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.
Jiwei Song1,2, Ye Yuan3, Sui Gu1, Xianyu Yang1, Ye Yue1, Jihua Cai1,* and Guosheng Jiang1 , *
1School of Engineering, China University of Geosciences, Wuhan 430074, China; 2115 Geological Team, Bureau of Geology and Mineral Exploration and Development of Guizhou Province, Guiyang 551400, China; 3Chengdu Team of Hydrogeology and Engineering Geology, Chengdu 610072, China.
Academic Editor: Dongsheng Wen
Received: 13 January 2017; Accepted: 2 May 2017; Published: 9 May 2017
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.
In the oil and gas industry, 75% of all footage was drilled in shale formations which are responsible for 90% of wellbore stability problems [1,2,3]. The main cause of shale instability for both soft and hard shales is water absorption and the subsequent swelling and sloughing of the wellbore . Wellbore 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 .
Viable types of engineered drilling fluids have been developed to address wellbore stability issues in shale formations. Chenevert  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  found that the best possible way of preventing contact between argillaceous rock and water was to seal off exposed clayey surfaces. Carminati et al.  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.  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.  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.  discovered the mechanism of polyether diamine improving shale wellbore stability in water-based drilling fluids. Van Oort et al.  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 [11,12,13,14,15,16,17]. Therefore, the past decade has seen an increase in NP use to improve wellbore stability in shales [18,19,20,21,22,23,24,25,26,27,28,29,30,31]. 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. . Hoxha et al.  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.  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.  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.  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 . The time dependent borehole stability is mainly caused by chemical and thermal diffusion. Huang et al.  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.  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 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.  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.  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.  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 , 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.
3. 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.
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 .
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 . 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.
Figure 1. Atoka shale sample used in the pressure transmission tests (PTTs).
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 contact with the lower face of the shale. The “simulated pore fluid” referred to was a 4 wt. % sea salt solution with a 0.98 water activity (aw). Its initial pressure was loaded to 0.34 MPa (50 psi). A test fluid flowed across the top of a shale sample (Figure 1) at a constant pressure of 2.07 MPa (300 psi) and the buildup of fluid pressure in a small sealed chamber located at the bottom of the shale was recorded automatically. The rate of pressure penetration provided a direct and quantitative measurement of shale permeability. Detailed equations for this computation were provided by Al-Bazali .
Figure 2. Experimental set up of PTT .
A three-step testing procedure was followed as we found that coring samples from the same 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 starting conditions. In step 2, 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 percent permeability reduction (Δk) was calculated based on the permeability obtained in the second step (times 100) .
2.3. PTT Results Analysis
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 close to the upstream pressure in approximately 20 h (Figure 3a), driven by the positive pressure difference. In the next step with the BM, the rising tendency of downstream pressure was still obvious for about 10 h. Finally, in the presence of SiO2 NP with the BM, the curve of the downstream pressure vs. time was almost flat (Figure 3a). A similar result was obtained when the tests were conducted with #2 Atoka shale sample (Figure 3b), revealing that SiO2 NP could effectively mitigate pore pressure transmission and the invasion tendency of water from the BM, therefore improving wellbore stability in shales.
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
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 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.
Table 2. Changes of NP on shale permeability.
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 . We speculated that only NP particles with a size in this range could enter and plug the pore throat of shale, therefore minimizing the fluid invasion tendency for shale. It must also be pointed out that a range of 7–15 nm NP worked well for Atoka shale; however, other sizes may be needed for other shale types. In addition, the specific type of shale, the specific type, size and concentration of NP, the interaction between NP and shale, and external factors such as pH, salinity, temperature require detailed investigation .
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, it could be simplified as a 2D fluid-solid coupling model in FLAC3D™ software, as shown in Figure 4. Here, σH, σh, and Pf referred to the maximum horizontal crustal press, minimum horizontal crustal press, and drilling fluid pressure, respectively.
Figure 4. Pressure load model of shale formation in numerical simulation.
Figure 5 shows the basic flow chart of the numerical simulation. The numerical simulation was based on the Mohr-Coulomb model, which belongs to the plane stress model. First, the seepage pattern starts. The left side represents the process of calculating the stress field, and the right side indicates the new step after considering the seepage process. The seepage simulation is mainly through the definition of seepage boundary, initial pore pressure, and mesh force setting to calculate. The software extracted results according to equation of motion, balance equation, and constitutive equation . According to the relationship between the stress and the strain, the strain corresponding to stress can be solved and used to observe the stress distribution around the wellbore and the distribution of the plastic zone.
Figure 5. Flow chart of numerical simulation.
The wellbore diameter was set 0.2 m and the length of the simulation area was set as 20 times the diameter (4.0 m). A radial grid subdivision method was used to improve computing speed and by considering that stress concentrations normally appeared near the wellbore, the division of the 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 the intuitive analysis of contour map in FLAC3D™.
Figure 6. Cell subdivision of the calculation model in numerical simulation (3600 grids and 7440 nodes).