Research Article  Open Access
The Research on Borehole Stability in Depleted Reservoir and Caprock: Using the Geophysics Logging Data
Abstract
Longterm oil and gas exploitation in reservoir will lead to pore pressure depletion. The pore pressure depletion will result in changes of horizontal insitu stresses both in reservoirs and caprock formations. Using the geophysics logging data, the magnitude and orientation changes of horizontal stresses in caprock and reservoir are studied. Furthermore, the borehole stability can be affected by insitu stresses changes. To address this issue, the dehydration from caprock to reservoir and roof effect of caprock are performed. Based on that, the influence scope and magnitude of horizontal stresses reduction in caprock above the depleted reservoirs are estimated. The effects of development on borehole stability in both reservoir and caprock are studied step by step with the above geomechanical model.
1. Introduction
During the development of oil and gas fields, the pore pressure in reservoir will decease dramatically due to the hydrocarbon exploitation. Decades of development experience reveal that the pore pressure change has great impact on horizontal insitu stresses. In some cases, the significant change of insitu stresses may even activate the instable faults. The accurate insitu stresses evaluation is one of the most important factors in safe drilling and hydraulic fracturing design [1–3]. For these reasons, researchers have done extensive works on the changes of insitu stresses caused by oil development [4–6].
Previous studies had paid much attention to the reservoir formations and the magnitude change of insitu stresses ignoring the orientation change and the change in caprock. However, some leak off tests in oil fields indicate that the insitu stresses in the caprock may also change significantly due to the depletion of reservoir pore pressure. So, it is meaningful and imperative to study the insitu stress change in caprock.
2. Geomechanical Effect of Exploitation on InSitu Stress Magnitude
The magnitude change of insitu stresses in reservoir caused by oil development has been investigated by several authors. Addis [7] showed that the magnitude of the change of the minimum horizontal stress has a linear relationship with that of the pore pressure by analyzing the insitu testing data of oil and gas fields of North America, North Sea such as Magnus, West Sole, and Wytch Farm fields. According to Addis, the minimum horizontal stress will decrease as the pore pressure decreases. But for different fault block fields, the proportional coefficient is generally different. For reservoirs with different boundary conditions and properties, Amadei et al. [8] provided the analytic solution of the proportional coefficient with uniaxial compression model. The analytic solution is presented in Table 1.

According to the porous linear elastic theory, supposing the reservoir is homogeneous, the change value of insitu stresses () has a linear relationship with that of the pore pressure () under the uniaxial compression condition. So, the horizontal insitu stresses of formations developed over a long period of time can be calculated by ((1a), (1b), and (1c)). All the other parameters can be obtained by geophysical logging data, for example, and ((1b)–(1c)) [9–12]:where and are the present maximum and minimum horizontal principle stresses, respectively; and are the original values; is the proportional coefficient; is the effective stress coefficient, is the change of the pore pressure; , are the elastic modulus and Poisson's ratio, respectively, which can be calculated by the and in (1c). is the internal frictional angle of fault, , are the coefficients of tectonic stress, is compressive wave velocity, m/s, and Vs is shear wave velocity, m/s.
Morita et al. [13] show that if the ratio of reservoir thickness and radius is smaller than 0.1 and the ratio between shear modulus of reservoir and caprock (GR/GC) is between 0.2 and 1.5, the result of (1a), (1b), and (1c) is relatively accurate.
3. Geomechanical Effect of Exploitation on InSitu Stress Orientation
For depleted fault block reservoirs, if the dip of fault and the orientation of horizontal stresses are not parallel, shear stress will present near the fault. Thus, the orientation of insitu stresses near the fault is not the same as that of the insitu stress far away from the fault. Sonder [14] analyzed the effect of development with geomechanical model (Figure 1). The assumptions of the model include (1) the fault F is impervious; (2) the change of formation temperature can be neglected; (3) the formation is homogeneous.
It can be seen from Figure 1 that the original orientation of horizontal stresses is parallel to the axis and the fault F is at an angle of to the orientation of maximum horizontal stress. The fault F divides the formation into two blocks, A and B. The pore pressure in the area A decreases dramatically due to the longperiod development, while the pore pressure of area B maintains the original value. The pore pressure difference between area A and B generates the normal traction force at both sides of the fault [15]. Because the direction of force and the axis are not parallel, the orientation of horizontal insitu stresses will rotate at some angle , and the angle can be calculated by the following equations [14]: where is the deflected angle of the horizontal stress near the fault; is the scaling factor; is the effective stress coefficient; is the change of the pore pressure; is the angel between the regional horizontal maximum stress and the dip of the fault.
According to the previous equations, the value of parameters can be assumed as follows: Poisson's ratio ; Biot’s coefficient ; the maximum horizontal insitu stress g/cm^{3}; the minimum horizontal insitu stress g/cm^{3}, and the depletion of pore pressure ranges from 0.1 g/cm^{3} to 0.8 g/cm^{3}, and then the relationship of the deflected angle and the angle is illustrated in Figure 2.
4. Geomechanical Effect of Exploitation on Caprock InSitu Stresses
For severely depleted reservoir, the insitu stresses in caprock will change due to the draining effect and top plate effect [16–18]. Morita and Fuh [19] showed that the change of the insitu stresses in caprock cannot be ignored after modeling its change degree with finite element model.
The pore pressure difference between the reservoir and caprock will drive the fluid from caprock into reservoir. Though the permeability of caprock is very low, decades of seepage will affect the reservoir insitu stresses [19–23]. This process is called draining effect of caprock. What’s more, the decrease of pore pressure causes the increasing of matrix stress and the caprock will deform accordingly. This phenomenon is called top plate effect. The influence of pore pressure depletion in the caprock can be calculated by the following equations [19]:
Initial Conditions. Consider
Governing Equations. Consider
Boundary Conditions. Consider
Based on the above equations, at time , the pore pressure with respect to can be given by the following equations [19]: where , is the present pore pressure in the caprock formations; is the original pore pressure of the caprock; is the present pressure of the depleted reservoir; is the vertical distance from the top of the reservoir to the interest point in the caprock; , , are the permeability, porosity, and fluid viscosity of the caprock, respectively. is the compressibility of the fluid; is the unit transformation ratio ; is the development time, years.
According to (3)–(7), we can calculate the pore pressure of caprock at different depth, by substituting the results into (1a), (1b), and (1c), the insitu stress of the caprock after the depletion of the reservoir is gained. The change of caprock formation of a certain field in BoHai Gulf Basin is present in Figure 3 based on the geophysics logging data. The involved parameters have the same value in Section 3.
In Figure 3, the filled triangular, square, and circle symbols represent pore pressure when the development time of reservoir is 3 years, 7 years, and 10 years, respectively. The open green triangular, square, and circle symbols represent minimum horizontal stresses when the development time of reservoir is 3 years, 7 years, and 10, years respectively. The open red triangular, square, and circle symbols represent maximum horizontal stresses when the development time of reservoir is 3 years, 7 years, and 10 years, respectively.
5. Borehole Stability Analysis
The insitu stress calculated by former chapter should be transformed form the geodetic coordinate systems (1, 2, 3) to borehole coordinate system (, , ). The coordinate conversion is presented in Figure 4. The conversion relation is as follows: where is the coordinate system transformation matrix. Consider
The basic approach to solve such problem consists of the stress distribution around wellbore and failure criterion, and calculating the safe mudweight windows subsequently. Based on reliable research [9, 23–27], the modeling is as follows.
The stress states of near wellbore are, respectively,
The principle stresses on borehole wall are calculated as follows [28, 29]:
The rock mechanical parameters, for example, uniaxial compressive strength, can be obtained by [30–32] where is shale content, GR is gamma ray log, and are, respectively, the gamma of pure sand and pure shale; G_{GCUR} is Hilchie index, which is related to geologic period, and it could be 3.7 for Tertiary and 2 for older formation; is shale content index.
The collapse pressure () and fracture pressure () can be calculated with (21) and (22), respectively, where is the minimum stress on the borehole wall, is critical pore pressure, and is tensile strength.
Based on the above equations and geomechanical parameters (shown in Figure 4), the safe mudweight window of depleted reservoir and caprock formations can be obtained. The calculation results of the vertical well are shown in Figure 5. The results show that the collapse pressure and fracture pressure both reduce with the development time.
Figures 6 and 7 show the current collapse pressure and fracture pressure versus the borehole inclination and azimuth in depleted reservoir after 7 years of development. They illustrate that the variation of critical mudweight is apparent, which are the safe ranges of drilling mud density to avoid borehole fracturing.
6. Conclusions
(1) The field development has a great effect on both magnitude and orientation of insitu stresses in reservoir, and the influence degree depends on the rock mechanical properties of reservoir, sealing of the fault, and the magnitude of original horizontal insitu stresses.
(2) The oil and gas field development will also have a significant impact on the insitu stresses in caprock. The impact is related to the development time, fluid viscosity, and rock permeability. Longterm development may affect the insitu stresses of caprock in dozens meters above the reservoir.
(3) The geomechanics effect of exploitation on insitu stress could reduce the collapse pressure and the fracture pressure significantly in reservoir, and the effection can not be negligible in caprock formation near the reservoir.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgments
This work is supported by the National Science Fund Innovative Research Groups (Project no. 51221003), the National Science Fund (Project no. 51174219), and the National Science and Technology Major Project (Project no. 2011ZX05009005).
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Copyright © 2013 Junliang Yuan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.