Wellbore instability in oil and gas drilling is resulted from both mechanical and chemical factors. Hydration is produced in shale formation owing to the influence of the chemical property of drilling fluid. A new experimental method to measure diffusion coefficient of shale hydration is given, and the calculation method of experimental results is introduced. The diffusion coefficient of shale hydration is measured with the downhole temperature and pressure condition, then the penetration migrate law of drilling fluid filtrate around the wellbore is calculated. Furthermore, the changing rules of shale mechanical properties affected by hydration and water absorption are studied through experiments.
Chuanliang Yan,1,2 Jingen Deng,1 and Baohua Yu1
1State Key Laboratory of Petroleum Resource and Prospecting, China University of Petroleum, Beijing 102249, China. 2Department of Petroleum Engineering, China University of Petroleum, Beijing 102249, China.
Received 28 April 2013; Accepted 18 June 2013
Copyright © 2013 Chuanliang Yan et al.
The relationships between shale mechanical parameters and the water content are established. The wellbore stability model chemical-mechanical coupling is obtained based on the experimental results. Under the action of drilling fluid, hydration makes the shale formation softened and produced the swelling strain after drilling. This will lead to the collapse pressure increases after drilling. The study results provide a reference for studying hydration collapse period of shale.
Maintaining wellbore stability is an important issue in oil and gas industry [1–10]. In the process of drilling, the economic losses caused by wellbore instability reaches more than one billion dollar every year , and the lost time is accounting for over 40% of all drilling related nonproductive time . It is also reported that shale account for 75% of all formations drilled by the oil and gas industry, and 90% of wellbore stability problems occur in shale formations [13–18]. When a well is drilled, the formation around the wellbore must sustain the load that was previously taken by the removed formation. As a result, an increase in stress around the wellbore and stress concentration will be produced [19–23]. If the strength of the formation is not strong enough the wellbore will be failure [24–28]. Wellbore stability is not only a pure rock mechanical problem, but also the interaction of drilling fluid and shale is a more important influence factor [29–35]. There are various chemicals in the drilling fluid which physically and chemically interact with shale formations. One hand, these interactions will result in the production of swelling stress [36–43]. On the other hand, it alleviates the mechanical strength of the wellbore wall rock [44–46]. Furthermore, it results in wellbore instability.
When studying the wellbore stability in shale, chemical factor must be combined with mechanical factor. Before the 1990s, the combinations are mainly on experimental study. Chenevert studied mechanical properties of shale after hydration since 1970s . The results showed that the hydration would decrease the shale strength. After 1990s, the combinations came into a quantitative research stage. Yew et al. (1990)  and Huang et al. (1995)  combined shale hydrated effect quantitatively into the mechanical model based on thermoelasticity theory. Their method attributed the rock mechanical properties change with total water content. Take shale as a semipermeable membrane, Hale et al. (1993) [48, 49], Deng et al. (2003) , and Zhang et al. (2009)  introduced equivalent pore pressure to study interaction of shale and water base drilling fluid. Ghassemi et al. (2009)  proposed a linear chemo-thermo-poroelasticity coupling model, which considers the influence of chemical potential and temperature. Wang et al. (2012) [53, 54] built a fluid-solid-chemistry coupling model, in which they considered electrochemical potential, fluid flow caused by ion diffusion.
The chemical effect of drilling fluid on shale can be ultimately attributed to the variation of rock mechanical properties and stress around the wellbore. Water migration in shale is the basement of all wellbore stability models with chemical-mechanical coupling. A new experimental equipment to measure in situ water diffusion coefficient of shale is developed in this paper. And a sample model to evaluate time-dependent collapse pressure with chemical-mechanical coupling is presented.
2. Experimental Research on the Hydration of Shale
The free water and ion will penetrate into shale under the driving force of chemical potential and pressure difference between the pore fluid and drilling fluid [55–58]. Water content of shale changes by various mechanisms such as osmosis flow, viscous flow and capillary flow. Osmosis flow, driving force is due to chemicals and ions with different composition in drilling fluid and pore fluid. In order to evaluate the hydration of drilling fluid, the coefficient of water absorption and diffusion and the swelling ratio must be determined first .
2.1. Experimental Research on the Water Absorption of Shale
2.1.1. Experimental Equipment
Cherevent let one end face of shale sample contact with drilling fluid and the other end face wrapped up by plastic film, then he measured the water content increment in different location. But his experiment can only be conducted in room temperature and with zero confining pressure. But during drilling process in deep formation, it is in the condition of high temperature and high pressure. Shale hydration is influenced by temperature and pressure seriously, so his experimental result was inconsistent with actual drilling. In order to test the coefficient of water diffusion of shale, we developed an in situ test equipment of water diffusion coefficient which can fit the downhole temperature and pressure condition while drilling (Figure 1).
Figure 1: The experimental equipment sketch.
Technical parameters of this designed equipment are as the following.(1)Temperature: room temperature to 150°C, which can imitate the temperature condition of the formation with 5000 meters depth.(2)Pressure: confining pressure 0 MPa to 70 MPa, axial pressure 0 MPa to 200 MPa.(3)Imitate the maximum differential pressure of drilling fluid with 10 MPa.(4)Sample size: ϕ 25 mm × 50 mm.
The experimental process are as follows.(1)Determine the original water content of the rock samples first, wrap the samples with separation sleeve, and put into the core holder. Put the drilling fluid into the tank and check the test system to make sure it is in good condition.(2)Turn on the temperature controller, warm the core samples to the same temperature with downhole condition. Then load the confining pressure and axial pressure to proper value and start timing.(3)During the test, data acquisition control system is used to keep the test values constant.(4)Cooling uninstall when the test time reaches the predetermined value (50 hours in this research), remove the rock samples quickly, and measure the water content at different distance from the end face.
2.1.2. Coefficient of Water Diffusion
According to conservation of mass, water diffusion equations can be established. Supposing is mass flow rate of the water diffusion, is the weight percentage of water at the time and distance away from the well axis; according to conservation of mass requirement, the following equation can be presented:
where ∇ is the gradient operator and 𝐷eff is the coefficient of water diffusion. According to the above equations, water diffusion equation can be established as follows:
And the boundary conditions are
where rω is the wellbore radius; Cdf is the saturated water content of shale; C0 is the original water content.
Sign 𝑢 = 𝑟/√𝐷eff 𝑡, 𝐶𝑆 (𝑟, 𝑡) = 𝜙(𝑢), then the following equations can obtain that
Insert (5) to (3), then (6) can be obtained:
Equations (7) and (8) can obtain by integrating (6) that
Combining (8) and (4) the following equations can obtain that.
Thus, the water content of shale formation around the wellbore can be written as follows:
where J0() and N0() are the zero order of Bessel’s functions of group one and two, respectively.
In a short period of time after drilling and within a short distance from the wellbore wall, (10) can be simplified to
The water diffusion character of shale is measured using this designed experiment equipment. All the shale core samples used in this paper were collected from Bohai Bay Basin of China. The drilling fluid which contacted the shale in this experiment was KCL drilling fluid. The experimental confining pressure was 20 MPa, and the differential pressure of the fluid was 6 MPa. Core samples were taken out after 50 hours and then cut into pieces to measure the water content of each piece. Three samples were tested in this research. The experimental results of core sample 1-1 are shown in Figure 2.
Figure 2: Experimental results of water diffusion in shale.
Substituting the experimental results into (11), the coefficient of water diffusion of shale can be obtained. All the calculated water diffusion coefficients and clay mineral contents of these three samples are shown in Table 1. Smectite is the mineral most prone to hydration [59, 60], and the water diffusion coefficient is higher with more smectite.
Table 1: Clay mineral contents and water diffusion coefficient of shale.
2.2. Chemical Effect of Drilling Fluid on Shale Mechanical Properties
The mechanical properties of shale can be altered seriously after contacting with drilling fluid. Existing forms of water in shale mainly include water vapor, solid water, bound water, adsorption water (film water), capillary water, and gravity water (free water) (Figure 3).
Figure 3: Water existing states in shale .