Synergistic anionic/zwitterionic mixed surfactant system with high emulsification efficiency for enhanced oil recovery in low permeability reservoirs

Emulsification is one of the important mechanisms of surfactant flooding. To improve oil recovery for low permeability reservoirs, a highly efficient emulsification oil flooding system consisting of anionic surfactant sodium alkyl glucosyl hydroxypropyl sulfonate(APGSHS) and zwitterionic surfactant octadecyl betaine(BS-18) is proposed. The performance of APGSHS/BS-18 mixed surfactant system was evaluated in terms of interfacial tension, emulsification capability, emulsion size and distribution, wettability alteration, temperature-resistance and salt-resistance. The emulsification speed was used to evaluate the emulsification ability of surfactant systems, and the results show that mixed surfactant systems can completely emulsify the crude oil into emulsions droplets even under low energy conditions. Meanwhile,the system exhibits good temperature and salt resistance. Finally, the best oil recovery of 25.45% is achieved for low permeability core by the mixed surfactant system with a total concentration of 0.3 wt%while the molar ratio of APGSHS:BS-18 is 4:6. The current study indicates that the anionic/zwitterionic mixed surfactant system can improve the oil flooding efficiency and is potential candidate for application in low permeability reservoirs.

Experimental study of the influencing factors and mechanisms of the pressure-reduction and augmented injection effect by nanoparticles in ultra-low permeability reservoirs

Nanoparticles(NPs)have gained significant attention as a functional material due to their ability to effectively enhance pressure reduction in injection processes in ultra-low permeability reservoirs.NPs are typically studied in controlled laboratory conditions,and their behavior in real-world,complex environments such as ultra-low permeability reservoirs,is not well understood due to the limited scope of their applications.This study investigates the efficacy and underlying mechanisms of NPs in decreasing injection pressure under various injection conditions(25—85℃,10—25 MPa).The results reveal that under optimal injection conditions,NPs effectively reduce injection pressure by a maximum of 22.77%in core experiment.The pressure reduction rate is found to be positively correlated with oil saturation and permeability,and negatively correlated with temperature and salinity.Furthermore,particle image velocimetry(PIV)experiments(25℃,atmospheric pressure)indicate that the pressure reduction is achieved by NPs through the reduction of wall shear resistance and wettability change.This work has important implications for the design of water injection strategies in ultra-low permeability reservoirs.

Permeability Estimation of Shale Oil Reservoir with Laboratory-derived Data: A Case Study of the Chang 7 Member in Ordos Basin

The shale oil reservoir within the Yanchang Formations of Ordos Basin harbors substantial oil and gas resources and has recently emerged as the primary focus of unconventional oil and gas exploration and development.Due to its complex pore and throat structure,pronounced heterogeneity,and tight reservoir characteristics,the techniques for conventional oil and gas exploration and production face challenges in comprehensive implementation,also indicating that as a vital parameter for evaluating the physical properties of a reservoir,permeability cannot be effectively estimated.This study selects 21 tight sandstone samples from the Q area within the shale oil formations of Ordos Basin.We systematically conduct the experiments to measure porosity,permeability,ultrasonic wave velocities,and resistivity at varying confining pressures.Results reveal that these measurements exhibit nonlinear changes in response to effective pressure.By using these experimental data and effective medium model,empirical relationships between P-and S-wave velocities,permeability and resistivity and effective pressure are established at logging and seismic scales.Furthermore,relationships between P-wave impedance and permeability,and resistivity and permeability are determined.A comparison between the predicted permeability and logging data demonstrates that the impedance–permeability relationship yields better results in contrast to those of resistivity–permeability relationship.These relationships are further applied to the seismic interpretation of shale oil reservoir in the target layer,enabling the permeability profile predictions based on inverse P-wave impedance.The predicted results are evaluated with actual production data,revealing a better agreement between predicted results and logging data and productivity.

A novel profile modification HPF-Co gel satisfied with fractured low permeability reservoirs in high temperature and high salinity

Conformance control and water plugging are a widely used EOR method in mature oilfields.However,majority of conformance control and water plugging agents are unavoidable dehydrated situation in high-temperature and high-salinity low permeability reservoirs.Consequently,a novel conformance control system HPF-Co gel,based on high-temperature stabilizer(CoCl_(2)·H_(2)O,CCH)is developed.The HPF-Co bulk gel has better performances with high temperature(120℃)and high salinity(1×10^(5)mg/L).According to Sydansk coding system,the gel strength of HPF-Co with CCH is increased to code G.The dehydration rate of HPF-Co gel is 32.0%after aging for 150 d at 120℃,showing excellent thermal stability.The rheological properties of HPF gel and HPF-Co gel are also studied.The results show that the storage modulus(G′)of HPF-Co gel is always greater than that of HPF gel.The effect of CCH on the microstructure of the gel is studied.The results show that the HPF-Co gel with CCH has a denser gel network,and the diameter of the three-dimensional network skeleton is 1.5-3.5μm.After 90 d of aging,HPF-Co gel still has a good three-dimensional structure.Infrared spectroscopy results show that CCH forms coordination bonds with N and O atoms in the gel amide group,which can suppress the vibration of cross-linked sites and improve the stability at high temperature.Fractured core plugging test determines the optimized polymer gel injection strategy and injection velocity with HPF-Co bulk gel system,plugging rate exceeding 98%.Moreover,the results of subsequent waterflooding recovery can be improved by 17%.

Optimization of Gas-Flooding Fracturing Development in Ultra-Low Permeability Reservoirs

Ultra-low permeability reservoirs are characterized by small pore throats and poor physical properties, which areat the root of well-known problems related to injection and production. In this study, a gas injection floodingapproach is analyzed in the framework of numerical simulations. In particular, the sequence and timing of fracturechanneling and the related impact on production are considered for horizontal wells with different fracturemorphologies. Useful data and information are provided about the regulation of gas channeling and possible strategiesto delay gas channeling and optimize the gas injection volume and fracture parameters. It is shown that inorder to mitigate gas channeling and ensure high production, fracture length on the sides can be controlled andlonger fractures can be created in the middle by which full gas flooding is obtained at the fracture location in themiddle of the horizontal well. A Differential Evolution (DE) algorithm is provided by which the gas injectionvolume and the fracture parameters of gas injection flooding can be optimized. It is shown that an improvedoil recovery factor as high as 6% can be obtained.

Development of Superhydrophobic Nano-SiO_(2)and Its Field Application in Low-permeability,High-temperature,and High-salinity Oil Reservoirs

In this study,to meet the stringent requirements on the hydrophobicity of nano-SiO_(2)particles for use in depressurization and enhanced injection operations in high-temperature and high-salinity oil reservoirs,secondary chemical grafting modification of nano-SiO_(2)is performed using a silane coupling agent to prepare superhydrophobic nano-SiO_(2) particles.Using these superhydrophobic nano-SiO_(2)particles as the core agent,and liquid paraffin or diesel as the dispersion medium,a uniform dispersion of nano-SiO_(2)particles is achieved under high-speed stirring,and a chemically enhanced water injection system with colloidal stability that can be maintained for more than 60 d is successfully developed.Using this system,a field test of depressurization and enhanced injection is carried out on six wells in an oilfield,and the daily oil production level is increased by 11 t.The cumulative increased water injection is 58784 m^(3),the effective rate of the measures was 100%,and the average validity period is 661 d.

Numerical Simulation of Oil-Water Two-Phase Flow in Low Permeability Tight Reservoirs Based on Weighted Least Squares Meshless Method

In response to the complex characteristics of actual low-permeability tight reservoirs,this study develops a meshless-based numerical simulation method for oil-water two-phase flow in these reservoirs,considering complex boundary shapes.Utilizing radial basis function point interpolation,the method approximates shape functions for unknown functions within the nodal influence domain.The shape functions constructed by the aforementioned meshless interpolation method haveδ-function properties,which facilitate the handling of essential aspects like the controlled bottom-hole flow pressure in horizontal wells.Moreover,the meshless method offers greater flexibility and freedom compared to grid cell discretization,making it simpler to discretize complex geometries.A variational principle for the flow control equation group is introduced using a weighted least squares meshless method,and the pressure distribution is solved implicitly.Example results demonstrate that the computational outcomes of the meshless point cloud model,which has a relatively small degree of freedom,are in close agreement with those of the Discrete Fracture Model(DFM)employing refined grid partitioning,with pressure calculation accuracy exceeding 98.2%.Compared to high-resolution grid-based computational methods,the meshless method can achieve a better balance between computational efficiency and accuracy.Additionally,the impact of fracture half-length on the productivity of horizontal wells is discussed.The results indicate that increasing the fracture half-length is an effective strategy for enhancing production from the perspective of cumulative oil production.

An overview of efficient development practices at low permeability sandstone reservoirs in China

Low permeability sandstone reservoirs in China typically have more complicated geological conditions, pore structures, and flow characteristics as compared to medium-to-high-permeability sandstone reservoirs. Traditional geological and seepage theories, and engineering methods are not applicable to the development of these low permeability reservoirs, and wells drilled into them often produce oil and gas at very low rates. Recent breakthroughs in reservoir exploitation technology have greatly improved the productivity of low permeability reservoirs, making them the primary target for oil exploration and extraction in China. The development theories and practices applied to low permeability reservoirs in China are reviewed in this study— based on relevant geological and engineering practices, including drilling, fracturing, recovery, and surface engineering. A unique series of technological advances that aid the development of low permeability reservoirs in China are summarized here. This study may serve as a meaningful guide in achieving scale efficiency for the development of low permeability reservoirs.

Experimental and Numerical Assessment of the Influence of Bottomhole Pressure Drawdown on Terrigenous Reservoir Permeability and Well Productivity

During oil and gas fields development,a decrease in reservoir and bottomhole pressure has often a detrimental effect on reservoir properties,especially permeability.This study presents the results of laboratory tests conducted to determine the response of terrigenous reservoir core-sample permeability to changes in the effective stresses and a decrease in the reservoir pressure.The considered samples were exposed for a long time to a constant high effective stress for a more reliable assessment of the viscoplastic deformations.According to these experiments,the decrease of the core samples permeability may reach 21%with a decrease in pressure by 9.5 MPa from the initial reservoir conditions.Numerical simulations have been also conducted.These have been based on the finite element modeling of the near-wellbore zone of the terrigenous reservoir using poroelasticity relations.The simulation results show a limited decrease in reservoir permeability in the near-wellbore zone(by 17%,which can lead to a decrease in the well productivity by 13%).

Adaptability of Development Methods for Offshore Gas Cap Edge Water Reservoirs under Different Permeability Levels

The BZ 34-1 oilfield is a typical gas cap edge water reservoir in the Bohai oilfield. The main characteristics of the oilfield were multi-phase sand body stacking and the sand body was composed of three parts: gas cap, oil reservoir, and edge water. The actual production site results show that the permeability difference of multi-layer sand bodies has a serious impact on the development effect. This article establishes a typical reservoir model numerical model based on the total recovery degree of the reservoir and the recovery degree of each layer, and analyzes the impact of permeability gradient. As the permeability gradient increases, the total recovery degree of all four well patterns decreases, and the total recovery degree gradually decreases. The recovery degree of low permeability layers gradually decreases, and the recovery degree of high permeability layers gradually increases. As the permeability gradient increases, the degree of recovery gradually decreases under different water contents. As the permeability gradient increases, the reduction rate of remaining oil saturation in low permeability layers is slower, while the reduction rate of remaining oil saturation in high permeability layers was faster. By analyzing the impact of permeability gradient on the development effect of oil fields, we could further deepen our understanding of gas cap edge water reservoirs and guide the development of this type of oil field.

Research on Well Testing Interpretation of Low Permeability Deformed Dual Medium Reservoir

Considering the influence of quadratic gradient term and medium deformation on the seepage equation, a well testing interpretation model for low permeability and deformation dual medium reservoirs was derived and established. The difference method was used to solve the problem, and pressure and pressure derivative double logarithmic curves were drawn to analyze the seepage law. The research results indicate that the influence of starting pressure gradient and medium deformation on the pressure characteristic curve is mainly manifested in the middle and late stages. The larger the value, the more obvious the upward warping of the pressure and pressure derivative curve;the parameter characterizing the dual medium is the crossflow coefficient. The channeling coefficient determines the time and location of the appearance of the “concave”. The smaller the value, the later the appearance of the “concave”, and the more to the right of the “concave”.

A Well Productivity Model for Multi-Layered Marine and Continental Transitional Reservoirs with Complex Fracture Networks

Using the typical characteristics of multi-layered marine and continental transitional gas reservoirs as a basis,a model is developed to predict the related well production rate.This model relies on the fractal theory of tortuous capillary bundles and can take into account multiple gas flow mechanisms at the micrometer and nanometer scales,as well as the flow characteristics in different types of thin layers(tight sandstone gas,shale gas,and coalbed gas).Moreover,a source-sink function concept and a pressure drop superposition principle are utilized to introduce a coupled flow model in the reservoir.A semi-analytical solution for the production rate is obtained using a matrix iteration method.A specific well is selected for fitting dynamic production data,and the calculation results show that the tight sandstone has the highest gas production per unit thickness compared with the other types of reservoirs.Moreover,desorption and diffusion of coalbed gas and shale gas can significantly contribute to gas production,and the daily production of these two gases decreases rapidly with decreasing reservoir pressure.Interestingly,the gas production from fractures exhibits an approximately U-shaped distribution,indicating the need to optimize the spacing between clusters during hydraulic fracturing to reduce the area of overlapping fracture control.The coal matrix water saturation significantly affects the coalbed gas production,with higher water saturation leading to lower production.

An Experimental Study on the Effect of a Nanofluid on Oil-Water Relative Permeability

The low porosity and low permeability of tight oil reservoirs call for improvements in the current technologies for oil recovery.Traditional chemical solutions with large molecular size cannot effectively flow through the nanopores of the reservoir.In this study,the feasibility of Nanofluids has been investigated using a high pressure high temperature core-holder and nuclear magnetic resonance(NMR).The results of the experiments indicate that the specified Nanofluids can enhance the tight oil recovery significantly.The water and oil relative permeability curve shifts to the high water saturation side after Nanofluid flooding,thereby demonstrating an increase in the water wettability of the core.In the Nanofluid flooding process the oil recovery was enhanced by 15.1%,compared to waterflooding stage.The T2 spectra using the NMR show that after Nanofluid flooding,a 7.18%increment in oil recovery factor was gained in the small pores,a 4.9%increase in the middle pores,and a 0.29%increase in the large pores.These results confirm that the Nanofluids can improve the flow state in micro-sized pores inside the core and increase the ultimate oil recovery factor.

Changes in filtration and capacitance properties of highly porous reservoir in underground gas storage:CT-based and geomechanical modeling

The paper presents the results of comprehensive studies of filtration and capacitance properties of highly porous reservoir rocks of the aquifer of an underground gas storage facility.The geomechanical part of the research included studying the dependence of rock permeability on the stress-strain state in the vicinity of the wells,and physical modeling of the implementation of the method of increasing the permeability of the wellbore zone-the method of directional unloading of the reservoir.The digital part of the research included computed tomography(CT)-based computer analysis of the internal structure,pore space characteristics,and filtration properties before and after the tests.According to the results of physical modeling of deformation and filtration processes,it is found that the permeability of rocks before fracture depends on the stress-strain state insignificantly,and this influence is reversible.However,when downhole pressure reaches 7-8 MPa,macrocracks in the rock begin to grow,accompanied by irreversible permeability increase.Porosity,geodesic tortuosity and permeability values were obtained based on digital studies and numerical modeling.A weak degree of transversal anisotropy of the filtration properties of rocks was detected.Based on the analysis of pore size distribution,pressure field and flow velocities,high homogeneity and connectivity of the rock pore space is shown.The absence of pronounced changes in pore space characteristics and pore permeability after non-uniform triaxial loading rocks was shown.On the basis of geometrical analysis of pore space,the reasons for weak permeability anisotropy were identified.The filtration-capacitance properties obtained from the digital analysis showed very good agreement with the results of field and laboratory measurements.The physical modeling has confirmed the efficiency of application of the directional unloading method for the reservoir under study.The necessary parameters of its application were calculated:bottomhole geometry,stage of operation,stresses and pressure drawdown value.

Numerical study on gas production via a horizontal well from hydrate reservoirs with different slope angles in the South China Sea

It is important to study the effect of hydrate production on the physical and mechanical properties of low-permeability clayey–silty reservoirs for the largescale exploitation of hydrate reservoirs in the South China Sea.In this study,a multiphysical-field coupling model,combined with actual exploration drilling data and the mechanical experimental data of hydrate cores in the laboratory,was established to investigate the physical and mechanical properties of low-permeability reservoirs with different slope angles during 5-year hydrate production by the depressurization method via a horizontal well.The result shows that the permeability of reservoirs severely affects gas production rate,and the maximum gas production amount of a 20-m-long horizontal well can reach186.8 m3/day during the 5-year hydrate production.Reservoirs with smaller slope angles show higher gas production rates.The depressurization propagation and hydrate dissociation mainly develop along the direction parallel to the slope.Besides,the mean effective stress of reservoirs is concentrated in the near-wellbore area with the on-going hydrate production,and gradually decreases with the increase of the slope angle.Different from the effective stress distribution law,the total reservoir settlement amount first decreases and then increases with the increase of the slope angle.The maximum settlement of reservoirs with a 0°slope angle is up to 3.4 m,and the displacement in the near-wellbore area is as high as2.2 m after 5 years of hydrate production.It is concluded that the pore pressure drop region of low-permeability reservoirs in the South China Sea is limited,and various slope angles further lead to differences in effective stress and strain of reservoirs during hydrate production,resulting in severe uneven settlement of reservoirs.

The coupling of dynamics and permeability in the hydrocarbon accumulation period controls the oil-bearing potential of low permeability reservoirs:a case study of the low permeability turbidite reservoirs in the middle part of the third member of Shahejie

The relationships between permeability and dynamics in hydrocarbon accumulation determine oil- bearing potential （the potential oil charge） of low perme- ability reservoirs. The evolution of porosity and permeability of low permeability turbidite reservoirs of the middle part of the third member of the Shahejie Formation in the Dongying Sag has been investigated by detailed core descriptions, thin section analyses, fluid inclusion analyses, carbon and oxygen isotope analyses, mercury injection, porosity and permeability testing, and basin modeling. The cutoff values for the permeability of the reservoirs in the accumulation period were calculated after detailing the accumulation dynamics and reservoir pore structures, then the distribution pattern of the oil-bearing potential of reservoirs controlled by the matching relationship between dynamics and permeability during the accumulation period were summarized. On the basis of the observed diagenetic features and with regard to the paragenetic sequences, the reservoirs can be subdivided into four types of diagenetic facies. The reservoirs experienced two periods of hydro- carbon accumulation. In the early accumulation period, the reservoirs except for diagenetic facies A had middle to high permeability ranging from 10 × 10-3 gm2 to 4207 × 10-3 lain2. In the later accumulation period, the reservoirs except for diagenetic facies C had low permeability ranging from 0.015 × 10-3 gm2 to 62× 10-3 -3m2. In the early accumulation period, the fluid pressure increased by the hydrocarbon generation was 1.4-11.3 MPa with an average value of 5.1 MPa, and a surplus pressure of 1.8-12.6 MPa with an average value of 6.3 MPa. In the later accumulation period, the fluid pressure increased by the hydrocarbon generation process was 0.7-12.7 MPa with an average value of 5.36 MPa and a surplus pressure of 1.3-16.2 MPa with an average value of 6.5 MPa. Even though different types of reservoirs exist, all can form hydrocarbon accumulations in the early accumulation per- iod. Such types of reservoirs can form hydrocarbon accumulation with high accumulation dynamics; however, reservoirs with diagenetic facies A and diagenetic facies B do not develop accumulation conditions with low accumu- lation dynamics in the late accumulation period for very low permeability. At more than 3000 m burial depth, a larger proportion of turbidite reservoirs are oil charged due to the proximity to the source rock, Also at these depths, lenticular sand bodies can accumulate hydrocarbons. At shallower depths, only the reservoirs with oil-source fault development can accumulate hydrocarbons. For flat surfaces, hydrocarbons have always been accumulated in the reservoirs around the oil-source faults and areas near the center of subsags with high accumulation dynamics.

Profile improvement during CO_2 flooding in ultra-low permeability reservoirs

Gas flooding such as CO2 flooding may be effectively applied to ultra-low permeability reservoirs, but gas channeling is inevitable due to low viscosity and high mobility of gas and formation heterogeneity. In order to mitigate or prevent gas channeling, ethylenediamine is chosen for permeability profile control. The reaction mechanism of ethylenediamine with CO2, injection performance, swept volume, and enhanced oil recovery were systematically evaluated. The reaction product of ethylenediamine and CO2 was a white solid or a light yellow viscous liquid, which would mitigate or prevent gas channeling. Also, ethylenediamine could be easily injected into ultra-low permeability cores at high temperature with protective ethanol slugs. The core was swept by injection of 0.3 PV ethylenediamine. Oil displacement tests performed on heterogeneous models with closed fractures, oil recovery was significantly enhanced with injection of ethylenediamine. Experimental results showed that using ethylenediamine to plug high permeability layers would provide a new research idea for the gas injection in fractured, heterogeneous and ultra-low permeability reservoirs. This technology has the potential to be widely applied in oilfields.

The tectonic fracture modeling of an ultra-low permeability sandstone reservoir based on an outcrop analogy: A case study in the Wangyao Oilfield of Ordos Basin, China

Due to inherent limits of data acquisition and geophysical data resolution, there are large uncertainties in the characterization of subsurface fractures. However, outcrop analogies can provide qualitative and quantitative information on a large number of fractures, based on which the accuracy of subsurface fracture characterization can be improved. Here we take the tectonic fracture modeling of an ultra-low permeability sandstone reservoir based on an outcrop analogy, a case study of the Chang6t~ Formation of the Upper Triassic Yanchang Group of the Wangyao Oilfield in the Ordos Basin of China. An outcrop at the edge of the basin is a suitable analog for the reservoir, but the prerequisite is that they must have equivalent previous stress fields, similar final structural characteristics, relative timing and an identical depositional environment and diagenesis. The relationship among fracture density, rock type and bed thickness based on the outcrop is one of the most important fracture distribution models, and can be used to interpret fracture density in individual wells quantitatively. Fracture orientation, dip, geometry and scale, also should be described and measured in the outcrop, and can be used together with structure restoration and single well fracture density interpretation to guide fracture intensity prediction on bed surfaces and to constrain the construction of the 3D fracture geometry model of the subsurface reservoir. The application of the above principles shows the outcrop-based tectonic fracture models of the target ultra-low permeability sandstone reservoir are consistent with fractures inferred from microseismic interpretation and tracer tests. This illustrated that the fracture modeling based on the outcrop analogy is reliable and can reduce the uncertainty in stochastic fracture modeling.

Advances in enhanced oil recovery technologies for low permeability reservoirs

Low permeability oil and gas resources are rich and have great potential all over the world, which has gradually become the main goal of oil and gas development. However, after traditional primary and secondary exploitation, there is still a large amount of remaining oil that has not been recovered.Therefore, in recent years, enhanced oil recovery(EOR) technologies for low permeability reservoirs have been greatly developed to further improve crude oil production. This study presents a comprehensive review of EOR technologies in low permeability reservoirs with an emphasis on gas flooding, surfactant flooding, nanofluid flooding and imbibition EOR technologies. In addition, two kinds of gel systems are introduced for conformance control in low permeability reservoirs with channeling problems. Finally,the technical challenges, directions and outlooks of EOR in low permeability reservoirs are addressed.

Effects of effective stress and temperature on permeability of sandstone from CO2-plume geothermal reservoir

Rock is generally complex and heterogeneous,therefore the heterogeneity effects of effective stress and temperature on permeability should be taken into account.In this study,two-part Hooke’s model（TPHM） is introduced to understand the influences of effective stress and temperature on permeability of soft and hard parts（two parts） of rock based on coupling thermo-hydro-mechanical tests.Under a fixed temperature level（25 ℃.35 ℃.50 ℃.65 ℃.80 ℃.90 ℃ and 95 ℃）.the tests were carried out in a conventional triaxial system whereas the confining pressure was remained at 50 MPa.and the pore pressure was increased to the specified levels step by step.i.e.8 MPa,18 MPa.28 MPa.38 MPa.41 MPa,44 MPa.46 MPa and 48 MPa.The temperature-dependent relationships for two parts permeabilities are proposed on the basis of the initial test results.We point out that temperature of 65 ℃-90 ℃ is the threshold for the development of CO2-plume geothermal（CPC） reservoir sandstone cracking under low effective stress（2-9 MPa） based on the relationship between temperature and soft part permeability.Furthermore,we discuss the effect of temperature on the two parts in the rock.The results indicate that as the temperature increases from 25 ℃ to 65 ℃.the flow channel in the hard part has a stronger response to temperature than that in the soft part at a fixed effective stress level,which is opposite to the situation of effective stress.Considering that natural rock is generally heterogeneous with non-uniform pore structure,we suggest a physical interpretation of the phenomenon that before the thermal cracking threshold the two parts have different responses to temperature.