Mitigating lost circulation: A numerical assessment of wellbore strengthening

Journal of Petroleum Science and Engineering 157 (2017) 657–670

Contents lists available at ScienceDirect

Journal of Petroleum Science and Engineering journal homepage: www.elsevier.com/locate/petrol

Mitigating lost circulation: A numerical assessment of wellbore strengthening Peidong Zhao a, *, Claudia L. Santana b, Yongcun Feng a, Kenneth E. Gray a a b

The University of Texas at Austin, United States Halliburton, Houston, TX, United States

A R T I C L E I N F O

A B S T R A C T

Keywords: Wellbore stability Lost circulation Wellbore strengthening Rock mechanics Hydraulic fracturing

Drilling in complex geological settings often possesses significant risk for unplanned events that could potentially impede already cost-demanding operations. Lost circulation, a major challenge in well construction, refers to the loss of drilling fluid into formation during drilling operations. When excessive wellbore pressure appears, lost circulation is induced by tensile failure or reopening of natural fractures at the wellbore. Over years of research efforts and field practices, wellbore strengthening techniques have been successfully applied in the field to mitigate lost circulation and have proved effective in extending the drilling margin to access undrillable formations. In fact, wellbore strengthening contributes additional resistance to fractures so that an equivalent circulating density higher than the estimated fracture gradient can be exerted on the wellbore. In this study, a fully coupled hydraulic fracture propagation model based on the cohesive zone model is presented. By implementing the model, an extensive parametric study is conducted to investigate factors involved in lost circulation. The parametric influences emphasizing the mass balance within the fracture reveal mechanisms of lost circulation mitigation. Simulation studies on wellbore strengthening are conducted in two parts, hoop stress enhancement and fracture resistance enhancement. First, a near-wellbore stress analysis characterizes wellbore mechanical responses during lost circulation. The results show elevated hoop stress during fracture width development, which validates the hypothesis of hoop stress enhancement. Also, beneficial influences from poroelastic effect and high rock stiffness are demonstrated. Then, a novel method to simulate fracture sealing is introduced to quantify fracture gradient extension for field practices. With this method, a case study on fracture sealing investigates the roles of sealing permeability and sealing length. The results show inhibition of fracture repropagation and conclude that fracture tip protection is achieved through fracture sealing and fracture fluid dissipation. From the case study, operational insights on wellbore strengthening design are derived.

1. Introduction The mud weight window (MWW) compels the annular pressure profile by a lower limit to prevent fluid influx and wellbore instability and by an upper limit (i.e., fracture gradient) to avoid wellbore breakdown and lost circulation (Zhang et al., 2008). A narrow MWW commonly appears in drilling depleted reservoirs where fluid production reduces the fracture gradient and extended-reach wells with large annulus pressure fluctuation. Drilling in the above settings is often plagued with lost circulation and its chain reactions (e.g., wellbore instability, underground blowout, unplanned casing point, etc.), causing protracted nonproductive time and exorbitant expense to remediate the issues (Cook et al., 2011).

* Corresponding author. E-mail address: [email protected] (P. Zhao). http://dx.doi.org/10.1016/j.petrol.2017.07.052 Received 28 February 2017; Received in revised form 20 June 2017; Accepted 19 July 2017 Available online 20 July 2017 0920-4105/© 2017 Elsevier B.V. All rights reserved.

Lost circulation is caused by unintentional hydraulic fracturing of a wellbore. Excessive wellbore pressure (i.e., annular pressure) can originate from surge effect, annulus pack-off, high annulus friction losses, etc. When wellbore pressure exceeds fracture initiation pressure (FIP) and fracture propagation pressure (FPP), hydraulic fracturing is induced (Feng et al., 2016); then, drilling fluid invades the induced fracture and is lost into the formation. For an intact wellbore, FIP at the wellbore can be higher than far-field FPP because its circular geometry magnifies the insitu stresses into a more compressive form (Hubbert and Willis, 1957). However, if fractures are induced or natural fractures exist, the wellbore fails when wellbore pressure equals FPP (Lee et al., 2004). Therefore, to prevent lost circulation for a fractured wellbore, fracture gradient is governed by FPP. In complex drilling environments, limited casing points

P. Zhao et al.

Journal of Petroleum Science and Engineering 157 (2017) 657–670

2012; Feng et al., 2015; Mehrabian et al., 2015; Zhang et al., 2016, Zhong et al., 2017). Field observations have also shown the improvement of a wellbore's pressure-sustaining capability after treatment (Aston et al., 2004; Dupriest, 2005; Song and Rojas, 2006; Aston et al., 2007). The objective of the fracture resistance enhancement method is to raise the apparent FPP (noting that fracture repropagation occurs after the reopening). In this method, the immobile mass acts as a sealant, which prevents wellbore pressure from transmitting to the fracture tip (as shown in Fig. 2). In theory, the opening and the propagation of a hydraulic fracture is governed by the net pressure, which is fracture fluid pressure minus the minimum in-situ stress (Yew and Weng, 2014). As immobile mass inhibits fluid flow across, the net pressure in the vicinity of the tip is reduced. Thus, the fracture propagation is suppressed. The DEA-13 project conducted by the Drilling Engineering Association pioneered the fracture resistance enhancement method (Morita et al., 1990, 1996; Onyia, 1994). From their experiments, a mud dehydrated zone was observed in the vicinity of the tip, and water-based mud fracturing presented higher FPPs than oil-based mud. The dehydrated zone is believed to isolate the fracture tip from the wellbore pressure, restricting the propagation until fluid breaks through the immobile mass and pressurizes the fracture tip. Hence, a better dehydration capability of LCM contributes to higher FPPs in water-based mud fracturing. Fuh et al. (1992, 2007) presented the tip screen-out model with mathematical descriptions and field trials. Kaageson-Loe et al. (2009) investigated the fracture sealing capability of particulate-based LCM and detailed a fracture-sealing-mechanism hypothesis. van Oort et al. (2011) proposed the fracture propagation resistance model. Since particle aggregation yields a low permeability when it is poorly sorted, many experiments found that optimum particle-sized distribution exists in elevating the FPP (van Oort et al., 2011; Razavi et al., 2015). Guo et al. (2014) stated that preventive treatment with low-concentration LCM is more effective than remedial treatment with higher concentration. Previous WBS studies have contributed considerable knowledge for the drilling community. Due to the complexity of bottomhole conditions, simplification must be applied in the model for field implementation. In previous hoop stress enhancement studies, assumptions have often been made on linear elastic rock properties and predefined fracture length (Alberty and McLean, 2004; Wang et al., 2007; Morita and Fuh, 2012; van Oort and Razavi, 2014; Feng and Gray, 2016). Even though these assumptions offer quick assessment for WBS operations, they might underestimate the fracture gradient extension without considering the pressure dissipation within the fracture. In addition, experimental and field observations presenting enhanced pressure-containing capability after WBS treatment are independently explained with very different concepts and lack quantitative validations. However, it might be too difficult to perform real-time monitoring in a laboratory or at a field to detect, for example, the fracture reopening and dehydration location inside fracture. Therefore, the fundamental mechanisms of WBS are still in dispute within the industry. In this paper, a fully coupled hydraulic fracturing model based on the cohesive zone model (CZM) is presented. The model explicitly simulates the dynamic process of fracture growth during lost circulation, along with mechanical wellbore behaviors. By utilizing the model, an extensive parametric study is conducted to investigate drilling-induced fractures under various rock properties and bottomhole conditions. Inspecting parametric influences pinpoints the controllable factors impeding fracture growth, which are believed to serve principal roles in WBS treatment. This paper also aims to validate the proposed hypotheses of WBS. First, hoop stress enhancement is validated by comparing wellbore mechanical responses during fracture propagation. Then, a novel simulation method is introduced that integrates fracture resistance enhancement (i.e., fracture sealing for tip protection) into the hydraulic fracturing simulation. This method explicitly accounts for the dynamic diffusion across the immobile mass, captures the time-dependent responses of an induced fracture, and offers the capability of quantifying the fracture gradient extension for drilling operations. Lastly, a case study on fracture

exist in order to reach the target depth so that necessary mud weight reduction at a hole section is constrained by the subsequent drilling plan. Hence, mitigating lost circulation, which aims for widening the MWW, is essential for the well-being of drilling operations. Wellbore strengthening (WBS) techniques have been widely practiced. From field observations, WBS can improve resistance to the induced or natural fracture so that the wellbore can sustain the equivalent circulating density (ECD) higher than the estimated fracture gradient. In general, current WBS techniques originate from two hypotheses: hoop stress enhancement method (e.g., the stress cage) and fracture resistance enhancement method (e.g., the tip screen-out). Nevertheless, in all of the techniques, lost circulation material (LCM) is added into drilling fluid and is engineered for particular sizes and mechanical properties based on the predicted fracture geometry. Upon circulating to the fractured depth, LCM is expected to deposit within the fracture and form a particle aggregation (or immobile mass). Since LCM is carried by the mud, dehydration of the aggregation dictates the success of WBS. For this reason, WBS in permeable formations (e.g., sandstone) is more effective than in low-permeable formations (e.g., shale). Lost circulation issues in fractured or vugular formations (e.g., carbonate) can be extreme cases, where applying WBS is impractical or uneconomical (Masi et al., 2011). Therefore, this paper only speaks to lost circulation issues in clastic rocks such as sandstone and shale. The purpose of the hoop stress enhancement method is to modify the local compressive hoop stress. Hoop stress is the tangential stress with respect to wellbore circumference. A fracture at the wellbore is essentially held closed by compressive hoop stress. Applying displacement at the fracture surface builds the hoop stress, which in turn raises the required wellbore pressure to reopen the fracture and extends the margin of ECD (as shown in Fig. 1). With this objective, the immobile mass (formed by the dehydration of particle aggregation) intends to prop the fracture. Alberty and McLean (2004) introduced the stress cage model. A stress cage projects that LCM deposits near the fracture mouth, acting as a proppant to modify the hoop stress in the near-wellbore region and as a seal to isolate a fracture from wellbore pressure. Dupriest (2005) presented the fracture closure stress (FCS) model. Different from the stress cage model, the FCS model seeks stress modification on a longer scale along the fracture. Additionally, this model emphasizes tip isolation, enhancing the resistance of fracture propagation. Theoretical studies have found that hoop stress can be significantly increased in the vicinity of particle aggregation and have underlined the strong influence of insitu stress anisotropy, propping location, and formation rock stiffness (Alberty and McLean, 2004; Wang et al., 2007, 2009; Morita and Fuh,

Fig. 1. A schematic of hoop stress enhancement for half of the wellbore. The dotted line indicates the displacement of the fracture surface after enhancement. 658

P. Zhao et al.

Journal of Petroleum Science and Engineering 157 (2017) 657–670

Fig. 2. A schematic of fracture resistance enhancement for half of the wellbore. Dotted lines represent fluid seepage at the fracture surface to the formation. The shortening of dotted lines toward the tip indicates fracture fluid pressure reduction generated by the immobile mass.

media, Reynold's lubrication theory for fracturing fluid flow, the tractionseparation constitutive law for cohesive fracture modeling, and Bernoulli's equation for fluid flow in the pipe (Abaqus, 2016).

sealing conditions is demonstrated, providing constructive insights for field practices of WBS. 2. Numerical model

2.2.1. Fluid flow in porous media Pore fluid is assumed to be single-phase and fully saturating the porous medium. A continuity equation equating the increase rate of fluid volume, V, stored at a point to the rate of volume of fluid flowing across the surface, S, into the point within the time increment is as follows:

2.1Methodology description Abaqus Standard, a software for finite element analysis, is adopted in this study. The fully coupled hydraulic fracturing code based on CZM offers coupling of the physical processes during lost circulation, including (1) pore fluid flow within the porous medium, (2) porous medium deformation due to fluid pressurization at the opening surface and poroelastic effect generated by pore fluid flow, (3) fracture fluid flow and seepage loss within the fracture, and (4) irreversible fracture propagation. In this model, two-dimensional (2D) plane strain is assumed to minimize computation of the parametric study. The advantage of CZM is considering the fracture process zone ahead of the crack tip to capture nonlinear fracture mechanics behavior on the basis of energy condition, which implies that fracture propagation occurs when the energy release rate reaches a critical value in the process zone. Different from the linear elastic fracture mechanics characteristics of fracture dimension and loading condition, CZM models the crack tip as a process zone experiencing progressive damage with material softening due to microcracks and pore space (Barenblatt, 1959, 1962), and it estimates distribution and intensity of cohesive stress based on material properties. Validation of the numerical tool used here against semianalytical fracture propagation solutions is documented by Zielonka et al. (2014). Fracturing experiments have also confirmed the applicability of the numerical model used here (Ning et al., 2015). Yao et al. (2010) compared cohesive fracture results with a pseudo-threedimensional (pseudo-3D) model and the Perkins-Kern-Nordgren model, and they showed that CZM can predict hydraulic fracture geometry more accurately. Shin and Sharma (2014) and Haddad and Sepehrnoori (2014) investigated stress interference during multifracture propagation. Kostov et al. (2015) illustrated an automated workflow to estimate fracture geometry for optimizing wellbore integrity. Wang et al. (2016a) investigated plasticity effect during fracture propagation.

d dt




 ∫ ρw ϕdV V

¼  ∫ ρw ϕnvw dS

(1)

S

where ρw is the mass density of pore fluid, ϕ is the porosity of the porous medium, vw is the average velocity of pore fluid relative to the solid phase (the seepage velocity), and n is the outward normal vector to surface S. Constitutive behavior of pore fluid flow is governed by Darcy's law as follows:

b⋅ ϕvw ¼  K

∂ψ ∂X

(2)

b is where ϕvw is the volumetric flow rate of the liquid through surface S, K b ¼ Kgρw converts permeability (in the hydraulic conductivity in which K μ

Darcy's unit) to hydraulic conductivity, μ is the fluid viscosity, and ψ is the fluid pressure head. Gravitational effect is ignored in this study. 2.2.2. Porous medium deformation The porous medium is assumed to be isotropic, poroelastic material. The theory of poroelasticity (Biot, 1941) is employed for coupling linear elastic rock deformation and pore pressure. Effective stress (σ ij ) dictates the material behavior and is expressed in terms of total stress (Sij ) as follows:

σ ij ¼ Sij þ pp δij

(3)

Stress equilibrium for the solid phase of the material in terms of the principle of virtual work for the volume under consideration in its current configuration at time t is as follows:

2.2Governing equations

  ∫ σ ij  pp I : δεdV ¼ ∫ t⋅δvdS þ ∫ f ⋅δvdS

In the hydraulic fracturing model, the governing equations are Darcy's law for pore fluid flow, Biot's theory of poroelasticity for porous

V

659

s

V

(4)

P. Zhao et al.

Journal of Petroleum Science and Engineering 157 (2017) 657–670

where δε is the virtual rate of deformation, I is the unit matrix, t are surface tractions per unit area, and f are body forces (excluding fluid weight) per unit volume. Negative stress value denotes for compressive stress in Abaqus. 2.2.3. Fluid flow in the fracture Fluid flow in the fracture is modeled by the cohesive element. The fluid constitutive response is reflected by tangential flow within the gap and normal flow across the gap (as shown in Fig. 3). Mass balance within the fracture is governed as follows:

∂g ∂qf þ þ vT þ vB ¼ 0 ∂t ∂s

Fig. 3. Fluid flow within the cohesive element (Zielonka et al., 2014).

(5)

where g is the fracture aperture, qf ¼ vf ⋅g is the rate of fracture fluid flowing within the fracture, and vT and vB are the volumetric flux of fluid leaking through the fracture surfaces into the rock. Incompressible, Newtonian fluid through a narrow slit comprises the momentum equation as follows:

g3 ∂pf qf ¼  12μf ∂s

(6)

where μf is the fracture fluid viscosity. Fluid leak-off is characterized by a linear model as follows:

vT ¼ CT ðpF  pT Þ

(7)

vB ¼ CB ðpF  pB Þ

(8)

Fig. 4. A typical traction-separation law (Zielonka et al., 2014).

is the critical fracture energy, Gc .

where pF , pT , and pB are the fracture fluid pressure and pore fluid pressure on the top and bottom surface of the fracture, and CT and CB are the leak-off coefficients for each surface. Leak-off coefficients define permeability damage at the fracture surface by drilling fluid (i.e., mud cake), and two nodal points with a plane strain thickness define the crossing surface.

2.2.5. Fluid flow in the pipe Fluid pipe elements are used to model fluid flow at the wellbore annulus. Steady-state, incompressible, and single phase are assumed. Pressure boundary condition is prescribed at the pipe inlet simulating the ECD at the wellbore annulus. Pipe flow pressure loss is governed by Bernoulli's equation as follows:

2.2.4. Fracture initiation and propagation A layer of coupled pressure/deformation cohesive elements is placed in the direction of maximum horizontal stress and predefines the propagating path of a planar fracture. Material damage (fracture propagation) is constituted by a modified CZM with an additional degree of freedom for pore pressure. Initially, the material is modeled with linear elastic behavior. When stress applied at the interface satisfies damage initiation criteria, fluid invades the cohesive element and applies a traction on the fracture surface. Then, gradual damage begins as the surface traction counteracts the in-situ compressive stress. A traction-separation law governs the progressive loss of mechanical strength. After being fully damaged, the cohesive element becomes an irreversibly fractured material. Fig. 4 illustrates the traction-separation law adopted in the model. Initial stiffness, Ko , defines the constitutive behavior of linear elastic material prior to damage initiation. Damage initiation is defined by the quadratic nominal stress criterion as follows:



Nn NOn

2

 þ

Ns NOs

2

 þ

Nt NOt


ΔP ¼



ρv2 2

(10)

where ΔP is the pressure loss between two nodes, ρ is the fluid density, Ki is the directional loss term, f is the frictional factor of pipe, L is the pipe length, and Dh is the pipe diameter. 2.3Model setup The model comprises a semicircular plate and a fluid pipe (as shown in Fig. 5). Plane strain thickness is 1 m; the external boundary is 15 m away from the wellbore center; the wellbore radius is 0.125 m; and the fluid pipe is 1 m long. Pressure loss at the fluid pipe is negligible. A tie constraint is applied between the last node of the fluid pipe and all nodes along the wellbore surface so that these nodes share the same pore pressure, maintaining mass conservation at the wellbore. A layer of mud cake exists by the wellbore surface, representing a net effect of formation damage by drilling fluid. By predefining the stress field, the fracture propagates along the layer of cohesive elements placed along the azimuth of SHmax. Materials are assumed homogeneous and isotropic. Overall, the simulation model consists of fluid pipe elements (FP2D2), cohesive elements (COH2D4P), and pore fluid/stress elements (CPE4P). The simulation model follows three steps: initialization, wellbore excavation, and lost circulation. The first step initializes porosity, pore pressure, and effective in-situ stresses. Zero radial displacement boundary condition is assigned to the outer surface and wellbore surface. Zero normal displacement is assigned to the symmetric surface. The second step simulates the stress perturbation due to drilling, where material is

2 ¼1

fL þ Ki Dh

(9)

where the superscript indicates the direction of stress (i.e., N n , N s ; N t represent stress applied in the normal, the first, and the second shear stress direction), and No is the corresponding cohesive strength. After damage initiation, the cohesive layer changes from g0 , where maximum traction meets, to g1 , where the layer is fully damaged. Then, it is free to open beyond this separation as complete damage. If the interface is unloaded before complete damage, a linear traction ramp-down is applied with damaged stiffness, Kp . Linear softening is assumed in our study. The area under the softening part of the traction-separation curve 660

P. Zhao et al.

Journal of Petroleum Science and Engineering 157 (2017) 657–670

Fig. 5. Left: Model geometry with mesh. Right: Model geometry in the near-wellbore region.

properties of the base case are listed in Table 1. The mud cake layer characterizes a net effect of formation damage in the near-wellbore region. Mud cake buildup experiments showed an initial permeability of 0.01 mD and a permeability range of 0.0005–0.01 mD after a few minutes (Jaffal, 2016). Considering the narrow fracture opening and rapid fracture propagation, cake development at the fracture surface in the early propagation process should be incomplete. Therefore, within this 5s fracture propagation simulation, 0.1 mD (10 times higher than the initial permeability in the experiments) is used as the damaged permeability (expressed by leak-off coefficient) at the fracture surface. Mud cake shares the same mechanical properties as rock. An injection case is additionally performed on the base case to estimate FPP (as shown in Fig. 7). FPP, which is the injection pressure recorded at the pipe inlet, is above minimum horizontal stress in the injection case. A pressure of 78 MPa is selected as a boundary condition at the wellbore for all lost circulation simulations, which is higher than the simulated FPP but lower than the analytical breakdown pressure (i.e., 78.8 MPa calculated by the Hubbert-Willis equation). The final fracture geometry of the base case is significantly larger than the injection case (as shown in Fig. 8). This is because the average rate of fluid entering the fracture is about tripled in the base case (as shown in Fig. 9). Base case fracture length is about 11 m after wellbore pressure is

removed and mud pressure is applied at the wellbore surface. In this step, zero radial displacement at the wellbore surface is disabled and replaced with a mechanical load that equals the fluid pressure in the wellbore. This loading condition implies a pressure balance between drilling fluid and formation fluid. In the third step, a constant wellbore pressure (i.e., ECD) is assigned at the pipe inlet to simulate excessive pressure overbalance of lost circulation. A constant pore pressure is assigned to the external boundary with a value of initial pore pressure. With two pressure boundary conditions defined, fracture propagation is computed through a transient coupled pore pressure/effective stress analysis. In this step, wellbore surface traction is always equal to the fluid pressure at the fracture mouth. The solving process of this coupled system is shown in Fig. 6. 3. Parametric study of lost circulation The purpose of this analysis is to investigate lost circulation patterns under various material properties and downhole conditions. The focused subjects are final geometry of induced fracture and rate of lost circulation. A base case is generated as a benchmark for the parametric study. The base case simulates lost circulation occurring in a vertical wellbore with a 3 000-m true vertical depth. Estimations of in-situ conditions and rock

Table 1 Input parameters for base case.

Fig. 6. Solution flow diagram for fracture propagation procedure (Wang, 2015). 661

Parameter

Value

Unit

True vertical depth Overburden gradient Vertical stress (Sv ) K (Sv /Shmin ) Minimum horizontal stress (Shmin ) K (Sv /SHmax ) Maximum horizontal stress (SHmax ) Pore pressure gradient Pore pressure Wellbore pressure Young's modulus Poisson's ratio Biot's coefficient Porosity Formation rock permeability Mud cake permeability Pore fluid specific gravity Pore fluid viscosity Cohesive strength Fracture energy Fracture fluid viscosity Leak-off coefficient

3 000 23 69 0.79 54.51 0.82 56.58 9.8 29.4 78 1Eþ07 0.2 1 0.2 100 0.0005 9.8 1 1 250 0.1 20 1E–07

m MPa/km MPa MPa MPa MPa/km MPa MPa kPa

mD mD kN/m3 cp kPa kJ/m2 cp m3/KPa/s

P. Zhao et al.

Journal of Petroleum Science and Engineering 157 (2017) 657–670

longer fracture (as shown in Fig. 10). When stiffness is lower, rock is more compliant with deformation so that the fracture width becomes wider under the same traction. On the other hand, when stiffness is higher, stress concentration at the fracture tip is easier to aggregate, and strain energy buildup at the fracture tip tends to be fostered. As a result, fractures propagate faster. Overall, the influence of rock stiffness on width is greater than that on length based on the simulation results. Because stiffer rock generates a smaller fracture mouth opening, the smaller width restricts incoming fluid. Therefore, with a constant pressure held at the wellbore, fluid flow tends to be less in a stiffer rock with a smaller fracture mouth opening. Studying rock mechanical properties also highlights the effect of fracturing criteria, in which a higher fracture critical energy contributes more resistance to fracture propagation and results in a shorter fracture length (as shown in Fig. 11). The flow rates show negligible influence from the fracturing resistance of rock. Mud loss rate is significantly influenced by rock permeability, which is expressed by hydraulic conductivity in the simulation and by ECD, which drives mud loss into the rock system. If pore pressure, leak-off coefficient, and wellbore pressure are the same, a larger fluid volume is driven into the rock system when conductivity is high. Therefore, a wider, longer fracture is generated in a more permeable formation. Similarly, higher ECD leads to more fluid flow into the rock and causes a longer, wider fracture. In the study of stress anisotropy, minimum horizontal stress is assumed fixed and maximum horizontal stress is altered, so the net pressures are kept the same. As a result, fracture propagations among all cases are nearly identical, and minimal influence is observed on final fracture geometry and loss rate. In theory, larger horizontal stress contrast leads to greater stress concentration at the wellbore, with FIP under such conditions being lower. Because constant wellbore pressure (defined higher than FIP) is a boundary condition, the more-noticeable influence on FIP is bypassed. Within the fracture domain, the fracture fluid pressure and volume play an important role in final fracture geometry. When fluid leak-off at the fracture surface is restricted (as shown in Fig. 12) or when fracture fluid is less viscous (as shown in Fig. 13), more fluid flows to the fracture tip and pressurizes the fracture surface near the tip. As a result, strain energy buildup at the fracture tip becomes easier and stimulates fracture propagation. On the other hand, higher fracture fluid pressure generates larger surface traction that further widens the fracture opening. Because leak-off rate and mud viscosity can be controlled by adjusting mud formulation, these properties might be the breakpoints to mitigate lost circulation.

Fig. 7. Injection pressure of the injection case. Fluid is injected at 0.01 m3/s for 5 s.

Fig. 8. Comparison of final fracture geometry between base case and injection case.

4. Hoop stress analysis during lost circulation The base case in the parametric study is investigated and is then compared with a high-stiffness case. Simulation results are extracted at different time steps during the lost circulation simulation. The fracture mouth opening is plotted in Fig. 14. Data are obtained along a nodal path near the wellbore circumference (as shown in Fig. 15). Effective hoop stresses along the wellbore wall at 1–2 s in the base case are extracted. As width increases about 0.001 m from 1 to 2 s, effective hoop stress increases approximately 3 MPa (becoming more compressive) at an azimuth of Shmin (i.e., 0 in Fig. 15); however, it decreases by approximately 4 MPa at an azimuth of SHmax (i.e., 90 in Fig. 15). In fact, the reduction of effective hoop stress is due to the elevated pore pressure by fluid invasion and the increased surface traction (i.e., wellbore pressure) applied at the wellbore circumference. Having assumed Biot's coefficient of 1, total hoop stresses along this path (as shown in Fig. 17) are calculated by adding pore pressures (as shown in Fig. 16) to effective stresses. Initially, all the total hoop stresses are elevated about 10 MPa from the intact condition to the fractured condition at 1 s because a displacement results from surface traction applied after fracture initiation. From 1 to 2 s, as the fracture

Fig. 9. Comparison of volumetric flow rate between base case and injection case.

held for 5 s. Assuming an infinite fluid source, a constant wellbore pressure, as the boundary condition, drives fluid flow into the fracture to compensate for the pressure drawdown caused by fluid leak-off and new fracture volume. Subsequently, the flow rates fluctuate with respect to time, and a higher flow rate contributes to greater fracture growth. Overall, the variation of flow rate demonstrates the difference between the lost circulation event and leak-off test. Increasing Young's modulus (i.e., stiffness) results in a narrower and 662

P. Zhao et al.

Journal of Petroleum Science and Engineering 157 (2017) 657–670

Fig. 10. Effect of Young's modulus on final fracture geometry and volumetric flow rate.

Fig. 11. Effect of fracture energy on final fracture geometry and volumetric flow rate.

Fig. 12. Effect of leak-off coefficient on final fracture geometry and volumetric flow rate.

closed fracture, the fracture fluid pressure has to overcome the fracture closure stress, which is the total hoop stress acting at the fracture surface. Therefore, based on the results, fracture width growth will enhance the hoop stress that holds the fracture closed, despite the reduction of effective hoop stress. Because of poroelasticity, rock volume in the near-wellbore region can be dilated if the local pore fluid cannot rapidly drain to the far field. Then, additional poroelastic backstress is generated, resulting in more closure stress at the fracture surface, which could further enhance stress building. Along with the fracture widening, this poroelastic effect also

continuously widens in a smaller magnitude, an increase of total hoop stress still occurs, and total stresses in the vicinity of 90 stay constant at about 78 MPa, which is the amount of surface traction applied by fracture fluid (fracture fluid pressure is close to wellbore pressure). It is also interesting to notice that rock near the fracture surface experiences more intense pore pressure buildup (i.e., 90 in Fig. 16), because fracture fluid invades rock at the fracture surface and pressure transient propagates along the wellbore tangential direction in the near-wellbore region. Recalling the motivation of the hoop stress enhancement mechanism, a fracture is essentially held closed by the hoop stress. To reopen the

663

P. Zhao et al.

Journal of Petroleum Science and Engineering 157 (2017) 657–670

Fig. 13. Effect of mud viscosity on final fracture geometry and volumetric flow rate.

Fig. 14. Fracture mouth widths of base case and high-stiffness case.

contributes to the total hoop stress enhancement shown in Fig. 17. However, if the invaded pore fluid is later dissipated to the far field or is withdrawn from the rock as wellbore pressure is lowered, such additional stress enhancement will vanish. Thus, poroelastic effect can be beneficial in hoop stress modification but is a time-dependent phenomenon. Total hoop stress of the high-stiffness case follows an identical trend to the base case (as shown in Fig. 18). The fracture mouth opening from the base case is larger than the high-stiffness case at all times. However, under the same loading condition, a higher stiffness assists the local stress buildup. In Fig. 18, the total hoop stress at the azimuth of Shmin (i.e., 0 ) increases about 13 MPa from 0 to 1 s in the high-stiffness case, while the base case increases 9 MPa at the same node. Hence, Young's modulus stimulates the effect of hoop stress enhancement.

Fig. 15. Effective hoop stress along the path from the base case. Data are obtained from red dotted nodes in the lower picture.

an immobile mass compressed by LCM imposes resistance on longitudinal flow within a fracture and isolates part of the fracture. Then, fracture fluid pressure at the isolated section equilibrates with nearby pore pressure, and stress intensity at the tip reduces. As a net outcome, fracture resistance is enhanced.

5. Fracture resistance enhancement By screening parametric effects, high mud viscosity and high leak-off quantity (i.e., coefficient) are found to be satisfactory for fracture resistance enhancement; meanwhile, both are operationally viable to be adjusted. Effect of mud viscosity shows that a viscous fluid requires a high differential pressure to drive to the tip and eventually reduces propagation rate and fracture length. Fluid leak-off at the fracture surface dissipates hydraulic power to the rock and weakens the tendency of fracture propagation. In the tip screen-out model (Fuh et al., 1992) and the FCS model (Dupriest, 2005), a certain volume of solids deposition within the fracture apertures is required, despite the instructed different operational philosophies. Similar to the mud viscosity measuring fluid flow friction,

5.1Simulation methodology for fracture sealing To quantify fracture resistance enhancement, a novel simulation method is proposed. This method explicitly considers the reduction of longitudinal fracture fluid flow due to particle sealing (i.e., the immobile mass) and the time-dependent fracture responses, as well as provides a method for drilling engineers to assess WBS outcomes through fracture sealing. Many experimental methods have been developed to measure 664

P. Zhao et al.

Journal of Petroleum Science and Engineering 157 (2017) 657–670

Reynold's equation modeling tangential fluid flow of the simulator is modified for Darcy's equation modeling linear fluid flow in porous media. The diffusive term from Darcy's equation and the conductivity term in Reynold's equation are equalized as follows:

g3 kA ¼ 12μf μfiltrate

(11)

assuming the width of fracture aperture g as the initial width ginitial after the material is fractured (i.e., ginitial ¼ 0.002 m ¼ 2000 μm is a default value in Abaqus), assuming the cross-sectional area of porous media, A, to be Ainitial ¼ ginitial  plane strain thickness, and identifying μfiltrate as the filtrate viscosity. Then, the above equation is reorganized as follows:

μ*f ¼ Fig. 16. Pore pressure along the path from the base case.

g3initial μfiltrate 12kAinitial

(12)

where μ*f is the modified viscosity of fracture fluid and an input parameter to the simulator. Because hydraulic conductivity increases as a fracture widens, immobile mass will become more permeable than the initial configuration during the width development. Thus, this method quantifies fracture resistance in a conservative manner where sealing capability is not exaggerated in the simulation. Limitations still exist in this method, however, such as ignoring transport and aggregation mechanisms of immobile mass, disregarding the mechanical strength of immobile mass that constitutes the dissipation of packed particles due to fracture aperture movement and creeping movement, and not considering timedependent fracture surface permeability damage. These limitations demonstrate challenges for improving simulation models in the near future. 5.2Case study on fracture sealing conditions Based on the proposed method, a case study on fracture sealing investigates the effect of sealing permeability and sealing length. An ECD of 90 MPa, which is 12 MPa higher than the ECD of inducing the fracture, is held for 60 s in this case study. All material properties and the simulation setup are the same as the base case, the fracture is predamaged according to the final fracture length of the base case (i.e., about 11 m), and modification is conducted based on the tip screen-out model and FCS model. Therefore, this case study simulates the fracture reopening process after the resistance enhancement.

Fig. 17. Calculated total hoop stresses along the path from the base case.

the permeability of immobile mass, for example, using a slot disk (Wang et al., 2016b) or high-pressure fracture test cell (Kaageson-Loe et al., 2009). By adopting the experimental measurement of LCM to this simulation method, fracture sealing can be effectively assessed under complex bottomhole conditions. This method is based on Abaqus modeling resources, but it can be adapted to any other fracture simulator.

Fig. 18. Comparison of calculated total hoop stresses along the path from the base case and high-stiffness case. 665

P. Zhao et al.

Journal of Petroleum Science and Engineering 157 (2017) 657–670

5.2.1. A case study on sealing permeability The case study on sealing permeability is guided by the tip screen-out model. This model is known as a preventive treatment that continuously circulates LCM within fluid while drilling. The suggested sealing location is in the narrow fracture tip zone. For this case study, an immobile mass (i.e., LCM) with a length of 0.5 m is placed 1.5 m behind the fracture tip (as shown in Fig. 19). 50 mD, 500 mD, and 5 000 mD are defined for the immobile mass (as listed in Table 2). An injection test for Case P-1 is performed to detect the signature of fracture sealing with respect to injection pressure. The same injection condition from the parametric study is applied to Case P-1 for 60 s. In Fig. 20, the final fracture geometry shows compelling results—the blue circled area, where the LCM is located, has a minimal opening. Most importantly, the isolated fracture section is not pressurized and has no width growth during the injection period. Thus, no further fracture propagation is observed, indicating the success of tip isolation and enhanced fracture resistance. The reduction of width in the middle of the fracture, labeled by the blue arrow in Fig. 20, is due to the poroelastic backstress. Since fracture propagation is terminated, the volume of the porous medium is dilated by the prolonged fluid invasion. Consequently, more compressive backstress toward the fracture surface is generated and closes the fracture. Hence, this observation proves the statement made in the previous section that poroelastic backstress could further assist hoop stress enhancement. Fig. 21(a) shows injection pressure, which constantly increases beyond the average FPP after 20 s. This elevation of FPP, along with the good fracture stability, indicates an enhancement of fracture resistance. The simulated result is qualitatively consistent with the experimental data from the DEA-13 project (as shown in Fig. 21(b)) and published leak-off test data. The green line in Fig. 21(b) records the initial injection using drilling fluid, and the red line records the secondary injection to reopen the induced fracture by using LCM-blended drilling fluid. In fact, the difference of this simulation study compared to the experiment is that the LCM is assumed to be immobile and mechanically strong. Fig. 22 shows the fracture geometry after 60-s pressure holding at the wellbore. The green box labels the LCM location. Case P-1, with 50-mD permeability, presents a great capability of tip protection, where no further propagation appears. In Case P-2, with 500-mD permeability, the pre-existing fracture extends its length to ~14 m. The fracture propagation resumes at about 9 s. However, as additional fracture surface is generated at the isolated section, reduced fluid influx can momentarily dissipate into the rock matrix, and fracture growth is inhibited at 40 s. These two cases show narrow fracture widths at the isolated section, so the fracture is stabilized and the wellbore is strengthened in both conditions. In Case P-3, with 5 000-mD permeability, fracture propagation restarts at about 2 s and reaches the external boundary. Fig. 23 shows the reduction of fracture fluid pressure through the LCM, as well as the influence on the fluid pressure at the isolated section. With a lower

Table 2 List of inputs for the case study on sealing permeability. Case

LCM (mD)

Wellbore pressure (MPa)

P-1 P-2 P-3

50 500 5 000

90 90 90

Fig. 20. Final fracture geometry for Case P-1 after a 60-s injection.

permeability of LCM, the fracture fluid pressure at the isolated section is lower in Case P-1 than in Case P-2. The mud loss rates from Cases P-1 and P-2 (as shown in Fig. 24) are very close. Case P-2, with a higher permeability, induces ~0.2 m3 more in total loss volume than Case P-1. In Fig. 24, the early peak indicates the completed reopening of the nonisolated fracture section. Then, the drop of flow rate indicates fracture plugging by the LCM, which constrains the longitudinal fracture fluid flow. 5.2.2. A case study on sealing length The case study on sealing length is guided by the FCS model. The FCS model can be categorized as a remedial treatment that instructs a hesitation-squeezing operation to prevent fracture reopening or propagation after lost circulation. Fig. 25 shows the sealing condition of this study, where an immobile mass (i.e., LCM) with a length of 9 m is placed 2 m behind the fracture tip. With the same set of permeabilities from the previous case study (as listed in Table 3), the overall fracture sealing capability improves remarkably as sealing length increases. As expected, Cases L-1 and L-2 both show small fracture widths in the near-wellbore region (as shown in Fig. 26). Case P-3, with 5 000-mD permeability of tip screen-out configuration, shows the failure of preventing fracture propagation. However, in Case L-3, with extended sealing length, only 0.5 m of new

Fig. 19. The immobile mass placement used in the case study of sealing permeability. 666

P. Zhao et al.

Journal of Petroleum Science and Engineering 157 (2017) 657–670

Fig. 21. (a) Simulated injection pressure from Case P-1. (b) DEA-13 fracturing experiment data show an elevation of injection pressure (modified from Black et al., 1985).

Fig. 24. Comparison of fluid loss rate between Cases P-1 and P-2.

Fig. 22. Comparison of final fracture geometry between Cases P-1 and P-2.

Case P-3. The significant delay in resuming propagation is facilitated by the sealing length. Overall, all three cases show the success of WBS. Fracture fluid pressure along the fracture length is shown in Fig. 27. As permeability decreases, fracture fluid pressure drops sharply. In Case L-3, even though the fracture fluid pressure at the isolated section is much higher than the other two cases, it still cannot produce enough strain energy at the tip and is more or less under an equilibrium condition of “barrel in, barrel out.” Fig. 28 shows the fluid loss rates of the three cases. Despite the highest permeability by orders of magnitude in Case L-3, LCM length compensates for the deficiency of fluid flow constraint and yields a drastic reduction of fluid loss rate similar to the other two. In addition, Case L-1, with the lowest permeability, merely induces ~0.09 m3 of total mud loss, which is ~1 m3 less total loss than Case P-1.

5.3Discussion of the results A notable fracture fluid pressure drop in the immobile mass is observed in all cases. Decreasing immobile mass permeability or increasing immobile mass length aids tip protection and contributes to fracture resistance enhancement. Some sealing cases reflect a resumption of fracture propagation. But fracture propagation stops after generating enough opening surface to allow fluid to dissipate to the rock matrix,

Fig. 23. Comparison of fracture fluid pressure between Cases P-1 and P-2.

fracture is induced, and the resumed propagation soon stops as enough opening surface is generated to dissipate the fracture fluid to rock. Fracture propagation occurs at 45 s in Case L-3, while it occurs at 2 s in 667

P. Zhao et al.

Journal of Petroleum Science and Engineering 157 (2017) 657–670

Fig. 25. The immobile mass placement used in the case study of sealing length.

Table 3 List of inputs for the case study on sealing length. Case

LCM (mD)

Wellbore pressure (MPa)

L-1 L-2 L-3

50 500 5 000

90 90 90

Fig. 28. Comparison of fluid loss rate among Cases L-1, L-2, and L-3.

which in turn mitigates stress intensity at the tip. In addition, the existence of immobile mass can delay the resumption of fracture propagation. Rate of mud loss is significantly reduced after sealing. Even with a high-permeability immobile mass, the reduction of volumetric flow rate is phenomenal. Overall, the reduction of mud loss rate depends on the seal capability that constrains the fluid flow inside the fracture. Suggestions for WBS treatment can be derived from these simulation results. Preventive treatment, which continuously keeps LCM within the drilling fluid, is always beneficial because a minimal amount of LCM can effectively increase the apparent FPP. For remedial treatment, the squeezing volume of LCM should be carefully estimated because a larger isolated fracture space can assist fluid leak-off to the rock matrix, ultimately mitigating the strain energy buildup at the fracture tip. For the same reason, injection rate during the squeezing treatment should be maintained as low as possible, giving more response time for fracture fluid dissipation in the vicinity of the fracture tip. To maximize fracture resistance, LCM should be designed with a low permeability after deposition. Moreover, even with a high-permeability LCM, increasing LCM concentration for a longer sealing length can compensate such a deficiency of material.

Fig. 26. Comparison of final fracture geometry among Cases L-1, L-2, and L-3.

6. Conclusion A parametric study is performed on lost circulation. The parametric study on rock properties first emphasizes the competition between induced strain energy at the fracture tip and fracturing resistance, where a high Young's modulus accelerates strain energy buildup and where high fracture energy and high tensile strength improve fracturing resistance. Secondly, mud loss rate is highly influenced by rock permeability and

Fig. 27. Comparison of fracture fluid pressure among Cases L-1, L-2, and L-3.

668

P. Zhao et al.

Journal of Petroleum Science and Engineering 157 (2017) 657–670

ECD. With a higher loss rate, a wider and longer fracture is generated. Lastly, studies on leak-off coefficient and mud viscosity highlight the mass balance within the fracture. When fluid leak-off is restricted or when fracture fluid is less viscous, fluid accumulation at the fracture tip accelerates and, in turn, fosters fracture propagation. Filtration control and viscosity can be customized in mud formulation. These parameters are possible alternatives for mitigating lost circulation. The differences between leak-off test and lost circulation event are discussed. In lost circulation, the flow rate fluctuates with respect to time to compensate the fluid pressure drop from fracture propagation. Since the wellbore pressure that induces lost circulation is higher than the FPP, the induced fracture geometry from the lost circulation case is longer and wider than the injection case. After the fracture is sealed with immobile mass, injection pressure can elevate above FPP without triggering further propagation. The hoop stress enhancement mechanism is validated in this numerical simulation. Since the total hoop stress dictates fracture closure, elevated total hoop stresses are observed as the fracture is widened. Therefore, WBS can be achieved through propping the fracture. Furthermore, the increase in pore pressure can dilate the porous rock and results in more closure stress for the fracture. However, the pore pressure in the near-wellbore region will change with time. Thus, poroelastic effect can temporarily assist hoop stress enhancement. The analysis of hoop stress enhancement also indicates that elevated Young's modulus further increases hoop stress. A proposed novel simulation method honors the fracture resistance enhancement mechanism aiming for tip protection. This method explicitly considers the dynamic diffusion across the immobile mass and time-dependent fracture behaviors, as well as provides a tool to assess the extended fracture gradient by fracture sealing. Based on the method, a case study on fracture sealing conditions investigates the effect of sealing permeability and sealing length. Results show that fracture fluid pressure loss, fracture width at the isolated section, and rate of mud loss are sharply reduced. According to results, immobile mass length and permeability are mutually beneficial in enhancing fracture resistance. As fluid leaks off to rock, a certain length of opening surface in the vicinity of the fracture tip can also assist lost circulation mitigation. Therefore, suggestions for WBS treatment emphasize the benefits of fracture sealing and the interplay among sealing permeability, sealing length, and fluid leak-off in the vicinity of the fracture tip.

Biot, M.A., 1941. General theory of three-dimensional consolidation. J. Appl. Phys. 12 (2). http://dx.doi.org/10.1063/1.1712886. Black, A., et al., 1985. DEA 13 (Phase Ӏ) Final Report: Investigation of Lost Circulation Problems and Apparent Fracture Gradient Reduction Encountered in the Field with Oil-based Drilling Fluids during Large-scale Laboratory Fracturing Experiences. Cook, J., Growcock, F., Guo, Q., Hodder, M., van Oort, E., 2011. Stabilizing the wellbore to prevent lost circulation. Oilfield Rev. 23 (4), 2012. Dupriest, F.E., 2005. Fracture closure stress (FCS) and lost returns practices. In: Presented at the SPE/IADC Drilling Conference. Amsterdam, Netherlands, 23—23 February. SPE-92192-MS. http://dx.doi.org/10.2118/92192-MS. Feng, Y., Arlanoglu, C., Podnos, E., et al., 2015. Finite-element studies of hoop-stress enhancement for wellbore strengthening. SPE Drill. Complet. 30 (1). SPE-168001-PA. http://dx.doi.org/10.2118/168001-PA. Feng, Y., Jones, J.F., Gray, K.E., 2016. A review on fracture-initiation and -propagation pressures for lost circulation and wellbore strengthening. SPE Drill. Complet. 31 (2). SPE-181747-PA. http://dx.doi.org/10.2118/181747-PA. Feng, Y., Gray, K.E., 2016. A fracture-mechanics-based model for wellbore strengthening applications. J. Nat. Gas. Sci. Eng. 29, 392–400. https://doi.org/10.1016/j.jngse. 2016.01.028. Fuh, G.-F., Morita, N., Boyd, P.A., et al., 1992. A new approach to preventing lost circulation while drilling. In: Presented at the SPE Annual Technical Conference and Exhibition. Washington, DC, 4—7 October. SPE-24599-MS. http://dx.doi.org/10. 2118/24599-MS. Fuh, G.-F., Beardmore, D.H., Morita, N., 2007. Further development, field testing, and application of the wellbore strengthening technique for drilling operations. In: Presented at the SPE/IADC Drilling Conference. Amsterdam, Netherlands, 20—22 February. SPE-105809-MS. http://dx.doi.org/10.2118/105809-MS. Guo, Q., Cook, J., Way, P., et al., 2014. A comprehensive experimental study on Wellbore strengthening. In: Presented at the IADC/SPE Drilling Conference and Exhibition. Fort Worth, Texas, 4—6 March. SPE-167957-MS. http://dx.doi.org/10.2118/ 167957-MS. Haddad, M., Sepehrnoori, K., 2014. Simulation of multiple-stage fracturing in quasibrittle shale formations using pore pressure cohesive zone model. In: Presented at the Unconventional Resources Technology Conference. Denver, Colorado, 25—27 August. SPE-2014-1922219-MS. http://dx.doi.org/10.2118/2014-1922219-MS. Hubbert, M.K., Willis, D.G., 1957. Mechanics of hydraulic fracturing. Petroleum transactions. AIME 210, 153–168. Jaffal, H.A., 2016. Evaluation of Mudcake Buildup and its Mechanical Properties. MS thesis. The University of Texas at Austin. Kaageson-Loe, N., Sanders, M.W., Growcock, F., et al., 2009. Particulate-based lossprevention material–the secrets of fracture sealing revealed! SPE Drill. Complet. 24 (4). SPE-112595. http://dx.doi.org/10.2118/112595. Kostov, N., Ning, J., Gosavi, S.V., 2015. Advanced drilling induced fracture modeling for wellbore integrity prediction. In: Presented at the SPE Annual Technical Conference and Exhibition. Houston, Texas, 28 January—30 September. SPE-174911-MS. http:// dx.doi.org/10.2118/174911-MS. Lee, D., Bratton, T., Birchwood, R., 2004. Leak-off test interpretation and modeling with application to geomechanics. In: Presented at the North America Rock Mechanics Symposium. Houston, Texas, 5—9 June. ARMA-04–547. Masi, S., Molaschi, C., Zausa, F., et al., 2011. Managing circulation losses in a harsh drilling environment: conventional solution vs. CHCD through a risk assessment. SPE Drill. Complet. 26 (2). SPE-128225-PA. http://dx.doi.org/10.2118/128225-PA. Mehrabian, A., Jamison, D.E., Teodorescu, S.G., 2015. Geomechanics of lost-circulation events and wellbore-strengthening operations. SPE J. 20 (6). SPE-174088-PA. http:// dx.doi.org/10.2118/174088-PA. Morita, N., Black, A.D., Guh, G.-F., 1990. Theory of lost circulation pressure. In: Presented at the SPE Annual Technical Conference and Exhibition. New Orleans, Louisiana, 23—26 September. SPE-20409-MS. http://dx.doi.org/10.2118/20409-MS. Morita, N., Black, A.D., Fuh, G.F., 1996. Borehole breakdown pressure with drilling fluids—I. Empirical results. Int. J. Rock Mech. Min. Sciences&Geomechanics Abstr. 33 (1). http://dx.doi.org/10.1016/0148-9062(95)00028-3. Morita, N., Fuh, G.F., 2012. Parametric analysis of wellbore-strengthening methods from basic rock mechanics. SPE Drill. Complet. 27 (2). SPE-145765-PA. http://dx.doi.org/ 10.2118/145765-PA. Ning, J., Kao, G., Kostov, N., et al., 2015. Experimental validation of simulation capabilities for hydraulic fractures propagation in a porous medium. In: Presented at the 2015 SIMULIA Community Conference (Berlin, Germany). Onyia, E.C., 1994. Experimental data analysis of lost-circulation problems during drilling with oil-based mud. SPE Drill. Complet. 9 (1). SPE-22581-PA. http://dx.doi.org/10. 2118/22581-PA. Razavi, O., Vajargah, A.K., Van Oort, E., et al., 2015. How to effectively strengthen wellbores in narrow drilling margin wells: an experimental investigation. In: Presented at the SPE Annual Technical Conference and Exhibition. Houston, Texas, 28—30 September. SPE-174976-MS. http://dx.doi.org/10.2118/174976-MS. Shin, D., Sharma, M.K., 2014. Factors controlling the simultaneous propagation of multiple competing fractures in a horizontal well. In: Presented at the SPE Hydraulic Fracturing Technology Conference. The Woodlands, Texas, 4—6 February. SPE168599-MS. http://dx.doi.org/10.2118/168599-MS. Song, J., Rojas, J.C., 2006. Preventing mud losses by wellbore strengthening. In: Presented at the SPE Russian Oil and Gas Technical Conference and Exhibition. Moscow, Russian, 3—6 October. SPE-101593-MS. http://dx.doi.org/10.2118/ 101593-MS. van Oort, E., Friedheim, J.E., Pierce, T., et al., 2011. Avoiding losses in depleted and weak zones by constantly strengthening wellbores. SPE Drill. Complet. 26 (4). SPE-125093PA. http://dx.doi.org/10.2118/125093-PA.

Acknowledgements The authors wish to thank the Wider Windows Industrial Affiliate Program at the University of Texas at Austin for financial and logistical support of this work. Financial support from Wider Windows sponsors BHP Billiton, British Petroleum, Chevron, ConocoPhillips, Halliburton, Marathon, National Oilwell Varco, Occidental Oil and Gas, and Shell are gratefully acknowledged. References Abaqus Analysis User’s Manual, 2016, Version 2016, Dassault Systemes Simulia Corp., Providence, Rhode Island. Alberty, M.W., McLean, M.R., 2004. A physical model for stress cages. In: Presented at the SPE Annual Technical Conference and Exhibition. Houston, Texas, 26—29 September. SPE-90493-MS. http://dx.doi.org/10.2118/90493-MS. Aston, M.S., Alberty, M.W., McLean, M.R., 2004. Drilling fluids for wellbore strengthening. In: Presented at the IADC/SPE Drilling Conference. Dallas, Texas, 2—4 March. SPE-87130-MS. http://dx.doi.org/10.2118/87130-MS. Aston, M.S., Alberty, M.W., Duncum, S.D., 2007. A new treatment for wellbore strengthening in shale. In: Presented at the SPE Annual Technical Conference and Exhibition. Anaheim, Montana, 11—14 November. SPE-110713-MS. http://dx.doi. org/10.2118/110713-MS. Barenblatt, G.I., 1959. The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. Axially-symmetric cracks. J. Appl. Math. Mech. 23 (3). http://dx.doi.org/10.1016/0021-8928(59)90157-1. Barenblatt, G.I., 1962. The mathematical theory of equilibrium cracks in brittle fracture. Adv. Appl. Mech. 7. http://dx.doi.org/10.1016/S0065-2156(08)70121-2.

669

P. Zhao et al.

Journal of Petroleum Science and Engineering 157 (2017) 657–670 Yao, Y., Gosavi, S.V., Searles, K.H., et al., 2010. Cohesive fracture mechanics based analysis to model ductile rock fracture. In: Presented at the 44th U.S. Rock Mechanics Symposium and 5th U.S.-Canada Rock Mechanics Symposium. Salt Lake City, Utah. ARMA-10–140. Yew, C.H., Weng, X., 2014. Mechanics of Hydraulic Fracturing. Elsevier Science. Zhang, J., Standifird, W.B., Lenamond, C., 2008. Casing ultradeep, ultralong salt sections in deep water: a case study for failure diagnosis and risk mitigation in record-depth well. In: Presented at the SPE Annual Technical Conference and Exhibition. Denver, Colorado, 21—24 September. SPE-114273-MS. http://dx.doi.org/10.2118/114273MS. Zhang, J., Alberty, M., Blangy, J.P., 2016. A semi-analytical solution for estimating the fracture width in wellbore strengthening applications. In: Presented at the SPE Deepwater Drilling and Completions Conference. Galveston, Texas, 14—15 September. SPE-180296-MS. http://dx.doi.org/10.2118/180296-MS. Zhong, R., Miska, S., Yu, M., 2017. Parametric study of controllable parameters in fracture-based wellbore strengthening. J. Nat. Gas Sci. Eng. 43, 13–21. https://doi. org/10.1016/j.jngse.2017.03.018. Zielonka, M.G., Searles, K.H., Ning, J., et al., 2014. Development and validation of fullycoupled hydraulic fracturing simulation capabilities. In: Presented at the 2014 SIMULIA Community Conference (Providence, Rhode Island).

van Oort, E., Razavi, S.O., 2014. Wellbore strengthening and casing smear: the common underlying mechanism. In: Presented at the IADC/SPE Drilling Conference and Exhibition. Fort Worth, Texas, 4—6 March. SPE-168041-MS. http://dx.doi.org/10. 2118/168041-MS. Wang, H., Towler, B.F., Soliman, M.Y., 2007. Near wellbore stress analysis and wellbore strengthening for drilling depleted formations. In: Presented at the Rocky Mountain Oil&Gas Technology Symposium. Denver, Colorado, 16—18 April. SPE-102719-MS. http://dx.doi.org/10.2118/102719-MS. Wang, H., Soliman, M.Y., Towler, B.F., 2009. Investigation of factors for strengthening a wellbore by propping fractures. SPE Drill. Complet. 24 (3). SPE-112629-PA. http:// dx.doi.org/10.2118/112629-PA. Wang, H., 2015. Numerical modeling of non-planar hydraulic fracture propagation in brittle and ductile rocks using XFEM with cohesive zone method. J. Petroleum Sci. Eng. 135. http://dx.doi.org/10.1016/j.petrol.2015.08.010. Wang, H., Marongiu-Porcu, M., Economides, M.J., 2016. Poroelastic and poroplastic modeling of hydraulic fracturing in brittle and ductile formations. SPE Prod. Operations 31 (1). SPE-168600-MS. http://dx.doi.org/10.2118/168600-MS. Wang, H., Savari, S., Whitfill, D.L., et al., 2016b. Forming a seal independent of formation permeability to prevent mud losses—theory, lab tests, and case histories. In: Presented at the IADC/SPE Drilling Conference and Exhibition. Fort Worth, Texas, 1—3 March. SPE-178790-MS. http://dx.doi.org/10.2118/178790-MS.

670