2D Numerical Simulation of Improving Wellbore Stability in ... - MDPI

energies Article

2D Numerical Simulation of Improving Wellbore Stability in Shale Using Nanoparticles Based Drilling Fluid Jiwei Song 1,2 , Ye Yuan 3 , Sui Gu 1 , Xianyu Yang 1 , Ye Yue 1 , Jihua Cai 1, * and Guosheng Jiang 1, * 1

2 3

*

School of Engineering, China University of Geosciences, Wuhan 430074, China; [email protected] (J.S.); [email protected] (S.G.); [email protected] (X.Y.); [email protected] (Y.Y.) 115 Geological Team, Bureau of Geology and Mineral Exploration and Development of Guizhou Province, Guiyang 551400, China Chengdu Team of Hydrogeology and Engineering Geology, Chengdu 610072, China; [email protected] Correspondence: [email protected] (J.C.); [email protected] (G.J.)

Academic Editor: Dongsheng Wen Received: 13 January 2017; Accepted: 2 May 2017; Published: 9 May 2017

Abstract: The past decade has seen increased focus on nanoparticle (NP) based drilling fluid to promote wellbore stability in shales. With the plugging of NP into shale pores, the fluid pressure transmission can be retarded and wellbore stability can be improved. For better understanding of the interaction between shale and NP based drilling fluid based on previous pressure transmission tests (PTTs) on Atoka shale samples, this paper reports the numerical simulation findings of wellbore stability in the presence of NP based drilling fluid, using the 2D fluid-solid coupling model in FLAC3D™ software. The results of previous PTT are discussed first, where the steps of numerical simulation, the simulation on pore fluid pressure transmission, the distribution of stress and the deformation of surrounding rock are presented. The mechanisms of NP in reducing permeability and stabilizing shale are also discussed. Results showed that fluid filtrate from water-based drilling fluid had a strong tendency to invade the shale matrix and increase the likelihood of wellbore instability in shales. However, the pore fluid pressure near wellbore areas could be minimized by plugging silica NP into the nanoscale pores of shales, which is consistent with previous PTT. Pore pressure transmission boundaries could also be restricted with silica NP. Furthermore, the stress differential and shear stress of surrounding rock near the wellbore was reduced in the presence of NP. The plastic yield zone was minimized to improve wellbore stability. The plugging mechanism of NP may be attributed to the electrostatic and electrodynamic interactions between NP and shale surfaces that are governed by Derjaguin-Landau-Verwey-Overbeek (DLVO) forces, which allowed NP to approach shale surfaces and adhere to them. We also found that discretization of the simulation model was beneficial in distinguishing the yield zone distribution of the surrounding rock in shales. The combination of PTT and the 2D numerical simulation offers a better understanding of how NP-based drilling fluid can be developed to address wellbore stability issues in shales. Keywords: shale; wellbore stability; drilling fluid; silica nanoparticles (NPs); pressure transmission test (PTT); numerical simulation

1. Introduction In the oil and gas industry, 75% of all footage was drilled in shale formations which are responsible for 90% of wellbore stability problems [1–3]. The main cause of shale instability for both soft and hard shales is water absorption and the subsequent swelling and sloughing of the wellbore [4]. Wellbore

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pressure penetrates the pore space when water invades the shale. This reduction of true overbalance, which acts as a support pressure for the borehole, can result in shale failure and wellbore instability [5]. Viable types of engineered drilling fluids have been developed to address wellbore stability issues in shale formations. Chenevert [4] suggested balanced-activity oil-continuous muds as a solution to address shale instability issues as there is no interaction between oil and shale. However, for environmental and economic considerations, water-based drilling fluids are preferred if the interaction between the drilling fluid and shale can be minimized. Hayatdavoudi and Apande [6] found that the best possible way of preventing contact between argillaceous rock and water was to seal off exposed clayey surfaces. Carminati et al. [7] showed that the most effective additives in controlling pore fluid pressure in formation and shale hardness, and consequently in preventing shale instability, were the silicates. Van Oort et al. [3] introduced environmentally friendly and inexpensive silicate-based muds as superior fluids for drilling troublesome formations like intact and (micro-) fractured shales and chalks. Reid et al. [8] regarded the interaction between potassium ions and polyols at the clay surface as the critical factor in the provision of shale inhibition. Zhong et al. [9] discovered the mechanism of polyether diamine improving shale wellbore stability in water-based drilling fluids. Van Oort et al. [10] used a high-performance water-based mud to improve wellbore stability in Tor/Ekofisk wells through careful shale-fluid compatibility optimization. However, unlike traditional sandstone and carbonate reservoirs, shales feature nano-sized pores. The pore diameter of gas shales in China and North America ranges from 5 to 300 nm and 8 to 100 nm, respectively [11–17]. Therefore, the past decade has seen an increase in NP use to improve wellbore stability in shales [18–31]. To assess wellbore stability in the presence of NP, triaxial failure tests, pressure transmission tests (PTTs), and modified thick walled cylinder (TWC) tests with drilling fluid exposure have been recommended by van Oort et al. [32]. Hoxha et al. [33] used the latter two tests combined with zeta potential measurements to investigate the interaction of NP and intact shales. Hydraulic conductivity and a “PTT delay factor” were used to measure fluid pressure transmission. Electrostatic and electrodynamic interaction between NP and shale surfaces, governed by Derjaguin-Landau-Verwey-Overbeek (DLVO) forces, is considered the main mechanism that leads to pore throat plugging in shales. They stated that NP use for practical shale stabilization required a dedicated, thoroughly engineered solution for each particular field application. Additionally, numerical simulation is another important method used to conduct rock-fluid interaction research, especially in shale formations. It can present visualized time dependent contour maps of stress and strain in near-wellbore areas for a better understanding of downhole wellbore instability issues and can supplement experimental appraisals on wellbore stability in shales. Frydman et al. [34] discussed the modeling aspects of the coupled process by comparing three formulations: An analytical elastic solution without the diffusion process, an analytical poroelasticity solution, and a numerical chemical hydro-mechanical model. Yu et al. [35] introduced a chemical-mechanical wellbore instability model for shales that accounted for solute diffusion and found that the onset of instability depended not only on water activity, but also on the properties of the solutes. Zhai et al. [36] developed a poro-thermo-mechanical model that integrated the effects of both thermal and hydraulic diffusion to determine the effects of drilling fluid and mud weight on the wellbore system. They found that the pressure differential effect was dominant in high mobility formation while thermal effect was important for low mobility formation. They subsequently improved this model by coupling the chemical-thermal-poro-mechanical effect on borehole stability [37]. The time dependent borehole stability is mainly caused by chemical and thermal diffusion. Huang et al. [38] obtained a chemo-poro-elastic stability model, incorporating drilling fluid-induced chemical osmotic in situ stress. It was found that both the compressive failure index and tensile failure index are a function of pore pressure. The salinity of drilling fluids cause chemical osmotic pressure and further affect the effective principle stresses. Wang et al. [39] reported a fluid-solid-chemistry coupling model that considered fluid flow and ion transmission (induced by shale-drilling) fluid system electrochemical potential osmosis, nonlinearity of flow and solute diffusion in the shale-drilling fluid system, and solid

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deformation resulted from fluid flow and ion transmission. They found that previous linear models overestimated the pore pressure and stress fields around the sidewall. Wen et al. [40] established a chemo-mechanical coupling model of wellbore stability in hard brittle shale that considered structure characteristics and targeted hydration. Accurate prediction of collapse pressure distribution was obtained by the chemo-mechanical coupling model, where borehole stability was ensured and the density of drilling fluid decreased as long as the drilling fluid activity was controlled in the window. Zhuang et al. [41] investigated the feasibility of utilizing hard rock for compressed air energy storage (CAES) by a couple thermo-hydro-mechanical model. It was found that mass control based CAES operation resulted in energy loss. Supplementary air injection was needed to maintain the required pressure level. Zhu et al. [42] developed a nonlinear semi-concurrent multi-scale method for modeling crack propagation (evolving from micro-structure) for non-linear material behavior and found that it was effective for modeling dynamic damage evolution for brittle materials. Based on our previous PTT with Atoka shale [19], this paper reports the numerical simulation findings of wellbore stability in the presence of silica (SiO2 ) NP based drilling fluid, using the 2D fluid-solid coupling model in FLAC3D™ software (Version 3.0, Minneapolis, MN, USA). The results of our previous PTT is first discussed. The steps of numerical simulation, the simulation on fluid pressure transmission in shales, the distribution of stress, and the deformation of surrounding rock are presented. The mechanism of NP in reducing the permeability and stabilizing shale is also discussed. 2. Pressure Transmission Tests on Shale 2.1. Experimental Materials Two types of SiO2 NP (denoted as NP-A and NP-B, respectively) were employed and their basic properties are shown in Table 1. Table 1. Basic properties of SiO2 NP dispersions. No.

Density (g/cm3 )

NP Size (nm)

NP (wt. %)

pH

NP-A NP-B

1.22 1.20

7 10–15

30.2 30.4

10 10

In this study, hard and preserved Atoka shale samples were numbered as #1 and #2, which comprised 52% quartz, 15% feldspar and 33% clay mineral—which included kaolinite (32%), chlorite (7%), illite (31%), smectite (19%) and mixed-layer (11%). It had an average pore size of 30 nm, and thus, it had relatively strong water sensitivity. Great care was taken to preserve the samples with its native water activity [32,43]. The bentonite mud (BM) used had a plastic viscosity of 41 mPa·s, a yield point of 25 Pa and an API fluid loss of 8.6 mL [19]. 2.2. Methodology PTT measures the tendency of a mud filtrate, applied at overbalance pressure, to invade the shale fabric and elevate the near wellbore pore pressure [3,44,45]. This “mud pressure penetration” effect can be an important cause of time-delayed shale failure. Pore pressure transmission in shales is at least one to two orders of magnitude faster than solute or ion diffusion, which in turn is one or two orders of magnitude faster than the Darcy flow of mud filtrate [46]. Therefore, PTT can be used to conduct fundamental investigations on shale-fluid interactions, and for the development of drilling fluids to promote wellbore stability. The detailed mechanics and procedures of the test can be found in the related literature [3,44,45]. The sliced shale cores were fixed with cured epoxy resin to create a confining pressure, as shown in Figure 1. The symbol on the shale sample was marked for reorganization in the original tests. The setup of PTT (Figure 2) consists of several devices to achieve a continuous flow of the test fluid across the top face of the shale sample while the simulated pore fluid was kept in

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Energies 2017,the 10, 651 4 of 23 contact with lower face of the shale. The “simulated pore fluid” referred to was a 4 wt. % sea salt solution with a 0.98 water activity (a ). Its initial pressure was loaded to 0.34 MPa (50 psi). A test fluid (50 psi). A test fluid flowed across w the top of a shale sample (Figure 1) at a constant pressure of 2.07 (50 psi). A test fluid flowed across the top of a 1) shale (Figure 1) atofa 2.07 constant 2.07the flowed across theand topthe of a shale sample at aasample constant pressure MPaatpressure (300 psi)ofand MPa (300 psi) buildup of fluid(Figure pressure in small sealed chamber located the bottom of MPa (300 psi) and the buildup of fluid pressure in a small sealed chamber located at the bottom of buildup of fluid pressure in a small sealed chamber located at the bottom of the shale was recorded the shale was recorded automatically. The rate of pressure penetration provided a direct and the shale was recorded automatically. The rate of pressure penetration provided a direct and automatically. The rate of pressure provided a direct and quantitative measurement quantitative measurement of shalepenetration permeability. Detailed equations for this computation were of quantitative measurement of shale permeability. Detailed equations for this computation were shale permeability. Detailed provided by Al-Bazali [45]. equations for this computation were provided by Al-Bazali [45]. provided by Al-Bazali [45].

Figure1.1.Atoka Atoka shale sample sample used in the pressure Figure pressuretransmission transmissiontests tests(PTTs). (PTTs). Figure 1. Atokashale shale sampleused used in in the the pressure transmission tests (PTTs). V3 V3 Vaccum Vaccum Injection Pump Injection Pump Back Pressure Back Pressure Regulator Regulator

V6 V6

V10 V10

V14 V14 BPR BPR QC QC

rr

Fresh Fresh Water Water Reservoi Reservoi

QC QC

Cyliner Cyliner P1 P1 Upstream Upstream Pressure Pressure

V3 V3

Cyliner Cyliner QC QC

P2 P2

QC QC

Test Cell Test Cell

N2 N2

QC QC Pressure Pressure Transducer Transducer

V7 V7

Out to Out to Waste Waste

V2 V2 P9 P9 Downstream Downstream Pressure Pressure

V11 V11 Manual Pump Manual Pump

Sea Sea Water Water Reservoir Reservoir

Figure 2. Experimental set up of PTT [19]. Figure2.2.Experimental Experimental set set up Figure up of of PTT PTT[19]. [19].

A three-step testing procedure was followed as we found that coring samples from the same A three-step testing procedure was followed as we found that coring samples from the same shale rock did not have procedure the same original permeability. It was decided to first flow sea water through A three-step testing was followed as we found that coring samples from the same shale shale rock did not have the same original permeability. It was decided to first flow sea water through shale samples until equilibrium was reached to produce saturated shale samples that had the same rock did not have the same original permeability. It was decided to first flow sea water through shale shale samples until equilibrium was reached to produce saturated shale samples that had the same startinguntil conditions. In step a PTT was run using BM to obtain ‘base mud’ forstarting that samples equilibrium was2, to produce saturated shale samples thatpermeability had the same starting conditions. In step 2,reached a PTT was run using BM to obtain ‘base mud’ permeability for that sample. Finally, the test was run using the BM that contained 10 wt. % silica NP (BM plus NP). The sample. Finally, the test was run using the BM that contained 10 wt. % silica NP (BM plus NP). The

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conditions. In step 2, a PTT was run using BM to obtain ‘base mud’ permeability for that sample. percent the permeability reduction (Δk)BM was calculated based on the permeability thepercent second Finally, test was run using the that contained 10 wt. % silica NP (BM obtained plus NP).inThe step (times 100) [19]. permeability reduction (∆k) was calculated based on the permeability obtained in the second step (times 100) [19]. 2.3. PTT Results Analysis 2.3. PTT Results Analysis 2.3.1. Pore Fluid Pressure Transmission from Drilling Fluid to Shale 2.3.1. Pore Fluid Pressure Transmission from Drilling Fluid to Shale In step 1, the downstream pressure of shale in contact with sea water (brine) quickly climbed the downstream of shale in contact with sea water (brine) quickly climbed close closeIntostep the 1,upstream pressurepressure in approximately 20 h (Figure 3a), driven by the positive pressure to the upstream pressure in approximately 20 h (Figure 3a), driven by the positive pressure difference. difference. In the next step with the BM, the rising tendency of downstream pressure was still obvious In next10step with the the risingoftendency downstream obvious for about forthe about h. Finally, inBM, the presence SiO2 NP of with the BM, thepressure curve ofwas the still downstream pressure 10 Finally, the presence of SiO with theresult BM, the of thewhen downstream vs. time 2 NP vs.h.time was in almost flat (Figure 3a). A similar wascurve obtained the testspressure were conducted was almost flat (Figure 3a). A similar result was obtained when the tests were conducted with #2 with #2 Atoka shale sample (Figure 3b), revealing that SiO2 NP could effectively mitigateAtoka pore shale sample (Figure 3b), that tendency SiO2 NP could effectively pore pressure transmission pressure transmission andrevealing the invasion of water from themitigate BM, therefore improving wellbore and the invasion stability in shales.tendency of water from the BM, therefore improving wellbore stability in shales. 2.50

Upstream Pressure

2.50

Downstream Pressure

2.00

brine,k =0.18nD

Pressure,MPa

Pressure,MPa

2.00 1.50

Upstream Pressure

BM,k =0.015nD BM+NP-A,k =0.0001nD

1.00 0.50

BM,k =0.050nD

1.50 BM+NP-B,k =0.003nD 1.00

brine,k =0.476nD

0.50

0.00 0.00

Downstream Pressure

0.00

10.00

20.00

30.00 Time,hr

(a)

40.00

50.00

60.00

0.00

10.00

20.00

30.00

40.00

50.00

60.00

Time,hr

(b)

Figure 3. PTT of Atoka shale. (a) #1 Atoka shale sample; (b) #2 Atoka shale sample. Figure 3. PTT of Atoka shale. (a) #1 Atoka shale sample; (b) #2 Atoka shale sample.

2.3.2. The Influence of NP on Shale Permeability 2.3.2. The Influence of NP on Shale Permeability The permeability of shale samples in contact with the three types of fluids above-mentioned was The permeability of shale samples in contact with the three types of fluids above-mentioned was calculated, and is shown in Table 2. The permeability reduction rates (Δk) based on the permeability calculated, and is shown in Table 2. The permeability reduction rates (∆k) based on the permeability of shales in contact with the BM was as high as 99.33% and 94.00%, respectively, indicating that the of shales in contact with the BM was as high as 99.33% and 94.00%, respectively, indicating that the perfect plugging performance of SiO2 NP into the Atoka shale samples was obtained. perfect plugging performance of SiO2 NP into the Atoka shale samples was obtained.

Shale #1 #2

Table 2. Changes of NP on shale permeability. Table 2. Changes of NP on shale permeability. Permeability, nD Shale Nanoparticles Δk, % Permeability, nD + NP Sea Water BM BM Nanoparticles #1 NP-A Sea Water 0.18 0.015 0.0001 99.33 BM BM + NP #2 NP-B 0.476 0.050 0.003 94.00 NP-A 0.18 0.015 0.0001 NP-B 0.476 0.050 0.003

∆k, % 99.33 94.00

It was also found that NP with size varying from 7 to 15 nm had better plugging performance than those with size greater than 20 nm [19]. We speculated that only NP particles with a size in this was also found that the NP pore withthroat size varying from 7 to 15minimizing nm had better plugging performance rangeItcould enter and plug of shale, therefore the fluid invasion tendency than those with size greater than 20 nm [19]. We speculated that only NP particles with a size this for shale. It must also be pointed out that a range of 7–15 nm NP worked well for Atoka in shale; range could enter and plug the pore throat of shale, therefore minimizing the fluid invasion tendency however, other sizes may be needed for other shale types. In addition, the specific type of shale, the for shale.type, It must pointed out that a range of 7–15 nmbetween NP worked wellshale, for Atoka shale; however, specific sizealso andbe concentration of NP, the interaction NP and and external factors other sizes may be needed for other shale types. In addition, the specific type of shale, the specific such as pH, salinity, temperature require detailed investigation [33]. type, size and concentration of NP, the interaction between NP and shale, and external factors such as pH, salinity, temperature detailed investigation [33]. Analysis 3. Numerical Simulationrequire Parameters for Wellbore Stability To better understand the interaction, a numerical simulation for wellbore stability in shales was conducted. By assuming that the shale was isotropic and the wellbore was geometrically

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3. Numerical Simulation Parameters for Wellbore Stability Analysis To better understand the interaction, a numerical simulation for wellbore stability in shales was conducted. By assuming that the shale was isotropic and the wellbore was geometrically symmetrical, Energies 2017, 10, 651 6 of 23 it could be simplified as a 2D fluid-solid coupling model in FLAC3D™ software, as shown in Figure 4. Energies 2017, 10, 651 6 of 23 Here,symmetrical, σH , σh , anditPfcould referred to the maximum horizontal crustalmodel press,in minimum horizontal crustal be simplified as a 2D fluid-solid coupling FLAC3D™ software, as press, and drilling fluid pressure, respectively. symmetrical, it could be simplified a 2D fluid-solid couplinghorizontal model in crustal FLAC3D™ shown in Figure 4. Here, σH, σh, and as Pf referred to the maximum press,software, minimumas Figure shows basic chart of the numerical simulation. The numerical simulation shown in5 Figure 4.the Here, σH,flow σdrilling h, and Pfluid f referred to the maximum horizontal crustal press, minimumwas horizontal crustal press, and pressure, respectively. horizontal crustal press, drilling fluidof pressure, Figure 5 shows the and basic flowwhich chart the numerical simulation. numerical simulation based on the Mohr-Coulomb model, belongs torespectively. the plane stressThe model. First, the seepagewas pattern Figure 5side shows the basicthe flow chart ofofthe numerical simulation. The model. numerical simulation was on Mohr-Coulomb model, which belongs to the plane First, theside seepage starts.based The leftthe represents process calculating the stressstress field, and the right indicates pattern The left side represents the process of The calculating thestress stressmodel. field,isand thethe right side the based onstarts. the Mohr-Coulomb model, which belongs to the plane First, seepage the new step after considering the seepage process. seepage simulation mainly through indicates the The new left stepside after considering the seepage process. The seepage simulation isright mainly pattern starts. represents the process of calculating the stress field, and the side definition of seepage boundary, initial pore pressure, and mesh force setting to calculate. The software through the seepage boundary, initial pore pressure, forcesimulation setting to calculate. indicates thedefinition new stepofafter considering the seepage process. and The mesh seepage is mainly extracted results according to equation of motion, balance equation, and constitutive equation [47]. The software extracted according to initial equation ofpressure, motion, balance equation, and constitutive through the definition ofresults seepage boundary, pore and mesh force setting to calculate. According to the relationship between the stress and the strain, the strain corresponding to stress can equation [47]. According to according the relationship between the stress and the strain, the strain The software extracted results to equation of motion, balance equation, and constitutive be solved and used to observe the stress distribution around the wellbore and the distribution of the corresponding stress can be and used to observe stress distribution around thethe wellbore equation [47]. to According to solved the relationship betweenthethe stress and the strain, strain plastic zone. and the distribution of the zone. corresponding to stress can plastic be solved and used to observe the stress distribution around the wellbore and the distribution of the plastic zone.

Figure 4. Pressure load model of shale formation in numerical simulation.

Figure 4. Pressure load model of shale formation in numerical simulation. Figure 4. Pressure load model of shale formation in numerical simulation.

Figure 5. Flow chart of numerical simulation.

The wellbore diameterFigure was set m chart and length of simulation. the simulation area was set as 20 times Figure Flow chartthe of numerical 5.5.0.2 Flow of numerical simulation. the diameter (4.0 m). A radial grid subdivision method was used to improve computing speed and The wellbore diameter was set 0.2 m normally and the length of the simulation area the wasdivision set as 20oftimes by considering that stress concentrations appeared near the wellbore, the The wellbore diameter wasgrid setwellbore 0.2 m and the length ofthe thecalculation simulation areawas wasdivided set as into 20 times the diameter (4.0 m). A radial subdivision was used to improve computing speed and grid was only encrypted near the area.method As a whole, model the diameter (4.0 m). A radial grid subdivision method was used to improve computing speed by considering concentrations normally appeared near the wellbore, the division of the 3600 grids andthat 7440stress nodes. The cell subdivision with finite difference method (FDM) is shown in and ® software by considering that stress concentrations normally near thesubsequent wellbore, the divided divisioninto of the Figure Surfer (Version 8.0, Golden, USA) was used for processing, grid was6.only encrypted near the wellbore area.CO, As aappeared whole, the calculation model data was and the intuitive analysis of contour map in FLAC3D™. 3600 grids and 7440 nodes. The cell subdivision with finite difference method (FDM) is shown in Figure 6. Surfer® software (Version 8.0, Golden, CO, USA) was used for subsequent data processing, and the intuitive analysis of contour map in FLAC3D™.

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grid was only encrypted near the wellbore area. As a whole, the calculation model was divided into 3600 grids and 7440 nodes. The cell subdivision with finite difference method (FDM) is shown in Figure 6. Surfer® software (Version 8.0, Golden, CO, USA) was used for subsequent data processing, and Energies the intuitive analysis of contour map in FLAC3D™. 2017, 10, 651 7 of 23 In this model, the simulation parameters were adopted from related references [48,49] where In this model, simulation parameters from related [48,49] where the maximum and thethe minimum horizontal inwere situ adopted stress gradient werereferences 3 MPa per 100 m andthe 2 MPa maximum and the minimum horizontal in situ stress gradient 3 MPa m and MPa per per 100 m, respectively. The pore fluid pressure gradient waswere 1 MPa per per 100 100 m and the2 depth of the 3 100 m, respectively. The pore fluid pressure gradient was 1 MPa per 100 m and the depth of the well well was 2500 m. The density of the drilling fluid was 1.40 g/cm , thus had a hydraulic pressure of 3, thus had a hydraulic pressure of 35 MPa. was 2500 The density of the drilling fluid was 1.40PTT g/cmwith 35 MPa. Them. permeability obtained in the previous #1 Atoka shale was set as the seepage The permeability obtained in the previous PTT with #1 Atoka shale was set as the seepage parameter parameter in the simulation. The parameters of the model are shown in Table 3. The pore fluid pressure in the simulation. The parameters of the model are shown in Table 3. The pore fluid pressure transmission, the stress, and deformation of the surrounding rock in contact with drilling fluid, with transmission, the stress, and deformation of the surrounding rock in contact with drilling fluid, with or without NP, were analyzed in detail in the following. or without NP, were analyzed in detail in the following.

Figure 6. Cell subdivision of the calculation model in numerical simulation (3600 grids and 7440 nodes).

Figure 6. Cell subdivision of the calculation model in numerical simulation (3600 grids and 7440 nodes). Table 3. Shale parameters used in the model. Parameter Value Table 3. Shale parameters used in the model. Porosity Shale density (ρ) Parameter Viscosity of water (μ) Porosity Maximum horizontal crustal stress (σH) Shale density (ρ)crustal stress (σh) Minimum horizontal Viscosity water (µ) (Po) Poreoffluid pressure Maximum horizontal crustal stress (P (σfH Drilling fluid pressure )) Minimum horizontal crustal stress (σ(E) Elasticity modulus of shale h) Pore fluidPoisson's pressureratio (Po ) (μ) Drilling fluid Cohesion pressure (C) (Pf ) Elasticity modulus ofangle shale(φ) (E) Friction Poisson’s ratio strength (µ) Tensile Cohesion (C) with sea water Shale permeability Friction angle (φ) with the BM Shale permeability Tensile strengthwith BM plus NP Shale permeability

4% 2600 kg/m3 Value 1.2 × 10−3 Pa·s 75 MPa 4% 2600 kg/m3 50 MPa × 10−3 Pa·s 251.2 MPa 75 MPa 35 MPa 50 MPa 45.9 GPa 0.25 25 MPa 35 MPa 22.73 MPa 34.8°45.9 GPa 2.94 MPa0.25 22.73 cm2MPa 1.8 × 10−18 ◦ −18 cm2 0.15 × 10 34.8 2.94 0.1 × 10−20 cm2MPa

Shale permeability with sea water 1.8 × 10−18 cm2 −18 cm2 Shale permeability with the BM 0.15 × 10 There is no dispute that 3D simulation would be more convincing than 2D simulation. In the Shale permeability with BM plus NP 0.1 × 10−20 cm2 future, we will conduct similar research as permeability might be as variable in 3D simulation. It could forecast that positive results will be derived in the presence of nano-SiO2 in contact with shale. However, thedispute anisotropy shale should be takenbe into consideration, the differences There is no thatof3D simulation would more convincingotherwise, than 2D simulation. In the between 2Dconduct simulation and 3D will beas minimal even with the time-consuming future, we will similar research permeability might be as variable inwork. 3D simulation. It could

forecast that positive results will be derived in the presence of nano-SiO2 in contact with shale. 4. Results and Discussion However, the anisotropy of shale should be taken into consideration, otherwise, the differences between 2D Fluid simulation 3D will be minimalofeven theInvasion time-consuming work. 4.1. Pore Pressureand Transmission Simulation Shalewith with the of Drilling Fluid 4.1.1. The Law of Pore Fluid Pressure Transmission of Shale in Contact with Sea Water

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4. Results and Discussion 4.1. Pore Fluid Pressure Transmission Simulation of Shale with the Invasion of Drilling Fluid EnergiesThe 2017,Law 10, 651 4.1.1. of Pore Fluid Pressure Transmission of Shale in Contact with Sea Water

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In transmission lawlaw of shale in contact withwith drilling fluidfluid (sea In this this section, section,the thepore porefluid fluidpressure pressure transmission of shale in contact drilling water) was was first first studied. When drilling fluidfluid pressure (Pf ) (P is f)higher than pore fluid pressure (Po )(Pof (sea water) studied. When drilling pressure is higher than pore fluid pressure o) shale formation, sea water will gradually penetrate the shale formation due to the hydraulic differential of shale formation, sea water will gradually penetrate the shale formation due to the hydraulic pressure, resulting in the gradual of pore fluid pressure of shale. For example, fluid differential pressure, resulting in increase the gradual increase of pore fluid pressure of shale. the Forpore example, pressure of shale increased from 25 MPa (Figure 7a) to 35 MPa (the drilling fluid pressure) in 24 h the pore fluid pressure of shale increased from 25 MPa (Figure 7a) to 35 MPa (the drilling fluid (Figure 7b). pressure) in 24 h (Figure 7b).

(a)

(b)

Figure 7. Time dependent pore fluid pressure contour map. The unit of pressure is defaulted as Pa in Figure 7. Time dependent pore fluid pressure contour map. The unit of pressure is defaulted as Pa in FLAC3D™, the same as below. (a) 1 h; (b) 24 h. FLAC3D™, the same as below. (a) 1 h; (b) 24 h.

Figures 8 and 9 show the distance and time dependent pore fluid pressure transmission from Figures 8 and showdependent the distancepore and fluid time dependent fluid pressure transmission from the the wellbore. The 9time pressure atpore different distances from the wellbore wellbore. timeexception, dependentindicating pore fluidthe pressure at different distances from of theshale wellbore increased increased The without possibility of wellbore instability in contact with without exception, indicating the possibility of wellbore instability of shale in contact with water sea water (Figure 8). Near the wellbore, the pore fluid pressure increased to 33.30 MPa in 24sea h (Figure (Figure Nearfrom the wellbore, the pore fluidfluid pressure increased to 33.30 MPa in 24(Figure h (Figure 8), while 8), while8).away the wellbore, the pore pressure increased rather slowly 9). The fluid away from the wellbore, the pore fluid pressure increased rather slowly (Figure 9). The fluid filtrate filtrate invasion gradually (typically in the order of several days) equilibrates the drilling fluid invasion (typically in the order of several days) effective equilibrates the drilling fluid pressure and pressure gradually and the near-wellbore pore pressure, whereby drilling fluid pressure support is the near-wellbore pore pressure, whereby effective drilling fluid pressure support is lost. Shale may lost. Shale may yield in shear or tensile models because of this pore-pressure elevation that, in yield in shearwith or tensile models because of this pore-pressure that, in combination withthat the combination the repulsive hydration stress, will reduceelevation the near-wellbore effective stress repulsive hydration stress, will reduce the near-wellbore effective stress that hold shale together [3]. hold shale together [3]. nearby wellbore 0.4m

35

Pore fluid pressure, MPa

34

0.2m 0.9m

33 32 31 30 29 28 27 26 25 0

4

8

12 16 20 24 28 32 36 40 44 48 Time, hr

Figure 8. Pore fluid pressure of shale in contact with sea water vs. time at different distance. Figure 8. Pore fluid pressure of shale in contact with sea water vs. time at different distance.

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pressure, PorePore fluidfluid pressure, MPaMPa

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35 34 35 33 34 32 33 31 32 30 31 29 30 28 29 27 28 26 27 25 26 24 25

24 0.1 0.1

0.25h 0.5h 0.25h 1h 0.5h 2h 1h 2h

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.2Axis0.3 0.5 0.6 0.8 m 0.9 distance0.4 from borehole along x0.7 direction, Axis distance from borehole along x direction, m

Figure 9. Pore fluid pressure of shale in contact with sea water vs. distance at different time. Figure 9. Pore fluid pressure of shale in contact with sea water vs. distance at different time. Figure 9. Pore fluid pressure of shale in contact with sea water vs. distance at different time.

4.1.2. Influence of Drilling Fluid Density on the Transmission of Pore Fluid Pressure 4.1.2. 4.1.2. Influence Influence of of Drilling Drilling Fluid Fluid Density Density on on the the Transmission Transmissionof ofPore PoreFluid FluidPressure Pressure In this section, the influence of drilling fluid density on pore fluid pressure transmission was In this section, the influence of drilling fluid density on pore fluid pressure transmission was In this section, the influence drilling fluid pore fluid pressure transmission investigated. Figure 10a,b presentsof the contour mapdensity of poreon fluid pressure for 1 h and 24 h whenwas the investigated. Figure 10a,b presents the map of pore fluid pressure for h the 3 toof 3 and investigated. Figure 10a,b presentsfrom the contour contour map pore fluid pressure for 311, respectively, h and and 24 24 h h when when the drilling fluid density was adjusted 1.40 g/cm 1.22 g/cm 1.63 g/cm and the 3 to 1.22 g/cm3 and 1.63 g/cm3 , respectively, and the drilling fluid density was adjusted from 1.40 g/cm 3 to 1.22 g/cm3 and 1.63 g/cm3, respectively, and the drilling fluid density was adjusted from 1.40 g/cm corresponding drilling fluid pressure was 30.50 MPa and 40.75 MPa. With a given pore fluid pressure, corresponding drilling was MPa and 40.75 With aa given given pore pore fluid fluid pressure, corresponding drilling fluid fluid pressure pressurecould was 30.50 30.50 MPathe and 40.75 MPa. MPa. With the decrease in drilling fluid density mitigate positive pressure differential betweenpressure, drilling the decrease in drilling fluid density could mitigate the positive pressure differential between drilling the decrease drilling could mitigate thealleviation positive pressure between drilling fluid pressureinand porefluid fluiddensity pressure, resulting in the of poredifferential fluid pressure transmission fluid pressure and pore fluid pressure, resulting in the alleviation of pore fluid pressure transmission fluid pressure and pore fluid pressure, resulting in the alleviation of pore fluid pressure transmission (Figure 10c). Furthermore, the increase in drilling fluid density will accelerate the transmission of (Figure 10c). Furthermore, the in in drilling fluid density willwill accelerate the transmission of pore (Figure 10c). Furthermore, theincrease increase drilling fluid density accelerate the transmission of pore fluid pressure (Figure 10d). fluid pressure (Figure 10d). pore fluid pressure (Figure 10d).

(a) (a)

(b) (b)

(c) (d) (c) (d) Figure 10. Pore fluid pressure contour map with different drilling fluid pressure. (a) 1 h at 30 MPa Figure 10. Pore fluid pressure contour map with different drilling fluid 1 h30atMPa 30 MPa f); (b)10. 1 hPore at 40fluid MPapressure (Pf); (c) 24 h at 30map MPa (P f);different and (d) 24 h at 40 MPa (Ppressure. f). (P Figure contour with drilling fluid pressure. (a) 1(a) h at (Pf ); f); (b) 1 h at 40 MPa (Pf); (c) 24 h at 30 MPa (Pf); and (d) 24 h at 40 MPa (Pf). (P (b) 1 h at 40 MPa (P ); (c) 24 h at 30 MPa (P ); and (d) 24 h at 40 MPa (P ). f

f

f

4.1.3. The Influence of NP on the Transmission of Pore Fluid Pressure 4.1.3. The Influence of NP on the Transmission of Pore Fluid Pressure (1) The influence of NP on pore fluid pressure transmission of the shale in contact with the BM. (1) The influence of NP on pore fluid pressure transmission of the shale in contact with the BM. In this section, various fluids (4% sea water, BM, BM + NP) successively in contact with the shale In this section, various fluidsfluid (4% sea water,(P BM, BMinitial + NP)pore successively in contact sample were simulated. Drilling pressure f) and fluid pressure (Po)with werethe 35 shale MPa sample were simulated. Drilling fluid pressure (Pf) and initial pore fluid pressure (Po) were 35 MPa

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4.1.3. The Influence of NP on the Transmission of Pore Fluid Pressure (1)

The influence of NP on pore fluid pressure transmission of the shale in contact with the BM

In this section, various fluids (4% sea water, BM, BM + NP) successively in contact with10the shale Energies 2017, 10, 651 of 23 sample were simulated. Drilling fluid pressure (Pf ) and initial pore fluid pressure (Po ) were 35 MPa andand 25 MPa, respectively. ToTo the viscositycompared compared water difficult 25 MPa, respectively. theBM, BM,itithad had higher higher viscosity toto seasea water andand waswas difficult to invade the compact formation. However, the fluid pore pressure fluid pressure still to invade into into the compact shaleshale formation. However, with with time,time, the pore still increased. increased. After 48 pressure h, pore fluid near the wellbore climbed 32.4 MPa (Figure 11a), the After 48 h, pore fluid nearpressure the wellbore climbed to 32.4 MPato(Figure 11a), indicating indicating the possibility of wellbore instability withreduction the BM. This reduction of true(which overbalance possibility of wellbore instability with the BM. This of true overbalance acts as a (which acts as a support pressure for the hole) can result in shale failure and wellbore instability. To NP support pressure for the hole) can result in shale failure and wellbore instability. To the BM plus the BM plus NP (BM + NP), no pore fluid pressure transmission was observed in the first 8 h (Figure (BM + NP), no pore fluid pressure transmission was observed in the first 8 h (Figure 11). After 48 h, 11). After 48 h, pore fluid pressure near the wellbore and at the distance two times from the wellbore pore fluid pressure near the wellbore and at the distance two times from the wellbore (0.2 m) only (0.2 m) only increased to 29.90 MPa (Figure 11a) and 27.4 MPa (Figure 11b), respectively, showing increased to 29.90 MPa (Figure 11a) and 27.4 MPa (Figure 11b), respectively, showing that the presence that the presence of SiO2 NP can effectively mitigate the transmission of fluid pressure into the shale of SiO effectively mitigatewellbore the transmission of fluid pressure into shale PTT formation 2 NP can formation and therefore improve stability, which is consistent with the previous results and therefore [19]. improve wellbore stability, which is consistent with previous PTT results [19]. 35

sea water

34

BM

35

BM+NP

34 Pore fluid pressure,MPa

Pore fluid pressure,MPa

33 32 31 30 29

33 32 31 30 29 28

sea water

27

BM

26

26

BM+NP

25

25

28 27

0

4

8

12

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28

Time, hr

(a)

32

36

40

44

48

0

4

8

12

16

20

24

28

32

36

40

44

48

Time, hr

(b)

Figure 11. Influence of drilling fluid types on pore fluid pressure transmission of shale. (a) Near the

Figure 11. Influence of drilling fluid types on pore fluid pressure transmission of shale. (a) Near the wellbore; (b) 0.2 m from the wellbore. wellbore; (b) 0.2 m from the wellbore.

(2) The influence of NP on the pore pressure transmission boundary of the shale in contact with the

(2) TheBM. influence of NP on the pore pressure transmission boundary of the shale in contact with the BM Figure shows the varietyininthe thepore pore pressure pressure transmission in the shale in contact Figure 12 12 shows the variety transmissionboundary boundary in the shale in contact with the BM and the BM plus SiO 2 NP. The red circles are considered the pore pressure transmission with the BM and the BM plus SiO2 NP. The red circles are considered the pore pressure transmission boundary. inside circles indicates increaseofofpore porefluid fluidpressure pressure while while outside outside the boundary. TheThe areaarea inside thethe circles indicates ananincrease the red red circles, the pore fluid pressure stays as the initial (25 MPa). To the BM, the boundary after 10 h circles, the pore fluid pressure stays as the initial (25 MPa). To the BM, the boundary after 10 h atatthe x the x direction and y direction was 0.88 m and 0.32 m (Figure 12a), respectively. After 24 h, the direction and y direction was 0.88 m and 0.32 m (Figure 12a), respectively. After 24 h, the boundary boundary at the x direction and y direction increased to 1.01 m and 0.6 m (Figure 12c), respectively. at the x direction and y direction increased to 1.01 m and 0.6 m (Figure 12c), respectively. After 48 h, After 48 h, the boundary at the x direction was out of scope (over than 2.0 m) and was 0.65 m at the the boundary at the x direction was out of scope (over than 2.0 m) and was 0.65 m at the y direction y direction (Figure 12c). In presence of SiO2 NP into the BM, the boundary after 10 h was only 0.64 m (Figure In at presence of SiO the BM, therespectively. boundary after 10after h was m and 0.12 2 NP into and 12c). 0.12 m the x and y directions (Figure 12b), Even 48 only h, the0.64 boundary onlym at the xincreased and y directions (Figure 12b), respectively. Even after 48 h, the boundary only increased to 0.72 m to 0.72 m and 0.16 m (Figure 12f), respectively. Therefore, the presence of SiO2 NP can andsignificantly 0.16 m (Figure 12f),the respectively. Therefore, the presence NP can significantly reduce reduce pore pressure transmission boundaryofofSiO the2 shale in contact with the BM, the poretherefore pressure transmission boundary of the shale in contact with the BM, therefore mitigating the mitigating the likelihood of wellbore instability. Theofinvasion ofinstability. water into the shale formation not only leads to secondary distribution of pore likelihood wellbore fluid also causes of hydration stress dueto tosecondary the water adsorption of clay The pressure, invasionbut of water into the generation shale formation not only leads distribution of pore which the original cementation status of shale particles. strength, the fluidminerals pressure, butdestroy also causes the generation of hydration stress due toTherefore, the waterthe adsorption of clay cohesion, and the friction angle of the surrounding rock will decrease. In the presence of NP into the minerals which destroy the original cementation status of shale particles. Therefore, the strength, BM, the invasion of water into the shale formation can be mitigated, and the wellbore stability of the cohesion, and the friction angle of the surrounding rock will decrease. In the presence of NP into shale can be significantly improved. the BM, the invasion of water into the shale formation can be mitigated, and the wellbore stability of However, for the convenience of numerical simulation, the permeability was set as a constant shale can be significantly improved. with the addition of NP. This is the limitation of this 2D model. In reality, permeability decreases gradually, and depends on the matching degree of NP size and the pore throats of shales, as well as on other factors such as pH, salinity, etc. In Figure 3a, we can see that the decrease of permeability

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was faster than that of Figure 3b. Furthermore, the pressure difference between the upstream and the downstream faster Energies 2017, 10, of 651the shale should affect this process. Higher pressure difference will lead to 11 of 23 accumulation of NP on the surface of shale. 2

y ,m 2

1.5

y ,m

1.5

1

BM+NP

1

BM

0.5

0.5

0.32 m 0

0.12 m

0.88 m

0

-0.5

-0.5

-1

-1

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-2 -2

-1.5

-1

-0.5

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x ,m

0.64 m

-2 -2

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-1

-0.5

(a)

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0.5

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2

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2

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2

x,m

(b)

y,m

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0

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0

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-2 -2

2

-1.5

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(c) 2

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y ,m

0.16 m 0

0

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-1

-1.5

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-2 -1.5

-1

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(e)

x,m

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-2

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(d)

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0.5

0

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1

1.5

2

x,m

0.72 m

-2 -2

-1.5

-1

-0.5

0

0.5

x ,m

(f)

Figure 12. 12. Time Time dependent dependent pore pore pressure pressure transmission transmission boundary boundary in in the the shale. shale. (a) 10 h h (BM); (BM); (b) (b) 10 10 h h Figure (a) 10 (BM + NP); (c) 24 h (BM); (d) 24 h (BM + NP); (e) 48 h (BM); and (f) 48 h (BM + NP). (BM + NP); (c) 24 h (BM); (d) 24 h (BM + NP); (e) 48 h (BM); and (f) 48 h (BM + NP).

4.2. The Influence of Drilling Fluid Invasion with or without NP on the Stress and Deformation of However, for the convenience of numerical simulation, the permeability was set as a constant Surrounding Rock with the addition of NP. This is the limitation of this 2D model. In reality, permeability decreases gradually, depends on theofmatching degree of NP the pore throats of shales, as well as 4.2.1. Stressand Distribution Law Surrounding Rock withsize theand Invasion of Sea Water on other factors such as pH, salinity, etc. In Figure 3a, we can see that the decrease of permeability Figurethan 13 presents the stress of the surrounding at the between x and y directions withand sea was faster that of Figure 3b. contour Furthermore, the pressure rock difference the upstream water in contact with shale formation after one hour and 48 h, respectively. When the wellbore is the downstream of the shale should affect this process. Higher pressure difference will lead to faster accumulation of NP on the surface of shale.

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4.2. The Influence of Drilling Fluid Invasion with or without NP on the Stress and Deformation of Surrounding Rock 4.2.1. Stress Distribution Law of Surrounding Rock with the Invasion of Sea Water Figure 13 presents the stress contour of the surrounding rock at the x and y directions with sea water in contact with shale formation after one hour and 48 h, respectively. When the wellbore is opened, the stress difference between the x and y directions has a maximum at the minimum horizontal in situ stress direction, so shear failure is most likely to happen. With sea water invasion into the shale formation, the transmission of pore fluid pressure leads to secondary stress distribution and the stress concentration area spreads to the periphery of the surrounding rock. At the minimum horizontal in situ stress direction, the stress differential between the x and y directions climbed rapidly at the beginning of sea water invasion, which increased the likelihood of shear failure and reached stable stress differential at 10 h (Figure 14). Energies 2017, 10, 651 12 of 23 Based on Figure 15, the shear stress of the surrounding rock presents symmetric distribution in the horizontal maximum (minimum) in situ stresses direction plus/minus 45◦ . Along with the opened, the stress difference between the x and y directions has a maximum at the minimum invasion for 1 h to 48 h, the maximum shear stress of the surrounding rock (tensile stress or stress) horizontal in situ stress direction, so shear failure is most likely to happen. With sea water invasion increased from 40.62 MPa to 41.95 MPa, which increased the risk of shear failure. into the shale formation, the transmission of pore fluid pressure leads to secondary stress distribution It is acknowledged that shale has a typical compact formation with a very low permeability (i.e., and the stress concentration area spreads to the periphery of the surrounding rock. At the minimum − 12 10 to 10−6 Darcy) and if fractures are not taken into consideration, the seepage process is rather slow. horizontal in situ stress direction, the stress differential between the x and y directions climbed Shales lack the protection of a filter cake as they do not experience normal fluid loss from water-based rapidly at the beginning of sea water invasion, which increased the likelihood of shear failure and drilling fluid at over balance. However, even this slow fluid filtrate invasion will gradually equilibrate reached stable stress differential at 10 h (Figure 14). the drilling fluid pressure and the near-wellbore pore pressure, whereby effective drilling pressure Based on Figure 15, the shear stress of the surrounding rock presents symmetric distribution in support is lost [3]. Therefore, long-term seepage is still unfavorable for wellbore stability. For sea water, the horizontal maximum (minimum) in situ stresses direction plus/minus 45°. Along with the pore fluid pressure still spread after 48 h and therefore the stress of the surrounding rock continued to invasion for 1 h to 48 h, the maximum shear stress of the surrounding rock (tensile stress or stress) change. The wellbore loses its stability once the stress exceeds the strength of shale formation. increased from 40.62 MPa to 41.95 MPa, which increased the risk of shear failure.

(a)

(b)

(c)

(d)

y direction ,MPa

Figure 13. Time stress contour contour map. map. The to Figure 13. Time dependent dependent stress The symbol symbol “−” “−” before before the the numbers numbers refers refers to compressive stress. Otherwise, it refers to tensile stress, the same as follows. (a) x direction stress for compressive stress. Otherwise, it refers to tensile stress, the same as follows. (a) x direction stress for 1 h; (b) (b) yy direction direction stress stress for for 11 h; h; (c) (c) xx direction direction stress stress for for 48 48h; h; and and(d) (d)yydirection directionstress stressfor for48 48h. h. 1 h;

105 104 103 102

(c)

(d)

Figure 13. Time dependent stress contour map. The symbol “−” before the numbers refers to compressive stress. Otherwise, it refers to tensile stress, the same as follows. (a) x direction stress for Energies 2017, 10, 651 13 of 23 1 h; (b) y direction stress for 1 h; (c) x direction stress for 48 h; and (d) y direction stress for 48 h.

Stress difference between x and y direction ,MPa

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98 97 96 95 0

4

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12

16

20

24

28

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36

40

44

48

Time, hr

Figure 14. Time dependent stress near the wellbore at the minimum horizontal horizontal stress stress direction. direction. Energies 2017, 10, 651

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(a)

(b)

Figure 15. Shear stress distribution at different times with sea water. (a) 1 h; (b) 48 h.

It is acknowledged that shale has a typical compact formation with a very low permeability (i.e., 10−12 to 10−6 Darcy) and if fractures are not taken into consideration, the seepage process is rather slow. Shales lack the protection of a filter cake as they do not experience normal fluid loss from water-based drilling fluid at over balance. However, even this slow fluid filtrate invasion will gradually equilibrate the drilling fluid pressure and the near-wellbore pore pressure, whereby effective drilling pressure support is lost [3]. Therefore, long-term seepage is still unfavorable for wellbore stability. (a) (b) stress of the surrounding For sea water, pore fluid pressure still spread after 48 h and therefore the rock continued to change. wellbore losesatits stability once thesea stress exceeds of shale Figure 15. ShearThe stress distribution different times with water. (a) 1 h;the (b) strength 48 h. Figure 15. Shear stress distribution at different times with sea water. (a) 1 h; (b) 48 h. formation. It is acknowledged that shale has a typical compact formation with a very low permeability (i.e., 4.2.2. Deformation Distribution Law Law of Surrounding Surrounding Rock Invasion of Sea −12 to 4.2.2. Deformation Distribution Rock with with the thethe Invasion ofprocess Sea Water Water 10 10−6 Darcy) and if fractures areof not taken into consideration, seepage is rather slow. The displacement direction ofcake the surrounding surrounding rock towardsnormal the wellbore wellbore in the the process process of sea Shales lack the protection of a filter as they do notrock experience fluid loss from water-based The displacement direction of the towards the in of sea water contacted with shale can be found and the displacement of the wellbore at the minimum drilling fluid at over balance. However, even this slow fluid filtrate invasion will gradually water contacted with shale can be found and the displacement of the wellbore at the minimum and and maximum horizontal situ direction stress direction was given atwhereby x and y(Figure directions equilibrate the drilling pressure and the near-wellbore poreatpriority pressure, effective drilling maximum horizontal influid situin stress was given priority the x and ythe directions 16), (Figure 16), respectively. pressure support is lost [3]. Therefore, long-term seepage is still unfavorable for wellbore stability. respectively. For sea water, pore fluid pressure still spread after 48 h and therefore the stress of the surrounding rock continued to change. The wellbore loses its stability once the stress exceeds the strength of shale formation. 4.2.2. Deformation Distribution Law of Surrounding Rock with the Invasion of Sea Water The displacement direction of the surrounding rock towards the wellbore in the process of sea water contacted with shale can be found and the displacement of the wellbore at the minimum and maximum horizontal in situ stress direction was given priority at the x and y directions (Figure 16), respectively. (a)

(b)

Figure 16. Displacement contour map around the surrounding rock. (a) x direction displacement for Figure 16. Displacement contour map around the surrounding rock. (a) x direction displacement for 1 h; (b) y direction displacement for 1 h. 1 h; (b) y direction displacement for 1 h.

Figure 17 presents the displacement curve at the x and y directions. Even at the y direction, the displacement was only 170 μm after 48 h, showing that the shale sample was a hard and brittle rock and wellbore shrinkage would not happen, which is consistent with the former X-ray diffraction analysis results [19]. Collapse and breaking will become the main model of wellbore instability.

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Figure 17 presents the displacement curve at the x and y directions. Even at the y direction, the displacement was only 170 µm after 48 h, showing that the shale sample was a hard and brittle rock and wellbore shrinkage would not happen, which is consistent with the former X-ray diffraction analysis results [19]. Collapse and breaking will become the main model of wellbore instability. Energies 2017, 10, 651 14 of 23

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43 43 41 41 39 39 37 37 35 35 33 33 31 31 29 2927

2725 25 0 4 8 12 16 20 24 28 32 36 40 44 48 0 4 8 12 16 20 24 28 32 36 40 44 48 Time, hr Time, hr

Displacement at yatdirection, μmμm Displacement y direction,

Displacement at x direction, μm Displacement at x direction, μm

180 180 170 170 160 160 150 150 140 140 130 130 120 120 0 0

4 4

8 8

12 16 20 24 28 32 36 40 44 48 12 16 20 24 28 32 36 40 44 48 Time, hr Time, hr

(a) (b) (a) (b) Figure 17. Displacement change trend of the surrounding rock. (a) x direction at the minimum Figure 17. Displacement change trend of the surrounding rock. (a) x direction at the the minimum minimum Figure 17. Displacement trend ofatthe rock. (a)stress x direction at horizontal stress direction;change (b) y direction the surrounding maximum horizontal direction. horizontal stress direction; (b) y direction at the maximum horizontal stress direction. horizontal stress direction; (b) y direction at the maximum horizontal stress direction.

Tensile deformation and shear deformation appeared at the maximum and minimum in situ Tensile deformation and deformation appeared at the the maximum and minimum in situ stress Tensile deformation andshear shear maximum and minimum stress directions, respectively, in thedeformation first 24 h of appeared sea water at invasion (Figure 18a). In the nextin24situ h, directions, respectively, in the first 24 h of sea water invasion (Figure 18a). In the next 24 h, stress directions, respectively, in the first 24 h of sea water invasion (Figure 18a). In the next shear 24 h, yield shear deformation occupied the primary position and the radius of the yielding zoneyield increased deformation occupied the primary position and the radius the yielding zone increased a certain yield shear deformation occupied primary position andof the radius of the yielding zonetoincreased to a certain extent (Figure 18b). the extent (Figure 18b).(Figure 18b). to a certain extent

None shear-n None tension-n shear-n tension-n

(a)

None shear-n None tension-n shear-n tension-n

(b)

(a) (b) Figure 18. Plastic yield distribution of the surrounding rock. (a) 24 h; and (b) 48 h. Figure 18. Plastic yield distribution of the surrounding rock. (a) 24 h; and (b) 48 h. Figure 18. Plastic yield distribution of the surrounding rock. (a) 24 h; (b) 48 h.

4.2.3. The Influence of Fluid Density on the Deformation of the Surrounding Rock

4.2.3. of Density on the of Surrounding Rock effect of fluid density on the yielding zone is shown in Figure 19. The shear failure 4.2.3. The The Influence Influence of Fluid Fluid Density onplastic the Deformation Deformation of the the Surrounding Rock 3. As the density of the drilling zone is only observed when the fluid density decreased to 1.22 g/cm The effect of offluid fluiddensity densityononthe the plastic yielding zone is shown in Figure 19. The failure The effect plastic yielding zone is shown in Figure 19. The shearshear failure zone 3 and the corresponding drilling fluid 3. Aspressure fluidis increased to 1.63 g/cm was 40.75 MPa, zone only observed when the fluid density decreased to 1.22 g/cm the density of the drilling is only observed when the fluid density decreased to 1.22 g/cm3 . As the density of the drilling fluid respectively, thetotensile yield3 zone the wellbore appeared atfluid the beginning of drilling fluid increased 1.63 g/cm and near the corresponding drilling 40.75 fluid MPa, 3 and increased to 1.63 g/cm the corresponding drilling fluid pressure was pressure 40.75 MPa,was respectively, the invasion (Figure 19b), indicating that higher density might lead to tensile failure. With further respectively, the tensile yield zone near the wellbore appeared at the beginning of drilling tensile yield zone near the wellbore appeared at the beginning of drilling fluid invasion (Figure fluid 19b), invasion, shear failure became the possible instability model and the to yield zone failure. of shear With deformation invasion 19b),density indicating density might tensile further indicating(Figure that higher mightthat leadhigher to tensile failure. With lead further invasion, shear failure became 3), indicating occupied less than that of lower density (1.22 g/cm that higher density might be helpful invasion, shear failure became thethe possible instability model and the yield zoneless of shear deformation the instability model and yield zone of shear deformation occupied thanfluid that density of lower in possible decreasing the radius of yield zone (Figure 19c,d). This can be explained by higher 3), indicating occupied less than that of lower density (1.22 g/cm that higher density might be of helpful 3 density (1.22 g/cm ), indicating that higher density might be helpful in decreasing the radius yield bringing higher effective support to the wellbore. However, it may also speed up the invasion of in decreasing the radius of yield zone (Figure 19c,d). This can be explained by higher fluid density zone (Figure 19c,d). This can be explained by higher fluid density bringing higher effective support to water into shales and weaken the rock, possibly However, even causing newalso fractures or lost bringing higher effective support tospeed the wellbore. it may speed upweaken the circulation. invasion of the wellbore. However, it may also up the invasion of water into shales and the rock, Therefore, the density drillingthe fluid should be controlled in a rational range. or lost circulation. water into shales and of weaken rock, possibly even causing new fractures possibly even causing new fractures or lost circulation. Therefore, the density of drilling fluid should Therefore, the density of drilling fluid should be controlled in a rational range. be controlled in a rational range.

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None shear-n None tension-n shear-n tension-n

None shear-n None tension-n shear-n tension-n

(a) (a)

None shear-n None tension-n shear-n

(b) (b)

None shear-n None tension-n shear-n

tension-n

tension-n (c) (d) (c) (d) Figure 19. Contrast on plastic yield distribution of the surrounding rock with different fluid density. Figure 19. Contrast on plastic yield distribution of the surrounding rock with different fluid density. Figureat 19. Contrast on plastic yield distribution of the30 surrounding rock with different fluidf).density. (a) (a) 11 h h at 30 30 MPa MPa (P (Pff);); (b) (b) 11 hh at at 40 40 MPa MPa (P (Pff);); (c) (c) 24 24 hh at at 30 MPa MPa (P (Pff););and and(d) (d)24 24hhat at40 40MPa MPa(P (Pf ). (a) 1 h at 30 MPa (Pf); (b) 1 h at 40 MPa (Pf); (c) 24 h at 30 MPa (Pf); and (d) 24 h at 40 MPa (Pf).

Stress difference between x and Stress difference between x and y y direction, direction, MPaMPa

4.2.4. The Influence of SiO2 NP on the Stress and Deformation of the Surrounding Rock 4.2.4. The The Influence Influence of of SiO SiO22 NP NP on on the the Stress Stress and and Deformation Deformation of of the the Surrounding Surrounding Rock 4.2.4. Rock The stress differential between the x and y directions at the wellbore of minimum horizontal in The stress stress differential differential between betweenthe thexxand and ydirections directionsatatthe thewellbore wellbore of minimum horizontal The minimum horizontal situ stress direction reached a maximum (105y MPa) with the invasion ofofthe BM lasting for 16 in h in situ stress direction reached a maximum (105 MPa) with the invasion of the BM lasting for 16 16 h situ stress reached a maximum (105BM MPa) with thestress invasion of the was BM only lasting for (Figure 20).direction In the presence of SiO 2 NP into the for 48 h, the differential 98.10 MPa,h (Figure In the presence presence of SiO22 NP NP into into the the BM BM for for 48 48h, h,the thestress stressdifferential differential was was only 98.10 98.10 MPa, MPa, (Figure 20). 20).that In the of SiO indicating the BM containing NP had excellent capability to lower the possibilityonly of shear failure indicating that the BM containing NP had excellent capability to lower the possibility of shear failure indicating the BM containing NP had excellent capability to lower the possibility of shear failure and tendedthat to improve wellbore stability. and tended to improve wellbore stability. and tended to improve wellbore stability. 105

BM+NP

104 105 103 104

BM+NP BM BM

102 103 101 102 100 101 99 100 98 99 97 98 96 97 95 96 95 0 0

4

8

12 16 20 24 28 32 36 40 44 48

4

8

12 16 20Time, 24 hr 28 32 36 40 44 48 Time, hr

Figure 20. Contrast in the stress difference of the surrounding rock with/without NP. Figure 20. Contrast in the stress difference of the surrounding rock with/without NP. Figure 20. Contrast in the stress difference of the surrounding rock with/without NP.

The maximum shear stress near the wellbore was 40.26 MPa and 41.02 MPa (Figure 21a,c) when The maximum shear stress near the wellbore was4840.26 MPa and 41.02 MPa 21a,c) the invasion of the BM into the shale lasted 10 h and h, respectively, while the(Figure BM with SiOwhen 2 NP, The maximum shear stress near the wellbore was 40.26 MPa and 41.02 MPa (Figure 21a,c) the invasion of shear the BMstress into the lasted32.32 10 h MPa and 48and h, respectively, while the BM with SiOwhen 2 NP, the maximum onlyshale reached 37.55 MPa (Figure 21b,d), respectively. the invasion ofshear the BM intoonly the shale lasted 10 MPa h andand 48 h, respectively, while the BM with SiO2 the maximum stress reached 32.32 37.55 MPa (Figure 21b,d), respectively. Therefore, the BM containing SiO2 NP has much less possibility for shear failure. NP, the maximum shear stressSiO only reached 32.32 MPa and 37.55 MPa (Figure 21b,d), respectively. Therefore, the BM containing 2 NP has much less possibility for shear failure. Therefore, the BM containing SiO2 NP has much less possibility for shear failure.

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(a)

(b)

(a)

(b)

(c)

(d)

Figure 21. Contrast of the shear stress distribution of the surrounding rock with/without NP. (a) BM

Figurefor 21. Contrast of the shear stress distribution of the surrounding rock with/without NP. (a) BM 10 h; (b) “BM + NP” for 10 h; (c) BM for 48 h; and (d) “BM + NP” for 48 h. for 10 h; (b) “BM + NP” for(c) 10 h; (c) BM for 48 h; and (d) “BM + NP” for(d) 48 h. Figure 22 Contrast shows the effect of stress the BM with or without SiO2 NP on plastic yield zone Figure 21. of the shear distribution of the surrounding rock with/without NP.distribution (a) BM near the wellbore. In the first 10 h, no yield zones were observed when the shale was in contact with 10shows h; (b) “BM forof 10 the h; (c)BM BM with for 48 h; (d) “BMSiO + NP” for 48 h. Figurefor22 the+ NP” effect orand without NP on plastic yield zone distribution 2 the BM containing NP and even after 48 h, the yield zone was much smaller compared to the shale near the wellbore. In the first 10 h, no yield zones were observed when the shale was in contact with with Figure only the Thethe physical SiOor 2 NP into the nano-sized pores yield mitigated invasion 22BM. shows effect plugging of the BMofwith without SiO 2 NP on plastic zone the distribution the BM containing NPdrilling and even after 48 h, the formation yield zone was much decreased smaller compared to the shale of water from the fluid into the shale and therefore the effects onwith the near the wellbore. In the first 10 h, no yield zones were observed when the shale was in contact with only the BM. The physical plugging of SiO NP into the nano-sized pores mitigated the invasion stress and yield zones theeven surrounding Therefore, the wellbore stability in shale to formations the BM containing NP of and after 48 h,rock. the2yield zone was much smaller compared the shale of water the drilling fluid into the shale and therefore decreased the effects on the could be improved. withfrom only the BM. The physical plugging of SiOformation 2 NP into the nano-sized pores mitigated the invasion

stress of and yield zones of the surrounding rock.formation Therefore, the wellbore stability shaleon formations water from the drilling fluid into the shale and therefore decreased theineffects the and yield zones of the surrounding rock. Therefore, the wellbore stability in shale formations could stress be improved. could be improved.

None shear-n tension-n

None

(a) None shear-n tension-n

(b) None

(a)

None shear-n tension-n

(b)

None shear-n

(c)

(d)

None Contrast shear-n tension-n

Figure 22. on the yield zone distribution ofNone the surrounding rock with/without the NP. (a) BM for 10 h; (b) “BM + NP” for 10 h; (c) BM for 24 h;shear-n and (d) “BM + NP” for 24 h. (c) (d) Figure 22. Contrast on the yield zone distribution of the surrounding rock with/without the NP.

Figure 22. Contrast on the yield zone distribution of the surrounding rock with/without the NP. (a) BM (a) BM for 10 h; (b) “BM + NP” for 10 h; (c) BM for 24 h; and (d) “BM + NP” for 24 h. for 10 h; (b) “BM + NP” for 10 h; (c) BM for 24 h; and (d) “BM + NP” for 24 h.

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5. Discussion 5. Discussion 5.1. The Mechanism of Silica NP Stabilizing Shale 5.1. The Mechanism of Silica NP Stabilizing Shale Similar PTTs (as those in Section 2) and following scanning electron microscope (SEM) tests were Similar (as those in Section 2) and following scanning electron microscope (SEM) tests were conducted toPTTs confirm the successful plugging of NP (nano-SiO 2) into shale, as shown in Figure 23. conducted to confirm the successful plugging of NP (nano-SiO ) into shale, as shownfrom in Figure 23. 2 The nano-SiO2 used in this study was a milky white dispersion and was procured Nanjing The nano-SiO used in this study was a milky white dispersion and was procured from Nanjing 2 Haitai Nano Materials Co., Ltd., Nanjing, China. The diameter of nano-SiO2 ranged from 10 to 20 nm. Haitai Nano Materials Co., Nanjing,of China. The diameter of nano-SiO from 10 to 20 nm. 2 ranged The shale sample was fromLtd., the outcrop Longmaxi Group, collected from Xiushan, Chongqing in The shale sample was from the outcrop of Longmaxi Group, collected from Xiushan, Chongqing in Southwest China. X-ray diffraction (XRD) results of the shale showed that it included 47% quartz, Southwest X-ray10% diffraction results and of the shale showed that it included 47% quartz, 25% 25% calcite,China. 10% illite, chlorite,(XRD) 5% feldspar 3% dolomite. calcite, 10% illite, 10% chlorite, 5% feldspar and 3% dolomite. The experimental data in Figure 23 showed that 5% nano-SiO2 by weight could retard liquid The transmission experimentaleffectively data in Figure 23 showed that nano-SiOwellbore couldwhich retardproved liquid 2 by weight pressure and was beneficial in 5% maintaining stability, pressure transmission and of was that NP can be used toeffectively seal the pores thebeneficial shale. in maintaining wellbore stability, which proved that NP can be used to seal the pores of the shale. SEM tests of shale samples after PTT were run to check the effects of NP in decreasing the SEM tests shale after PTT were run to effects NPenlarged in decreasing the permeability of of shale. Thesamples SEM pictures of shale before andcheck after the contact withofNP 2400 times permeability of shale. The SEM of respectively. shale before and after24b contact with enlarged 2400 times and 30,000 times are shown in pictures Figure 24, Figure shows thatNP nano-SiO 2 attached to and 30,000 times are shown in Figure 24, respectively. Figure 24b shows that nano-SiO attached to but the 2 the shale surface or penetrated the pores of shale. The nano-SiO2 consolidated and became larger, shale surface penetrated the pores ofto shale. The nano-SiO andmagnification became larger, we 2 consolidated we still foundorthat NP attached stably the surfaces of shale. By increasing tobut 30,000 still found that NP attached stably to the surfaces of shale. By increasing magnification to 30,000 times, times, we could clearly see that the pores of the original shale (Figure 24c) and the blocked pores of we could clearlywith see that pores24d). of the original shale (Figure 24c) and the blocked pores of shale in shale in contact NP the (Figure It indicates that nano-SiO 2 can plug the shale pore effectively, contact withits NPpermeability (Figure 24d). and It indicates thatretarding nano-SiO2the canpore plug the shale pore effectively,todecreasing decreasing therefore pressure transmission maintain its permeability and therefore retarding the pore pressure transmission to maintain wellbore stability. wellbore stability. Statistical ofof Figure 24c,d areare shown in Figure 25. Statistical diagrams diagramsof ofpore poresize sizedistribution distributionofofSEM SEMpictures pictures Figure 24c,d shown in Figure The average porepore sizessizes of shale were 0.275 and 0.137 respectively. After plugging, the average 25. The average of shale were µm 0.275 μm andµm, 0.137 μm, respectively. After plugging, the pore size was reduced by a ratio of 50.18%. The SEM pictures and statistical diagrams of pore size average pore size was reduced by a ratio of 50.18%. The SEM pictures and statistical diagrams of pore distribution of shale furtherfurther confirmed the successful plugging of nano-SiO pores, resulting 2 into shale size distribution of shale confirmed the successful plugging of nano-SiO 2 into shale pores, in the decrease of shale permeability. resulting in the decrease of shale permeability.

Figure 23. PTT shale in in China China with with different different solutions. solutions. Figure 23. PTT curves curves of of Longmaxi Longmaxi group group shale

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(a)

(b)

(a)

(b)

(c)

(d)

Figure 24. SEM pictures(c) of the shale. (a) Original shale magnified by 2400 times; (b) Shale contacted Figure 24. SEM pictures of the shale. (a) Original shale magnified by 2400(d) times; (b) Shale contacted with nano-SiO2 in PTT magnified by 2400 times; (c) Original shale magnified by 30,000 times; and (d) with nano-SiO2 in PTT magnified by 2400 times; (c) Original shale magnified by 30,000 times; and Figure 24. SEM pictures of the 2shale. (a)magnified Original shale magnified in PTT by 30,000 times. by 2400 times; (b) Shale contacted Shale contacted with nano-SiO (d) Shale contacted with nano-SiO2 in PTT magnified by 30,000 times. with nano-SiO2 in PTT magnified by 2400 times; (c) Original shale magnified by 30,000 times; and (d) Shale contacted with nano-SiO2 in PTT magnified by 30,000 times. 16.00%

16.00% 12.00%

Percentage, % Percentage, %

Percentage, % Percentage, %

16.00%

12.00% 8.00% 8.00% 4.00% 4.00% 0.00%

16.00% 12.00% 12.00% 8.00% 8.00% 4.00% 4.00% 0.00%

0.08 0.22 0.24 0.28 0.29 0.32 0.33 0.35 0.36 0.41 0.00%

Pore size, μm 0.08 0.22 0.24 0.28 0.29 0.32 0.33 0.35 0.36 0.41

(a)

Pore size, μm

0.00%

0.07 0.08 0.08 0.09 0.12 0.13 0.17 0.21 0.24 0.25 Pore size, μm 0.07 0.08 0.08 0.09 (b)0.12 0.13 0.17 0.21 0.24 0.25 Pore size, μm

Figure 25. Statistics of (a)pore size distribution of SEM pictures. (a) Original shale; (b) (b) Shale contacted with nano-SiO2. Figure 25. Statistics of pore size distribution of SEM pictures. (a) Original shale; (b) Shale contacted Figure 25. Statistics of pore size distribution of SEM pictures. (a) Original shale; (b) Shale contacted 2. with nano-SiO In terms of how NP stabilizes shales, Hoxha et al. [33] provided an in-depth explanation by with nano-SiO 2.

addressing the “force” that “drives” NP to block shale pore throats, decrease shale permeability, and In fluid termspressure of how transmission. NP stabilizesNP shales, Hoxha et al. [33]surface-active provided an properties in-depth explanation by reduce exhibits phenomenal with their high In terms of how NP stabilizes shales, Hoxha et pore al. [33] provided an in-depth explanation by addressing the “force” that “drives” NP to block shale throats, decrease shale permeability, and surface-to-volume ratio, allowing for their customized attachment to compounds which can be addressing the “force”transmission. that “drives”NP NPexhibits to blockphenomenal shale pore throats, decrease shale permeability, and reduce surface-active theirshale high utilizedfluid for pressure “fit-for-purpose” applications. Hoxha et al. [33] stated that properties attraction with between surface-to-volume allowing for their compounds whichpressure can be surfaces and NP isratio, the main mechanism thatcustomized will lead toattachment pore throattoplugging reducing utilized for “fit-for-purpose” applications. Hoxha et al. [33] stated that attraction between shale surfaces and NP is the main mechanism that will lead to pore throat plugging reducing pressure

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reduce fluid transmission. NP exhibits phenomenal surface-active properties with their Energies 2017,pressure 10, 651 19 of high 23 surface-to-volume ratio, allowing for their customized attachment to compounds which can be utilized Energies 2017, 10, 651 19 of 23 whichapplications. in turn benefits borehole stability by slowing down near-wellbore pore-pressure fortransmission, “fit-for-purpose” Hoxha et al. [33] stated that attraction between shale surfaces and elevation and effective stress reduction. inter-molecular shaledown NP interaction should allow for NP is the main mechanism that willborehole leadThe to stability pore throat plugging reducing pressure transmission, transmission, which in turn benefits by slowing near-wellbore pore-pressure NP to approach the borehole shale surface andby beslowing able to down adherenear-wellbore to them. Thispore-pressure means that electrostatic which in turn benefits stability elevation elevation and effective stress reduction. The inter-molecular shale NP interaction should allowand for repulsion needs to be sufficiently slow so that NP can NP “diffuse” through any present repulsive barrier, effective stress reduction. inter-molecular shale interaction should for NP to approach NP to approach the shaleThe surface and be able to adhere to them. Thisallow means that electrostatic and reach the shale surface, in plugging the shale pores.that They also advocated the use of NP to the shale surface be ableresulting to slow adhere to them. This means electrostatic repulsion repulsion needs toand be sufficiently so that NP can “diffuse” through any present repulsiveneeds barrier, at optimized concentrations of up to 5% by weight. be slowsurface, so that resulting NP can “diffuse” through anypores. present repulsive barrier, and reach the andsufficiently reach the shale in plugging the shale They also advocated the use of NP shale surface, resulting in plugging the shale pores. They also advocated the use of NP at optimized at 5.2. optimized concentrations of up Discretization to 5% by weight. The Influence of the Underlying on the Simulation Results concentrations of up to 5% by weight. identifyofthe of discretization on the simulation results, by taking Figure 22 (the yield 5.2. TheTo Influence theeffect Underlying Discretization on the Simulation Results 5.2.zone Thedistribution Influence of of thethe Underlying Discretization the Simulation Results the mesh into a sparse and surrounding rock) as anon example, we transformed To identify the effect of discretization on the the simulation results, by yield taking Figure 22 (the yield denser one (Figure 26), separately, and simulated deformation of the zone distribution of To identify the effect of discretization on the simulation results, by taking Figure 22 (the yield zone zone distribution of the surrounding rock) as an example, we transformed the mesh into a sparse shear failure. As a whole, the calculation model was divided into 1800 grids and 3720 nodes for theand distribution of the surrounding rock)and as an example, the we transformed the mesh intozone a sparse and denser denser (Figure 26), separately, simulated of the yield sparseone one, and the calculation was divided into 7200deformation grids and 14,880 nodes for the distribution denser one, of one (Figure simulated the deformation the1800 yield zone distribution shear shear failure.26), As separately, a whole, theand calculation model was dividedof into grids and 3720 nodesoffor the respectively. failure. As a whole, the calculation model was divided into 1800 grids and 3720 nodes for the sparse sparse one, and the calculation was divided into 7200 grids and 14,880 nodes for the denser one, one, and the calculation was divided into 7200 grids and 14,880 nodes for the denser one, respectively. respectively.

(a)

(b)

Figure 26. A sparse and dense cell subdivision result of the calculation model in numerical simulation. (a) 1800 grids and 3720 nodes; (b) (a)7200 grids and 14880 nodes. (b)

Figure 26.the A sparse and dense cellofsubdivision result of the calculation model numerical When became a half the previous model (Figure 6), only the in BM solution simulation. had a plastic Figure 26. A grid sparse and dense cell subdivision result of the calculation model in numerical simulation. (a) 1800 grids and 3720 nodes; (b) 7200area, gridsand and there 14880was nodes. shear zone for 10 h in the near wellbore no plastic zone for 24 h. When using “BM (a) 1800 grids and 3720 nodes; (b) 7200 grids and 14880 nodes.

+ NP”, there was no plastic zone nearby the wellbore for both 10 h and 24 h (Figure 27). When the grid a half of the previous (Figure 6), only themore BM than solution a plastic When the gridbecame was doubled, the plastic zonemodel of the “BM + NP” varied that had of the BM When the 10 grid became a half of the area, previous model (Figure 6), only thefor BM24solution had a plastic shear zone for h in the near wellbore and there was no plastic zone h. When using “BM nearby the wellbore for 10 h and 24 h, and the change of the plastic zone was more detailed than that shear zone for 10 h in the near wellbore area, and there was no plastic zone for 24 h. When using + NP”, was no plastic zone thethe wellbore for both 10plastic h and zone 24 h (Figure 27). in thethere article. However, it can be nearby seen from propagation of the that the seepage speed “BM + NP”, there was nodoubled, plastic zone nearby the for28). h andmore 24 h (Figure 27). of the “BM + NP” is much slower than that ofzone the wellbore BM (Figure When the grid was the plastic of the “BM +both NP”10varied than that of the BM

nearby the wellbore for 10 h and 24 h, and the change of the plastic zone was more detailed than that in the article. However, it can be seen from the propagation of the plastic zone that the seepage speed of the “BM + NP” is much slower than that of the BM (Figure 28).

None shear-n

None

(a) None shear-n

(b)

Figure 27. Cont.

None

(a)

(b)

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None

None

(c)

(d)

Figure 27. Contrast on the yield zone distribution of shear failure of the surrounding rock Figure 27. Contrast on the yield zone distribution of shear failure of the surrounding rock with/without with/without the NP and with more sparse mesh. (a) BM for 10 h; (b) “BM + NP” for 10 h; (c) BM for the NP and with more sparse mesh. (a) BM for 10 h; (b) “BM + NP” for 10 h; (c) BM for 24 h; and 24 h; and (d) “BM + NP” for 24 h. (d) “BM + NP” for 24 h. None

None

When the grid was doubled, the plastic zone of the “BM + NP” varied more than that of the BM (c) (d) nearby the wellbore for 10 h and 24 h, and the change of the plastic zone was more detailed than that Figure 27. Contrast on the yield zone distribution of shear failure of the surrounding rock in the article. However, it can be seen from the propagation of the plastic zone that the seepage speed with/without the NP and with more sparse mesh. (a) BM for 10 h; (b) “BM + NP” for 10 h; (c) BM for of the “BM + NP” is much slower than that of the BM (Figure 28). 24 h; and (d) “BM + NP” for 24 h.

None shear-n tension-n

None shear-n tension-n

(a)

None shear-n tension-n

(b)

None shear-n tension-n

(a)

(b) None shear-n tension-n

None shear-n tension-n

(c)

(d)

Figure 28. Contrast on the yield zone distribution of shear failure of the surrounding rock with/without the NP and with denser mesh. (a) BM for 10 h; (b) “BM + NP” for 10 h; (c) BM for 24 h; None and (d) “BM +None NP” for 24 h. shear-n shear-n tension-n

tension-n

Therefore, discretization (c) is beneficial in distinguishing the (d) yield zone distribution of the surrounding rock in shales. However, it will also greatly decrease the computing efficiency if all the Figure 28. Contrast on the yield zone distribution of shear failure of the surrounding rock Figure is 28.divided Contrast on the yield zone distribution of shear failure of the surrounding rock with/without wellbore into too many grids. with/without the NP and with denser mesh. (a) BM for 10 h; (b) “BM + NP” for 10 h; (c) BM for 24 h; the NP with+ NP” denser mesh. (a) BM for 10 h; (b) “BM + NP” for 10 h; (c) BM for 24 h; and andand (d) “BM for 24 h.

(d) “BM + NP” for 24 h. 6. Conclusions

Therefore, discretization is beneficial in distinguishing the yield zone distribution of the The combination of PTT and 2D numerical simulation with FLAC3D™ software offers a better surrounding rock in shales. However, it will in alsodistinguishing greatly decreasethe the computing efficiency if all the Therefore, discretization is between beneficial of the understanding of the interaction shale and NP-based drillingyield fluid. zone Baseddistribution on previous PTT wellbore is divided into too many grids.

surrounding shales. will also simulation greatly decrease theofcomputing efficiency if all with Atoka rock shale,inthe paper However, reports theitnumerical findings wellbore stability in the the wellbore is divided into too many grids. presence of NP based drilling fluid with the fluid-solid coupling model in FLAC3D™ software. The 6. Conclusions results of previous PTT were discussed. The steps of numerical simulation, simulation on pore fluid The combination of PTT and 2Dofnumerical simulation with FLAC3D™ software rock offerswere a better 6. pressure Conclusions transmission, distribution stress, and deformation of surrounding also understanding of the interaction between shale and NP-based drilling fluid. Based on previous PTT presented. The mechanism of NP in reducing the permeability and stabilizing shale was discussed The of PTT 2D numerical simulation with FLAC3D™ software offers a better with combination Atoka shale, the paperand reports the numerical simulation findings of wellbore stability in the and the following keyinteraction conclusionsbetween were reached: understanding of the shale and NP-based drilling fluid. Based on previous presence of NP based drilling fluid with the fluid-solid coupling model in FLAC3D™ software. The

PTT with shale,PTT thewere paper reports The the steps numerical simulation findings of wellbore in resultsAtoka of previous discussed. of numerical simulation, simulation on porestability fluid pressure transmission, distribution of stress, and deformation of surrounding rock were also presented. The mechanism of NP in reducing the permeability and stabilizing shale was discussed and the following key conclusions were reached:

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the presence of NP based drilling fluid with the fluid-solid coupling model in FLAC3D™ software. The results of previous PTT were discussed. The steps of numerical simulation, simulation on pore fluid pressure transmission, distribution of stress, and deformation of surrounding rock were also presented. The mechanism of NP in reducing the permeability and stabilizing shale was discussed and the following key conclusions were reached: (1)

(2) (3)

(4)

The numerical simulation results showed that water from the water-based drilling fluids had a strong tendency to invade shale, driven by the positive pressure differential between drilling fluid pressure and pore fluid pressure which increased the likelihood of shale instability. However, the transmission of pore fluid pressure could be mitigated in the presence of silica NP, which is consistent with previous results of PTT. The pore pressure transmission boundary of the shale in contact with the drilling fluid could also be restricted with silica NP. The stress differential and shear stress of surrounding rock near the wellbore can be reduced in the presence of NP. The plastic yield zone is minimized to improve wellbore stability. The plugging of silica NP on the surface of the shale plays an important role in decreasing the permeability of shale. The plugging mechanism of NP may be attributed to the electrostatic and electrodynamic interaction between NP and shale surfaces, governed by DLVO forces, which allows the NP to approach shale surfaces and adhere to them. Discretization of the simulation model is beneficial in distinguishing the yield zone distribution of the surrounding rock in shales.

Acknowledgments: Thanks to Martin E. Chenevert and Mukul M. Sharma from the University of Texas at Austin for the patient and careful supervision of pressure transmission tests. Meanwhile, the study is supported by the National Science Foundation of China (No. 41072111), the Innovation Foundation of China National Petroleum Corporation (No. 2014D-5006-0308), and the Key Project of Natural Science Foundation of Hubei Province (No. 2015CFA135). Author Contributions: Jiwei Song prepared the initial manuscript; Ye Yuan completed the initial 2D numerical simulation; Sui Gu helped to complete the PTT on Atoka shale; Xianyu Yang carried out the 2D numerical simulation according to the reviewers’ suggestions and the PTT on shale sample in China; Ye Yue completed the SEM analysis after PTT; Jihua Cai and Guosheng Jiang were responsible for the academic ideas and the responses to the reviewers’ and the editor’s suggestions. Conflicts of Interest: The authors declare no conflict of interest.

References 1. 2. 3. 4. 5. 6. 7. 8.

9.

Lal, M. Shale Stability: Drilling fluid interaction and shale strength. In Proceedings of the SPE Asia Pacific Oil and Gas Conference and Exhibition, Jakarta, Indonesia, 20–22 April 1999. Steiger, R.P.; Leung, P.K. Quantitative determination of the mechanical properties of shales. SPE Drill. Eng. 1992, 7, 181–185. [CrossRef] Van Oort, E.; Hale, A.H.; Mody, F.K.; Roy, S. Transport in shales and the design of improved water-based shale drilling fluids. SPE Drill. Complet. 1996, 11, 137–146. [CrossRef] Chenevert, M.E. Shale control with balanced-activity oil-continuous muds. J. Pet. Technol. 1970, 22, 1309–1316. [CrossRef] Ewy, R.T.; Morton, E.K. Wellbore-stability performance of water-based mud additives. SPE Drill. Complet. 2009, 24, 390–397. [CrossRef] Hayatdavoudi, A.; Apande, E. A theoretical analysis of wellbrore failure and stability in shales. In Proceedings of the 27th U.S. Symposium on Rock Mechanics, Tuscaloosa, AL, USA, 23–25 June 1986. Carminati, S.; Del Gaudio, L.; Brignoli, M. Shale stabilisation by pressure propagation prevention. In Proceedings of the SPE Annual Technical Conference and Exhibition, Dallas, TX, USA, 1–4 October 2000. Reid, P.I.; Dolan, B.; Cliffe, S. Mechanism of shale inhibition by polyols in water-based drilling fluids. In Proceedings of the SPE International Symposium on Oilfield Chemistry, San Antonio, TX, USA, 14–17 February 1995. Zhong, H.; Qiu, Z.; Huang, W.; Cao, J. Shale inhibitive properties of polyether diamine in water-based drilling fluid. J. Pet. Sci. Eng. 2011, 78, 510–515. [CrossRef]

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