When exploiting the deep resources, the surrounding rock readily undergoes the hole shrinkage, borehole collapse, and loss of circulation under high temperature and high pressure. A series of experiments were conducted to discuss the compressional wave velocity, triaxial strength, and permeability of granite cored from 3500 meters borehole under high temperature and three-dimensional stress. In light of the coupling of temperature, fluid, and stress, we get the thermo-fluid-solid model and governing equation. ANSYS-APDL was also used to stimulate the temperature influence on elastic modulus, Poisson ratio, uniaxial compressive strength, and permeability. In light of the results, we establish a temperature-fluid-stress model to illustrate the granite’s stability. The compressional wave velocity and elastic modulus, decrease as the temperature rises, while poisson ratio and permeability of granite increase. The threshold pressure and temperature are 15 MPa and 200°C, respectively. The temperature affects the fracture pressure more than the collapse pressure, but both parameters rise with the increase of temperature. The coupling of thermo-fluid-solid, greatly impacting the borehole stability, proves to be a good method to analyze similar problems of other formations.
Deep resources such as oil, gas, and solid mineral have drawn more interest. Generally, the deeper drill is characterized by higher pressure and temperature, which make the drilling and borehole stability harder [
When the fluid circles, the upper surrounding rock will be heated; when the fluid ceases to work, however, the lower one will be heated. Balanced by the fluid column pressure and the rock confining pressure [
Wang et al.’s research [
Since the 1980s, in order to dispose the permanent nuclear waste, people began researching the coupling of THM (thermo-hydro-mechanical) [
The sample, obtained from a 1000 meter deep borehole in Mount Yan, North China, is about 100 mm with a diameter of 50 mm. The density is about 2.54 g/cm3. TAW-1000 deep pore pressure servo experimental system was employed to test the sample. It consists of quartz, feldspar, and hornblende. All the samples were processed on the basis of Chinese national standard of GB50128-94 (shown in Figure
Granite samples for testing.
The experiments were conducted in a 1000°C electrothermal furnace whose space is 300 × 200 × 120 mm. The samples were placed at the center of the furnace, to whose front and rear it is about 3 mm far from the sample. All the samples were divided into 5 groups, with each was heated to room temperature, 100°C, 200°C, 300°C, 400°C and insulated for 2 hours, respectively. Compared with the original sample in Figure
Rock samples correlation under different temperature.
Figure
Longitudinal wave velocity variation curve with temperature in granite.
Figure
Uniaxial strength variation curve with temperature in granite.
Peak strain variation curve with temperature in granite.
Below 200 centigrade, the peak stress increases slowly but rapidly when it is over 200 centigrade. It shows that the threshold temperature is 200 centigrade, which accords with the outcome obtained from the link between the temperature and the uniaxial strength.
The thermal damage is introduced to reflect the fluctuation of the elastic modulus of the samples before and after the heating the sample. The thermal stress will be produced between different mineral compositions due to the temperature change [
The elastic modulus decreases with the increase of the temperature. Additionally,
Figure
Thermal damage curve under different temperatures in granite.
The Poisson ratio is characterized by polymeric. As shown in Figure
Poisson ratio curve under different temperatures in granite.
The sample was experimentally damaged under uniaxial pressure in three ways as shown in Figure
Ordinary damage states under uniaxial pressure.
Figure
Triaxial compressive strength curve with confining pressure and temperature.
The link between elastic modulus and confining pressure was displayed in Figure
Relationship between elastic modulus and confining pressure under 300°C.
Figures
Relationship between triaxial compressive strength and temperature with constant confining pressure.
Peak strain variation curve with temperature with constant confining pressure.
Elastic modulus variation with temperature with constant confining pressure.
Tested by deep pore pressure servo experimental system, the samples were broken by two ways: (I) when heated to 200°C or lower, the sample undergoes the brittle fracture. However, when the confining pressure increased to 20 MPa, the shear and tension fracture dominated. (II) When heated over 200°C, the sample undergoes the compression shear and fracture (Figure
Ordinary damage states under triaxial stress.
The permeability was measured by TAW-1000 deep pore pressure servo experimental system. The sample was enwrapped by a 3 mm thickness hot pyrocondensation pipe. Pressed around by 20 MPa, the sample’s one end was ventilated by N2 and a highly precise gas flowmeter was installed at its other end. Figure
Permeability curve under different temperatures in granite.
Adopting the definition of Biot’s effective stress, the relationship between effective stress and total stress is
The mass conservation equation of fluid is
The energy conservation equation of solid is
The energy conservation equation of fluid is
Assume that at any point inside the solid phase and liquid phase has the same temperature, the total energy conservation equation [
The total heat flux density of rock and fluid can be expressed as
Based on mixture theory, the equivalent thermal conductivity can be defined; namely,
According to the principle of virtual displacement, the whole equilibrium differential equations in solution domain can be represented as
We take the effective stress of rock skeleton equation into (
Based on indoor experiment of this study paper, it was found that the dynamic evolution equations of elastic modulus, Poisson ratio, uniaxial compressive strength, and permeability of Granite with temperature can be represented as
The paper uses the ANSYS secondary development function of the fluid-solid interaction module and temperature-structure coupling calculation module for the solver, according to the decoupling method; firstly we do numerical calculation of the granite-borehole temperature field and then put the results into ANSYS fluid-solid interaction of calculation module.
The units’ segmentation of temperature field and the units’ segmentation of flow-solid coupling calculation is the same, such that the plane-strain problems use four-node units. The dynamic evolution of elastic modulus, Poisson ratio, uniaxial compressive strength, and permeability of granite using secondary development of the ANSYS parametric design language (ANSYS Parameter Design Language-APDL) to achieve. Firstly, to extract the temperature of the unit in the process of thermal analysis calculation, and modify the unit parameters of the thermal and mechanical properties, to form Loop iteration control process, and realize the Granite-borehole temperature coupling.
The stimulation was performed on a one-fourth sample of symmetry. The sample was divided into 612 four-point units in Figure
Plane model of borehole.
Temperature distribution near borehole.
The influence that impacted the granite strata borehole wall stability in the temperature field, the stress field, and the seepage field mainly was exerted by changing the stress state of the borehole [
Figures
Distribution of the radial stress in borehole under different conditions.
Distribution of the tangential stress in borehole under different conditions.
The shear fracture of the rock, subject to Mohr-Coulomb, expressed by the main stress is described as
The layer will collapse when the tangential effective stress is over the tensile strength of the rock:
The stress distribution is calculated on the basis of finite element. Considering the shear failure and tensile failure, the collapse pressure and tensile pressure are calculated. Suppose the uniaxial compressive strength is subject to temperature. Based on Griffith,
The variations of collapse pressure and fracture pressure with temperature increase and decrease are shown in Figures
Variation of collapse pressure and fracture pressure with temperature increase.
Variation of collapse pressure and fracture pressure with temperature decrease.
A filter cake can be developed as the fluid seeps through the permeable reservoir. In this case where the fluid will be constrained, the pore pressure is not equal to the drilling fluid column pressure.
Figure
Variation of collapse pressure and fracture pressure with permeability.
Risk distribution of collapse pressure when permeability coefficient is 0.5.
Risk distribution of collapse pressure when temperature drop is 25°C.
Risk distribution of collapse pressure under coupling of thermo-fluid-solid.
Suppose north-south and east-west as the directions along which the horizontal maximum and minimum stresses developed, respectively. It can be concluded that the seepage can cut the maximum and add the minimum collapse pressures; the decrease of the temperature, however, leads to the increase of the maximum and minimum collapse pressure. What is more, Figure
Risk distribution of fracture pressure when permeability coefficient is 0.5.
Risk distribution of fracture pressure when temperature drop is 25°C.
Risk distribution of fracture pressure under coupling of thermo-fluid-solid.
When drilling along the direction of the minimum principal stress, the fracture pressure reached the biggest, increasing the upper boundary of the fluid’s density. It shows that the wider the window of the fluid is, the safer the drilling is. When drilling along the direction of the maximum stress, the fracture pressure reaches the minimum. As a result, it is suggested that in order to ensure the borehole stability, we should drill along the direction of the maximum stress. If the fracture pressure is beyond the expectation, the sloughing formation will be developed.
It is shown that the threshold temperature of strength and elastic modulus of granite are both 200 centigrade. Below this, the sample mainly undergoes the brittle fracture and the rupture surface is along the axial direction under small confining pressure, while shear compression failure is the main state when the confining pressure is over 20 MPa. Above 200 centigrade, the damage modes are mixing shear compression and brittle fracture failure, and shear compression failure is positively correlated with the increasing of confining pressure and temperature. The compressional wave velocity, elastic modulus, and uniaxial compression strength will decrease as the temperature rises. Additionally, when the temperature is given, the elastic modulus and strength will increase as the surrounding pressure rises. The threshold pressure and temperature are 15 MPa and 200°C, respectively. The threshold thermal fracture temperature is 200°C. The permeability will dramatically increase with the rise of temperature up to 10−3~10−4 mD. The coupling borehole stability model of thermo-fluid-solid is developed by the ANASYS-APDL. The dynamic evolution equations of elastic modulus, Poisson ratio, uniaxial compressive strength, and permeability of granite with temperature are built and run. The results show that the radical stress and tangential stress are greatly different in full coupling model and in other physical field models. The results simulated by full coupling model are more precise and reliable than other models. The temperature affects the fracture pressure more than the collapse pressure. In order to avoid losing fluid, we suggest lowering the fluid’s density when the temperature of the borehole wall decreases. As for the permeability, its rise leads to the decrease of the fracture pressure but increase of the collapse pressure, which indicates that the low-density fluid is better. The seepage degrades the upper limit of collapse pressure and heightens the lower limit. The fall of temperature heightens both upper and lower limits of collapse pressure in borehole. As a result, in order to accurately predict the collapse pressure, the seepage and temperature are supposed to be taken into account.
Thermal damage coefficient
Temperature, °C
Elastic modulus at
Elastic modulus at 20°C, GPa
Elastic modulus, GPa
Goodness of fit
Triaxial compressive strength, MPa
Confining pressure, MPa
Matrix of effective stress, MPa
Matrix of total stress, MPa
Second-order unit tensor
Absolute value of pressure, MPa
Porosity
Permeability coefficient of fluid
Velocity of flow coefficient affected by temperature
Viscosity coefficient of fluid
Density of fluid,
Hydraulic pressure, Pa
Acceleration of gravity of fluid,
Specific heat capacity,
Density of rock,
Heat flux density of rock,
Energy conversion coefficient,
Specific heat capacity of fluid,
Relative density of fluid
Heat flow,
Total heat flux density,
Heat flux density of fluid,
Heat transfer coefficient of rock,
Heat transfer coefficient of fluid,
Equivalent thermal conductivity coefficient,
Strain
Three-dimensional force,
Plane vector force,
Cake permeability
Poisson ratio
Uniaxial compressive strength, MPa
Permeability, mD
Maximum main stress, MPa
Minimum main stress, MPa
Internal friction angle, rad
Cohesive force,
Tangential effective stress in borehole, MPa
Effective stress coefficient
Pore pressure, MPa
Tensile strength, MPa
Uniaxial compressive strength, MPa
Drilling fluid column pressure, MPa
Borehole pore pressure, MPa
Formation pore pressure.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors gratefully acknowledge the support by the Fundamental Research Funds for the Central Universities (Grant no. 2652011273), the International Scientific and Technological Cooperation projects (Grants nos. 2010DFR70920 and 2011DFR71170), the National Natural Science Foundation of China (Grant no. 51004086), and the open Funds of Key Laboratory on Deep Geo-Drilling Technology, Ministry of Land and Resources (Grant no. NLSD201210). Meanwhile, great thanks also go to former researchers for their excellent works, which was of great help to our academic study.