The evolution of the reservoir stress state throughout the history of production

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1 International Journal of Petroleum and Geoscience Engineering (IJPGE) 2 (2): 181- ISSN Academic Research Online Publisher Research paper The evolution of the reservoir stress state throughout the history of production Mohsen Saemi a, Morteza Ahmadi b, *, Hamid Hashem Al-Hosseini c a,b Rock Mechanics Department, Engineering Faculty, Tarbiat Modares University, Tehran, Iran. c Mining Faculty, Isfahan University of Technology, Isfahan, Iran * Corresponding author. Tel.: address: moahmadi@modares.ac.ir A b s t r a c t Keywords: Coupled Reservoir, Geomechanics modelling, Rock permeability, Stress Path, Elastic constants, Pressure depletion, Effective stress, Reservoir compaction. Accepted:30 June2014 Based on principle stress theorem, the effective stress changes in the reservoir and its surrounding formation tightly coupled with pore pressure changes due to reservoir fluid withdraw or injection. Rock mechanical deformation induced by evolution of effective stress would be controlled through paths in which the reservoir stress follows during pore pressure alterations. The stress path that the reservoir conforms all over history of production undoubtedly affects the mechanical behaviour of the reservoir and fluid flow characteristics and could be one of the key factors in measurements and calculations of geomechanical instabilities related to pressure depletion/injection. The stress path additionally, has a considerable influence on recovery drive mechanism, straightly through compaction drive, and indirectly through permeability variation. Furthermore, the stress modifications in the reservoir and bounding formation possibly lead to changes in seismic attributes and consequently disturbing time-lapse (4D) seismic response. Other associated geomechanical problems include wellbore instability, casing collapse and solid production are strongly related to the stress path that reservoir and its burdens follow during production. Reservoir stress path and its changes throughout reservoir depletion are strongly dependent on several geological and mechanical factors such as reservoir boundary, reservoir dimension and its shape, constitutive behavior of reservoir rock and surrounding formations, and so on. A coupled hydromechanical model that includes above mentioned parameters was extended to more precisely forecast the reservoir stress state changes and to investigate the influences of these factors on reservoir behaviour. The main goals of this Paper are to explore which factors have the significant impact on the stress path, and to consider the effects of stress path on hydromechanical behaviour of a depleting reservoir. Numerical modelling results confirm that reservoir stress path is associated with the dimension and geometry of the reservoir and on poroelastic properties of the reservoir rock and bounding formations. Also we have shown that permeability reduction of the reservoir through fluid withdraw strongly depend on magnitude of the reservoir stress path. Academic Research Online Publisher. All rights reserved.

2 1. Introduction Pore pressure reduction due to the reservoir production induces dramatically changes in the reservoir stress distribution within the reservoir and the surrounding strata. This stress alteration is the crucial factor that might be causing serious troubles frequently took place through production such as casing collapse or fault reactivation. Based on effective stress law reservoir fluid withdraw raises the load conveyed by the reservoir rock matrix. It directly promotes deformation mechanisms in microscales like grain contact spreading, microcrack growth, closure, cement crashing and grain replacements [1,2]. In these situations, rocks usually experience compaction due to porosity reduction, and therefore acoustic velocity would be raised due to compression and density increasing. Numerous challenging consequences of reservoir deformation caused by production have been observed, Carbognin et al. [3] reported some of these problems in different cases. These geomechanical issues covering some hazardous phenomena like subsidence[4], casing damage [4], earthquakes [5] and some troublesome problems like reduction of reservoir permeability [6,7], sanding and borehole instability. Furthermore, the stress state evolution associated with reservoir depletion demonstrates the stability of cap rock and fault reactivation, and also could be effective on hydraulic fracture design [8,9]. In addition, from a reservoir management point of view, compaction-induced changes in porosity and permeability need to be understood and modeled in order to optimize the drilling and completion strategy and the drawdown as a function of time and reservoir fluid pressure [10]. The stress path is implicitly outlined the parameters that specify the magnitude of stress arching and stress anisotropy that appear during reservoir depletion. The in-situ measured stress path in the reservoirs is totally different from the experimental uniaxial strain model and might be either substantially less or larger than the measured laboratory stress path [11]. This discrimination inherently caused by dissimilar conditions of geologic and geomechanical characteristics of rock mass and core sample in the lab [12]. These factors include boundary conditions on the reservoir, size and geometry of the reservoir, poroelastic deformation behavior of reservoir rock and bounding formations, and other parameters. In this study, a coupled reservoir geomechanics numerical model has developed to illustrate the reservoir stress path due to the reservoir fluid drawdown. Various mechanical and geometrical properties have been assigned to model to assess how these different conditions affect the reservoir stress path during production. In this work, we investigate the impact of the reservoir geometry, discriminations between mechanical properties of reservoir and the surrounding formations, elastic anisotropic properties, and scale on stress patch and furthermore the influence of the stress path on 182 P a g e

3 permeability of the reservoir was studied. This work demonstrates the results of a comprehensive 3D numerical hydro-mechanical coupled modeling that consider the impact of reservoir geometry and rock mechanical behavior on the reservoir stress path. In addition, the coupled simulations have shown how stress path variations in the reservoir can affect the matrix permeability of rocks. 2. Definition of Stress Path Parameters Based on principle stress theorem, the effective stress changes in the reservoir and its surrounding formation tightly coupled with pore pressure changes due to reservoir fluid withdraw or injection. Rock mechanical deformation induced by evolution of effective stress would be controlled through paths in wich the reservoir stress follows during pore pressure alterations. The stress changes during reservoir depletion turn principally on the initial stress state of the reservoir, reservoir geometry and rock properties of the reservoir and bounding strata, and can be commonly outlined in terms of the reservoir stress path parameters Usually it is reasonably believed that the maximum and minimum principal stresses are vertical and horizontal respectively in sedimentary formations. Stress path can be therefore explained by the ratio of the change in effective minimum horizontal stress ( sh) to the change in effective vertical stress ( sv) due to pressure reduction (Δp) from a reservoir, which according to effective stress law [12] leads to the change of the reservoir stresses from initial state: Δσ v= Δσv αδp (1) Δσ h= Δσh αδp (2) where Δσ v and Δσ h are respectively the effective vertical and minimum horizontal stresses, Δσv and Δσh are the total stress values, and α is the Biot s constant [12]. The stress path parameters present the evolution of the principal stresses during the reservoir fluid withdraw and can be shown as: For the horizontal stress path coefficients: (3) and vertical stress path coefficient (4) (5) (6) 183 P a g e

4 and is usually measured from field observations, but for calculation of K further assumptions need to be taken into account. Segura et al explained more in detail the stress path coefficients which mentioned in above equations. They described as the stress arching parameter as the horizontal stress path parameter and K as the deviatoric stress path parameter. The obtained results of hydraulic fracturing tests such as microfrac, LOT, XLOT or FIT are generally used to determine in the field. Stress arching represent the extra load of overburden induced by reservoir depletion on overlaid layers and can be described in term of parameter. Indeed, the stress arching transfers vertical stress unloading induced by production to sideburdens in the form of overloading. The parameter K outlines the progress of stress anisotropy in the reservoir due to pressure drawdown. The stress anisotropy can only increase when the stress arching does not occur in the reservoir (i.e. with low values ). In practice, it is convenient to be supposed that the reservoir compress uniaxially without lateral strain, and that the total load of the overburden is translated by the reservoir through history of depletion. Thus, according to linear poroelastic theory, one can rewrite the above equations as: Where the refers to the Poisson s ratio of rock framework. This relation is only valid when lateral dimension of the reservoir is much greater than its thickness, the contrast between the elastic properties of the reservoir and its bounding layers be insignificant, and the petrophysical properties of the reservoir do not change with location and demonstrating entity a homogeneous formation [13]. Generally, simplification to develop a comprehensive model increases the uncertainty and away the results from reality. To solve these problems that cause some limitations like unreliable geometry and heterogeneity, numerical modeling is required to solve complicated circumstances of a reservoir which included complex geometry with various mechanical properties. Morita et al. [14] used a finite element model to organize a series of empirical associations between the stress path and the reservoir geometry. Mulders, [15] also used a finite element simulation to consider the effect of rock plasticity on stress paths for an ellipsoidal reservoir. (7) 3. Reservoir Geomechanical Modeling In this study, we partially coupled a fluid flow simulation code to a finite element stress simulator. Using this numerical method, the stress changes induced by reservoir pressure reduction were determined in every element of the mechanical model. In the next stage, the associated deformation was converted to porosity and permeability changes, and then new hydraulic properties was imported 184 P a g e

5 to the fluid flow simulator to reestablish new static model. This new dynamic model recomputed new saturation and pressure in corresponding elements and therefore new values of stress and strain were obtained from the output of reservoir simulation. This circulation represents the exchange of fluid flow and geomechanics information between simulators which was updated in given time step. We construct a synthetic reservoir gridded using Cartesian cells in size of 20*20*3 and consist of four producer wells at the corners over a schedule of five-year production. The simulation started with a geostatic step in which the initial vertical and horizontal stress state was equilibrated. This was continued by setting of 10 load steps, which present accurately five years of production during natural depletion, from 2015 to The porosity and permeability in each cell are modified according to the implemented stress path and deviatoric stresses. Figure 1 shows a rectangular idealized reservoir mesh (Corner Point Geometry) as a conceptual model for coupled simulations. It is reasonably assumed to be extend m by ft in x and y directions and a depth of 500 ft. Fig. 1: the reservoir model embedded in geomechanical grids for numerical coupled simulation. In order to analysis of stress model, it is essential to model not only the reservoir but also its containment, to certify boundary conditions and mechanical interactions between reservoir and its bounding layers caused by production have appropriately implemented. The finite element mesh embedded with the reservoir geometry, additionally incorporates an overburden going from 0 to 7000 ft, an underburden going from 7500 ft to m, and sideburden extended ft from both lateral 185 P a g e

6 Porosity (%) Permeability (MD) Initial Pressure (PSI) Bubble Point Pressure (PSI) Saemi M. et al. / International Journal of Petroleum and Geoscience Engineering (IJPGE) 2 (2): 181- sides of the reservoir. Thus, the total dimensions of the stress mesh are ft by ft for a total height of ft (see Figure 1). Reservoir simulations are performed with a black oil simulator. Table 1 shows some petrophysical properties of different sectors of the model. Table 1: Fluid Flow and petrophysical Properties of the reservoir Elastic Properties Zone name Overburden Sideburdens Underburden Reservoir The initial stress state for the mechanical mesh is defined with the effective vertical stress in the reservoir and the ratios of the maximal and minimal effective horizontal stress with the vertical one. The total vertical stress was calculated from the weight of the overlying with the gradient of 1.15 Psi/ft3. To populate the mechanical and reservoir properties to every point of model, reservoir initialization was implemented. After initialization, fluid flow analysis was done until the reservoir reached a given pore pressure at a definite time (end of first time step). Current pressure and saturation then will insert to stress simulator to determine new effective stresses and associated strains. According to new calculated strains, porosity and permeability will be updated in each time step. The coupled reservoir geomechanical model was used to exactly determine the impact of hydromechanical properties and the reservoir dimension which control the stress path that the model of the reservoir has followed during production. In this study, the effects of reservoir geometry of synthetic reservoirs on stress path and contrasts in mechanical properties between the producing reservoir and surrounding strata have been assessed using the explained numerical method. 4. Factors Affecting the Reservoir Stress Path 4.1. Effect of Reservoir Geometry on Stress Path. 186 P a g e

7 The size and geometry of the reservoir are the most important factors that influence the stress path. When a reservoir and its surrounding media are isotropic with the same elastic properties, stress path declines with an extension in reservoir length (Figure 2). In other words, the stress path for an infinite, continuous reservoir is the lowest state and similar to the stress state in uniaxial strain condition. In this situation the stress path is only dependent to Poisson s ratio. Fig. 2: The aspect ratio of the reservoir length to height versus as reservoir stress path. As illustrated in figure 2 the geometry of the reservoir has changed by varying the length/thickness ratio of the reservoir zone from 1 to 10. The elastic properties of the reservoir and its burdens were supposed to be the same, and the initial conditions of the model were applied by gravitational loading and a pore pressure gradient. In general, the stress path is minimal when the ratio of reservoir length to its thickness be considerable. Therefore, the flat and persistent reservoirs usually have high orders of stress path rather than sectored reservoirs that are uncontinues in one direction The Effect of Different Elastic Properties between the Reservoir and Bounding Formations To assess how the eluviation of elastic properties affects the reservoir stress path, we were set different young modulus between the reservoir model and bounding formations. The lower part of figure 3 shows the results of the isotropic reservoirs with much stiffness than the bounding rocks and in the upper part, the young modulus of the reservoir is lower than its burdens. E1 and E2 represent the elastic modulus of the burdens and the reservoir respectively. As shown in lower part, the stress path has increased with an increase in the elastic moduli of the reservoir but when the reservoirs have a lower elastic modulus than the bounding formations, the stress path decreases with an increase in the contrast in elastic moduli. 187 P a g e

8 Fig. 3: The effect of different elastic properties between the reservoir and bounding formations on the reservoir stress path. The poisson s ratio is another independent elastic modulus that relates rock deformation to stress changes. Figure 4 demonstrating the impact of different Poisson s ratio between the reservoir and bounding formations on the stress path. This figure shows that practically the stress path is not varied when the poisson s ratio of the reservoir is fixed and the rock bounding poisson's ratio is changing. On the other hand, where the Poisson s ratio of surrounding area has set to be fixed, an increase in Poisson s ratio of the reservoir generally increases the reservoir stress path. Fig. 4: The impact of poisson s ratio variations on the reservoir stress path Effect of Transverse Isotropy in Elastic Properties. Naturally, because of horizontal layering in sedimentary rocks inherently most of the reservoir formations are transversely isotropic. Generally vertical loading of overburden leads to the elastic modulus be greater perpendicular to bedding than parallel to bedding. Figure 5 reveals how the contrast between Horizontal elastic modulus (Ex) and vertical elastic modulus (Ev) influences the 188 P a g e

9 reservoir stress path. The stress path increases only when the reservoir is transversely isotropic and high orders of anisotropy in the reservoir would be increased the stress path. Fig. 5: The effect of anisotropic elastic constants on the reservoir stress path Simulating Stress Path Effects on Permeability Figure 6 illustrates the permeability variations of the reservoir model versus production history for different predetermined stress path. As shown normalized permeability reduction due to pore pressure drawdown was depicted for a normal stress regime. This figure reveals the simulation results of geomechanical mode representing the large variation of permeability with fluid reservoir withdraw, particularly at high production rates. The matrix permeability of the reservoir was approximately declined exponentially with respect to decrease of reservoir pore pressure up to end of 2016 and beyond this point, permeability decreases with a very low slope rather than the first part. Indeed, in this point the vertical stress has exceeded from preconsolidation pressure. This is a critical pressure and demonstrates the greatest vertical stress which the reservoir has experienced in the past. The stresses more than preconsolidation pressure, lead rocks to receive irrecoverable deformation and consequently, associated strain hardening strengths the rock and causes more resistance to permeability modifications. 189 P a g e

10 Fig. 6: permeability variations of two different stress regimes versus production history. Three different depletion scenarios have been applied to model. The impact of the reservoir stress path on permeability in has shown in Figure 7. The results of numerous simulations in different boundary conditions obviously indicate that reservoir fluids withdraw decreases permeability and that permeability parallel and perpendicular to the maximum stress direction decrease at different rates. The minimum reduction in permeability is parallel to the maximum principal stress. Thus, stress-induced permeability anisotropy develops with pore pressure drawdown and the magnitude of permeability anisotropy increases at lower stress paths. In the other word, for low stress paths the minimum effective horizontal stress has increased at a slower rate than the effective vertical stress with pore pressure drawdown. The Figure 7. part A, reveals that Although a negligible permeability increase meets during dilatants deformation, substantial permeability reductions are related to the contracting behaviour at high levels of horizontal stress (see high stress paths in Figure 9A). In the other hand, in low stress paths where differential stress is considerable, the state of stress is on the left side of critical stress line. In this situation the shear stress is dominant and has a larger increase for a lower stress path. Therefore, different horizontal stresses in the reservoir led to meet different fluid flow conductivity, and the variation in permeability entirely associated both to horizontal stress, and to the constitutive mechanical behavior of the reservoir. 190 P a g e

11 B A Fig. 7: The impact of the reservoir stress path on permeability (A) and permeability anisotropy (B) in the reservoir rock. 5. Discussion Reservoir can be considered as a dynamic system that is continuously changing during fluid production history. According to the effective stress principle, a little production of reservoir fluids reduces the pore pressure, increases the effective stresses, and generally modifies the 3D stress field from the its initial state. In practice, the stress path followed by reservoir throughout of pressure depletion can be determined using the measurement of the least horizontal stress variations caused by reservoir fluid production. The importance of the implemented stress path on the reservoir would be understood when one notice that shear stresses increase more quickly with pressure drawdown for reservoirs following low stress paths than for reservoirs following high stress paths. Figures 2 to 7 show that reservoir stress path is dependent to several different geometrical and geomechanical parameters, such as boundary conditions on the reservoir, size, and dimensions of the reservoir, mechanical behavior of reservoir rock and surrounding formations, and so on. A coupled reservoir geomechanical model was developed to investigate how these factors can be influenced the stress state of the reservoir during depletion. In this paper, we studied the impact of reservoir geometry variations and contrasts in mechanical properties between the reservoir and its burdens. The simulation results of the model obviously express that the reservoir stress path is strongly associated to the geometry of the reservoir and constitutive behavior of the reservoir rock and bounding formations. In general, the stress path tends to be lower as the reservoir length becomes much longer 191 P a g e

12 than its thickness. The framework and attributes of this model in the next step have used to evaluate the changes of permeability and permeability anisotropy of reservoir rock during production. The significance of the reservoir stress path on reservoir permeability was verified through a coupled reservoir geomechanics modeling in which the reservoir was uniformly depleting in a given period of time. Anisotropic loading with fixed boundary condition was applied to model, and the initial conditions were assigned through gravitational loading. In this situation, permeability parallel and perpendicular to the maximum stress direction decreases at dissimilar rates. The minimum decrease in permeability is parallel to the maximum principal stress. Accordingly, the permeability anisotropy caused by stress changes evolves with pore pressure reduction and the extent of permeability anisotropy increases at lower stress paths. The degree of the permeability anisotropy is possibly depended to the configuration of pore space and initial permeability of the reservoir rock. 6. Conclusion In this study, we have shown that the coupled fluid flow and deformation simulation is able to accurately demonstrate the reliance and effect of the reservoir size, geometry, elastic properties and permeability on the reservoir stress. The numerical simulation results prove that the stress path followed by the reservoir has a tight relation to the size and geometry of the reservoir and to the reservoir rock mechanical parameters. The model demonstrates that the stress arching phenomenon is more significant in thin reservoirs with lower elastic properties compared to the bounding material. In these reservoirs, the stresses tend to be travel through the stiffer formations, and consequently the stress evolution most likely appears in the sideburdens. Thus, arching in a reservoir with high magnitude of elastic modulus and any size and geometry cannot occur. In addition, we conclude that the poission s ratio is a controlling factor of the stress path when the horizontal extension of the reservoir in longer than thickness. In this condition, the reservoir deforms uniaxilly in vertical direction due to reservoir pressure drawdown. Furthermore, the effect of the stress path on reservoir permeability and stress induced permeability anisotropy reveals that the permeability reduction induced by reservoir production totally shows different behavior for different stress paths and most reduction of permeability is parallel to minimum principal stress direction. Generally, the main achievements or conclusions of this investigation can be summarized as following: Rock mechanical deformation induced by evolution of effective stress would be controlled through paths in which the reservoir stress follows during pore pressure alterations. 192 P a g e

13 The simulation results of the model obviously express that reservoir stress path and its changes throughout reservoir depletion are strongly dependent on several geological and mechanical factors such as reservoir boundary, reservoir dimension and its shape, constitutive behavior of reservoir rock and surrounding formations, and so on. In general, the stress path tends to be lower as the reservoir length becomes much longer than its thickness. the poission s ratio is a controlling factor of the stress path when the horizontal extension of the reservoir in longer than thickness. Generally, an increase in Poisson s ratio of the reservoir would be increased the reservoir stress path. The stress path increases only when the reservoir is transversely isotropic and high orders of anisotropy in the reservoir would be increased the stress path. Permeability reduction of the reservoir through fluid withdraw strongly depend on magnitude of the reservoir stress path. In fact, the effect of the stress path on reservoir permeability and stress induced permeability anisotropy reveals that the permeability reduction induced by reservoir production totally shows different behavior for different stress paths and most reduction of permeability is parallel to minimum principal stress direction. References [1] Wong, Tf, Baud P. Mechanical compaction of porous sandstone. Oil & Gas Science and Technology, Rev. IFP, 1999; 54: [2] Schutjens PMTM et al. Compaction of a poorly consolidated quartz rich reservoir sandstone. Experiments for the analysis of compaction drive. 2000; In: Carbognin, L., G. Gambolati and A. I. Johnson (eds). Land Subsidence. [3] Carbognin L et al. Land Subsidence. Proceedings of the Sixth International Symposium on Land Subsidence. 2000; Ravenna (Italy), September [4] Freeze RA, Social decision making and land subsidence. In: Carbognin, L., G. Gambolati and A. I. Johnson (eds). Land Subsidence. 2000; Proc. 6th Symp. Land Subsidence. Ravenna (Italy), Sept. 00. p [5] Fredrich et al. Geomechanical modeling of reservoir compaction, surface subsidence, and casing damage at Belridge Diatomite Field. 2000; SPE Res. Eval. 3(4) Aug [6] Grasso JRP et al. Scaling of seismic response to hydrocarbon production: A tool to estimate both seismic hazard and reservoir behavior over time. Paper presented at EUROCK'94: Rock mass response to hydrocarbon production. 1994; Delft, The Netherlands. 193 P a g e

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