Tony Settari, SPE, TAURUS Reservoir Solutions Ltd., Calgary and University of ... main hydraulic fracture, new fracturing on the scale of microseismic events and ...
Peer Reviewed
Relationship between Microseismic Activity, Hydrofracture and Stimulated Zone Growth Based on a Numerical Damage Model Alice Guest, SPE, University of Calgary, Department of Chemical and Petroleum Engineering, currently at CGG, Calgary and Tony Settari, SPE, TAURUS Reservoir Solutions Ltd., Calgary and University of Calgary, Department of Chemical and Petroleum Engineering
Abstract In development of tight gas and shale, the key property controlling reservoir productivity is the permeability enhancement achieved by stimulation. Attempts are being made to estimate permeability of the stimulated zone around the hydraulic fracture using a statistical function of the spatial distribution of microseismic events. In order to quantify the effect of the stimulation on the permeability, we numerically model microseismicity occurring along the hydraulic fracture and compare it to the recorded microseismic activity. For this purpose, we developed a fully coupled fluid-geomechanical model of hydraulic fracture propagation in the heterogeneous reservoir. The fluid part is solved using the commercial code Geosim and the geomechanical and microseismic solutions are constructed using the damage mechanics. Permeability enhancement is calculated from the fracture displacement. We distinguish three fracture scales in terms of model implementation: the main hydraulic fracture, new fracturing on the scale of microseismic events and microfractures. Our model was successfully tested on the case study of hydraulic fracturing in Bossier sands, using the observed microseismicity distribution as a representation of pre-existing structures in the reservoir. The coupled modeling shows that new fracturing in the reservoir has an important effect on fluid leak-off and main fracture propagation, but the effect is dependent on the pre-existing heterogeneities of the reservoir. We conclude that the permeability enhancement and the increased leak-off determined from the microseismic distribution alone is not sufficient to characterize the total leak-off into the formation. As a result, the total permeability enhancement of the stimulated reservoir volume (SRV) appears to include both the scale of the microseismic events and all the scales that are smaller. The results also suggest that the permeability of the main fracture remains the main driving mechanism during the stimulation phase in the studied case and most likely in other similar cases where main hydraulic fracture develops.
Introduction The key properties controlling well productivity are reservoir permeability and size and conductivity of hydraulic fracture. Several attempts were made to estimate permeability of the stimulated zone around the hydraulic fracture using a statistical function of the spatial distribution of microseismic events. In this study, we have developed a numerical model of microseismicity occurring along the hydraulic fracture, which allows us to calibrate the geomechanical data by comparing it to the recorded (and interpreted) microseismic activity. Such model can be then used to predict changes of permeability of the reservoir based on the motion on the newly formed fractures (microseismic events). The permeability changes are then coupled with reservoir flow modeling and this coupled system is used to model the treatment itself as well as the effect of stimulation on production. During the hydraulic fracturing, reservoir permeability is changing due to the formation of fractures on various scales (primary single plane tensile fracture and shear fractures) and due to the opening and closing of the pre-existing joints, fractures and microfratures in the reservoir. We consider both effects in our model; however, this paper focuses on testing mainly the effect of the new fractures that are on the scale of microseismic events (5-50 ft scale). Since the occurrence of the microseismic events is necessarily linked to the fracture scales above and below the microseismic scale, in this paper, we distinguish three fracture scales in terms of model implementation: the main hydraulic fracture (above 50 ft scale), new fracturing on the scale of microseismic events (5 – 50 ft scale) and microfractures (under 5 ft scale). The numerical modeling of fracturing in heterogeneous materials presents problems related to the introduction of discontinuities in a model. We use damage theory (for overview see Mazar and Pijaudier-Cabot, 1989), where the discontinuity created by a forming fracture is approximated by the degradation of elastic properties of the material. This method is in principal very similar to the particle-flow models (Flekkoy and Malthe-Sorenssen, 2002, Hazzard et al., 2000, Zhao and Young, 2009), in which the degradation of the material is introduced through the failure of the bonds of the specific strength between the individual grains. The damage technique was used for variety of modeling problems including mining (Tang, 1997, Tang and Kaiser, 1998, Tang et al., 2002, Fang and Harrison, 2002), geotechnical (Wang et al., 2009), and rock-mechanics (Yang et al., 2004), and engineering (Zhu and Tang, 2004). We present a fully coupled fluid-geomechanical model of hydraulic fracture propagation in a heterogeneous reservoir. The fluid part is solved using the commercial code Geosim which is coupled with the geomechanical module with microseismic capability as described in this paper. In Geosim, special treatment has been developed to model rigorously the main hydraulic fracture and its propagation (Ji and Settari, 2009). However, we use damage mechanics to construct the geomechanical model, including the main hydraulic fracture. The practical application of this method to hydraulic fracturing stimulation problem is new. Following up on our earlier work introducing the method (Guest and Settari, 2010; Guest and Settari, 2011), we focus here on testing the proper implementation of fractures on various scales by comparing the numerical results to analytical solutions. The proper implementation is important because the degradation of the material properties rules the fracture opening and thus permeability. The damaged 14
Volume 1 - Number 2
Hydraulic Fracturing Journal | April 2014
material properties of the fractured medium are compared to the effective Young’s modulus of a composite material consisting of a matrix and a fracture determined from the joint theory. These comparisons allow us to include distribution of the in-situ (inherited) fractures in the reservoir as an initial heterogeneity. The paper is organized in the following parts. The first part introduces the basics of the damage theory and the equations used in the geomechanical modeling. In the second part, we investigate how to model the deformation of the three fracture scales by comparing the numerical results with analytical solutions of fracture opening in impermeable media (Sneddon and Lowengrub, 1969), porous media (Tran et al., 2012), and jointed media (Bagheri and Settari, 2006). In the third part, we apply the technique to a field case of hydraulic fracturing in Bossier Sands in Texas.
Damage Mechanics Damage mechanics was introduced for solid materials to describe the creation and growth of microvoids and microcracks in a medium considered continuous on a larger scale (for overview see Mazar and Pijaudier-Cabot, 1989; Lemaitre and Desmorat, 2005). The damage parameter D is defined as a loss of a surface (or volume) that can carry the load. If several mechanisms of damage occur, each mechanism can be represented by its own damage parameter characterizing the process. The goal is to quantify the damage on a continuous level through various mechanical properties of the material, such as Young’s modulus and strength. For the applications in hydraulic fracturing, the microscale is not practical because of the computation time and the method has to be scaled to the scale of fractures in the reservoir. This section describes the general implementation of damage mechanics into the geomechanical equations as adopted from Tang, 1997, Tang and Kaiser, 1998, Tang et al., 2002. The section “Fracture Characterization” describes our implementation of damage mechanics to the scale of hydraulic fracturing. Geomechanical Equations and the Damage Theory used in the Geomechanical Module. The local geomechanical equilibrium is based on solving the constitutive (linear elasticity) (1), geometrical (2), and mechanical equilibrium equations (3): EDν E Ãij = ε kk δ ij + D ε ij + α pδ ij + σ ijRδ ij σ (1)
(1 +ν )(1 − 2ν )
1 +ν
1 ∂u ∂u (2) ε ij = i + j ,
2 ∂x j
∂xi
∂σ ij (3) =0
∂x j
where σij is the total stress tensor, εij is the strain tensor, xi are the Cartesian coordinates, ui is the displacement vector, ED is the damaged Young’s modulus, v is the Poisson’s ratio, δij is the Kronecker delta (δij =0 except for i=j when δij =1), α is the Biot’s coefficient, p is the fluid pressure added to the system (i.e., total pressure minus the initial reservoir pressure), and σRij is the regional stress. As a simplification to the solution, we assume plain strain conditions in a horizontal plane with zero strain condition in vertical direction. This leads to the reduction of the 3D problem to a solution on 2D grid because the variables in the third direction can be solved independently. The initial stress conditions represent the regional stress state, and the boundary conditions at the boundaries of the horizontal plane are zero displacements (Fig. 1). The pressure distribution in (1) is input into the geomechanical code each time step and is obtained from a separate solution of the fluid flow problem with propagating fracture using a commercial code Geosim (Ji and Settari, 2009). The flow solution is solved first and uses the permeability field from the geomechanical solution of the previous time step. The passing of pressure from fluid flow code to the geomechanical module and permeability from the geomechanical module to the fluid flow represents the coupling between the codes. The fracture formation is solved using damage theory similarly to Tang and Kaiser (1998) (see also Tang, 1997; Tang et al., 2002; Yang et al., 2004; Zhu and Tang, 2004). The damage of the material initiates when the Mohr-Coulomb or tensile failure criteria (4) are satisfied locally:
σ 1' −
1 + sin φ ' cos φ σ 3 > 2c0 = f c 0 , or σ 3' < f t 0 1 − sin φ 1 − sin φ
(4)
where σ’1 and σ’3 are the maximum and minimum principal effective stresses, respectively, defined as σ’ij=σij-αpδij, fc0 is the compressive strength and ft0 is the tensile strength, c0 is cohesion, and ø is the friction angle. The damage variable D and the damaged Young’s modulus ED are then defined as:
λf c 0 E ε1
D = 1− (5) (6) E = (1 − cD) E D
where λ is a parameter determining the ratio between the initial and residual compressive strength (it describes damage to the strength of the material, i.e., the decreased cohesion of a fracture after the fracture slipped; it initiates with the failure and it is held constant afterwards.), fcr = λfc0, λ
