Supported by the China National Science and Technology Major Project. 2016ZX05037-003 Supported by the China National Science and Technology Major Project. 2017ZX05049-003
Abstract
Laboratory experiments were conducted on laboratory-made tight cores to investigate the stress-dependent permeability hysteresis of tight reservoirs during pressure loading and unloading process. Based on experiment results, and Hertz contact deformation principle, considering arrangement and deformation of rock particles, a quantitative stress dependent permeability hysteresis theoretical model for tight reservoirs was established to provide quantitative analysis for permeability loss. The model was validated by comparing model calculated results and experimental results. The research results show that during the early pressure-loading period, structural deformation and primary deformation worked together, rock permeability reduced dramatically with increasing effective stress. When the effective stress reached a certain value, the structural deformation became stable while the primary deformation continued; the permeability variation tended to be smooth and steady. In the pressure unloading process, the primary deformation recovered with the decreasing effective stress, while the structural deformation could not. The permeability thus could not fully recover, and the stress-dependent hysteresis was obvious.
CAO Nai, LEI Gang. Stress sensitivity of tight reservoirs during pressure loading and unloading process. [J], 2019, 46(1): 138-144 doi:
Introduction
The decreasing formation pressure in the developing process of reservoirs leads to an increase in the effective stress exerted on the porous media, elastoplastic deformation and permeability drop of formation rock, reduction of production and worsening of development effect successively[1,2]. Water and gas injection are often adopted to replenish and maintain the formation pressure in the development of tight reservoirs[3,4]. As the injection of fluid (water or gas), the reservoir energy recovers constantly, the physical parameters (permeability and porosity) of the reservoir cannot fully recover to the original state, this nature of rock is called the stress sensitivity hysteresis[5]. Compared with conventional reservoirs, tight reservoirs have a much more obvious stress sensitivity hysteresis[6]. The permeability hysteresis effect is the main reason of permanent permeability damage and has a significant impact on the production or recovery of tight reservoirs[7,8].
Many experimental work have been conducted to study and analyze stress sensitivity, the explanation of these results were mainly qualitative based on experience. In addition, most of these researches focused on the analysis of stress sensitivity during the pressure loading process with the effective stress increasing continuously. The research methods could be grouped into: (1) obtaining empirical formulas of permeability and porosity with effective stress based on a large number of laboratory experiments; (2) establishing rock particle composition model, and deriving formulas for permeability and porosity calculation under different effective stress through mechanical analysis. Due to discrepancies in experimental methods and rock physical properties, the research results had many inconsistencies. Moreover, since the stress sensitivity hysteresis occurs in the pressure unloading process, the research on it should put emphasis on the stress sensitivity of reservoir during the depressurization process.
Wissler and Simmons[9] analyzed the recoverability and irrecoverability of stress-dependent permeability of sandstone in 1985. Bernabe[10] found the stress sensitivity hysteresis effect of rock by experiments, and proposed that the rock stress sensitivity hysteresis effect of the core samples would be eliminated or minimized after aging treatment and the stress sensitivity hysteresis would not exist after multiple aging treatment, because the rock would no longer follow the stress path. Warpinski and Teufel[11,12] concluded through study that the rock stress sensitivity hysteresis would disappear after multiple aging cycles of rock samples. After stress sensitivity experiments on rock samples of different lithologies and scales, Tadesse and Li[13] found that the stress sensitivity hysteresis of nano-scale rock samples was more obvious than that of micron and millimeter-scale rock samples, and so the rock stress sensitivity hysteresis effect was affected by the size and distribution of pores and the mineral composition of rock sample, in other words, different rocks had different stress sensitivity hysteresis. Shi, Yujiang et al.[14] tested the stress sensitivity hysteresis effect of rock by exerting an increasing net overpressure on the tight rock and two kinds of return pressure after the overpressure reached the maximum value (45 MPa). The experimental results showed that the stress sensitivity hysteresis effect of lithic sandstone and mudstone were stronger than that of quartz sandstone, and the stress sensitivity hysteresis effect of sandstone with low porosity and permeability sandstone was more obvious than that of sandstone with high porosity and permeability. Ruan Min et al. [15] believed that when the low-permeability tight sandstone was under pressure, the muddy matter between the particles would plastically deform and be squeezed around, thereby blocking the pores. At this stage, the rock permeability decreased rapidly. When the pressure increased further, more particles would come into direct contact, leading to some elastoplastic deformation of rock; when the pressure was unloaded, the elastic deformation could restore, but the plastic deformation of the muddy matter and micro-throat couldn’t restore to the original state, so the permeability recovery of the rock was relatively small. Wang Xiujuan[16] reached the finding through study that the reservoir permeability recovered to different extents as the water injection time increased, and the recovery extent was related to the initial permeability of the reservoir: the lower the original permeability of the reservoir, the more obvious the stress sensitivity hysteresis effect would be.
The researches mentioned above on stress sensitivity during pressure unloading process were mainly qualitative works conducted based on experiments, while few theoretical studies have been done. Therefore, it is necessary to do quantitative analysis of the reservoir stress sensitivity hysteresis from a theoretical perspective. In this work, based on the results of stress sensitivity experiments during pressure loading and unloading process and Hertz contact theory, a theoretical calculation model of stress sensitivity hysteresis has been established. The model was verified by comparing the calculation results from the model and experimental results. Stress sensitivity hysteresis of tight reservoir was quantitatively analyzed based on the calculation results. The rock deformation during the pressure loading and unloading process was explained theoretically based on a tight four-particle packing unit, which provides a reasonable explanation for the experimental results and theoretical basis for the stress sensitivity hysteresis of tight reservoirs.
1. Experiment
1.1. Samples
In this experiment, the artificial homogeneous tight cores were prepared by epoxy resin pressing cementation[17], and in the process of core preparation, quartz sands with particle size intervals of 0.1-0.15 mm and 0.15-0.2 mm were used. The cores were cured at 21 °C for 6.5 h. By conducting flooding and stress sensitivity experiments, the prepared cores were proved to be similar with natural cores in porosity, permeability, displacement effect and mechanical properties. Six artificial homogeneous tight cores were selected for experiment and the basic physical parameters of them are shown in Table 1.
The setup of the experiment is shown in Fig. 1. The pump was the source of the driving force to provide high pressure gas, dry nitrogen, in this experiment. The parameters of the pump included: displacement of 0.01-50 mL/min, pump speed accuracy of 0.011 μL /min, working pressure of 7 kPa, and pump pressure of 0.068-68.000 MPa. The core holder was utilized to fix the core. The confining pressure was provided by manual pump, and the pressure drop from the core inlet to outlet ends was recorded by a pressure transducer.
The core samples were washed and dried for 48 h, the experiment was conducted at room temperature. According to the SY/T-2016 China's oil and gas industry standard, "Method for measuring porosity and permeability of rocks under overburden pressure", the stress sensitivity of tight cores during pressure loading and unloading process were evaluated by changing the confining pressure. The experimental results were obtained under a constant inlet pressure. The detailed procedure is: (1) In the pressure loading stage, under a constant inlet pressure, the confining pressure was gradually in-creased from 5 MPa to 15 MPa; the permeability was measured when the core outlet flow became stable. (2) In the pressure unloading process, the confining pressure was gradually reduced from 15 MPa to 5 MPa, and the permeability was measured when the flow rate at outlet was stable. The effective stress calculation formula adopted in this experiment is[18,19]:
$\sigma ={{\sigma }_{c}}-\eta p$
The effective stress coefficient η in formula (1) is generally taken as the rock porosity[20,21].
The experimental results are shown in Fig. 2, from which we can see all the six cores have similar shape of permeability retention rate curves (ratio of permeability after deformation to initial permeability of the core). In the early increasing stage of effective stress, namely, from 5 MPa to 10 MPa, the permeability dropped significantly with the increase of effective stress. When the effective stress exceeded 10 MPa, the change of core permeability became weak. All the tested cores showed stress sensitivity hysteresis, namely, their permeability cannot fully recover after the pressure was unloaded. When the effective stress changed in the range from 5 MPa to 10 MPa, though both the core permeability decrease during the pressure loading process and the recovery of core permeability in the pressure unloading process were obvious, there was a noticeable difference between the permeability under the same stress in these two processes. When the effective stress exceeded a certain value, the curves of the two stages coincided. This suggests that in the early increasing stage of effective stress, the core samples had both body deformation and structural deformation, consequently, the permeability reduced drastically; while after the effective stress exceeded a certain value, the structural deformation tended stable, the body deformation became the dominant factor, so the permeability became stable.
Fig. 2.
Experimental result of permeability retention rate of the tested cores.
2. Modeling
2.1. Hertz Contact Deformation Theory
As shown in Fig. 3, the initial contact state of the two spherical particles (whose radii are respectively R1 and R2) is point contact, and when they are subjected to external stress, a deformation occurs. After the deformation, the contact area between the two particles is a circle with a radius of a.
Fig. 3.
Hertz deformation diagram of two contacted spheres.
The Hertz deformation theory assumes that the pressure is in semi-elliptical spherical distribution, which is related to the point position on the contact area[22]. The contact area between the two particles is very small compared to the volume of the spherical particles, thus, this deformation process can be regarded as a force exerting on semi-infinite volume but distributing on a very small area. The contact radius satisfies[17,18,19,20]:
2.2. Theoretical model of stress sensitivity hysteresis
The assumptions of the newly established theoretical model for stress sensitivity hysteresis during pressure loading and unloading process are as follow:
(1) The rock pores are formed by aggregation of particles with the same size, and the aggregation unit is made up of four particles[23,24,25]. The initial state of the rock pore is shown in Fig. 4a: R is the particle radius; the inner angles of the quadrilateral O1O2O3O4 before deformation are θ1, θ2, θ3 and θ4, among which, θ1=θ3, θ2=θ4.
(2) In the pressure loading process, the pore has both body deformation and structural deformation[21]. The body deformation follows the Hertz deformation theory, the contact of the particles turns from initial point contact to surface contact after deformation (Fig. 4b), the contact area is a circle with the radius of a; the structural deformation is caused by the change of the arrangement of four spherical particles (Fig. 4c); the comprehensive deformation of the rock pore is obtained by the combining the body and structural deformations together (Fig. 4d). The inner angles of the quadrilateral O1O2O3O4 after deformation are θ'1, θ'2, θ'3 and θ'4, and θ'1=θ'3, θ'2=θ'4.
(3) In the pressure unloading process, the body deformation of rock gradually recovers, while the structural deformation, namely, the arrangement of the four spherical particle cannot recover.
In the pressure loading process, according to Hertz theory and the model assumptions, after substituting R1=R2=R, E1=E2=E and v1=v2=v into formula (2), the radius of contact surface and the vertical distance from the particle center to the contact surface are, respectively[24]:
In formula (7), θ is a function of effective stress, which decreases gradually with the increase of effective stress, with a variation range of π/3≤θ≤π/2. Considering the fact that the permeability of the cores tended stable after the effective stress reached a value twice the initial effective stress in the experiment, and the body deformation was the dominant factor after that, the segmental expression of effective stress function during the pressure loading process is:
From the formulas (7) and (8), the seepage area of rock after deformation is a function of particle radius and effective stress, and the porosity retention rate during loading process can be expressed as:
During the pressure unloading process, the body deformation of the particles can recover, in the other words, the particle contact radius decreases gradually with the decrease of the effective stress; while the structure deformation of the particles cannot recover, namely, the arrangement of the particles cannot recover. Assuming the pressure unloading process begins when the effective stress reaches the maximum value of σxpmax, and the effective stress function is θxp at this point. θxp gradually increases after the unloading begins, but cannot fully recover to θ. The radius of contact surface and the vertical distance from the particle center to the contact surface after deformation are respectively:
Based on the stress sensitivity hysteresis calculation model established in this work, by using the radius and lithology parameters of the 6 tight artificial homogeneous cores in the experiment above, the permeability retention rate of the cores were calculated by Matlab programming, and compared with experimental results (Fig. 5).
Fig. 5.
Comparison of permeability retention rates from calculation and from experiment.
The comparison shows that the calculated results of core permeability retention rate are in good consistency with the experimental results. Both of them have significant decrease at first and then gradually become stable in the pressure loading process; both of them also have an unrecoverable loss with almost the same extent after the effective stress decreases to the initial value, and the recovery trend of them are also similar.
3.2. Sensitivity analysis
In order to improve the model accuracy and explore the influences on the calculation results caused by different parameters, deformation factors are discussed as influencing factors in the sensitivity analysis.
The permeability retention rate during the pressure loading and unloading processes at different deformation rates, β, were calculated and analyzed by using the newly established model to find out the effect of β on permeability retention rate. As shown in Fig. 6, the retention rate of permeability decreases with the increase of β. The β and θ are positively correlated with the changing rate of the effective stress, namely, the larger the β is, the faster the θ changes, and a more dramatic deformation of the core structure follows. That is to say the change in permeability retention rate and the stress sensitivity hysteresis are more obvious. β is affected by Poisson ratio, elastic modulus, effective stress coefficient and particle radius, so its value is different for different lithologic reservoirs. Thus, by taking a correct β value, the prediction accuracy of permeability loss for different types of tight reservoirs (sandstone, mudstone, carbonate rocks, etc.) caused by the stress sensitivity hysteresis effect can be improved.
Fig. 6.
Permeability retention rate under different β.The deformation degree parameter γ is influenced by the effective stress coefficient and rock particle radius. For different γ, the retention rate of rock permeability during the pressure unloading process was calculated by using the established model to analyze the effect of γ on permeability retention rate. The calculation result was compared with the permeability retention rate in the pressure loading process. As shown in Fig. 7, in the pressure unloading process, with the increase of γ, the damage extent of θ increases, which leads to an increase in the non-recoverable damage extent of the rock structural deformation, in other words, the stress sensitivity hysteresis increases.
Fig. 7.
Permeability retention rate at different γ.
Tight reservoirs include many different types of rocks, and different types of rock are different in stress sensitivity hysteresis[13]. For tight reservoirs of different lithologies, the permeability loss of one type of reservoir caused by stress sensitivity hysteresis can be predicted by determining a proper deformation parameter for this kind of reservoir. It is necessary to take the lithologic parameter of the reservoir into consideration besides a reasonable production pressure drop in the development of tight reservoirs.
4. Conclusions
In this work, based on the results of stress sensitivity hysteresis experiments during pressure loading and unloading process on tight cores, a new theoretical model for the stress sensitivity hysteresis in tight reservoirs has been established. Validated by the experimental results, the model can be used as a means to do quantitative stress sensitivity hysteresis analysis, providing a theoretical basis for analyzing this phenomenon during development of tight reservoirs.
In the pressure loading process, in the early stage, body and structural deformations work together, and the permeability drops rapidly with the increase of effective stress, the structural deformation tends stable after the effective stress exceeds a certain value, the body deformation becomes the dominant factor of rock deformation, and the variation of the rock permeability turns stable.
During the pressure unloading process, the body deformation of the rock can recover while the structural deformation cannot. This results in a non-recoverable damage on the pore size of the rock, consequently, the permeability of the rock cannot fully recover to the initial state.
The stress sensitivity hysteresis increases with the increase of the deformation parameter. In the developing process of tight reservoirs, the permeability loss of one type of tight reservoirs caused by stress sensitivity hysteresis effect can be predicted by defining a proper deformation parameter for this kind of reservoir. It must be noted that the specific deformation parameters for different type of reservoirs need to be defined through further study to improve the accuracy of the permeability loss prediction, and in turn production prediction. Thus, when making development plan for tight reservoirs, in addition to a reasonable production pressure drop, the physical properties and lithology of the reservoirs should be considered.
Nomenclature
a—the radius of the contact area between the two sphere particles, m;
A, A°—the seepage area before and after the deformation in the pressure loading process, m2;
Axp—the seepage area in the pressure unloading process, m2;
b—the distance from the particle center to the contact surface, m;
E—the elastic modulus of spheroidal particles, Pa;
E1, E2— the elastic modulus of particle 1 and 2, Pa;
F, Fxp—the stress loaded on the particles in the pressure loading and unloading process, N;
K—the rock permeability after deformation in pressure loading process, 10-3 μm2;
K0—the initial rock permeability, 10-3 μm2;
Kxp—the rock permeability in the pressure unloading process, 10-3 μm2;
p—the fluid pressure, Pa;
R—the radius of the sphere particle, m;
R1, R2—the radius of particle 1 and 2, m;
β— the deformation parameter representing the changing rate of θ with the effective stress;
γ—the deformation parameter representing the changing extent of θ;
η— the effective stress coefficient;
θ, θxp— the effective stress function during the pressure loading and unloading process;
θ1, θ2, θ3, θ4——the inner angles of the quadrilateral O1O2O3O4 before deformation, (°);
${{\theta }_{1}}^{\prime }$, ${{\theta }_{2}}^{\prime }$, ${{\theta }_{3}}^{\prime }$, ${{\theta }_{4}}^{\prime }$—the inner angles of the quadrilateral O1O2O3O4 after deformation, (°);
v—the Poisson ratio of spheroidal particles;
ν1, ν2—the Poisson ratio of particle 1 and 2;
σ—the effective stress, Pa;
σ0—the initial effective stress, Pa;
σc—the rock overburden pressure, taken as the confining pressure in this work, Pa;
σjp—the effective stress in the pressure loading process, Pa;
σxp—the effective stress in the pressure unloading process, Pa;
σxpmax—the initial effective stress in the pressure unloading process, Pa;
ϕ—the rock porosity after deformation in the pressure loading process, %;
ϕ0—the initial rock porosity, %;
ϕxp—the rock porosity in the pressure unloading process, %.
The authors have declared that no competing interests exist.
The progress in pore structure characterization, hydrocarbon occurrence state, mechanism of oil and gas accumulation, main controlling factors and high production model of unconventional oil and gas is reviewed. The unconventional oil and gas geological research developed from observation of the nanopores to quantitative full scale and 3D pore structure characterization, from macroscopic occurrence state study to microscopic occurrence state evolution discussion, from differential pressure drive and preferential channel migration to staged accumulation and wettability preferential migration, from accumulation controlled by source to accumulation jointly controlled by source-reservoir assemblage and preservation conditions, from accumulation model to enrichment and high production model, revealing the research progresses and future trends of unconventional oil and gas geology. Challenges are presented in unconventional oil and gas geological theory, enrichment conditions and recoverable resources potential of deeply buried unconventional oil and gas, combination of unconventional oil and gas geological research and engineering technique, and basic geologic research for joint mining of different unconventional oil and gas resources.
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Development prospect and strategic significance of tight gas and shale gas in China
Based on the investigation of tight oil exploration and development in North America, the successful cases of tight oil exploration and development in North America are summarized. The geological differences between continental tight oil in China and marine tight oil in North America is analyzed to explore the technical strategies for the industrial development of continental tight oil in China. The experiences of large-scale exploration and profitable development of tight oil in North America can be taken as references from the following 6 perspectives, namely exploring new profitable strata in mature exploration areas, strengthening the economic evaluation of sweet spots and focusing on the investment for high-profitability sweet spots, optimizing the producing of tight oil reserves by means of repetitive fracturing and 3 D fracturing, optimizing drilling and completion technologies to reduce the cost, adopting commodity hedging to ensure the sustainable profit, and strengthening other resources exploration to improve the profit of whole project. In light of the high abundance of tight oil in China, we can draw on successful experience from North America, four suggestions are proposed in sight of the geological setting of China's lacustrine tight oil:(1) Evaluating the potential of tight oil resources and optimizing the strategic area for tight oil exploration;(2) selecting "sweet spot zone" and "sweet spot interval" accurately for precise and high efficient development;(3) adopting advanced tight oil fracturing technology to realize economic development;(4) innovating management system to promote the large-scale profitable development of tight oil.
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Low-permeability reservoir has been paid more attention to in exploration and development as conventional reserve decreases,while economical development and management for low-permeability reservoir are severely restricted by stress-sensitivity.A summary about previous on stress-sensitivity was made from evaluation method,fluid-solid coupling model and deliverability equation.It is indicated through analyzing that method based on in-situ stress compound with multinomial equation has a desirable accuracy in stress-sensitivity assessment;Development of numerical simulation softwares with regard to fluid-solid coupling and deliverability equation and water injectivity prediction will be the research priorities in this field.It is also pointed out that in no way can stress-sensitive mechanism be revealed merely based on phenomenology or theoretical derivation.It's proposed that a comprehensive evaluation system should be obtained taking into account experimental data,theoretical formula and reservoir characteristic;Establishing appropriate structural model of fracture plane and computer simulation method considering interaction between fracture network comprised of natural and hydraulic fractures is the choke point for fracture stress-sensitivity yet to be broken.
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Measuring permeability of rock has important meaning in oil field, water conservancy, waste dispose and environment engineering. Using the Porosity and Permeability Meter under high pressure, based on Darcy law, state equation and equation of continuity, a gas transit measurement and calculation method of permeability on rock has been studied. The results show that the method is suitable to low permeability rock, quick and simple as well. Meanwhile, it is easily extended to permeability measurement under temperature condition.
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Permanent and elastic strains have been measured in 19 dry sandstones as a function of hydrostatic stress to 200 MPa. Differential Strain Analysis (DSA), a high precision strain measurement technique, was used to measure the total strain inthree orthogonal directions. Samples were cyclically loaded and unloaded from atmospheric to successively higher maximum pressures. The total strain is separated into elastic and permanent components. Permanent strains are the measured strains remaining after a loading cycle. The permanent strains are well behaved functions of maximum confining pressure yet they can be a significant fraction (30%) of the total strain and can be highly anisotropic. Permanent strains are compactive at low pressures but may become dilational at higher pressures. Permanent and elastic strains are related in a piecewise linear manner with slope Ψ. Ψ values range from 0.4 to – 1.0 and decrease as a function of increasing pressure. Negative values of Ψ are obtained when permanent strain increments are dilational. Elastic response depends on the maximum pressure to which a sample has been exposed previously. Permanent strains reflect permanent changes in the rock microstructure. These changes are important factors to consider when interpreting laboratory measurements of physical properties made under stress.
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By experiment research,the pressure_sensitive effect in the development of low permeability oilfield is analyzed.The result shows that along with the oilfield's developing going on,formation pressure will drop gradually,and then the oil reservoir pressure will be reduced,so pressure sensitivity hurt to formation will unavoidable.Eventually,effect of permeability loss on low permeability oil field developing is strong.Research result shows due to existence of pressure_sensitive effect,formation permeability value nearby well wall is only around the 45% of that in feed flow border.When formation pressure drops by 5 MPa,output will drop by 13% around.
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Stress sensitivity and poroperm lower limit of deliverability in the low-permeability reservoir
core samples collected from Yushulin,Chaoyanggou and Toutai oilfields to the east of Daqing placanticline have been tested with the CMS-200 porosity and permeability tester.For the sake of observing the stress sensitivity of low permeability reservoir during the oilfield exploitation, initial pressure (initial formation pressure) and maximum confining pressure (maximum overburden pressure )have been chosen;and the recovery time of simulated pressure have properly been prolonged,due to the consideration of the protracted nature of field's waterflood development and the rheological property of the rocks. Experimental results show that the low-permeability reservoir is relatively sensitive to stress change, i.e. the permeability will have a relatively large decrease with the increase of stress.However, permeability has also recovered to a certain degree with the waterflooding to be prolonged, and the degree of recovery is related to the extent of initial permeability: the degree of recovery is greater with higher initial permeability; vice versa. Especially the low-permeability reservoir with permeability of less than 1.0×10 -3 μm 2 is very sensitive to stress change,and the resulting solid-liquid coupling effect is also very evident.The permeability of 1.0×10 -3 μm 2 can then be referred to as the limit of reservoir's stress sensitivity.From the viewpoint of oilfield development, the solid-liquid coupling effect will do more harm than good, so exploitation of low-permeability reservoirs should,as far as possible,be kept at the foramtion pressure to eliminate the influence of solid-liquid coupling. Except the factors of reservoir reformation and advanced development technique,the influence of solid-liquid coupling must also be considered while determining the low limit of productivity. It is suggested that the lower limit of productivity can be set at permeability ≥1.0×10 -3 μm 2 for reference while making strategic decision.
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Phenomenological models have been devised to determine the variation with pressure of the permeability of whole and fractures porous rock. For whole porous rock, the permeability variation with pressure is based upon the Hertzian theory of deformation of spheres. This model gives a permeability variation with pressure given by k(P) = k 0 {1 61 C 0[(P + P 1)/P 0] sol2 3} 4 where k 0 is the initial permeability of the loose-grain packing, C 0 is a constant depending upon the packing (and is of the order of 2), P 1 is the ‘equivalent pressure’ due to the cementation and permanent deformation of the grains and P 0 is the effective elastic modulus of the grains (and is of the order of the grain material bulk modulus). The permeability variation of a fracture (or fractured rock) with confining pressure is determined by using a ‘bed of nails’ model for the asperities of the fracture. Its functional dependence is k( P) = k 0 [1 61 ( P/ P 1) m] 3 where k o is the zero pressure permeability, P 1 is the effective modulus of the asperrities (and is of the order of one-tenth to one-hundredth of the asperity material bulk modulus) and m is a constant (0 < m < 1) which characterizes the distributions function of the asperity lengths. The above expression assumes a simple power-law variation for the asperity-length distribution. More complicated asperity-length distributions can be used, but the data quality and the fracture-to-fracture variability does not warrant the use of such distributions. A comparison of experimental data with the theoretical curves shows good correlation between the two and gives reasonable values for the constants k 0, P 1 and m.
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The process of water flooding met the law of non-Darcy flow and existed threshold pressure gradient in tight sandstone reservoirs. Porous medium would get deformed,and the permeability would decrease. The nanometer pore characteristics of tight sandstone through scanning electron microscope(SEM) experiment were researched. Based on the distribution of rock particles,a theory model which characterized stress sensitivity caused by medium deformation was established and medium deformation coefficient was derived. The comparison analysis of results between the theory model and experiment is performed. Moreover,a seepage mathematical model was established which took the deformation of tight sandstone into consideration. The coupling influences of the threshold pressure gradient and medium deformation on the oil-water two-phase nonlinear percolation feature are studied. The result shows that the flow resistance and formation pressure drawdown loss increase under the coupling effects of threshold pressure gradient and medium deformation. Moreover,with the increase of production duration,amplitude of pressure drawdown loss would increase.
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Progress and development trend of unconventional oil and gas geological research
1
2017
... The decreasing formation pressure in the developing process of reservoirs leads to an increase in the effective stress exerted on the porous media, elastoplastic deformation and permeability drop of formation rock, reduction of production and worsening of development effect successively[1,2]. Water and gas injection are often adopted to replenish and maintain the formation pressure in the development of tight reservoirs[3,4]. As the injection of fluid (water or gas), the reservoir energy recovers constantly, the physical parameters (permeability and porosity) of the reservoir cannot fully recover to the original state, this nature of rock is called the stress sensitivity hysteresis[5]. Compared with conventional reservoirs, tight reservoirs have a much more obvious stress sensitivity hysteresis[6]. The permeability hysteresis effect is the main reason of permanent permeability damage and has a significant impact on the production or recovery of tight reservoirs[7,8]. ...
Development prospect and strategic significance of tight gas and shale gas in China
1
2012
... The decreasing formation pressure in the developing process of reservoirs leads to an increase in the effective stress exerted on the porous media, elastoplastic deformation and permeability drop of formation rock, reduction of production and worsening of development effect successively[1,2]. Water and gas injection are often adopted to replenish and maintain the formation pressure in the development of tight reservoirs[3,4]. As the injection of fluid (water or gas), the reservoir energy recovers constantly, the physical parameters (permeability and porosity) of the reservoir cannot fully recover to the original state, this nature of rock is called the stress sensitivity hysteresis[5]. Compared with conventional reservoirs, tight reservoirs have a much more obvious stress sensitivity hysteresis[6]. The permeability hysteresis effect is the main reason of permanent permeability damage and has a significant impact on the production or recovery of tight reservoirs[7,8]. ...
Profitable exploration and development of continental tight oil in China
1
2018
... The decreasing formation pressure in the developing process of reservoirs leads to an increase in the effective stress exerted on the porous media, elastoplastic deformation and permeability drop of formation rock, reduction of production and worsening of development effect successively[1,2]. Water and gas injection are often adopted to replenish and maintain the formation pressure in the development of tight reservoirs[3,4]. As the injection of fluid (water or gas), the reservoir energy recovers constantly, the physical parameters (permeability and porosity) of the reservoir cannot fully recover to the original state, this nature of rock is called the stress sensitivity hysteresis[5]. Compared with conventional reservoirs, tight reservoirs have a much more obvious stress sensitivity hysteresis[6]. The permeability hysteresis effect is the main reason of permanent permeability damage and has a significant impact on the production or recovery of tight reservoirs[7,8]. ...
1
2014
... The decreasing formation pressure in the developing process of reservoirs leads to an increase in the effective stress exerted on the porous media, elastoplastic deformation and permeability drop of formation rock, reduction of production and worsening of development effect successively[1,2]. Water and gas injection are often adopted to replenish and maintain the formation pressure in the development of tight reservoirs[3,4]. As the injection of fluid (water or gas), the reservoir energy recovers constantly, the physical parameters (permeability and porosity) of the reservoir cannot fully recover to the original state, this nature of rock is called the stress sensitivity hysteresis[5]. Compared with conventional reservoirs, tight reservoirs have a much more obvious stress sensitivity hysteresis[6]. The permeability hysteresis effect is the main reason of permanent permeability damage and has a significant impact on the production or recovery of tight reservoirs[7,8]. ...
A misunderstanding in reservoir rock stress sensitivity: In reply to Dr Liu Xiaoxu
1
2008
... The decreasing formation pressure in the developing process of reservoirs leads to an increase in the effective stress exerted on the porous media, elastoplastic deformation and permeability drop of formation rock, reduction of production and worsening of development effect successively[1,2]. Water and gas injection are often adopted to replenish and maintain the formation pressure in the development of tight reservoirs[3,4]. As the injection of fluid (water or gas), the reservoir energy recovers constantly, the physical parameters (permeability and porosity) of the reservoir cannot fully recover to the original state, this nature of rock is called the stress sensitivity hysteresis[5]. Compared with conventional reservoirs, tight reservoirs have a much more obvious stress sensitivity hysteresis[6]. The permeability hysteresis effect is the main reason of permanent permeability damage and has a significant impact on the production or recovery of tight reservoirs[7,8]. ...
Study of stress sensitivity and its influence on oil development in low permeability reservoir
1
2011
... The decreasing formation pressure in the developing process of reservoirs leads to an increase in the effective stress exerted on the porous media, elastoplastic deformation and permeability drop of formation rock, reduction of production and worsening of development effect successively[1,2]. Water and gas injection are often adopted to replenish and maintain the formation pressure in the development of tight reservoirs[3,4]. As the injection of fluid (water or gas), the reservoir energy recovers constantly, the physical parameters (permeability and porosity) of the reservoir cannot fully recover to the original state, this nature of rock is called the stress sensitivity hysteresis[5]. Compared with conventional reservoirs, tight reservoirs have a much more obvious stress sensitivity hysteresis[6]. The permeability hysteresis effect is the main reason of permanent permeability damage and has a significant impact on the production or recovery of tight reservoirs[7,8]. ...
Review and prospect about study on stress-sensitivity of low-permeability reservoir
1
2011
... The decreasing formation pressure in the developing process of reservoirs leads to an increase in the effective stress exerted on the porous media, elastoplastic deformation and permeability drop of formation rock, reduction of production and worsening of development effect successively[1,2]. Water and gas injection are often adopted to replenish and maintain the formation pressure in the development of tight reservoirs[3,4]. As the injection of fluid (water or gas), the reservoir energy recovers constantly, the physical parameters (permeability and porosity) of the reservoir cannot fully recover to the original state, this nature of rock is called the stress sensitivity hysteresis[5]. Compared with conventional reservoirs, tight reservoirs have a much more obvious stress sensitivity hysteresis[6]. The permeability hysteresis effect is the main reason of permanent permeability damage and has a significant impact on the production or recovery of tight reservoirs[7,8]. ...
Gas transit measurement method of permeability on rock
1
1999
... The decreasing formation pressure in the developing process of reservoirs leads to an increase in the effective stress exerted on the porous media, elastoplastic deformation and permeability drop of formation rock, reduction of production and worsening of development effect successively[1,2]. Water and gas injection are often adopted to replenish and maintain the formation pressure in the development of tight reservoirs[3,4]. As the injection of fluid (water or gas), the reservoir energy recovers constantly, the physical parameters (permeability and porosity) of the reservoir cannot fully recover to the original state, this nature of rock is called the stress sensitivity hysteresis[5]. Compared with conventional reservoirs, tight reservoirs have a much more obvious stress sensitivity hysteresis[6]. The permeability hysteresis effect is the main reason of permanent permeability damage and has a significant impact on the production or recovery of tight reservoirs[7,8]. ...
The physical properties of a set of sandstones: Part II. Permanent and elastic strains during hydrostatic compression to 200 MPa
1
1985
... Wissler and Simmons[9] analyzed the recoverability and irrecoverability of stress-dependent permeability of sandstone in 1985. Bernabe[10] found the stress sensitivity hysteresis effect of rock by experiments, and proposed that the rock stress sensitivity hysteresis effect of the core samples would be eliminated or minimized after aging treatment and the stress sensitivity hysteresis would not exist after multiple aging treatment, because the rock would no longer follow the stress path. Warpinski and Teufel[11,12] concluded through study that the rock stress sensitivity hysteresis would disappear after multiple aging cycles of rock samples. After stress sensitivity experiments on rock samples of different lithologies and scales, Tadesse and Li[13] found that the stress sensitivity hysteresis of nano-scale rock samples was more obvious than that of micron and millimeter-scale rock samples, and so the rock stress sensitivity hysteresis effect was affected by the size and distribution of pores and the mineral composition of rock sample, in other words, different rocks had different stress sensitivity hysteresis. Shi, Yujiang et al.[14] tested the stress sensitivity hysteresis effect of rock by exerting an increasing net overpressure on the tight rock and two kinds of return pressure after the overpressure reached the maximum value (45 MPa). The experimental results showed that the stress sensitivity hysteresis effect of lithic sandstone and mudstone were stronger than that of quartz sandstone, and the stress sensitivity hysteresis effect of sandstone with low porosity and permeability sandstone was more obvious than that of sandstone with high porosity and permeability. Ruan Min et al. [15] believed that when the low-permeability tight sandstone was under pressure, the muddy matter between the particles would plastically deform and be squeezed around, thereby blocking the pores. At this stage, the rock permeability decreased rapidly. When the pressure increased further, more particles would come into direct contact, leading to some elastoplastic deformation of rock; when the pressure was unloaded, the elastic deformation could restore, but the plastic deformation of the muddy matter and micro-throat couldn’t restore to the original state, so the permeability recovery of the rock was relatively small. Wang Xiujuan[16] reached the finding through study that the reservoir permeability recovered to different extents as the water injection time increased, and the recovery extent was related to the initial permeability of the reservoir: the lower the original permeability of the reservoir, the more obvious the stress sensitivity hysteresis effect would be. ...
The effective pressure law for permeability during pore pressure and confining pressure cycling of several crystalline rocks
1
1987
... Wissler and Simmons[9] analyzed the recoverability and irrecoverability of stress-dependent permeability of sandstone in 1985. Bernabe[10] found the stress sensitivity hysteresis effect of rock by experiments, and proposed that the rock stress sensitivity hysteresis effect of the core samples would be eliminated or minimized after aging treatment and the stress sensitivity hysteresis would not exist after multiple aging treatment, because the rock would no longer follow the stress path. Warpinski and Teufel[11,12] concluded through study that the rock stress sensitivity hysteresis would disappear after multiple aging cycles of rock samples. After stress sensitivity experiments on rock samples of different lithologies and scales, Tadesse and Li[13] found that the stress sensitivity hysteresis of nano-scale rock samples was more obvious than that of micron and millimeter-scale rock samples, and so the rock stress sensitivity hysteresis effect was affected by the size and distribution of pores and the mineral composition of rock sample, in other words, different rocks had different stress sensitivity hysteresis. Shi, Yujiang et al.[14] tested the stress sensitivity hysteresis effect of rock by exerting an increasing net overpressure on the tight rock and two kinds of return pressure after the overpressure reached the maximum value (45 MPa). The experimental results showed that the stress sensitivity hysteresis effect of lithic sandstone and mudstone were stronger than that of quartz sandstone, and the stress sensitivity hysteresis effect of sandstone with low porosity and permeability sandstone was more obvious than that of sandstone with high porosity and permeability. Ruan Min et al. [15] believed that when the low-permeability tight sandstone was under pressure, the muddy matter between the particles would plastically deform and be squeezed around, thereby blocking the pores. At this stage, the rock permeability decreased rapidly. When the pressure increased further, more particles would come into direct contact, leading to some elastoplastic deformation of rock; when the pressure was unloaded, the elastic deformation could restore, but the plastic deformation of the muddy matter and micro-throat couldn’t restore to the original state, so the permeability recovery of the rock was relatively small. Wang Xiujuan[16] reached the finding through study that the reservoir permeability recovered to different extents as the water injection time increased, and the recovery extent was related to the initial permeability of the reservoir: the lower the original permeability of the reservoir, the more obvious the stress sensitivity hysteresis effect would be. ...
Determination of the effective stress law for permeability and deformation in low-permeability rocks
1
1992
... Wissler and Simmons[9] analyzed the recoverability and irrecoverability of stress-dependent permeability of sandstone in 1985. Bernabe[10] found the stress sensitivity hysteresis effect of rock by experiments, and proposed that the rock stress sensitivity hysteresis effect of the core samples would be eliminated or minimized after aging treatment and the stress sensitivity hysteresis would not exist after multiple aging treatment, because the rock would no longer follow the stress path. Warpinski and Teufel[11,12] concluded through study that the rock stress sensitivity hysteresis would disappear after multiple aging cycles of rock samples. After stress sensitivity experiments on rock samples of different lithologies and scales, Tadesse and Li[13] found that the stress sensitivity hysteresis of nano-scale rock samples was more obvious than that of micron and millimeter-scale rock samples, and so the rock stress sensitivity hysteresis effect was affected by the size and distribution of pores and the mineral composition of rock sample, in other words, different rocks had different stress sensitivity hysteresis. Shi, Yujiang et al.[14] tested the stress sensitivity hysteresis effect of rock by exerting an increasing net overpressure on the tight rock and two kinds of return pressure after the overpressure reached the maximum value (45 MPa). The experimental results showed that the stress sensitivity hysteresis effect of lithic sandstone and mudstone were stronger than that of quartz sandstone, and the stress sensitivity hysteresis effect of sandstone with low porosity and permeability sandstone was more obvious than that of sandstone with high porosity and permeability. Ruan Min et al. [15] believed that when the low-permeability tight sandstone was under pressure, the muddy matter between the particles would plastically deform and be squeezed around, thereby blocking the pores. At this stage, the rock permeability decreased rapidly. When the pressure increased further, more particles would come into direct contact, leading to some elastoplastic deformation of rock; when the pressure was unloaded, the elastic deformation could restore, but the plastic deformation of the muddy matter and micro-throat couldn’t restore to the original state, so the permeability recovery of the rock was relatively small. Wang Xiujuan[16] reached the finding through study that the reservoir permeability recovered to different extents as the water injection time increased, and the recovery extent was related to the initial permeability of the reservoir: the lower the original permeability of the reservoir, the more obvious the stress sensitivity hysteresis effect would be. ...
1
1991
... Wissler and Simmons[9] analyzed the recoverability and irrecoverability of stress-dependent permeability of sandstone in 1985. Bernabe[10] found the stress sensitivity hysteresis effect of rock by experiments, and proposed that the rock stress sensitivity hysteresis effect of the core samples would be eliminated or minimized after aging treatment and the stress sensitivity hysteresis would not exist after multiple aging treatment, because the rock would no longer follow the stress path. Warpinski and Teufel[11,12] concluded through study that the rock stress sensitivity hysteresis would disappear after multiple aging cycles of rock samples. After stress sensitivity experiments on rock samples of different lithologies and scales, Tadesse and Li[13] found that the stress sensitivity hysteresis of nano-scale rock samples was more obvious than that of micron and millimeter-scale rock samples, and so the rock stress sensitivity hysteresis effect was affected by the size and distribution of pores and the mineral composition of rock sample, in other words, different rocks had different stress sensitivity hysteresis. Shi, Yujiang et al.[14] tested the stress sensitivity hysteresis effect of rock by exerting an increasing net overpressure on the tight rock and two kinds of return pressure after the overpressure reached the maximum value (45 MPa). The experimental results showed that the stress sensitivity hysteresis effect of lithic sandstone and mudstone were stronger than that of quartz sandstone, and the stress sensitivity hysteresis effect of sandstone with low porosity and permeability sandstone was more obvious than that of sandstone with high porosity and permeability. Ruan Min et al. [15] believed that when the low-permeability tight sandstone was under pressure, the muddy matter between the particles would plastically deform and be squeezed around, thereby blocking the pores. At this stage, the rock permeability decreased rapidly. When the pressure increased further, more particles would come into direct contact, leading to some elastoplastic deformation of rock; when the pressure was unloaded, the elastic deformation could restore, but the plastic deformation of the muddy matter and micro-throat couldn’t restore to the original state, so the permeability recovery of the rock was relatively small. Wang Xiujuan[16] reached the finding through study that the reservoir permeability recovered to different extents as the water injection time increased, and the recovery extent was related to the initial permeability of the reservoir: the lower the original permeability of the reservoir, the more obvious the stress sensitivity hysteresis effect would be. ...
Experimental Investigation on permeability and porosity hysteresis of tight formations
2
2017
... Wissler and Simmons[9] analyzed the recoverability and irrecoverability of stress-dependent permeability of sandstone in 1985. Bernabe[10] found the stress sensitivity hysteresis effect of rock by experiments, and proposed that the rock stress sensitivity hysteresis effect of the core samples would be eliminated or minimized after aging treatment and the stress sensitivity hysteresis would not exist after multiple aging treatment, because the rock would no longer follow the stress path. Warpinski and Teufel[11,12] concluded through study that the rock stress sensitivity hysteresis would disappear after multiple aging cycles of rock samples. After stress sensitivity experiments on rock samples of different lithologies and scales, Tadesse and Li[13] found that the stress sensitivity hysteresis of nano-scale rock samples was more obvious than that of micron and millimeter-scale rock samples, and so the rock stress sensitivity hysteresis effect was affected by the size and distribution of pores and the mineral composition of rock sample, in other words, different rocks had different stress sensitivity hysteresis. Shi, Yujiang et al.[14] tested the stress sensitivity hysteresis effect of rock by exerting an increasing net overpressure on the tight rock and two kinds of return pressure after the overpressure reached the maximum value (45 MPa). The experimental results showed that the stress sensitivity hysteresis effect of lithic sandstone and mudstone were stronger than that of quartz sandstone, and the stress sensitivity hysteresis effect of sandstone with low porosity and permeability sandstone was more obvious than that of sandstone with high porosity and permeability. Ruan Min et al. [15] believed that when the low-permeability tight sandstone was under pressure, the muddy matter between the particles would plastically deform and be squeezed around, thereby blocking the pores. At this stage, the rock permeability decreased rapidly. When the pressure increased further, more particles would come into direct contact, leading to some elastoplastic deformation of rock; when the pressure was unloaded, the elastic deformation could restore, but the plastic deformation of the muddy matter and micro-throat couldn’t restore to the original state, so the permeability recovery of the rock was relatively small. Wang Xiujuan[16] reached the finding through study that the reservoir permeability recovered to different extents as the water injection time increased, and the recovery extent was related to the initial permeability of the reservoir: the lower the original permeability of the reservoir, the more obvious the stress sensitivity hysteresis effect would be. ...
... Tight reservoirs include many different types of rocks, and different types of rock are different in stress sensitivity hysteresis[13]. For tight reservoirs of different lithologies, the permeability loss of one type of reservoir caused by stress sensitivity hysteresis can be predicted by determining a proper deformation parameter for this kind of reservoir. It is necessary to take the lithologic parameter of the reservoir into consideration besides a reasonable production pressure drop in the development of tight reservoirs. ...
Stress sensitivity analysis of Changqing tight clastic reservoir
1
2001
... Wissler and Simmons[9] analyzed the recoverability and irrecoverability of stress-dependent permeability of sandstone in 1985. Bernabe[10] found the stress sensitivity hysteresis effect of rock by experiments, and proposed that the rock stress sensitivity hysteresis effect of the core samples would be eliminated or minimized after aging treatment and the stress sensitivity hysteresis would not exist after multiple aging treatment, because the rock would no longer follow the stress path. Warpinski and Teufel[11,12] concluded through study that the rock stress sensitivity hysteresis would disappear after multiple aging cycles of rock samples. After stress sensitivity experiments on rock samples of different lithologies and scales, Tadesse and Li[13] found that the stress sensitivity hysteresis of nano-scale rock samples was more obvious than that of micron and millimeter-scale rock samples, and so the rock stress sensitivity hysteresis effect was affected by the size and distribution of pores and the mineral composition of rock sample, in other words, different rocks had different stress sensitivity hysteresis. Shi, Yujiang et al.[14] tested the stress sensitivity hysteresis effect of rock by exerting an increasing net overpressure on the tight rock and two kinds of return pressure after the overpressure reached the maximum value (45 MPa). The experimental results showed that the stress sensitivity hysteresis effect of lithic sandstone and mudstone were stronger than that of quartz sandstone, and the stress sensitivity hysteresis effect of sandstone with low porosity and permeability sandstone was more obvious than that of sandstone with high porosity and permeability. Ruan Min et al. [15] believed that when the low-permeability tight sandstone was under pressure, the muddy matter between the particles would plastically deform and be squeezed around, thereby blocking the pores. At this stage, the rock permeability decreased rapidly. When the pressure increased further, more particles would come into direct contact, leading to some elastoplastic deformation of rock; when the pressure was unloaded, the elastic deformation could restore, but the plastic deformation of the muddy matter and micro-throat couldn’t restore to the original state, so the permeability recovery of the rock was relatively small. Wang Xiujuan[16] reached the finding through study that the reservoir permeability recovered to different extents as the water injection time increased, and the recovery extent was related to the initial permeability of the reservoir: the lower the original permeability of the reservoir, the more obvious the stress sensitivity hysteresis effect would be. ...
Low-permeability of oilfield development and pressure-sensitive effect
1
2002
... Wissler and Simmons[9] analyzed the recoverability and irrecoverability of stress-dependent permeability of sandstone in 1985. Bernabe[10] found the stress sensitivity hysteresis effect of rock by experiments, and proposed that the rock stress sensitivity hysteresis effect of the core samples would be eliminated or minimized after aging treatment and the stress sensitivity hysteresis would not exist after multiple aging treatment, because the rock would no longer follow the stress path. Warpinski and Teufel[11,12] concluded through study that the rock stress sensitivity hysteresis would disappear after multiple aging cycles of rock samples. After stress sensitivity experiments on rock samples of different lithologies and scales, Tadesse and Li[13] found that the stress sensitivity hysteresis of nano-scale rock samples was more obvious than that of micron and millimeter-scale rock samples, and so the rock stress sensitivity hysteresis effect was affected by the size and distribution of pores and the mineral composition of rock sample, in other words, different rocks had different stress sensitivity hysteresis. Shi, Yujiang et al.[14] tested the stress sensitivity hysteresis effect of rock by exerting an increasing net overpressure on the tight rock and two kinds of return pressure after the overpressure reached the maximum value (45 MPa). The experimental results showed that the stress sensitivity hysteresis effect of lithic sandstone and mudstone were stronger than that of quartz sandstone, and the stress sensitivity hysteresis effect of sandstone with low porosity and permeability sandstone was more obvious than that of sandstone with high porosity and permeability. Ruan Min et al. [15] believed that when the low-permeability tight sandstone was under pressure, the muddy matter between the particles would plastically deform and be squeezed around, thereby blocking the pores. At this stage, the rock permeability decreased rapidly. When the pressure increased further, more particles would come into direct contact, leading to some elastoplastic deformation of rock; when the pressure was unloaded, the elastic deformation could restore, but the plastic deformation of the muddy matter and micro-throat couldn’t restore to the original state, so the permeability recovery of the rock was relatively small. Wang Xiujuan[16] reached the finding through study that the reservoir permeability recovered to different extents as the water injection time increased, and the recovery extent was related to the initial permeability of the reservoir: the lower the original permeability of the reservoir, the more obvious the stress sensitivity hysteresis effect would be. ...
Stress sensitivity and poroperm lower limit of deliverability in the low-permeability reservoir
1
2003
... Wissler and Simmons[9] analyzed the recoverability and irrecoverability of stress-dependent permeability of sandstone in 1985. Bernabe[10] found the stress sensitivity hysteresis effect of rock by experiments, and proposed that the rock stress sensitivity hysteresis effect of the core samples would be eliminated or minimized after aging treatment and the stress sensitivity hysteresis would not exist after multiple aging treatment, because the rock would no longer follow the stress path. Warpinski and Teufel[11,12] concluded through study that the rock stress sensitivity hysteresis would disappear after multiple aging cycles of rock samples. After stress sensitivity experiments on rock samples of different lithologies and scales, Tadesse and Li[13] found that the stress sensitivity hysteresis of nano-scale rock samples was more obvious than that of micron and millimeter-scale rock samples, and so the rock stress sensitivity hysteresis effect was affected by the size and distribution of pores and the mineral composition of rock sample, in other words, different rocks had different stress sensitivity hysteresis. Shi, Yujiang et al.[14] tested the stress sensitivity hysteresis effect of rock by exerting an increasing net overpressure on the tight rock and two kinds of return pressure after the overpressure reached the maximum value (45 MPa). The experimental results showed that the stress sensitivity hysteresis effect of lithic sandstone and mudstone were stronger than that of quartz sandstone, and the stress sensitivity hysteresis effect of sandstone with low porosity and permeability sandstone was more obvious than that of sandstone with high porosity and permeability. Ruan Min et al. [15] believed that when the low-permeability tight sandstone was under pressure, the muddy matter between the particles would plastically deform and be squeezed around, thereby blocking the pores. At this stage, the rock permeability decreased rapidly. When the pressure increased further, more particles would come into direct contact, leading to some elastoplastic deformation of rock; when the pressure was unloaded, the elastic deformation could restore, but the plastic deformation of the muddy matter and micro-throat couldn’t restore to the original state, so the permeability recovery of the rock was relatively small. Wang Xiujuan[16] reached the finding through study that the reservoir permeability recovered to different extents as the water injection time increased, and the recovery extent was related to the initial permeability of the reservoir: the lower the original permeability of the reservoir, the more obvious the stress sensitivity hysteresis effect would be. ...
Study on the development of man-made core and the influencing factors of permeability
2
2017
... In this experiment, the artificial homogeneous tight cores were prepared by epoxy resin pressing cementation[17], and in the process of core preparation, quartz sands with particle size intervals of 0.1-0.15 mm and 0.15-0.2 mm were used. The cores were cured at 21 °C for 6.5 h. By conducting flooding and stress sensitivity experiments, the prepared cores were proved to be similar with natural cores in porosity, permeability, displacement effect and mechanical properties. Six artificial homogeneous tight cores were selected for experiment and the basic physical parameters of them are shown in Table 1. ...
... The Hertz deformation theory assumes that the pressure is in semi-elliptical spherical distribution, which is related to the point position on the contact area[22]. The contact area between the two particles is very small compared to the volume of the spherical particles, thus, this deformation process can be regarded as a force exerting on semi-infinite volume but distributing on a very small area. The contact radius satisfies[17,18,19,20]: ...
Variation of whole and fractured porous rock permeability with confining pressure
2
1978
... The core samples were washed and dried for 48 h, the experiment was conducted at room temperature. According to the SY/T-2016 China's oil and gas industry standard, "Method for measuring porosity and permeability of rocks under overburden pressure", the stress sensitivity of tight cores during pressure loading and unloading process were evaluated by changing the confining pressure. The experimental results were obtained under a constant inlet pressure. The detailed procedure is: (1) In the pressure loading stage, under a constant inlet pressure, the confining pressure was gradually in-creased from 5 MPa to 15 MPa; the permeability was measured when the core outlet flow became stable. (2) In the pressure unloading process, the confining pressure was gradually reduced from 15 MPa to 5 MPa, and the permeability was measured when the flow rate at outlet was stable. The effective stress calculation formula adopted in this experiment is[18,19]: ...
... The Hertz deformation theory assumes that the pressure is in semi-elliptical spherical distribution, which is related to the point position on the contact area[22]. The contact area between the two particles is very small compared to the volume of the spherical particles, thus, this deformation process can be regarded as a force exerting on semi-infinite volume but distributing on a very small area. The contact radius satisfies[17,18,19,20]: ...
Stress-dependent permeability and porosity of coal and other geologic formations
2
1988
... The core samples were washed and dried for 48 h, the experiment was conducted at room temperature. According to the SY/T-2016 China's oil and gas industry standard, "Method for measuring porosity and permeability of rocks under overburden pressure", the stress sensitivity of tight cores during pressure loading and unloading process were evaluated by changing the confining pressure. The experimental results were obtained under a constant inlet pressure. The detailed procedure is: (1) In the pressure loading stage, under a constant inlet pressure, the confining pressure was gradually in-creased from 5 MPa to 15 MPa; the permeability was measured when the core outlet flow became stable. (2) In the pressure unloading process, the confining pressure was gradually reduced from 15 MPa to 5 MPa, and the permeability was measured when the flow rate at outlet was stable. The effective stress calculation formula adopted in this experiment is[18,19]: ...
... The Hertz deformation theory assumes that the pressure is in semi-elliptical spherical distribution, which is related to the point position on the contact area[22]. The contact area between the two particles is very small compared to the volume of the spherical particles, thus, this deformation process can be regarded as a force exerting on semi-infinite volume but distributing on a very small area. The contact radius satisfies[17,18,19,20]: ...
Effective stress law for permeability of tight gas reservoir sandstone
2
2011
... The effective stress coefficient η in formula (1) is generally taken as the rock porosity[20,21]. ...
... The Hertz deformation theory assumes that the pressure is in semi-elliptical spherical distribution, which is related to the point position on the contact area[22]. The contact area between the two particles is very small compared to the volume of the spherical particles, thus, this deformation process can be regarded as a force exerting on semi-infinite volume but distributing on a very small area. The contact radius satisfies[17,18,19,20]: ...
Double effective stress of porous media
2
1999
... The effective stress coefficient η in formula (1) is generally taken as the rock porosity[20,21]. ...
... (2) In the pressure loading process, the pore has both body deformation and structural deformation[21]. The body deformation follows the Hertz deformation theory, the contact of the particles turns from initial point contact to surface contact after deformation (Fig. 4b), the contact area is a circle with the radius of a; the structural deformation is caused by the change of the arrangement of four spherical particles (Fig. 4c); the comprehensive deformation of the rock pore is obtained by the combining the body and structural deformations together (Fig. 4d). The inner angles of the quadrilateral O1O2O3O4 after deformation are θ'1, θ'2, θ'3 and θ'4, and θ'1=θ'3, θ'2=θ'4. ...
The calculation method of Hertzian and non-Hertzian contact theory
1
2017
... The Hertz deformation theory assumes that the pressure is in semi-elliptical spherical distribution, which is related to the point position on the contact area[22]. The contact area between the two particles is very small compared to the volume of the spherical particles, thus, this deformation process can be regarded as a force exerting on semi-infinite volume but distributing on a very small area. The contact radius satisfies[17,18,19,20]: ...
Nonlinear seepage regularity of tight sandstone reservoirs with consideration of medium deformation
2
2013
... (1) The rock pores are formed by aggregation of particles with the same size, and the aggregation unit is made up of four particles[23,24,25]. The initial state of the rock pore is shown in Fig. 4a: R is the particle radius; the inner angles of the quadrilateral O1O2O3O4 before deformation are θ1, θ2, θ3 and θ4, among which, θ1=θ3, θ2=θ4. ...
... The pore seepage area of the rock before and after pore deformation are respectively[23]: ...
Study of stress- sensitivity of low-permeability reservoir based on arrangement of particles
2
2014
... (1) The rock pores are formed by aggregation of particles with the same size, and the aggregation unit is made up of four particles[23,24,25]. The initial state of the rock pore is shown in Fig. 4a: R is the particle radius; the inner angles of the quadrilateral O1O2O3O4 before deformation are θ1, θ2, θ3 and θ4, among which, θ1=θ3, θ2=θ4. ...
... In the pressure loading process, according to Hertz theory and the model assumptions, after substituting R1=R2=R, E1=E2=E and v1=v2=v into formula (2), the radius of contact surface and the vertical distance from the particle center to the contact surface are, respectively[24]: ...
Quantitative study of stress sensitivity for fractured tight reservoir with different filled patterns
1
2018
... (1) The rock pores are formed by aggregation of particles with the same size, and the aggregation unit is made up of four particles[23,24,25]. The initial state of the rock pore is shown in Fig. 4a: R is the particle radius; the inner angles of the quadrilateral O1O2O3O4 before deformation are θ1, θ2, θ3 and θ4, among which, θ1=θ3, θ2=θ4. ...
