbonate complex.

and discussed in detail in Appendix D):

$${\sigma }_{ij}={\sigma }_{ij,0}-\Delta {\sigma }_{ij}={\sigma }_{ij,0}-\left(\Delta {\sigma }^P+\Delta {\sigma }^T\right).$$

(7)

First-order changes are those caused by a temperature drop in the vicinity of the injection wells, but their extent is local and depends mainly on the thermal properties of the injected fluid and rock [38,51]. The temperature effects are partially compensated by second-order changes resulting from an increase in reservoir pressure, and these changes affect the rocks at the reservoir scale [9,23]. The evolution of the geomechanical state of the rock in the reservoir, accompanied by changes in the thermodynamic conditions of the fluids in the reservoir, can accelerate the escape of CO₂ through the fault zones and the caprock. The analysis of the geomechanical integrity of the reservoir was carried out, taking into account elastic and plastic deformations. It was investigated that elastic deformations influence the transport properties only to a small extent. Therefore, plastic deformation is considered to be the main cause of gas leakage, as it creates an optimal environment for the reactivation of fractures and for rock failure. The study of the impact of geomechanical state on reservoir stability during production history and forecast was carried out using a numerical method, combining reservoir fluid flow modeling and geomechanical effects. The performance of the oil reservoir, due to the evolution of rock transport properties during its life cycle, was also investigated and presented in Section 5.

The applied approach for coupled simulations is unique and differs in many aspects from the results previously presented in the literature [26,27,51,52]. First, it assumes an effective two-way coupling without using a geomechanical simulator. Secondly, the plastic behavior is considered to determine the failure as well as the changes in the basic geomechanical properties with temperature. The described method integrates the results of the fluid flow and thermal simulations with the results of the analytical calculations of the geomechanical state using a semi-automatic two-way coupling approach, which allows the results to be obtained in a much shorter time [21,22,46,51]. As a final result of these simulations, the author created a simulation model of an offshore oil reservoir using an effective hydro-thermo-mechanical (HTM) coupling. The geological modeling as well as the geomechanical calculations were performed with special workflows developed in a Petrel environment and through reservoir flow simulations with Eclipse.

IOR and EOR methods usually involve the injection of cold water and CO₂ at supercritical conditions that are much colder than the reservoir rock, leading to thermo-poroelastic phenomena [1,6,9,10,11,34,37]. The influence of both poroelastic and thermoelastic effects on geomechanical stability were investigated in detail, including fluid dynamics during the operational cycle of the offshore oil reservoir formation. In this study, the numerical solution was adapted to evaluate the scientific problem of oil formation integrity during cold fluid injection. The fluid flow and heat transfer simulations were effectively coupled with equations corresponding to stress–strain tensor changes. By combining a hydrothermal flow model and a large-scale geomechanical model in an integrated dynamic model that used a reduced grid volume, a significant increase in computational efficiency was achieved with a slight decrease in numerical accuracy [26,27,47,51].

The dynamic simulation environment presented in this study assumed variable characteristics based on the actual operating cycle of the offshore oil reservoir, including an increasing number of production and injection wells and variable production and injection rates. Injection fluid temperature and downhole production pump pressure were treated as constant factors. A reservoir formation consisting of a rock matrix with natural fractures is continuously subjected to elastic deformations until the fractures are reactivated or the rock fails. The numerical method is characterized by the reciprocal linking of hydrothermal flow simulations and geomechanical state calculations, which lead to modifications of the rock transport properties [48]. The numerical procedure begins with an Eclipse simulation to generate initial distributions of reservoir properties (pressure, temperature, and fluid saturation). Then, for this point in time, the geomechanical state is calculated to obtain initial stresses and strains as a reference for further changes. In the next step, the Eclipse simulator proceeds to calculate reservoir property distributions for subsequent time steps, up to the first coupled time step (at the end of the first year). The coupling process involves calculating stress and strain changes based on pressure and temperature changes relative to the initial state. Changes in the geomechanical state generate updates to distributions of transport properties (porosity and permeability), which are implemented in the next time step of the Eclipse simulation (at the beginning of the second year). After n-time steps between couplings, the Eclipse simulation proceeds to the second coupled time step (at the end of the second year). It is possible to manually define a larger number of coupled time steps to increase the continuity of the geomechanical state assessment. It was found that a yearly coupled time is sufficient to obtain reasonable results, due to the assumed interdependence between the geomechanical state and continuous pressure and temperature changes. In order to obtain a consistent solution, numerical simulations of the fluid and heat flows are performed, complemented by calculations of the stress and strain tensor at each reported time step. In the case of the hydrothermal model, the modifications of the basic output properties, including pore pressure ($P_p$), temperature ($T$), and fluid saturation ($S_w,S_o,{S_g,S}_{{CO}_2}$), are calculated continuously over a selected time interval ($t_i\to t_{i+1}$). The acceptable disadvantage of this method is the assumption that the changes in the transport properties ($k,\varnothing$) are delayed until the next time step ($t_{i+1}$), since the change in the elastic stiffness tensor ($c^{ijkl}$) must be calculated in advance. The numerical procedure is performed under the control of the Petrel workflow environment. The procedure involves alternating calls of the flow simulations with Eclipse and the geomechanical state computations. A schematic representation of the effective HTM coupling procedure applied to the integrated model for the selected time interval ($t_i\to t_{i+1}$) is shown in Figure 1.

2.3. Evolution of Transport Properties

Under non-isothermal conditions, the spread of the injected fluid in the formation leads to an expansion of the cooled zone around the injection wells. After a certain time from the start of injection, the volume of the cooled rock is less than the volume already saturated with the injected fluid. This effect is directly proportional to the ratio between the heat capacity of the injection fluid and the reservoir rocks. As a result, this phenomenon leads to rapid changes in the geomechanical stability of the reservoir formation. In order to predict and study the plastic deformation of the rock caused by pressure and temperature changes, the geomechanical state is resolved in specific time steps. The magnitude of the changes in the elastic stiffness tensor and the associated changes in the stress ($\Delta \sigma$) and strain ($\Delta \epsilon$) components are calculated on the basis of changes in pore pressure ($\Delta P_p$) and temperature ($\Delta T$). According to the Kozeny–Carman model [63], the solutions related to the changes in the stiffness tensor, with particular attention to the evolution of the volumetric strain ($\Delta {\epsilon }_V$), allow the quantification of the degree of changes in the transport properties ($\Delta k,\Delta \phi$). The change in porosity ($\Delta \phi$) due to variations in volumetric strain ($\Delta \epsilon$) is first determined as shown in Equation (8):

$$\Delta \phi =\alpha ·\Delta {\epsilon }_V$$

(8)

The modified permeability ($k_{i+1}$) is then calculated directly from its initial value ($k_i$) by taking into account the original (${\phi }_i$) and the modified porosity (${\phi }_{i+1}$), as shown in Equation (9):

$$k_{i+1}=k_i·\left({\displaystyle \frac{{{\phi }_{i+1}}^3}{{\left(1-{\phi }_{i+1}\right)}^2}}\right)/\left({\displaystyle \frac{{{\phi }_i}^3}{{\left(1-{\phi }_i\right)}^2}}\right)$$

(9)

As a result, the variations in the transport properties due to elastic deformations are spatially filled on the entire simulation grid. However, the influence of these deformations on the flow dynamics in the rock matrix is relatively small. The resulting permeability may not change significantly compared to the initial value, as the effects of the pressure increase and temperature decrease are not significant. If we consider the isothermal conditions in carbonate formations, the high injection pressures can induce elastic deformations that increase the permeability of the fractures by several orders of magnitude [27].

In naturally fractured reservoirs, the permeability of the fractures is the most important factor influencing the overall permeability. To determine the variation in fracture permeability under different geomechanical conditions, a stress-dependent model was adopted and modified according to the work of Min et al. [64] by combining the effects of normal and shear stress. In this work, a three-stage failure analysis was performed, which included continuous elastic deformations interrupted by plastic deformations such as fracture reactivation and rock failure. Plastic deformations can lead to rapid changes in fracture opening driven by dilatation mechanisms. The changes in fracture permeability ($k_{el,ratio}$) are then a function of the effective normal stress. The mechanism of elastic deformations has only a minor effect on the permeability, as at most a two-fold increase can be observed. The polynomial approximation of the permeability coefficient, which is defined as a function of the effective normal stress, was found based on the previously mentioned model from the literature [64], as shown in Equation (10):

$$k_{el,ratio}=0.00036·{{\sigma }_{n,eff}}^2-0.023·{\sigma }_{n,eff}+1.39$$

(10)

Optimally oriented fractures are those that are more prone to early reactivation. Shear stress induces traction, which leads to a strong permeability response, but only to a limited extent. The observed decrease in effective normal stress below 14 MPa does not lead to a significant increase in permeability, which means that this parameter tends asymptotically to its maximum factor of 16. The limitation of this model is that new fractures are required to further increase the permeability of the rock due to its failure. The concept of predicting changes in the permeability of fractured rock due to reactivation of fractures and formation of new ones was loosely inspired by the modified Barton–Bandis model [65]. The conversion of the effective normal stress to the change in permeability associated with the reactivation of fractures ($k_{re,ratio}$) up to the reactivation limit is given by the following Equation (11):

$$k_{re,ratio}={{-0.054·\sigma }_{n,eff}}^3+0.13·{{\sigma }_{n,eff}}^2-0.943·{\sigma }_{n,eff}+13.56$$

(11)

If we consider the worst-case scenario, where the fractures are not optimally aligned, reactivation starts when the $k_{ratio}$ reaches 1.08 and ${\sigma }_{n,eff}$ drops from the original value of 30 MPa to −10 MPa. In fractured rock masses, failure occurs when the effective normal stress falls below −6 MPa. This is associated with the formation of new fractures and can also multiply the permeability ($k_{fa,ratio}$) by the factor of 35. The relationship between the increase in permeability due to the failure of fractured rock and the opening of new fractures is shown in Equation (12):

$$k_{fa,ratio}=0.0019·{{\sigma }_{n,eff}}^4-0.124·{{\sigma }_{n,eff}}^3-3.01·{{\sigma }_{n,eff}}^2-32.17·{\sigma }_{n,eff}+92.89$$

(12)

Plastic deformation was hypothesized to be a major factor in increasing rock permeability, but it can also lead to the development of potential CO₂ leakage pathways. The schematic plot of permeability variations concerning fractured rocks implemented in the coupled simulation model of the analyzed oil reservoir is shown in Figure 2.

3. Geological Modeling

Structural Modeling

The three-dimensional (3D) structural model of the studied oil field was created based on 3D seismic and well data, including geophysical logs and the results of a special core analysis. The integrated modeling process included the volume of the reservoir formation, supplemented by the overlying caprock and the underlying base rock (Figure 3). The geological model of the analyzed oil field structure was created and supplemented with reservoir properties and thermal and geomechanical parameters. The oil-saturated volume was mapped, taking into account the results of the interpretation of the 3D seismic data, calibrated with the well data, and finally, confirmed with the results of the DSTs and well tests. Based on the parametric model, the fluid flow simulations were initialized, executed, and adjusted to the history.

The total number of grid blocks in the structural model is 1,522,248 (182 × 164 × 51), of which 410,363 are active. A static geologic model of the Middle Cambrian reservoir series was created with a fixed horizontal grid resolution of 75 × 75 m to match the available computational resources. The vertical resolution varied in the range of 1–3 m, with an average of about 1.50 m. The geological model covered a total thickness of about 70 m, of which about 40 m was the reservoir zone, about 15 m was the overburden, and about 15 m was the underlying strata. Water inflow rates were matched using a global grid approach at each well to within 2% of the error, and the total water production from the reservoir was balanced. Therefore, the construction of LGRs around individual wells was not mandatory in this case. In order to correctly reproduce the boundary conditions and reduce consumption of computational resources, including the lateral extent of the numerical aquifers, the horizontal extent of the model was limited to approximately 11.0 × 4.5 km.

The studied oil field is structurally sealed to the east by a fault zone. The western edge of the reservoir model is bounded by a linear no-flow zone mapped based on seismic data. These two sides of the structural model run parallel to each other in a north–south direction and are regarded as edges of the simulation model. However, the eastern fault zone is of regional importance. In the south, the studied oil field is bounded by the oil–water contact. As there are no direct measurements, the location of the northern boundary of the reservoir was approximated by analyzing seismic data in terms of seismic attributes and spectral decomposition. It was assumed that the northern boundary of the reservoir is facies-like. In this study, the classical approach of geological modeling of fault zone architecture was applied. Faults were implemented as part of a structural grid with an appropriate reduction in transmissibility between the blocks associated with the fault plane [66,67,68]. For the purposes of this study, the dislocation model was adopted based on data from the literature [69,70]. The conceptual model of dislocation used in this paper is shown in Figure 3. The chosen structural modeling approach enabled the explicit determination of the geomechanical stability of fault zones during the EOR process.

The structural model selected for this study assumes that the fault zone is divided into the barely permeable fault core and the conductive damage zone due to the occurrence of natural fractures [69]. The fault core is formed by the crushing of rock into a clay fraction and represents an effective barrier perpendicular to the direction of flow. The damage zone surrounding the fault core is a volume of rock traversed by a dense network of natural fractures that have developed close to the slip surface of the fault on both sides [70]. Therefore, the damage zone is characterized by increased permeability along the fault plane. The permeability of the damage zone in a direction perpendicular to the fault surface is usually lower, as most fractures are aligned with the main fault plane. The effectiveness of the fault zone system as a barrier was tested during the history-matching process. The results of history matching and division of the zones in the geological model are shown in Figure 4.

The substantial model configuration related to parameter description is discussed in detail in the Appendix. The petrophysical, geothermal, and geomechanical properties are discussed in subsequent Appendix A, Appendix B and Appendix C. The geomechanical modeling, failure criterion, and boundary conditions for the geomechanical model are expanded in subsequent Appendix D, Appendix E and Appendix F.

4. Initialization of Hydro-Thermal Dynamic Model

The dynamic modeling was initialized based on an integrated oil reservoir model comprising geological, geothermal, and geomechanical models. The starting point of the dynamic modeling was the implementation of the required components representing the equilibrium state of the reservoir. Therefore, the properties of the dynamic model take into account the initial distributions of the reservoir fluids, the transport properties of the reservoir fluid, and the thermodynamic properties of the hydrocarbon fluid. The dynamic model was supported by consistent input data for the initial conditions, including pressure, temperature, and fluid saturation distributions. The initial formation pressure was determined based on DST measurements and well tests in accordance with a hydrostatic gradient of 0.0108 MPa/m and ranged from 23.0 MPa to 25.0 MPa, with an average value of 24.0 MPa. The spatial heat distribution was determined based on a surface temperature of 15 °C and a geothermal gradient of 0.0312 °C/m, calculated from borehole measurements. The resultant temperature ranged from 78 °C to 81 °C, with an average value of 80 °C. The spatial distribution of reservoir fluids was introduced to saturate the geologic structure with oil and water under conditions of hydrostatic equilibrium. In this study, the standard Corey model with a power approximation was used to predict the wetting and non-wetting multiphase flow, considering the following systems: water–oil, oil–CO₂, water–CO₂, as well as a trapping mechanism [71]. Corey curves were calibrated separately for each lithofacies to account for the heterogeneity of flow within the reservoir. Reduced saturations ($S_{rx}$) were calculated using endpoint parameters ($k_{rx,max},S_{x,min},S_{x,max}$), as shown in Equation (13):

$$S_{rx}={\displaystyle \frac{S_x-S_{x,max}}{S_{x,max}-S_{x,min}}}$$

(13)

where $k_{rx}$—relative permeability, $S_{rx}$—reduced fluid saturation, $n_x$—exponent, and $k_{rx,max},S_{x,min},S_{x,max}$—point parameters.

The dependence of the relative permeability coefficients on the reduced saturations is given by Equation (14):

$$k_{rx}=k_{rx,max}·{\left(S_{rx}\right)}^{n_x},(x=w,C{O}_2)$$

(14)

The point parameters were inserted into the model according to data from the literature [72], and their values are given in

Table 1. Relative permeability curve parameters.

Phase	Parameter	Value
water	nw	2
water	Sw,min (=Srw)	0.05
water	Sw,max	0.8
CO2 (water–CO2 system)	nCO2	2
CO2 (water–CO2 system)	SCO2,min (=SrCO2)	0.22
CO2 (water–CO2 system)	S CO2,max	0.8

.

The realistic spatial distributions of the fluids in the oil reservoir were resolved using the hydrostatic equilibrium approach (J-function), according to Leverett [73] and assuming the initial absence of a gas cap. The subdivision into four facies zones was applied to the studied oil reservoir. It was supplemented by seventeen further regions in the central and eastern part of the reservoir, which were characterized by variable water wettability, and a northern region, which was associated with high water saturation. For the indicated regions, the procedure of fitting the Leverett J-function to the geophysical measurements of the water saturation profiles in boreholes was carried out. The general form of Leverett’s J-function was assumed according to Equation (15):

$$J\left({S_w}^{*}\right)=C·{\displaystyle \frac{{\left[1-{\left({S_w}^{*}\right)}^p\right]}^m}{{\left({S_w}^{*}\right)}^n}}=\sqrt{{\displaystyle \frac{k}{\varnothing }}}·{\displaystyle \frac{P_{cow}\left({S_w}^{*}\right)}{{\sigma }_{cow}·\cos \left({\theta }_{ow}\right)}}$$

(15)

where ${S_w}^{*}$—reduced water saturation, $k$—permeability, $\varnothing$—porosity, $P_{cow}$—capillary pressure for water–oil system, ${\sigma }_{cow}$—capillary pressure for water–oil system (25 dyn/cm), and ${\theta }_{ow}$—contact angle for water–oil system (0°).

The thermodynamic model of the black oil reservoir (water and oil saturated with natural gas and CO₂) was created using PVTSim software. The model was characterized by PVT correlations of a number of parameters for the defined fluid components, including density, viscosity, and solubility. The distributions of oil saturation (SOIL), pressure (PRES), and temperature (TEMP) for the initial state (t = 0) and the pre-injection phase (t = 10) are shown in Figure 5 in an exemplary vertical cross-section SW–NE.

As a boundary condition for the flow, two analytical aquifers of the Carter–Tracy type [74] were attached to the side walls of the dynamic model, namely in the north and in the south. The purpose of implementing an infinite-acting aquifer was to create a buffer zone outside the numeric model for the injected fluids during both IOR and EOR phases. This implementation significantly reduced the flow resistance around the injection wells and slowed the associated average reservoir pressure build-up, which was consistent with historical data. The boundaries of the dynamic model, including the top of the caprock and the bottom of the base rock, were considered as barriers preventing the flow of mass and energy.

In the base case, oil production is assumed to be supported by water flooding from the beginning of the reservoir production phase. Cold water is planned to be injected into the reservoir formation at an annual mass rate of 0.43 megatons/year using five wells over a 24-year period. In the alternative case, after eight years of water flooding, the method will be switched to EOR with continuous CO₂ injection into two southern and one western well. It is planned to inject cold fluids (water and CO₂) under non-isothermal conditions through five wells over a 24-year period, including 437 megatons/year of CO₂ through two southern wells and one western well, and 755 tons/day of water through the northern well. Non-isothermal injection conditions are achieved by an initial temperature gradient in the reservoir and a constant injection temperature in the range of 35–80 °C.

The complete set of initial and boundary conditions, as well as the schematic geometry of a coupled dynamic model, are shown in Figure 6.

5. Results Analysis

The numerical procedure was performed using the common structural mesh of the integrated HTM model. Fluid and heat flow simulations were combined with geomechanical state calculations to effectively predict the behavior of the offshore oil reservoir, including the evolution of transport properties caused by PT changes during the EOR process. All simulations that were performed considered realistic non-isothermal scenarios where the temperature of the injected fluid was lower than the reservoir temperature ($T_{inj}=35–70°\mathrm{C}$), except the isothermal base case. The simulation results were documented for all specified time steps.

5.1. Waterflooding and EOR-CO₂ Injection Assumptions

In the waterflooding simulation scenarios, water was injected through four wells at a rate adapted to the local transport properties of the reservoir. In the simulation variants related to CO₂-EOR, injection was performed by a combination of a single waterflooding well in the north and three CO₂ injection wells in the south. For both types of scenarios, the effect of oil sweep was tracked for 35 years, 18 years in the past and 16 years in the forecast. The main objective of the alternative injection program was to investigate the effect of the type of injection fluid on the total oil production of the field. In this work, the relaxation phase was not taken into account, so that the reservoir did not reach the HTM equilibrium state at the end of the simulated period. The IOR/EOR operations were controlled by the results of the geomechanical stability analysis. The standard protocol, which assumed formation stability, was changed when the top of the reservoir caprock failed and the injected gas was able to breach the caprock. Such an event was interpreted as a leak in the geologic structure of the oil reservoir and an inability to continue the IOR/EOR process.

The different operating assumptions were necessary to emphasize the thermal effects that influence the geomechanical stability of the selected oil reservoir. The production wells were controlled by a downhole pressure restriction of 100 bar to maintain the target oil production rates. Injection was performed over the entire interval of the reservoir formation to avoid the problem of increased injection pressure due to the flow resistance of the formation. The maximum wellhead pressure was set at 400 bar, which was intended to prevent excessive fracturing of the rock formations due to the applied overpressure. The maximum injection rate of the group was set at 1.1E6 sm³/d due to the technical capabilities of the waterflooding system. The minimum downhole temperature of the injection fluid was set above 30 °C ($T_{inj,min}=35°\mathrm{C}$) to ensure supercritical conditions of CO₂ flow during injection and to minimize the risk of CO₂ hydrate blockages.

Examples of pressure, temperature, and fluid saturation distributions for the initial state and after 10, 15, 20, 25, 30, and 35 years of the exploitation cycle of the oil reservoir are shown in Figure 7, Figure 8 and Figure 9.

5.2. Analysis of Coupled HTM Simulations

To maximize EOR enhanced oil production by creating an optimal oil displacement front, a configuration of peripheral injection wells was designed. The irregularity of the oil displacement front is consistent with the anisotropy of the reservoir formation’s transport properties, as shown in a comparison of Figure 2 and Figure 4. In some areas of the formation, the extent of oil displacement relative to the size of the CO₂ plume is structurally constrained by both sealing faults and small-scale faults within the formation. In contrast to the expansion of the volume occupied by the injected fluids in the reservoir, symmetry is also observed in the spread of the cooled zone in all horizontal directions. The maximum lateral extent of the cooled zone (after 35 years) was three times greater in cases with waterflooding than in the EOR-CO₂ scenarios, as shown in Figure 8. An exception to this rule can occur if the injection well is located close to the conductive fault. This situation was observed for the injection well in the north (XI-4). As a result, the oil displacement front and the cooled zone expanded rapidly along the fault zone during the first year of the EOR process. In this particular case, unlike the rock volume occupied by the injected water, the cooled zone could not extend far beyond the fault zone. The observed phenomenon of fault cooling is a negative symptom related to maintaining the tightness of the caprock. For this reason, the scenario of CO₂ injection through a borehole in the north was not taken into account in the integrated simulation model.

6. Analysis of the Geomechanical Stability of the Oil Reservoir Structure

The main topic of this article is the evaluation of the geomechanical stability of the studied oil reservoir structure during IOR/EOR-supported oil production. In this context, questions regarding the influence of temperature and pressure on the resulting stress and strain state, as well as mapping the occurrence of rock failure, were raised. In addition to the geomechanical analysis, the elastic strain distributions were also investigated in order to determine the magnitude of changes in the transport properties of intact rock. In the model zones where the Mohr–Coulomb failure criterion was met, a corresponding flag was set for the reactivation or failure event. The author studied five non-isothermal cases (${\Delta T}_{inj}=-10,-15,-25,-35,-45°\mathrm{C}$), as shown in

Table 2. List of simulation scenarios and general geomechanical stability results for injection zones.

Tinj	ΔT	Caprock		Reservoir
°C	°C	React	Failure	React	Failure
80	0	NO	NO	NO	NO
70	−10	NO	NO	NO	NO
65	−15	NO	NO	YES	NO
55	−25	NO	NO	YES	NO
45	−35	NO	NO	YES	NO
35	−45	NO	NO	YES	YES

Legend: T_inj—Temperature of injected fluid, ΔT—Temperature change between current and initial state, React—Reactivation mode, Failure—Failure mode, NO—no events observed, and YES—Reactivation/Failure events observed.

, to verify reservoir stability and caprock tightness. For the most realistic case (${\Delta T}_{inj}=-45°\mathrm{C}$), an additional detailed geomechanical analysis was performed, supplemented by Mohr circle diagrams for each stage of oil production supported by the EOR process.

6.1. Preliminary Results of the Geomechanical State and Stability

The spatial distribution of the diagonal components of both the stress and strain tensors in the zones close to the borehole after the start of the injection process is not uniform. The superposition of poroelastic and thermoelastic effects in the structure of the oil reservoir leads to a considerable change in the geomechanical state compared to the initial conditions. The development of these changes most likely correlates with the increase in the volume occupied by the cooled zone. The application of fluid injection at temperatures far below the formation temperature (${\Delta T}_{inj}=-45°\mathrm{C}$) leads to a strong thermoelastic unloading of both horizontal stress components (${\sigma }_H,{\sigma }_h$) around the injection wells, as documented in Figure 10 and Figure 11. At the end of the well test phase (the first 10 years), a slight decrease in vertical stresses (${\sigma }_v$) can be observed in the central part of the reservoir, which is due to partial depletion. However, in the EOR phase (after the 10th year), the injection of cold water or scCO₂ has no significant effect on the vertical stress component, as can be seen in Figure 12.

The propagation of the cooled zone also led to a local decrease in the magnitudes of the horizontal diagonal components of the strain tensor (${\epsilon }_{xx},{\epsilon }_{yy}$) in the central part of the model. This is observed mainly in the layers with higher porosity of the geological model due to the more pronounced contraction of the sandstone lithology with decreasing temperature. A similar negative effect to that described above can be observed for the volumetric strain in Figure 13. However, the positive deformation effects in the aquifers surrounding the injection zones are relatively weak (${\Delta \epsilon }_{xx}=1\mathrm{m}\mathrm{m},{\Delta \epsilon }_{yy}=1.5\mathrm{m}\mathrm{m},{\Delta \epsilon }_{zz}=1.5\mathrm{m}\mathrm{m}$). The negative thermoelastic effects cause a significant compensation of the deformations in the zones around the injection wells (${\Delta \epsilon }_{xx}=0–0.5\mathrm{m}\mathrm{m},{\Delta \epsilon }_{yy}=0–0.3\mathrm{m}\mathrm{m},{\Delta \epsilon }_{zz}=0–0.2\mathrm{m}\mathrm{m}$).

Thermoelastic-induced stress unloading causes a rotation of the original stress tensor, which is accompanied by a rapid transition from the strike-slip stress (SS) regime to the normal fault (NF) regime. The local extent of the occurrence of the NF stress regime can be seen in Figure 14. The observed change in stress state can have a significant impact on the failure mode and the kinetics of the induced dislocation movements. The compressive strike-slip regime favors the reactivation of critically stressed fractures or the development of shear fractures within the reservoir formation and caprock during horizontal displacement. The area affected by a normal faulting stress regime is more prone to the development of tensile fractures or the reopening of existing discontinuities with accompanying vertical rock displacements.

Any type of rock failure would have a significant impact on the flow conditions in the structure of the oil reservoir, as already described in Figure 2. Furthermore, damage to the overburden may result in the reservoir no longer being leak-tight, as potential CO₂ escape paths through the overburden will be created. The modeled temperature drop near the injection wells leads to a rapid failure of the rock in tensile mode, accompanied by the reopening of existing natural fractures. In the scenarios with waterflooding, the extent of the tensile failure zone increases as the IOR process progresses, as does the extent of the cooled zone. Compared to the EOR-CO₂ scenarios, the reservoir formation becomes more stable and the volume occupied by damaged rock decreases, as shown in Figure 15. The process of reactivation of natural fractures follows the directions of the reservoir volume affected by rock failure, but over a much larger area. For example, the area reactivated by the temperature drop thus surrounds the volume of the failed rock around the injection wells. The overpressure-induced reactivation of fractures occurs near the injection wells, mainly north of the southern wells (XI-1, XI-2) and to a lesser extent north of the northern well (XI-4). The failure of the rock in tensile mode increased the permeability of the zones near the injection wells, which led to a decrease in injection pressure due to the decrease in the flow resistance of the formation. The observed geomechanical response of the oil reservoir is consistent with the recorded events in the production history, particularly the accelerated water breakthrough from the south into the XP-4 production well and the increased communication with the aquifers through the reactivated zones.

The geomechanical stability analysis was based on the Coulomb–Mohr failure criterion, taking into account the plasticity function. Based on this assumption, the reservoir formation remained stable during the first nine years of the well-testing phase. The first occurrence of conditions favorable for the reactivation of fractures was observed in the fourth year of the EOR phase in the reservoir interval of all four injection wells (XI-1, XI-2, XI-3, and XI-4). The reactivated area increases as the EOR phase progresses. The reactivation process involves the sealing layers of the underlying base rock, from the eighth and tenth year of injection in the case of injection wells XI-2 and XI-1, with XI-4. Since the start of injection (fourth year of EOR), fractures in the reservoir interval near the XI-4 well were rapidly reactivated by transitioning into the basement and the damage zone of the nearby fault. After eight years of EOR, the entire modeled interval in this well is reactivated, except for the caprock, including the reservoir, base rock, and adjacent fault damage zone. Well XI-3 to the south was the least susceptible to reactivation due to the cessation of injection in the tenth year of EOR. In that well, reactivation only affected the zones near the wellbore in the reservoir interval since the eighth year of the EOR phase. In the case of the western hinge of the reservoir, the area around well XI-5 was not reactivated. The reactivation process mainly affects stiff lithologies, where the probability of natural fracture occurrence is higher, including the reservoir interval where fractures have been observed on borehole images. After 8 years of injection, the accumulation of compressive stresses caused by the increase in pore pressure leads to the formation of an extensive reactivation zone located outside the drilling zones of the southern injection wells in a radius of up to 1 km to the north. This phenomenon can be explained by the increased conductivity of the fractures for the water injected from the south and is related to the observed rapid increase in water production at well XP-4. Since there are no measurements, it is still a matter of debate whether there are natural fractures in the overlying carbonates. Small-scale calcite-healed fractures were found in only one core sample from the caprock at the offset well. In this study, it was assumed that there are pre-existing natural fractures in the caprock. Consequently, the structure of the oil reservoir will lose its integrity if the reactivation or failure zone develops simultaneously in the reservoir and the overburden.

The failure zone appears after the first year of the EOR phase in the most vulnerable reservoir interval of the two wells, XI-1 and XI-2, in the south. In these wells, the failure zone never extends beyond the reactivation zone and spreads in all directions, similarly to the reactivated area. Since the sixth year of EOR, the failure zone has been observed at the reservoir interval of the three boreholes XI-1, XI-2, and XI-4. The same situation occurs in the tenth year of the EOR phase at the well XI-3. At the end of the simulated time interval (after 35 years), the failure zone reaches 210 and 350 m from the injection wells XI-2 and XI-1, respectively. This horizontal extent of the failed rock correlates with a very pronounced negative horizontal thermoelastic effect due to the injected cold water (${\Delta \sigma }_{T,xx,yy}=-25\mathrm{M}\mathrm{P}\mathrm{a}$). After seven years of the waterflooding phase, numerous rock failure events were observed around the two southern injection wells (XI-1 and XI-2). The same situation occurred in the northern injection well (XI-4) after nine years of water injection. These events were not able to trigger the upward leakage paths of the injection fluid in the prediction scenarios. The results of the preliminary geomechanical stability analysis performed for the water injection case and related to the classical C-M criterion are presented in

Table 3. Results of geomechanical stability analysis performed according to Coulomb–Mohr (C-M) failure criterion for selected oil production with IOR-waterflooding. Reactiv.—fracture reactivation event, FM_S—rock failure in shear mode, FM_T—rock failure in tensile mode, Leak (NO/Up)—no observed CO₂ leakage/upward leakage through specific region, 1, 2, 3, 4, 5, and 6—numbers of regions determined in dynamic model enlisted in Figure 6, and NO—formation is stable.

Oil Reservoir Stability During Well Test and IOR Acc. C-M Failure Criterion
C-M Plascicity Function (FS)			Tinj = 35 °C, ΔT = −45 °C				Tinj = 35 °C, ΔT = −45 °C				Tinj = 35 °C, ΔT = −45 °C				Tinj = 35 °C, ΔT = −45 °C				Tinj = 35 °C, ΔT = −45 °C
			XI-1				XI-2				XI-3				XI-4				XI-5
Timstep	Elaps. Time	Stage	Reactiv.	FM_S	FM_T	Leak	Reactiv.	FM_S	FM_T	Leak	Reactiv.	FM_S	FM_T	Leak	Reactiv.	FM_S	FM_T	Leak	Reactiv.	FM_S	FM_T	Leak
Start	0	Initial	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO
1	1	Welltest	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO
2	2		NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO
3	6		NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO
4	10	IOR-waterflooding	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO
5	12		NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO
6	14		2	NO	NO	NO	2	NO	NO	NO	2	NO	NO	NO	2	NO	NO	NO	NO	NO	NO	NO
7	16		2	2	2	NO	2	2	2	NO	2	NO	NO	NO	2	2	2	NO	NO	NO	NO	NO
8	18		2	2	2	NO	2.6	2	2	NO	2	2	2	NO	2	2	2	NO	NO	NO	NO	NO
9	20		2.6	2	2	NO	2.6	2	2	NO	2	2	2	NO	2.6	2	2	NO	NO	NO	NO	NO
10	35		2.6	2	2	NO	2.6	2	2	NO	2	2	2	NO	2.6	2	2	NO	NO	NO	NO	NO

for comparison purposes.

During CO₂ injection into the southern wells (XI-1 and XI-2), the area of the failure zone stabilizes and remains constant throughout the forecast period, with the radius in both wells reaching approximately 200 m. Thermal effects also contribute to the rapid failure of the reservoir rock several years after the start of injection in well XI-4. In the sixth year of injection, the failure spreads to the damage zone of the nearby fault. Furthermore, since the eighth year of EOR, the entire modeled section of borehole XI-4 is covered by the reactivation zone, separated by intervals of failed rock. In the southwest, the failure zone occurs only in the vicinity of injection well XI-3, between the seventh and ninth year of the EOR phase. The failure is not observed at the XI-5 injection well, because water is injected into the depleted zone in the western part of the reservoir. The switch to scCO₂ injection in most wells from the eighth year of production leads to an increase in the overall horizontal permeability of the reservoir interval due to a lower cooling effect of CO₂ on the rocks and, consequently, to a more pronounced extension of the reactivation zone. However, the failure zone does not propagate upwards during the forecast, and the integrity of the caprock is maintained, so no leakage of the injected fluid is observed. The results of the preliminary geomechanical stability analysis performed for the scCO₂ injection case and related to the classical C-M criterion are presented in

Table 4. Results of geomechanical stability analysis performed according to Coulomb–Mohr (C-M) failure criterion for selected oil production with EOR-CO₂. Reactiv.—fracture reactivation event, FM_S—rock failure in shear mode, FM_T—rock failure in tensile mode, Leak (NO/Up)—no observed CO₂ leakage/upward leakage through specific region, 1, 2, 3, and 4—numbers of regions determined in the dynamic model enlisted in Figure 6, and NO—formation is stable.

Oil Reservoir Stability During Well Test and IOR Acc. C-M Failure Criterion
C-M Plascicity Function (FS)			Tinj = 35 °C, ΔT = −45 °C				Tinj = 35 °C, ΔT = −45 °C				Tinj = 35 °C, ΔT = −45 °C				Tinj = 35 °C, ΔT = −45 °C				Tinj = 35 °C, ΔT = −45 °C
			XI-1				XI-2				XI-3				XI-4				XI-5
Timstep	Elaps. Time	Stage	Reactiv.	FM_S	FM_T	Leak	Reactiv.	FM_S	FM_T	Leak	Reactiv.	FM_S	FM_T	Leak	Reactiv.	FM_S	FM_T	Leak	Reactiv.	FM_S	FM_T	Leak
Start	0	Initial	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO
1	1	Welltest	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO
2	2		NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO
3	6		NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO
4	10	IOR-waterfl.	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO
5	12		NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO	NO
6	14		2	NO	NO	NO	2	NO	NO	NO	2	NO	NO	NO	2	NO	NO	NO	NO	NO	NO	NO
7	16		2	2	2	NO	2	2	2	NO	2	NO	NO	NO	2	2	2	NO	NO	NO	NO	NO
8	18	EOR-CO2	2	2	2	NO	2.6	2	2	NO	2	2	2	NO	2	2	2	NO	NO	NO	NO	NO
9	20		2	2	2	NO	2.6	2	2	NO	2	2	2	NO	2.6	2	2	NO	NO	NO	NO	NO
10	35		2	2	2	NO	2	2	2	NO	2	2	2	NO	2	2	2	NO	NO	NO	NO	NO

for comparison purposes.

6.2. Analysis of the Impact of Poroelastic and Thermoelastic Effects

To establish the relationship that describes the influence of pore pressure and temperature variations in the reservoir ($\Delta P,\Delta T$) on the principal components of the stress tensor (${{\sigma }_H,{\sigma }_h,\sigma }_V$), the relative changes in pore pressure and temperature ($\Delta P/P,\Delta T/T$), as well as the relative changes in the stress tensor component (${\Delta \sigma }_H/{\sigma }_H,{\Delta \sigma }_h/{\sigma }_h,{\Delta \sigma }_V/{\sigma }_V$), must first be determined. As can be seen from Figure 16 and Figure 17, the thermal stress caused by temperature changes is, on average, more than twice as large as the effect of the pore pressure on the horizontal stress components. In addition, the superposition of the thermoelastic and poroelastic effects reduces the vertical stress component to practically zero. These two effects lead to modifications of the stress–strain tensor, especially its horizontal components, resulting in drastic changes in the geomechanical stability of the oil reservoir structure. As a result, the transport properties of the reservoir formation evolve together with the changes in the geomechanical state. Shortly after the start of the IOR waterflooding phase, and continuing during the EOR-CO₂ phase, the thermoelastic effects exceed the poroelastic effects three-fold in the near-wellbore zones where cold fluid has been injected. As a result, the magnitudes of the horizontal stress components decrease rapidly compared to the initial state. After several years of continuous injection of cold water, a decrease in the ratio of thermal stress to poroelastic stress (${\Delta \sigma }_T/{\Delta \sigma }_p$) to 1.7 can be observed, which is due to the pressure build-up.

In general, the resulting relative changes in the vertical stress component (${\Delta \sigma }_V/{\sigma }_V$) are negligible (−0.0021, 0.0023) due to the mutual compensation of temperature and pressure effects. Moreover, the relative change in vertical stress caused by the relative change in pressure ($\Delta P/P$) is seven times greater than that caused by the relative change in temperature. It can be concluded that the greatest influence of the relative change in temperature ($\Delta T/T$) on the relative change in the horizontal components of the stress tensor (${\Delta \sigma }_H/{\sigma }_H,{\Delta \sigma }_h/{\sigma }_h$) is observed shortly after the start of injection ($-0.35,-0.20$). As the injection approaches the minimum target temperature, the relative change in the horizontal components of the stress tensor reaches a minimum value ($-0.60,-0.40$). At the end of the first year of the injection phase, the relative change in pressure reaches a value of 0.32, resulting in a relative change in the horizontal stress components of 0.08 on average. After the EOR phase, the relative change in pressure reaches a maximum value of 0.53, which corresponds to a relative change in the horizontal stress components of 0.15.

The correlations described above represent a certain average trend of changes occurring in the blocks of the simulation model. It should be noted here that the observed anisotropy of the properties of the reservoir rocks suggests that different relationships should be determined for each block of the model. These relationships may have a larger spread, but they would be centered around the curves shown in Figure 16. The nonlinearity of the impact of temperature on the resultant stress tensor, shown in Figure 17, in the case of CO₂ injection, additionally makes it difficult to easily describe and predict the results of thermoelastic phenomena on the reservoir rocks. An easier case to describe is the effect of pressure on the resultant stress tensor; this relationship is also nonlinear but with a smoother course.

6.3. Detailed Analysis of Geomechanical Stability

In this work, an analysis of the change in the stress state and the geomechanical stability of the reservoir was also carried out using Mohr’s circle diagrams. The analysis refers to the blocks of the oil reservoir model where the strongest changes in stress state occurred and where the highest probability of leakage in the structure of the oil reservoir was identified. These include areas that have been previously plasticized, mainly due to strong temperature changes, i.e., near the well that is injecting the cold fluid, in the fault zone (damage zone). The detailed analysis was performed for two variants that differed in the type of injected fluid, but in both cases, the minimal injection temperature was constant, i.e., 35 °C. The central depleted part of the reservoir, where the oil production takes place, is where the reservoir formation remains stable throughout the entire operational life of the reservoir. Figure 18, Figure 19 and Figure 20 are introduced generally to be combined with Figure 21 and Figure 22 and to complement the detailed stability analysis. These figures were introduced to follow stress evolution trends at sample locations of high deviatoric stress through the exemplary time points to find stability loss events simultaneously on vertical sections and Mohr’s circle diagrams. The most important here are the key points relating to reactivation (RE) and failure in shear, hybrid, or tensile modes (SF, HF, and TF). These events are depicted in Figure 21 and Figure 22 and in the above mentioned discussion to emphasize their importance in enhancing the transport properties of the reservoir formation or opening potential escape routes for CO₂.

According to the result presented in Table 2, if we consider isothermal conditions (base case) and in most non-isothermal cases (${\Delta T}_{inj}=-10,-15,-25,-35°\mathrm{C}$), only critically stressed fractures are favorable to reactivate in the area of several hundred meters around the injection wells, mainly due to applied overpressure. When the EOR process advances and the temperature difference increases below −30 °C, thermoelastic stresses produce conditions favorable to tensile failure, but exclusively in the zones near the injection wells. As the temperature of the injected fluid approaches its minimum value ($35°\mathrm{C}$), there is an early decrease in the average, resulting in both horizontal stress components (${{\sigma }_h,\sigma }_H$), from about 3% at 70 °C to a maximum of 74% and 78% at 35 °C. These large changes in the two horizontal components of the stress tensor (${\sigma }_H,{\sigma }_h$) coincide with the predominant directions of cold fluid flow through the sequestration structure, i.e., along the meridional axis of the structure, and perpendicular to it. In the individual injection wells, such a decrease occurs at different times, e.g., in the southern wells after 11 years and in the northern well after 14 years from the start of the reservoir life cycle. The vertical component of the stress (${\sigma }_V$) does not change significantly during the entire simulated period (35 years). For this reason, the continuous cooling of the zones near the injection wells leads to a transition from the strike-slip stress regime (SS) to the normal faulting regime (NF). The increase in differential stresses creates optimal conditions for the reactivation of critically stressed natural fractures or directly causes a failure in shear, hybrid, or tensile modes. In the case of the zone around the south-eastern well (XI-2), the natural fractures are reactivated very quickly in the middle interval of the reservoir during the first year of water injection. Shear failure occurs one year later, and during the next five years the middle interval of XI-2 well switches to hybrid failure. Tensile failure conditions persist until the end of the forecast, as shown in Figure 18. The change in injection fluid from water to scCO₂ (year 18) also leads to a continuation of the stress failure conditions, but with a smaller opening of the hydraulic fractures, as seen by comparing the Mohr diagrams in Figure 21 and Figure 22. The near-well zone of the next southern well (XI-1) is subject to a similar development of the stress state. The difference is that a stress failure occurs in a wider zone around this well. After year 16, well XI-1 is under tensile failure conditions, but two years later, there is a slight relaxation due to reduced average injection rates, and the near-well zone re-enters a hybrid failure condition. This condition does not last long, because from year 19 until the end of the forecast, tensile failure conditions are mainly observed in the most unstable layers. The change from water injection to scCO₂ (year 19) leads to continued tensile failure conditions but causes smaller hydraulic fracture openings. The development of the changes in the stress state for wells XI-1 and XI-2 can be seen in Figure 15, Figure 18, and Figure 19. The zone around the south-western well (XI-3) remains stable until year 11, and from year 12 it is mostly reactivated with a single interval under shear failure conditions. After year 14, the near-well zone is under hybrid failure. From year 16 to the end of the history (year 19), tensile failure conditions prevail, with a decreasing aperture of hydraulic fractures. From year 20 to the end of the forecast (year 35), there is a period of incomplete relaxation caused by well abandonment, during which a gradual transition to shear failure occurs. The evolution of geomechanical changes in the vicinity of borehole XI-3 can be followed in Figure 21 and Figure 22. The development of the changes in geomechanical stability of the northern wells differs from the southern ones, e.g., because they started injecting a half-year later, when the conditions in the reservoir were different than at the beginning. In the case of the northern well (XI-4), the near-well zone remains stable until year 13. In the following years, the natural fractures are reactivated, including the adjacent small fault to the northeast. From year 14, a shear failure occurs, which quickly turns into a tensile failure (from year 16 to 35). The development of the failure of XI-4 is shown in Figure 20. The north-western well XI-5 remains stable until year 19 due to a late connection to the injection system. Since year 20, the unstable layers enter reactivation mode but gradually move towards a shear and hybrid failure mode until the end of the forecast. The caprock layers above the interval provided for the injection remain stable throughout the simulated history and forecast, demonstrating their sealing capacity in the waterflooding and EOR-CO₂ process, as can be observed in Figure 21 and Figure 22.

Figure 21 and Figure 22 are introduced generally to be combined with Figure 18, Figure 19 and Figure 20 and to complement the detailed stability analysis. These Figures were introduced to follow stress evolution trends at sample locations of high deviatoric stress through the exemplary time points to find stability loss events simultaneously on vertical sections and Mohr’s circle diagrams. The most important here are the key points relating to reactivation (RE) and failure in shear, hybrid, or tensile modes (SF, HF, and TF). These events are depicted in Figure 21 and Figure 22 and in the previously mentioned discussion to emphasize their importance in enhancing the transport properties of the reservoir formation or opening potential escape routes for CO₂.

Considering the results described in Section 5.1, an increase in the deviatoric effective stress can result in a significant increase in long-term permeability due to natural fracture reactivation or rock failure. A decrease in the effective stress to a level below 20 MPa can trigger fracture reactivation, leading to a ten- to sixteen-fold increase in permeability. If the decrease in effective stress below −5 MPa is associated with rock failure, the permeability can reach a factor of 35. Changes in permeability in intact rock due to elastic deformation and induced by temperature drop are considered to be a relatively weak factor due to their small magnitude (up to a two-fold increase). As mentioned earlier, the assessment of geomechanical stability is crucial because only inelastic deformations are able to significantly change the transport properties of the formation or increase the risk of loss of caprock integrity.

7. Summary and Conclusions

The research work described in this article deals with the analysis of the geomechanical stability of an oil reservoir during its production cycle, taking into account secondary (IOR-waterflooding) and tertiary (EOR-CO₂) methods. During the injection of water and CO₂ at a temperature much lower than the reservoir temperature, significant shear and tensile stresses were generated. The study focused on the practical issue of reservoir and caprock integrity, taking into account thermo-poroelastic effects. This paper is a summary of the presented research. Among other things, it contains assumptions, the numerical method used, and conclusions proving the validity of the selected production IOR and EOR methods. The analyses carried out enabled an attempt to optimize the production conditions of the oil reservoir with regard to the failure that occurred and to formulate conclusions from these analyses. As a result of performing the above tasks, the following conclusions were formulated as bullet points:

(1)

The quality of the geomechanical model was significantly improved by calibrating in-situ stress to the results of production test, injection tests, and mini-fracs.

(2)

A detailed geomechanical analysis with Mohr diagrams was performed exclusively for the most stressed areas of the oil reservoir, i.e., the zones around the injection wells and in the overburden layers above these wells.

(3)

The geomechanical calculations and heat flow simulations took into account the changes in the thermal, geomechanical, and transport properties of the reservoir rock due to the effects of temperature.

(4)

The injection of cold fluids (water and CO₂) into hot reservoir rock leads to a significant change in the initial stress tensor, mainly in the vicinity of the injection wells.

(5)

The cooling of the fault zones and the zones around the injection wells, as well as the temperature drop in the lower part of the caprock due to thermal conduction, leads to a transition from the strike-slip stress regime to normal faulting conditions. Transition to a normal faulting regime is risky and may lead to the initiation of tensile failure. The effect is more pronounced when cold water is injected rather than scCO₂.

(6)

The thermoelastic unloading in the reservoir leads to a significant reduction in the horizontal components of the stress tensor, while the vertical stresses remain practically unchanged (Δσ_H = −47 MPa and Δσ_V = −7 MPa for ΔT_inj = −45 °C).

(7)

The contribution of the thermoelastic component is more than twice as large as that of the poroelastic component to the overall change in the horizontal components of the stress tensor, which was presented in Section 6.2 in Figure 16 and Figure 17. For this reason, thermal stresses should always be considered when the change in the formation temperature exceeds 10 °C.

(8)

The primary factor for the growth of fractures is the thermal drawdown, as a result of increasing tensile stresses with decreasing temperature. The secondary factors are the azimuth of maximum horizontal stress (WNW-ESE) as well as the magnitude of vertical stress.

(9)

It has been found that higher injected fluid temperature (above 35 °C), especially in the case of scCO₂, can reduce or stop the hydraulic fracture opening mechanism due to lower tensile stresses, as shown in Section 6.3 in Figure 21 and Figure 22.

(10)

It has been estimated that changes in the geomechanical state of the oil reservoir can increase the formation permeability by sixteen times (fracture reactivation) to as much as thirty-five times (tensile failure).

(11)

Switching injection fluid from water to scCO₂ may reduce the likelihood of premature breakthrough of the injected water into the production wells and also prevent reactivation of critically stressed fractures in the caprock.

(12)

It should be emphasized that the phenomenon of tensile stress accumulation in the overburden may lead to the generation of leakage pathways, but in the case of the selected offshore reservoir overburden, they remained stable throughout the simulated period.

(13)

The conducted hydro-thermo-mechanical (HTM) coupled simulation proved its effectiveness in the field of time optimization. A single coupled time step period duration was about ten seconds, and the total elapsed time of the coupled simulations was extended by less than 1%.

(14)

The enhanced oil recovery supported by CO₂ injection (EOR-CO₂) should be conducted by maintaining the supercritical conditions of downhole CO₂ (80 bar > P_inj < 600 bar, 31 °C > T_inj > 80 °C). Such an approach guarantees the stability of the caprock throughout the whole prediction period.