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Coupled seepage-mechanical modeling to evaluate formation deformation and casing failure in waterflooding oilfields
Journal of Petroleum Science and Engineering 180 (2019) 124–129
Contents lists available at ScienceDirect
Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol
Coupled seepage-mechanical modeling to evaluate formation deformation and casing failure in waterflooding oilfields
T
Lihong Hana, Fei Yinb,∗, Shangyu Yanga,∗∗, Wei Liub, Yong Dengb a
State Key Laboratory for Performance and Structure Safety of Petroleum Tubular Goods and Equipment Materials, CNPC Tubular Goods Research Institute, Xi'an, 710077, China b State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu University of Technology, Chengdu, Sichuan, 610059, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Well integrity Waterflooding Formation deformation Casing failure Coupled model
Waterflooding implemented to enhance oil recovery could concomitantly induce formation deformation and casing failure. The adverse responses should be evaluated to ensure the safety and performance of wells. A coupled seepage-mechanical model is developed to analyze the responses of formation and wells in waterflooding oilfields. The fluid-solid coupling method is employed to capture the flow and deformation in interlayers. The behavior of casing is predicted from the mechanical interaction among the wellbore-cement sheathcasing system. This model is validated by the analytical result. Results indicate that injection-production unbalance causes nonuniform pressurization or depletion in formation. Under pressurization, the vertical displacement along wellbore increases with the increases of axial position and time and displays a sharp rise in mudstone layer. There is an offset in mudstone layer. Casing stress increases under continuous pressurization or depletion, and stress concentration occurs in the mudstone interval. The predicted casing yield situation is consistent with the failure location in oilfield. The incongruous displacement in mudstone is the mechanism of casing deformation. Sustaining injection-production balance and adopting no-cementation operation are the possible strategies for mitigating the adverse effects of waterflooding. The findings can be applied to evaluate and manage formation response and casing integrity in waterflooding oilfields.
1. Introduction Waterflooding aims to maintain formation pressure. It is implemented to produce oil and hot-dry-rock geothermal resource. Some significant responses of formations and wells arise during the process of water injection and oil production, which include pore pressure variation, stress field redistribution, fracturing, fault reactivation, microseismicity, subsequent reservoir compaction/dilation and casing failure (Dutta et al., 2018; Zoback and Gorelick, 2012). This problem attracts growing concerns from oil companies and environmental departments. Therefore, the evaluation of injection induced responses is necessary in view of well integrity and performance. In waterflooding oilfields, injection leads to reservoir dilation and deformation. It exhibits an opposite deformation under excessive production. Formation deformation induced by injection includes elastic pore expansion and shear dilation. Large pore pressure increase especially hydraulic fracturing causes tensile and shear failures (Lin et al., 2017; Rawal, 2012). The strain accumulation increases the shear stress,
∗
together with the decreasing normal and frictional stresses, thus formation is likely to slide along weak interfaces (such as fractures/joints/ beddings/faults) (McGarr, 2014). The faulting may initiate in two ways including reactivation of preexisting faults and generation of new fractures/faults. The microseismic and acoustic emission (AE) events have reflected the tensile failure, shear failure and pore collapse induced by water injection. Stanchits et al. (2011) found that brittle failure and fault nucleated at a cloud of AE events in all samples. Nemoto et al. (2008) measured the stepwise slip with the maximum slip displacement of 15 mm by conducting the injection-induced slip experiments. Injection induced a M4.6 earthquake at Cogdell Canyon Reef, Texas (Davis and Pennington, 1989). Injection and the related induced seismicity could cause small-displacement sliding on faults in Gulf Coast (Nicot et al., 2014). One intractable problem induced by injection is casing failure. As is well known, the failure rate of casings in waterflooding oilfields is abnormally high. Casing failure may lead to production suspending, economical loss and leakage risk. According to statistical data, the
Corresponding author. Corresponding author. E-mail addresses: [email protected] (F. Yin), [email protected] (S. Yang).
∗∗
https://doi.org/10.1016/j.petrol.2019.05.035 Received 5 July 2018; Received in revised form 27 April 2019; Accepted 13 May 2019 Available online 14 May 2019 0920-4105/ © 2019 Elsevier B.V. All rights reserved.
Journal of Petroleum Science and Engineering 180 (2019) 124–129
L. Han, et al.
2G ⎞ σij′ = 2Gεij + ⎛K − εkk δij 3 ⎠ ⎝
casing failure rates in production and injection wells were 15.23% and 31.45% respectively in Qinghai oilfield (in March 2016). The failure rate of casings was 15.8% in Tarim oilfield (Wang et al., 2011). The ground uplifted 0.4 m and 88% casings damaged in the S-1 block of Daqing oilfield. Casing failure rate decreased with the decrease of surface subsidence in Belridge oilfield (Wright et al., 1995). Huang and Liu (2010) inferred that the high pressure and the hydration of mudstone induced the slide of beddings or interlayers, and consequently caused casing failure. Han et al. (2010) thought the sandstone layer expand and claystone localized slide caused casing failure in Daqing Oilfield. The main failure modes of casings include deformation and dislocation. Yin et al. (2018) pointed that the slip of weak structural interfaces caused casing shear deformation in waterflooding oilfields. The previous researches haven't covered the factors of three-dimensional (3D) geomechanics, well barrier and engineering operations. To be more practical, a novel coupled flow-geomechanics model consisting of wells and interlayers is developed. Based on this model, pore pressure, stress field, deformation and displacement of interlayers are predicted during waterflooding. From the interaction between cased hole and formation, the load, stress and deformation of casings are evaluated. Moreover, possible optimal strategies are proposed to ensure well integrity.
(6)
Where G is the shear modulus, K is the bulk modulus of rock skeleton. Combining the mass conservation equation and Darcy's law, the momentum conservation equation of fluid flow in porous media is derived as (Moradi et al., 2017):
α
∂p k ∂ε = ∇⋅⎜⎛ ∇p ⎞⎟ + Qf + [φCf + (α − φ) Cr ] ∂t ∂t ⎝μ ⎠
(7)
Where φ is the porosity, Cf and Cr are the fluid compressibility and skeleton compressibility respectively, k is the permeability of porous media, μ is the viscosity of fluid, Qf is the fluid flow rate, t is time. Based on a set of governing equations and initial/boundary conditions, this coupled problem can be solved by either analytical or numerical methods. The skeleton deformation model with the added item of pore pressure is solved and the strain are inputted to the flow model. Then, the fluid flow model with the added item of strain is solved and the pore pressure is inputted to skeleton deformation model (Liu and Feng, 2004). Lastly, the coupled flow-solid model can be solved by iterative approach. 2.1.2. Shear failure Plane stress state and strength change can account for the shear failure mechanism. The normal stress and shear stress on an arbitrary inclined plane are given as:
2. Modeling 2.1. Mathematical formulation 2.1.1. Governing equations of flow-solid coupling model Formation as porous media consists of the rock skeleton and pores saturated with fluid. The deformation of porous media and the flow of fluid in pores interact. Thus, the flow equations and geomechanical equilibrium equations must be tightly coupled. We follow the convention of stress value: the compressive stress is positive and the tensile stress is negative. According to the poroelasticity, the total stress in formation is equal to the sum of effective stress and pore pressure. The effective stress of rock skeleton is:
Where σα, τα are the normal stress and shear stress on the inclined plane respectively, σ1, σ3 are the maximum and minimum principal stresses respectively, β is the rotational angle from the x-axis to the normal line on inclined plane. Mohr-Coulomb failure criterion is a common shear slip criterion for geomaterial, which is written linearly as:
σij′ = σij − αpδij
τmax = c + (σ − p)tan ϕ
1, i = j δij = ⎧ 0, i ≠ j ⎨ ⎩
1
1
τα = 2 (σ1 − σ3)sin 2 β
(1)
∂p k ∂ε = ∇⋅⎜⎛ ∇p ⎞⎟ +S ∂t ∂t ⎝μ ⎠
(2)
pcr =
(3)
(4)
Where f is the external force vector, ∇ is Hamiltonian operator. The strain-displacement equation of rock skeleton is described as:
ε=
1 (∇u + ∇T u) 2
(9)
1 1 (σ1 + σ3) + (σ1 − σ3)cos 2 β − 2 2
1 (σ 2 1
− σ3)sin 2 β − c tan ϕ
(10)
Where pcr is the critical pore pressure. The practical critical pore pressure may be lower than the value calculated by Eq. (10). This is because that the injected water could change the physical and mechanical properties of a formation. The stress state of a geomaterial can be described by Mohr's stress circle plotted in Fig. 1. These are three main variations induced by injection. Firstly, Mohr's circle moves left because the increase of pore pressure decreases the effective stress (σ′). Secondly, Mohr's circle diameter increases because of the increase of the differential stress. For example, the horizontal effective stress increases by a less amount compared to the vertical effective stress under depletion (Streit and Hillis, 2004). Thirdly, triaxial rock tests indicate the cohesion and internal friction angle decrease with the increase of moisture content. Thus, the failure envelope curve shrinks and the shear strength decreases. Rock will slide once the changed stress circle intersects the failure envelope line, i.e., the shear stress (τ) equals or exceeds the shear strength of rock. These three variations, affecting the stability of rock after injection, could promote faulting such as frictional sliding on preexisting faults and/or generation of new fractures/faults.
Where ε is strain, v is fluid velocity, S is storativity, k is the permeability, μ is the fluid viscosity, t is time. The equations of solid deformation include three groups: equilibrium equation, geometry equation and constitutive equation. The equilibrium equation of formation is expressed as:
∇⋅σ − f = 0
(8)
Where τmax is the shear strength, σ is the total normal stress, p is the pore pressure, c is the cohesion, ϕ is the internal friction angle. By combining Eq. (8) and Eq. (9), the critical pore pressure of formation shear failure is inferred as:
Where σij′ is the effective stress, σij is the total stress tensor, p is the pore pressure of fluid, α is the Biot coefficient, δij is the Kronecker delta. According to Darcy's law and the law of mass conservation, fluid flow equation is (Moradi et al., 2017):
α
1
σα = 2 (σ1 + σ3) + 2 (σ1 − σ3)cos 2 β
(5)
Where ε is strain, u is the displacement vector of rock skeleton. Under the assumptions of small deformation and elastic material, the constitutive equation of the rock skeleton is written as (Siriwardane et al., 2013): 125
Journal of Petroleum Science and Engineering 180 (2019) 124–129
L. Han, et al.
Fig. 1. Stress and strength changes induced by injection.
2.2. Finite element model The schematic diagram of formation response and potential casing failure in waterflooding oilfields is shown in Fig. 2. The “workflow” of injection-induced response is summarized as follows: injection/production changing pore pressure, then stress redistribution/formation deformation, even fault reactivation/interfaces slip/seismicity, subsequent casing failure and ground subsidence/heave after several decades. To simplify the model, the following assumptions are made:
Fig. 3. The geometrical model (a) and the coupled seepage-mechanical model in waterflooding oilfields (b).
• The rock material in each layer is homogeneous and isotropic; • Neglecting the properties of water and oil, the pores in the rock are saturated with a single-phase fluid; • One injection well and one production well are drilled in the local region; • The temperature and gravity effects are neglected.
layers in the center are sandwiched by the fractional overburden and underlayer. The highly nonlinear partial differential equations relate pressure and displacement variations in space and time throughout the porous media. Because solving these equations analytically is impractical, a numerical approach for solving equations is a good method (Kidambi et al., 2017). The fluid-solid coupling problem can be solved by employing the finite element code. The finite element model (FEM) of coupled seepage-mechanical model is developed to simulate formation response and well behavior, which is shown in Fig. 3. The simulation is conducted by using the software Abaqus. The numerical approach is a general prediction method for waterflooding projects (Lin et al., 2017). One half of the model is established due to its symmetry.
One injection-production unit is extracted from the well pattern, the distance from wellbore to model boundary (Db) is set as a half of well distance (Dw). An appropriate flow boundary condition is assigned based on field measurement to neglect the boundary effect. Thus, the length and width of the model are 4Db and Db respectively. The height of model could be assigned according to the actual thicknesses of reservoir and adjacent layers. Generally, the mudstone and sandstone
Fig. 2. Schematic diagram of formation response and casing failure in waterflooding oilfields. 126
Journal of Petroleum Science and Engineering 180 (2019) 124–129
L. Han, et al.
respectively, and the mudstone-sandstone interlayers are sandwiched by upper and under layers with the thickness of 15 m. The dip angle of formation is equal to 0°. The injection and production are implemented in the sandstone intervals with the flow rates of 90 and 80 m3/d respectively. The simulated time is 1000 days after waterflooding.
The symmetric boundary is imposed on the section, and the other three lateral sides are constrained in normal displacements. The bottom side is fixed and the top side can move freely. The boundaries can be assumed to be impermeable when the model is large enough and the injection time is short. The formation is meshed by using the displacement - pore pressure element, and casing and cement are meshed by using the displacement element. The grid network is refined near the mudstone/sandstone layers and injection/production wells. The negative/positive flow rates are applied on the injection/production wellbores at the sandstone intervals.
3.1. Responses of formation and well The distribution of vertical displacement along wellbore is shown in Fig. 5. It indicates that the vertical displacement of wellbore increases with axial position (from bottom to top of formation) and time. It should be noted that the increase rate in mudstone is higher than other layers. The distribution of horizontal displacement along wellbore is shown in Fig. 6. The negative value represents the direction of −z axis in the model. This figure demonstrates that formation and wellbore move or bend in the direction from injection well to production well. The distortion of curve in the mudstone reflects the discontinuous displacement. The offsets arise at the interfaces of sandstone-mudstone and mudstone-overburden. It's noteworthy that the mudstone will slide once the shear stress exceeds the shear strength. The distribution of casing Mises stress is shown in Fig. 7. It is obvious that stress concentration occurs in the mudstone interval and the maximum value lies in the mudstone-sandstone interface. Based on the statistical data of the 26 damaged wells from Qinghai oilfield, the 22 wells (casings) damaged in the mudstone-sandstone interfaces, together with 3 wells in the mudstone interval and 1 well in sandstone. The similar situation has presented in other waterflooding oilfields (Huang and Liu, 2010; Han et al., 2010). The predicted result is consistent with the practical situation in oilfield. We can conclude that wellbore incongruous displacement in mudstone is the main reason of casing deformation in waterflooding oilfields. The failure mechanism of casings in waterflooding oilfields is the tension/compression and slip of layers resulting to axial force and shear stress on casing. Thus, the failure modes of casing include shear deformation, tensile failure and buckling. While, the main failure mode is shear deformation in waterflooding oilfields. Evolutions of differential pore pressure at the top of reservoir and casing maximum Mises stress in injection and production wells are shown in Fig. 8. The differential pore pressure (Δp) refers to the difference between pore pressures after injection and the initial pore pressure. The Δp increases because injection flow rate is larger than production flow rate. The maximum Mises stress of casing increases linearly with time until yield. The casings in the injection and production wells are predicted to yield at the 151 and 153 days respectively. It should be explained that the assumed flow rate in the model is larger than the practical values and boundaries are impermeable, so the predicted failure time is shorter than that observed in waterflooding oilfields.
2.3. Validation of model The proposed numerical model is validated by the analytical solution of the two-dimensional consolidation problem. Under undrained condition, the vertical displacement at the surface observation point can be calculated by:
1 u y ⎛⎜x , y = 0⎞⎟ = π ⎝ ⎠
∫V εV ⎛ b2 + −(xb− a)2 ⎞ dV ⎜
⎟
⎝
⎠
(11)
Where a, b are the point source coordinates, uy is the vertical displacement, εV is the volumetric strain, V is the volume of formation element. The comparison the numerical result with the analytical result (Nanayakkara and Wong, 2009) is shown in Fig. 4. The relative small error validates the reliability of the proposed model. Some scholars have also adopted and validated the method (Lin et al., 2017; Haddad et al., 2017). 3. Case study The waterflooding development is implemented in one oilfield to enhance oil recovery. The phenomenon of casing failure soon after waterflooding makes it necessary to understand formation response and failure mechanism. The initial in-situ stress and pore pressure are assigned in the reservoir. The vertical, maximum horizontal and minimum horizontal effective stresses are 30, 25 and 20 MPa respectively. The initial pore pressure is 20 MPa. The well distance (Dw) in well pattern is about 100 m. The diameter of wellbore in the reservoir is 215.9 mm. The diameter and thickness of production casing are 139.7 and 9.17 mm respectively. The material properties of rocks, cement sheath and casing are listed in Table 1. The thicknesses of mudstone and sandstone layers are 10 and 10 m
3.2. Optimal strategies To enhance casing integrity in waterflooding oilfields, the optimal strategies are studied. Although many factors affect casing integrity in the complex underground environment, the controllable and effective factors may focus on flow rate and cementation operation. The flow rate in the injection well is assumed to be a variable, while the flow rate in the production well is still set as a constant 80 m3/d. The effect of the differential flow rate between injection and production wells (Δq = qi−qp) on casing failure is investigated. The effect of the differential flow rate on casing failure time is shown in Fig. 9. When the differential flow rate is 10 m3/d, the failure times of casings in injection and production wells are 151 and 153 days respectively. When the differential flow rate is −10 m3/d, the failure times of casings in injection and production wells are 153 and 150 days respectively. When the differential flow rate is zero, the casings in injection and production wells will never fail. With the increase of differential flow rate, casing
Fig. 4. Comparison numerical result with analytical result. 127
Journal of Petroleum Science and Engineering 180 (2019) 124–129
L. Han, et al.
Table 1 Material properties of rocks, cement and casing. Material
Young's modulus (MPa)
Poisson's ratio
Cohesion (MPa)
Internal friction angle (°)
Permeability (mD)
Void ratio
Sandstone Mudstone Overburden/Underlayer Cement Casing
16709.7 3976.7 20000 7000 210000
0.352 0.386 0.25 0.23 0.3
7.16 1.09 10 9.0 –
45.9 25 46 24.0 –
60 5 10 – –
0.4 0.2 0.3 – –
Fig. 5. Distribution of vertical displacement along wellbore.
Fig. 7. Distribution of casing Mises stress.
Fig. 8. Evolutions of pore pressure and casing stress. Fig. 6. Distribution of horizontal displacement along wellbore.
well barrier in waterflooding oilfields. failure time shortens. Injection well fails earlier when formation pressurization, conversely production well fails earlier when formation depletion. The casing Mises stress decreases when the Young's modulus of cement sheath decreases. Especially, the casing won't be directly affected by the formation displacements if there is no cement sheath between wellbore and casing. No-cementation may cause the lack of annulus seal, wellbore instability and casing corrosion. Wellbore instability at this time is unlikely to affect drilling, production and well integrity. Furthermore, we can mitigate the other risks by using packers to seal different layers and corrosion inhibitor etc. No-cementation operation is an alternative to achieve mechanical and seal integrity of
4. Conclusions
• The •
128
coupled seepage-mechanical model is adopted to simultaneously evaluate fluid flow, formation deformation and casing behavior induced by waterflooding. This model is validated by the analytical solution and observed data. In the case, the formation and wellbore move upwards and offset. The special incongruous displacements arise in the mudstone interval and its interfaces. Casing stress increases under continuous pressurization or depletion, and stress concentration occurs in the mudstone interval. It is the main mechanism of casing deformation.
Journal of Petroleum Science and Engineering 180 (2019) 124–129
L. Han, et al.
σ1, σ3 α τmax c ϕ a, b uy V
maximum and minimum principal stresses respectively rotational angle shear strength cohesion internal friction angle point source coordinates vertical displacement volume of formation element
Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.petrol.2019.05.035. References Davis, S.D., Pennington, W.D., 1989. Induced seismic deformation in the Cogdell oilfield of West Texas. Bull. Seismol. Soc. Am. 79 (5), 1477–1494. Dutta, Kumar, Bhardwaj, Gunasekaran, Mohammed, 2018. Production induced faulting risk assessment in a depleted reservoir: a case study from deepwater KrishnaGodavari basin, India. J. Pet. Sci. Eng. 161, 319–333. Haddad, M., Du, J., Gilbert, S.V., 2017. Integration of dynamic microseismic data with a true 3D modeling of hydraulic-fracture propagation in the Vaca Muerta Shale. SPE J. 1–25. Han, X., Li, Q., Li, J., et al., 2010. Mechanism analysis of casing damage induced by high pressure water injection in Daqing oilfield. Key Eng. Mater. 417–418, 81–84. Huang, X., Liu, J., 2010. Mechanism of casing's shear failure in water injection oilfield and its numerical simulation. Phys. Numer. Simul. Geotech. Eng. 51–56. Kidambi, Hanegaonkar, Dutt, Kumar, 2017. A fully coupled flow and geomechanics model for a tight gas reservoir: implications for compaction, subsidence and faulting. J. Nat. Gas Sci. Eng. 38, 257–271. Lin, Chen, Jin, 2017. Evaluation of reservoir deformation induced by water injection in SAGD wells considering formation anisotropy, heterogeneity and thermal effect. J. Pet. Sci. Eng. 157, 767–779. Liu, Feng, 2004. Application of fluid-solid coupling theory in oil field casing damage forecast. Geo-Engineering Book Series 2. pp. 635–640 (C). McGarr, A., 2014. Maximum magnitude earthquakes induced by fluid injection. J. Geophys. Res.: Solid Earth 119 (2), 1008–1019. Moradi, Shamloo, Dezfuli, 2017. A sequential implicit discrete fracture model for threedimensional coupled flow-geomechanics problems in naturally fractured porous media. J. Pet. Sci. Eng. 150, 312–322. Nanayakkara, A., Wong, S., 2009. How far does surface heave propagate? A discussion on analytical and numerical modeling of the surface heave induced by subsurface fluid injection. KSCE J. Civ. Eng. 13 (4), 297–303. Nemoto, K., Moriya, H., Niitsuma, H., 2008. Mechanical and hydraulic coupling of injection-induced slip along pre-existing fractures. Geothermics 37 (2), 157–172. Nicot, Meckel, Carr, Oldenburg, 2014. Impact of induced seismic events on seal integrity, Texas Gulf Coast. Energy Procedia 63, 4807–4815. Rawal, C., 2012. 3D Modeling of Coupled Rock Deformation and Thermo-PoroMechanical Processes in Fractures. Texas A&M University. Siriwardane, H., Gondle, R., Bromhal, G., 2013. Coupled flow and deformation modeling of carbon dioxide migration in the presence of a caprock fracture during injection. Energy Fuels 27 (8), 4232–4243. Stanchits, Mayr, Shapiro, Dresen, 2011. Fracturing of porous rock induced by fluid injection. Tectonophysics 503 (1), 129–145. Streit, Hillis, 2004. Estimating fault stability and sustainable fluid pressures for underground storage of CO2 in porous rock. Energy 29 (9), 1445–1456. Wang, Yang, Zhu, et al., 2011. Law and countermeasures for the casing damage of oil production wells and water injection wells in Tarim Oilfield. Petrol. Explor. Dev. 38 (3), 352–361. Wright, C.A., Conant, R.A., Golich, G.M., Bondor, P.L., Murer, A.S., Dobie, C.A., 1995. Hydraulic Fracture Orientation and Production/Injection Induced Reservoir Stress Changes in Diatomite Waterfloods. Society of Petroleum Engineers. Yin, Deng, He, et al., 2018. Mechanical behavior of casing crossing slip formation in waterflooding oilfields. J. Pet. Sci. Eng. 167, 796–802. Zoback, M.D., Gorelick, S.M., 2012. Earthquake triggering and large-scale geologic storage of carbon dioxide. Proc. Natl. Acad. Sci. U.S.A. 109 (26), 10164–10168.
Fig. 9. Effect of the differential flow rate on casing failure time.
• Injection-production balance and no-cementation operation are the
effective approaches to sustain well integrity in waterflooding oilfields.
Acknowledgment This paper was finically supported by Natural Science Foundation of China (51574278, U1762211), the National key Technologies R&D Program of China (2016ZX05022-005), CNPC Basic Research Project (2019A-3911) and Shaanxi Outstanding Youth Fund (2018JC-030). Nomenclature σ σij′ σij p α δij f ε εV u G K φ k μ Cf , Cr
Qf t σα, τα
total normal stress effective stress total stress tensor pore pressure Biot coefficient Kronecker delta external force vector strain volumetric strain displacement vector of rock skeleton shear modulus bulk modulus of rock skeleton porosity permeability of porous media viscosity of fluid fluid compressibility and skeleton compressibility respectively fluid flow rate time normal stress and shear stress respectively
129
Contents lists available at ScienceDirect
Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol
Coupled seepage-mechanical modeling to evaluate formation deformation and casing failure in waterflooding oilfields
T
Lihong Hana, Fei Yinb,∗, Shangyu Yanga,∗∗, Wei Liub, Yong Dengb a
State Key Laboratory for Performance and Structure Safety of Petroleum Tubular Goods and Equipment Materials, CNPC Tubular Goods Research Institute, Xi'an, 710077, China b State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Chengdu University of Technology, Chengdu, Sichuan, 610059, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Well integrity Waterflooding Formation deformation Casing failure Coupled model
Waterflooding implemented to enhance oil recovery could concomitantly induce formation deformation and casing failure. The adverse responses should be evaluated to ensure the safety and performance of wells. A coupled seepage-mechanical model is developed to analyze the responses of formation and wells in waterflooding oilfields. The fluid-solid coupling method is employed to capture the flow and deformation in interlayers. The behavior of casing is predicted from the mechanical interaction among the wellbore-cement sheathcasing system. This model is validated by the analytical result. Results indicate that injection-production unbalance causes nonuniform pressurization or depletion in formation. Under pressurization, the vertical displacement along wellbore increases with the increases of axial position and time and displays a sharp rise in mudstone layer. There is an offset in mudstone layer. Casing stress increases under continuous pressurization or depletion, and stress concentration occurs in the mudstone interval. The predicted casing yield situation is consistent with the failure location in oilfield. The incongruous displacement in mudstone is the mechanism of casing deformation. Sustaining injection-production balance and adopting no-cementation operation are the possible strategies for mitigating the adverse effects of waterflooding. The findings can be applied to evaluate and manage formation response and casing integrity in waterflooding oilfields.
1. Introduction Waterflooding aims to maintain formation pressure. It is implemented to produce oil and hot-dry-rock geothermal resource. Some significant responses of formations and wells arise during the process of water injection and oil production, which include pore pressure variation, stress field redistribution, fracturing, fault reactivation, microseismicity, subsequent reservoir compaction/dilation and casing failure (Dutta et al., 2018; Zoback and Gorelick, 2012). This problem attracts growing concerns from oil companies and environmental departments. Therefore, the evaluation of injection induced responses is necessary in view of well integrity and performance. In waterflooding oilfields, injection leads to reservoir dilation and deformation. It exhibits an opposite deformation under excessive production. Formation deformation induced by injection includes elastic pore expansion and shear dilation. Large pore pressure increase especially hydraulic fracturing causes tensile and shear failures (Lin et al., 2017; Rawal, 2012). The strain accumulation increases the shear stress,
∗
together with the decreasing normal and frictional stresses, thus formation is likely to slide along weak interfaces (such as fractures/joints/ beddings/faults) (McGarr, 2014). The faulting may initiate in two ways including reactivation of preexisting faults and generation of new fractures/faults. The microseismic and acoustic emission (AE) events have reflected the tensile failure, shear failure and pore collapse induced by water injection. Stanchits et al. (2011) found that brittle failure and fault nucleated at a cloud of AE events in all samples. Nemoto et al. (2008) measured the stepwise slip with the maximum slip displacement of 15 mm by conducting the injection-induced slip experiments. Injection induced a M4.6 earthquake at Cogdell Canyon Reef, Texas (Davis and Pennington, 1989). Injection and the related induced seismicity could cause small-displacement sliding on faults in Gulf Coast (Nicot et al., 2014). One intractable problem induced by injection is casing failure. As is well known, the failure rate of casings in waterflooding oilfields is abnormally high. Casing failure may lead to production suspending, economical loss and leakage risk. According to statistical data, the
Corresponding author. Corresponding author. E-mail addresses: [email protected] (F. Yin), [email protected] (S. Yang).
∗∗
https://doi.org/10.1016/j.petrol.2019.05.035 Received 5 July 2018; Received in revised form 27 April 2019; Accepted 13 May 2019 Available online 14 May 2019 0920-4105/ © 2019 Elsevier B.V. All rights reserved.
Journal of Petroleum Science and Engineering 180 (2019) 124–129
L. Han, et al.
2G ⎞ σij′ = 2Gεij + ⎛K − εkk δij 3 ⎠ ⎝
casing failure rates in production and injection wells were 15.23% and 31.45% respectively in Qinghai oilfield (in March 2016). The failure rate of casings was 15.8% in Tarim oilfield (Wang et al., 2011). The ground uplifted 0.4 m and 88% casings damaged in the S-1 block of Daqing oilfield. Casing failure rate decreased with the decrease of surface subsidence in Belridge oilfield (Wright et al., 1995). Huang and Liu (2010) inferred that the high pressure and the hydration of mudstone induced the slide of beddings or interlayers, and consequently caused casing failure. Han et al. (2010) thought the sandstone layer expand and claystone localized slide caused casing failure in Daqing Oilfield. The main failure modes of casings include deformation and dislocation. Yin et al. (2018) pointed that the slip of weak structural interfaces caused casing shear deformation in waterflooding oilfields. The previous researches haven't covered the factors of three-dimensional (3D) geomechanics, well barrier and engineering operations. To be more practical, a novel coupled flow-geomechanics model consisting of wells and interlayers is developed. Based on this model, pore pressure, stress field, deformation and displacement of interlayers are predicted during waterflooding. From the interaction between cased hole and formation, the load, stress and deformation of casings are evaluated. Moreover, possible optimal strategies are proposed to ensure well integrity.
(6)
Where G is the shear modulus, K is the bulk modulus of rock skeleton. Combining the mass conservation equation and Darcy's law, the momentum conservation equation of fluid flow in porous media is derived as (Moradi et al., 2017):
α
∂p k ∂ε = ∇⋅⎜⎛ ∇p ⎞⎟ + Qf + [φCf + (α − φ) Cr ] ∂t ∂t ⎝μ ⎠
(7)
Where φ is the porosity, Cf and Cr are the fluid compressibility and skeleton compressibility respectively, k is the permeability of porous media, μ is the viscosity of fluid, Qf is the fluid flow rate, t is time. Based on a set of governing equations and initial/boundary conditions, this coupled problem can be solved by either analytical or numerical methods. The skeleton deformation model with the added item of pore pressure is solved and the strain are inputted to the flow model. Then, the fluid flow model with the added item of strain is solved and the pore pressure is inputted to skeleton deformation model (Liu and Feng, 2004). Lastly, the coupled flow-solid model can be solved by iterative approach. 2.1.2. Shear failure Plane stress state and strength change can account for the shear failure mechanism. The normal stress and shear stress on an arbitrary inclined plane are given as:
2. Modeling 2.1. Mathematical formulation 2.1.1. Governing equations of flow-solid coupling model Formation as porous media consists of the rock skeleton and pores saturated with fluid. The deformation of porous media and the flow of fluid in pores interact. Thus, the flow equations and geomechanical equilibrium equations must be tightly coupled. We follow the convention of stress value: the compressive stress is positive and the tensile stress is negative. According to the poroelasticity, the total stress in formation is equal to the sum of effective stress and pore pressure. The effective stress of rock skeleton is:
Where σα, τα are the normal stress and shear stress on the inclined plane respectively, σ1, σ3 are the maximum and minimum principal stresses respectively, β is the rotational angle from the x-axis to the normal line on inclined plane. Mohr-Coulomb failure criterion is a common shear slip criterion for geomaterial, which is written linearly as:
σij′ = σij − αpδij
τmax = c + (σ − p)tan ϕ
1, i = j δij = ⎧ 0, i ≠ j ⎨ ⎩
1
1
τα = 2 (σ1 − σ3)sin 2 β
(1)
∂p k ∂ε = ∇⋅⎜⎛ ∇p ⎞⎟ +S ∂t ∂t ⎝μ ⎠
(2)
pcr =
(3)
(4)
Where f is the external force vector, ∇ is Hamiltonian operator. The strain-displacement equation of rock skeleton is described as:
ε=
1 (∇u + ∇T u) 2
(9)
1 1 (σ1 + σ3) + (σ1 − σ3)cos 2 β − 2 2
1 (σ 2 1
− σ3)sin 2 β − c tan ϕ
(10)
Where pcr is the critical pore pressure. The practical critical pore pressure may be lower than the value calculated by Eq. (10). This is because that the injected water could change the physical and mechanical properties of a formation. The stress state of a geomaterial can be described by Mohr's stress circle plotted in Fig. 1. These are three main variations induced by injection. Firstly, Mohr's circle moves left because the increase of pore pressure decreases the effective stress (σ′). Secondly, Mohr's circle diameter increases because of the increase of the differential stress. For example, the horizontal effective stress increases by a less amount compared to the vertical effective stress under depletion (Streit and Hillis, 2004). Thirdly, triaxial rock tests indicate the cohesion and internal friction angle decrease with the increase of moisture content. Thus, the failure envelope curve shrinks and the shear strength decreases. Rock will slide once the changed stress circle intersects the failure envelope line, i.e., the shear stress (τ) equals or exceeds the shear strength of rock. These three variations, affecting the stability of rock after injection, could promote faulting such as frictional sliding on preexisting faults and/or generation of new fractures/faults.
Where ε is strain, v is fluid velocity, S is storativity, k is the permeability, μ is the fluid viscosity, t is time. The equations of solid deformation include three groups: equilibrium equation, geometry equation and constitutive equation. The equilibrium equation of formation is expressed as:
∇⋅σ − f = 0
(8)
Where τmax is the shear strength, σ is the total normal stress, p is the pore pressure, c is the cohesion, ϕ is the internal friction angle. By combining Eq. (8) and Eq. (9), the critical pore pressure of formation shear failure is inferred as:
Where σij′ is the effective stress, σij is the total stress tensor, p is the pore pressure of fluid, α is the Biot coefficient, δij is the Kronecker delta. According to Darcy's law and the law of mass conservation, fluid flow equation is (Moradi et al., 2017):
α
1
σα = 2 (σ1 + σ3) + 2 (σ1 − σ3)cos 2 β
(5)
Where ε is strain, u is the displacement vector of rock skeleton. Under the assumptions of small deformation and elastic material, the constitutive equation of the rock skeleton is written as (Siriwardane et al., 2013): 125
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Fig. 1. Stress and strength changes induced by injection.
2.2. Finite element model The schematic diagram of formation response and potential casing failure in waterflooding oilfields is shown in Fig. 2. The “workflow” of injection-induced response is summarized as follows: injection/production changing pore pressure, then stress redistribution/formation deformation, even fault reactivation/interfaces slip/seismicity, subsequent casing failure and ground subsidence/heave after several decades. To simplify the model, the following assumptions are made:
Fig. 3. The geometrical model (a) and the coupled seepage-mechanical model in waterflooding oilfields (b).
• The rock material in each layer is homogeneous and isotropic; • Neglecting the properties of water and oil, the pores in the rock are saturated with a single-phase fluid; • One injection well and one production well are drilled in the local region; • The temperature and gravity effects are neglected.
layers in the center are sandwiched by the fractional overburden and underlayer. The highly nonlinear partial differential equations relate pressure and displacement variations in space and time throughout the porous media. Because solving these equations analytically is impractical, a numerical approach for solving equations is a good method (Kidambi et al., 2017). The fluid-solid coupling problem can be solved by employing the finite element code. The finite element model (FEM) of coupled seepage-mechanical model is developed to simulate formation response and well behavior, which is shown in Fig. 3. The simulation is conducted by using the software Abaqus. The numerical approach is a general prediction method for waterflooding projects (Lin et al., 2017). One half of the model is established due to its symmetry.
One injection-production unit is extracted from the well pattern, the distance from wellbore to model boundary (Db) is set as a half of well distance (Dw). An appropriate flow boundary condition is assigned based on field measurement to neglect the boundary effect. Thus, the length and width of the model are 4Db and Db respectively. The height of model could be assigned according to the actual thicknesses of reservoir and adjacent layers. Generally, the mudstone and sandstone
Fig. 2. Schematic diagram of formation response and casing failure in waterflooding oilfields. 126
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respectively, and the mudstone-sandstone interlayers are sandwiched by upper and under layers with the thickness of 15 m. The dip angle of formation is equal to 0°. The injection and production are implemented in the sandstone intervals with the flow rates of 90 and 80 m3/d respectively. The simulated time is 1000 days after waterflooding.
The symmetric boundary is imposed on the section, and the other three lateral sides are constrained in normal displacements. The bottom side is fixed and the top side can move freely. The boundaries can be assumed to be impermeable when the model is large enough and the injection time is short. The formation is meshed by using the displacement - pore pressure element, and casing and cement are meshed by using the displacement element. The grid network is refined near the mudstone/sandstone layers and injection/production wells. The negative/positive flow rates are applied on the injection/production wellbores at the sandstone intervals.
3.1. Responses of formation and well The distribution of vertical displacement along wellbore is shown in Fig. 5. It indicates that the vertical displacement of wellbore increases with axial position (from bottom to top of formation) and time. It should be noted that the increase rate in mudstone is higher than other layers. The distribution of horizontal displacement along wellbore is shown in Fig. 6. The negative value represents the direction of −z axis in the model. This figure demonstrates that formation and wellbore move or bend in the direction from injection well to production well. The distortion of curve in the mudstone reflects the discontinuous displacement. The offsets arise at the interfaces of sandstone-mudstone and mudstone-overburden. It's noteworthy that the mudstone will slide once the shear stress exceeds the shear strength. The distribution of casing Mises stress is shown in Fig. 7. It is obvious that stress concentration occurs in the mudstone interval and the maximum value lies in the mudstone-sandstone interface. Based on the statistical data of the 26 damaged wells from Qinghai oilfield, the 22 wells (casings) damaged in the mudstone-sandstone interfaces, together with 3 wells in the mudstone interval and 1 well in sandstone. The similar situation has presented in other waterflooding oilfields (Huang and Liu, 2010; Han et al., 2010). The predicted result is consistent with the practical situation in oilfield. We can conclude that wellbore incongruous displacement in mudstone is the main reason of casing deformation in waterflooding oilfields. The failure mechanism of casings in waterflooding oilfields is the tension/compression and slip of layers resulting to axial force and shear stress on casing. Thus, the failure modes of casing include shear deformation, tensile failure and buckling. While, the main failure mode is shear deformation in waterflooding oilfields. Evolutions of differential pore pressure at the top of reservoir and casing maximum Mises stress in injection and production wells are shown in Fig. 8. The differential pore pressure (Δp) refers to the difference between pore pressures after injection and the initial pore pressure. The Δp increases because injection flow rate is larger than production flow rate. The maximum Mises stress of casing increases linearly with time until yield. The casings in the injection and production wells are predicted to yield at the 151 and 153 days respectively. It should be explained that the assumed flow rate in the model is larger than the practical values and boundaries are impermeable, so the predicted failure time is shorter than that observed in waterflooding oilfields.
2.3. Validation of model The proposed numerical model is validated by the analytical solution of the two-dimensional consolidation problem. Under undrained condition, the vertical displacement at the surface observation point can be calculated by:
1 u y ⎛⎜x , y = 0⎞⎟ = π ⎝ ⎠
∫V εV ⎛ b2 + −(xb− a)2 ⎞ dV ⎜
⎟
⎝
⎠
(11)
Where a, b are the point source coordinates, uy is the vertical displacement, εV is the volumetric strain, V is the volume of formation element. The comparison the numerical result with the analytical result (Nanayakkara and Wong, 2009) is shown in Fig. 4. The relative small error validates the reliability of the proposed model. Some scholars have also adopted and validated the method (Lin et al., 2017; Haddad et al., 2017). 3. Case study The waterflooding development is implemented in one oilfield to enhance oil recovery. The phenomenon of casing failure soon after waterflooding makes it necessary to understand formation response and failure mechanism. The initial in-situ stress and pore pressure are assigned in the reservoir. The vertical, maximum horizontal and minimum horizontal effective stresses are 30, 25 and 20 MPa respectively. The initial pore pressure is 20 MPa. The well distance (Dw) in well pattern is about 100 m. The diameter of wellbore in the reservoir is 215.9 mm. The diameter and thickness of production casing are 139.7 and 9.17 mm respectively. The material properties of rocks, cement sheath and casing are listed in Table 1. The thicknesses of mudstone and sandstone layers are 10 and 10 m
3.2. Optimal strategies To enhance casing integrity in waterflooding oilfields, the optimal strategies are studied. Although many factors affect casing integrity in the complex underground environment, the controllable and effective factors may focus on flow rate and cementation operation. The flow rate in the injection well is assumed to be a variable, while the flow rate in the production well is still set as a constant 80 m3/d. The effect of the differential flow rate between injection and production wells (Δq = qi−qp) on casing failure is investigated. The effect of the differential flow rate on casing failure time is shown in Fig. 9. When the differential flow rate is 10 m3/d, the failure times of casings in injection and production wells are 151 and 153 days respectively. When the differential flow rate is −10 m3/d, the failure times of casings in injection and production wells are 153 and 150 days respectively. When the differential flow rate is zero, the casings in injection and production wells will never fail. With the increase of differential flow rate, casing
Fig. 4. Comparison numerical result with analytical result. 127
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Table 1 Material properties of rocks, cement and casing. Material
Young's modulus (MPa)
Poisson's ratio
Cohesion (MPa)
Internal friction angle (°)
Permeability (mD)
Void ratio
Sandstone Mudstone Overburden/Underlayer Cement Casing
16709.7 3976.7 20000 7000 210000
0.352 0.386 0.25 0.23 0.3
7.16 1.09 10 9.0 –
45.9 25 46 24.0 –
60 5 10 – –
0.4 0.2 0.3 – –
Fig. 5. Distribution of vertical displacement along wellbore.
Fig. 7. Distribution of casing Mises stress.
Fig. 8. Evolutions of pore pressure and casing stress. Fig. 6. Distribution of horizontal displacement along wellbore.
well barrier in waterflooding oilfields. failure time shortens. Injection well fails earlier when formation pressurization, conversely production well fails earlier when formation depletion. The casing Mises stress decreases when the Young's modulus of cement sheath decreases. Especially, the casing won't be directly affected by the formation displacements if there is no cement sheath between wellbore and casing. No-cementation may cause the lack of annulus seal, wellbore instability and casing corrosion. Wellbore instability at this time is unlikely to affect drilling, production and well integrity. Furthermore, we can mitigate the other risks by using packers to seal different layers and corrosion inhibitor etc. No-cementation operation is an alternative to achieve mechanical and seal integrity of
4. Conclusions
• The •
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coupled seepage-mechanical model is adopted to simultaneously evaluate fluid flow, formation deformation and casing behavior induced by waterflooding. This model is validated by the analytical solution and observed data. In the case, the formation and wellbore move upwards and offset. The special incongruous displacements arise in the mudstone interval and its interfaces. Casing stress increases under continuous pressurization or depletion, and stress concentration occurs in the mudstone interval. It is the main mechanism of casing deformation.
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σ1, σ3 α τmax c ϕ a, b uy V
maximum and minimum principal stresses respectively rotational angle shear strength cohesion internal friction angle point source coordinates vertical displacement volume of formation element
Appendix A. Supplementary data Supplementary data to this article can be found online at https:// doi.org/10.1016/j.petrol.2019.05.035. References Davis, S.D., Pennington, W.D., 1989. Induced seismic deformation in the Cogdell oilfield of West Texas. Bull. Seismol. Soc. Am. 79 (5), 1477–1494. Dutta, Kumar, Bhardwaj, Gunasekaran, Mohammed, 2018. Production induced faulting risk assessment in a depleted reservoir: a case study from deepwater KrishnaGodavari basin, India. J. Pet. Sci. Eng. 161, 319–333. Haddad, M., Du, J., Gilbert, S.V., 2017. Integration of dynamic microseismic data with a true 3D modeling of hydraulic-fracture propagation in the Vaca Muerta Shale. SPE J. 1–25. Han, X., Li, Q., Li, J., et al., 2010. Mechanism analysis of casing damage induced by high pressure water injection in Daqing oilfield. Key Eng. Mater. 417–418, 81–84. Huang, X., Liu, J., 2010. Mechanism of casing's shear failure in water injection oilfield and its numerical simulation. Phys. Numer. Simul. Geotech. Eng. 51–56. Kidambi, Hanegaonkar, Dutt, Kumar, 2017. A fully coupled flow and geomechanics model for a tight gas reservoir: implications for compaction, subsidence and faulting. J. Nat. Gas Sci. Eng. 38, 257–271. Lin, Chen, Jin, 2017. Evaluation of reservoir deformation induced by water injection in SAGD wells considering formation anisotropy, heterogeneity and thermal effect. J. Pet. Sci. Eng. 157, 767–779. Liu, Feng, 2004. Application of fluid-solid coupling theory in oil field casing damage forecast. Geo-Engineering Book Series 2. pp. 635–640 (C). McGarr, A., 2014. Maximum magnitude earthquakes induced by fluid injection. J. Geophys. Res.: Solid Earth 119 (2), 1008–1019. Moradi, Shamloo, Dezfuli, 2017. A sequential implicit discrete fracture model for threedimensional coupled flow-geomechanics problems in naturally fractured porous media. J. Pet. Sci. Eng. 150, 312–322. Nanayakkara, A., Wong, S., 2009. How far does surface heave propagate? A discussion on analytical and numerical modeling of the surface heave induced by subsurface fluid injection. KSCE J. Civ. Eng. 13 (4), 297–303. Nemoto, K., Moriya, H., Niitsuma, H., 2008. Mechanical and hydraulic coupling of injection-induced slip along pre-existing fractures. Geothermics 37 (2), 157–172. Nicot, Meckel, Carr, Oldenburg, 2014. Impact of induced seismic events on seal integrity, Texas Gulf Coast. Energy Procedia 63, 4807–4815. Rawal, C., 2012. 3D Modeling of Coupled Rock Deformation and Thermo-PoroMechanical Processes in Fractures. Texas A&M University. Siriwardane, H., Gondle, R., Bromhal, G., 2013. Coupled flow and deformation modeling of carbon dioxide migration in the presence of a caprock fracture during injection. Energy Fuels 27 (8), 4232–4243. Stanchits, Mayr, Shapiro, Dresen, 2011. Fracturing of porous rock induced by fluid injection. Tectonophysics 503 (1), 129–145. Streit, Hillis, 2004. Estimating fault stability and sustainable fluid pressures for underground storage of CO2 in porous rock. Energy 29 (9), 1445–1456. Wang, Yang, Zhu, et al., 2011. Law and countermeasures for the casing damage of oil production wells and water injection wells in Tarim Oilfield. Petrol. Explor. Dev. 38 (3), 352–361. Wright, C.A., Conant, R.A., Golich, G.M., Bondor, P.L., Murer, A.S., Dobie, C.A., 1995. Hydraulic Fracture Orientation and Production/Injection Induced Reservoir Stress Changes in Diatomite Waterfloods. Society of Petroleum Engineers. Yin, Deng, He, et al., 2018. Mechanical behavior of casing crossing slip formation in waterflooding oilfields. J. Pet. Sci. Eng. 167, 796–802. Zoback, M.D., Gorelick, S.M., 2012. Earthquake triggering and large-scale geologic storage of carbon dioxide. Proc. Natl. Acad. Sci. U.S.A. 109 (26), 10164–10168.
Fig. 9. Effect of the differential flow rate on casing failure time.
• Injection-production balance and no-cementation operation are the
effective approaches to sustain well integrity in waterflooding oilfields.
Acknowledgment This paper was finically supported by Natural Science Foundation of China (51574278, U1762211), the National key Technologies R&D Program of China (2016ZX05022-005), CNPC Basic Research Project (2019A-3911) and Shaanxi Outstanding Youth Fund (2018JC-030). Nomenclature σ σij′ σij p α δij f ε εV u G K φ k μ Cf , Cr
Qf t σα, τα
total normal stress effective stress total stress tensor pore pressure Biot coefficient Kronecker delta external force vector strain volumetric strain displacement vector of rock skeleton shear modulus bulk modulus of rock skeleton porosity permeability of porous media viscosity of fluid fluid compressibility and skeleton compressibility respectively fluid flow rate time normal stress and shear stress respectively
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