A method for calculating the force of gas storage structure

Abstract

The present invention discloses a method for calculating the force of a gas storage structure, including: constructing a force model of a lined gas storage under high internal pressure load; based on the force model of the lined gas storage under high internal pressure load, obtaining the stress field function and radial displacement function of the lined gas storage; wherein the stress field function and the radial displacement function both include undetermined coefficients; the undetermined coefficients are used to characterize the size of the stress field and the displacement field; based on the preset boundary conditions of the lined gas storage, solving the undetermined coefficients, obtaining the radial stress of the lined gas storage, and based on the radial stress of the lined gas storage, obtaining the load sharing ratio of the lined gas storage, and completing the force calculation of the lined gas storage under high internal pressure load. Under the premise of ensuring the calculation precision and accuracy, the present invention avoids the problems of long time-consuming numerical simulation, slow analysis and calculation, and huge amount of calculation, and the calculation efficiency is significantly improved, which is more convenient for engineering and technical personnel to use in the site selection, design, and construction of compressed gas energy storage lined gas storage.

Description

Technical Field

[0001] The invention belongs to the technical field of compressed air energy storage, and in particular relates to a method for calculating the force of a gas storage structure. Background Art

[0002] The access ratio of new energy sources such as wind power and solar energy and the requirements for the time-space allocation of power resources are getting higher and higher, resulting in an urgent need for power energy storage on the power supply side, the grid side and the load side. Compressed Air Energy Storage (CAES) is a new physical energy storage technology that uses high-pressure air as a medium to store electricity and generate electricity. Its gas storage can be built in salt caverns, abandoned mines, oil and gas reservoirs, aquifers and artificial hard rocks. However, there are geographical restrictions on the site selection of salt caverns, depleted oil and gas reservoirs and aquifers. Therefore, artificially excavated lined gas storage in rocks has become a more suitable gas storage solution for CAES power stations. Compared with pumped storage and electrochemical storage, lined gas storage has attracted widespread attention due to its advantages such as long life, large scale, low cost, environmental friendliness, wide range of alternative sites and convenient maintenance. It is currently one of the most commercially promising energy storage technologies. Different from traditional underground projects without internal pressure, compressed air energy storage (CAES) lined gas storage bears the expansion load of alternating temperature and pressure cycles. The theoretical system of the coordinated stress mechanism, deformation characteristics and load sharing mechanism of the surrounding rock-support-sealing structure, which is the basis for its design and construction, has not yet been established, and relevant research is urgently needed.

[0003] Under the complex stress mode and operating environment, the theoretical system of the coordinated stress mechanism, deformation characteristics and load sharing mechanism of the surrounding rock-support-seal structure of the gas storage reservoir has not yet been established. These key issues involve the selection of sealing materials, the selection of concrete lining strength and thickness, the selection of sites, and the determination of the strength and range of surrounding rock reinforcement. Therefore, it is urgent to propose a method for calculating the stress of the gas storage reservoir structure. Summary of the invention

[0004] The purpose of the present invention is to propose a method for calculating the force of a gas storage structure. Without considering the temperature load caused by the operating temperature change of the gas storage, based on the theory of multi-layer thick-walled cylinders, the force of the lined gas storage is simplified according to the axisymmetric problem and the analytical solution of its stress and displacement as well as the load sharing ratio of each structure are obtained.

[0005] To achieve the above object, the present invention provides a method for calculating the force of a gas storage structure, comprising:

[0006] Construct the stress model of lined gas storage under high internal pressure load;

[0007] Based on the force model of the lined gas storage under high internal pressure load, the stress field function and radial displacement function of the lined gas storage are obtained; wherein the stress field function and radial displacement function both include undetermined coefficients; the undetermined coefficients are used to characterize the magnitude of the stress field and radial displacement field;

[0008] Based on the preset boundary conditions of the lined gas storage reservoir, the undetermined coefficients in the stress field function and radial displacement function of the lined gas storage reservoir are solved to obtain the radial stress of the lined gas storage reservoir, and based on the radial stress of the lined gas storage reservoir, the load sharing ratio of the lined gas storage reservoir is obtained to complete the force calculation of the lined gas storage reservoir under high internal pressure load.

[0009] Optionally, a stress model of the lined gas storage under high internal pressure load is constructed, including:

[0010] Based on the stress model of a single-layer thick-walled cylinder under high internal pressure load, the stress model of a multi-layer thick-walled cylinder under high internal pressure load is obtained;

[0011] The stress model of the multi-layer thick-walled cylinder under high internal pressure load is regarded as the stress model of the lined gas storage under high internal pressure load.

[0012] Optionally, the stress model of the lined gas storage under high internal pressure load includes: a stress model of a steel lining, a stress model of a concrete lining and a stress model of surrounding rock;

[0013] The stress model of the lined gas storage under high internal pressure load is:

[0014]

[0015] Among them, A1, A2, A3, C1, C2, C3 are all unknown coefficients, which are determined by boundary conditions. The coefficient A represents the degree to which the radial / circumferential stress changes with the radial distance, the coefficient C represents the degree to which the radial / circumferential stress remains unchanged with the radial distance, and r is the radial distance. is the stress function of the steel lining, is the stress function of the concrete lining, is the stress function of the surrounding rock.

[0016] Optionally, the stress field function of the lined gas storage is:

[0017]

[0018] Among them, σ r1 is the radial stress of the steel lining, σ θ1 is the hoop stress of the steel lining, σ r2 is the radial stress of the concrete lining, σ θ2 is the hoop stress of the concrete lining, σ r3is the radial stress of the surrounding rock, σ θ3 is the hoop stress of the surrounding rock, A1, A2, A3, C1, C2, C3 are all unknown coefficients, which are determined by the boundary conditions. The coefficient A represents the degree of change of radial / hoop stress with radial distance, the coefficient C represents the degree of invariance of radial / hoop stress with radial distance, and r is the radial distance.

[0019] Optionally, the radial displacement function of the lined gas storage is:

[0020]

[0021] Among them, u r1 、u r2 、u r3 are the radial displacements of steel lining, concrete lining and surrounding rock respectively; E1′, E2′, E3′ are the elastic moduli of steel lining, concrete lining and surrounding rock respectively required for analyzing plane strain problems; v1′, v2′, v3′ are the Poisson’s ratios of steel lining, concrete lining and surrounding rock respectively required for analyzing plane strain problems.

[0022] Optionally, the preset boundary conditions of the lined gas storage reservoir include: internal stress boundary conditions of the gas storage reservoir, external stress boundary conditions of the gas storage reservoir, boundary conditions at the junction of the steel lining and the concrete lining, and boundary conditions at the junction of the concrete lining and the surrounding rock;

[0023] The internal stress boundary conditions of the gas storage reservoir and the external stress boundary conditions of the gas storage reservoir are:

[0024]

[0025] Among them, σ r1 is the radial stress of the steel lining, σ r3 is the radial stress of the surrounding rock, r0 is the inner radius of the steel lining, r3 is the influence radius, p0 is the internal pressure of the gas storage, and p3 is the in-situ stress simplified to a uniform stress field;

[0026] The stress boundary conditions at the junction of the steel lining and the concrete lining, and at the junction of the concrete lining and the surrounding rock are:

[0027]

[0028] Among them, σ r2 is the radial stress of the concrete lining, r1 is the outer radius of the steel lining and the inner radius of the concrete lining, and r2 is the outer radius of the concrete lining and the inner radius of the surrounding rock;

[0029] The displacement boundary conditions at the junction of the steel lining and the concrete lining, and at the junction of the concrete lining and the surrounding rock are:

[0030]

[0031] Among them, u r1 is the radial displacement of the steel lining, u r2 is the radial displacement of the concrete lining, u r3 is the radial displacement of the surrounding rock.

[0032] Optionally, the method for solving the undetermined coefficients is:

[0033]

[0034] Substitute the unknown coefficients into the stress field function and displacement field function of the lined gas storage, and then obtain the radial stress, hoop stress and radial displacement of the steel lining, concrete lining and surrounding rock.

[0035] Optionally, the load sharing ratio of the lined gas storage is:

[0036]

[0037] Among them, α i is the load sharing ratio of each structure, Δp i is the radial stress p on the interface of each structure i-1 The radial stress p i Δp is the difference between the internal pressure of the gas storage p0 and the ground stress p3.

[0038] The present invention has the following beneficial effects:

[0039] The present invention obtains the stress field and displacement field of each structure through the stress function of each structure of the lined gas storage reservoir, draws the radial stress, hoop stress and radial displacement curves of the lined gas storage reservoir and obtains the load sharing ratio of each structure (steel lining, concrete lining and surrounding rock); by analyzing the influence of parameters such as the maximum gas storage internal pressure, ground stress, deformation modulus of surrounding rock, thickness and strength of concrete lining on the mechanical response of the lined gas storage reservoir, it can judge the favorable or unfavorable working conditions for the lined gas storage reservoir. Under the premise of ensuring the calculation precision and accuracy, it avoids the problems of long time-consuming numerical simulation, slow analysis and calculation, and huge amount of calculation, and the calculation efficiency is significantly improved, which is more convenient for engineering and technical personnel to use in the site selection, design and construction of compressed gas energy storage lined gas storage reservoirs. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0041] Figure 1 A schematic diagram of a compressed gas energy storage liner gas storage system according to an embodiment of the present invention;

[0042] Figure 2It is a simplified schematic diagram of the forces acting on the lined gas storage tank according to an embodiment of the present invention;

[0043] Figure 3 This is a schematic diagram of the influence radius of the lined gas storage according to an embodiment of the present invention;

[0044] Figure 4 It is a schematic diagram of radial stress of a lined gas storage tank according to an embodiment of the present invention;

[0045] Figure 5 A schematic diagram of the hoop stress of a lined gas storage tank according to an embodiment of the present invention;

[0046] Figure 6 It is a schematic diagram of radial displacement of a lined gas storage reservoir according to an embodiment of the present invention;

[0047] Figure 7 The present invention is a flow chart of a method for calculating the force of a gas storage structure according to an embodiment of the present invention. DETAILED DESCRIPTION

[0048] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0049] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0050] like Figure 7 As shown, this embodiment proposes a method for calculating the force of a gas storage structure, including:

[0051] Construct the stress model of lined gas storage under high internal pressure load;

[0052] Specifically, the stress model of the lined gas storage under high internal pressure load includes: a stress model of the steel lining, a stress model of the concrete lining and a stress model of the surrounding rock; based on the multi-layer thick-walled cylinder theory, this embodiment simplifies the lined gas storage into a plane strain problem of a three-layer structure of steel lining, concrete lining and surrounding rock, and obtains the stress functions of the steel lining, concrete lining and surrounding rock under axisymmetric load;

[0053] Based on the stress model of the lined gas storage under high internal pressure load, the stress field function and radial displacement function of the lined gas storage are obtained; wherein the stress field function and the radial displacement function both include undetermined coefficients; the undetermined coefficients are used to characterize the magnitude of the stress field and the radial displacement field;

[0054] Specifically, based on the stress functions of the steel lining, concrete lining and surrounding rock, the stress field and displacement field of each structure are obtained.

[0055] Based on the stress model of the lined gas storage under high internal pressure load, the stress field function and radial displacement function of the lined gas storage are obtained; wherein, the stress field function and radial displacement function both include undetermined coefficients; the undetermined coefficients are used to characterize the magnitude of the stress field and radial displacement field. Boundary conditions are the conditions that stress or displacement on the boundary of a system needs to meet in order to satisfy the force balance and deformation coordination of the system.

[0056] Specifically, the unknown coefficients are solved by solving the stress and displacement boundary conditions of the gas storage reservoir, and then the radial stress, annular stress and radial displacement of the steel lining, concrete lining and surrounding rock are obtained; the load sharing ratio of each structure is solved according to the radial stress of the steel lining, concrete lining and surrounding rock.

[0057] Step 1: Derive the theoretical formula of multi-layer thick-walled cylinder based on the theory of single-layer thick-walled cylinder

[0058] The stress function of a single-layer thick-walled cylinder subjected to an axisymmetric load is:

[0059]

[0060] Where: A and C are unknown coefficients, which are determined by boundary conditions. Coefficient A represents the degree to which radial / circumferential stress changes with radial distance, coefficient C represents the degree to which radial / circumferential stress remains unchanged with radial distance, r is the radial distance, is the stress function of a single-layer thick-walled cylinder.

[0061] The corresponding stress and displacement are given by equations (2) to (3):

[0062]

[0063] Among them, the stress components include radial stress and hoop stress, σ r is the radial stress; σ θ is the hoop stress.

[0064]

[0065] In the formula, u r is the radial displacement; uθ is the circumferential displacement; E′ and v′ are the elastic modulus and Poisson’s ratio required for analyzing plane strain problems, respectively.

[0066]

[0067]

[0068] Where: E and v are the elastic modulus and Poisson's ratio of the material respectively.

[0069] The lined gas storage is simplified as a three-layer thick-walled cylinder. According to formula (1), the stress functions of the steel lining, concrete lining and surrounding rock are as follows:

[0070]

[0071] Among them, A1, A2, A3, C1, C2, and C3 are all unknown coefficients, which are determined by boundary conditions. The coefficient A represents the degree to which the radial / circumferential stress changes with the radial distance, and the coefficient C represents the degree to which the radial / circumferential stress remains unchanged with the radial distance. r is the radial distance. is the stress function of the steel lining, is the stress function of the concrete lining, is the stress function of the surrounding rock.

[0072] The corresponding stress and displacement are given by equations (7) to (8):

[0073]

[0074]

[0075] Where: subscripts 1, 2, and 3 represent steel lining, concrete lining, and surrounding rock, respectively, σ r1 is the radial stress of the steel lining, σ θ1 is the hoop stress of the steel lining, σ r2 is the radial stress of the concrete lining, σ θ2 is the hoop stress of the concrete lining, σ r3 is the radial stress of the surrounding rock, σ θ3 is the hoop stress of the surrounding rock.

[0076] Step 2: Determine the boundary conditions of the lined gas storage reservoir and solve the unknown coefficients and the stress and displacement of each structure

[0077] The unknown coefficients A1, A2, A3, C1, C2, C3 in equations (7) to (8) are determined by the boundary conditions.

[0078] The internal and external stress boundary conditions of the gas storage are:

[0079]

[0080] Considering that all structures are in full contact, there are two boundary conditions at the junction of the steel lining and the concrete lining, and at the junction of the concrete lining and the surrounding rock (Equation (10), Equation (11)):

[0081]

[0082]

[0083] Combining the four stress boundaries and two displacement boundaries in equations (9) to (11), we can obtain:

[0084]

[0085] The coefficients A1, A2, A3, C1, C2, and C3 can be solved by formula (12), and then the radial stress, annular stress, and radial displacement of the gas storage reservoir can be obtained by formula (7) and formula (8).

[0086] Step 3: Calculate the load sharing ratio of each structure of the liner gas storage according to the radial stress;

[0087] Based on the radial stress of the steel lining, concrete lining and surrounding rock of the lined gas storage, the proportion of load borne by each structure can be calculated:

[0088]

[0089] Where: α i is the load sharing ratio of each structure; Δp i is the radial stress p on the interface of each structure i-1 The radial stress p i Δp is the difference between the internal pressure of the gas storage p0 and the ground stress p3.

[0090] In a specific embodiment, the configuration of the compressed gas energy storage liner gas storage is as follows: Figure 1 , Figure 2 shown.

[0091] Before conducting mechanical response analysis of lined gas storage, it is necessary to determine the influence radius of surrounding rock under high internal pressure. The radius of gas storage is selected as 7.5m, the thickness of steel lining is 20mm, the thickness of concrete lining is C40, the deformation modulus of surrounding rock is 5GPa, and the ground stress is 3MPa. Calculate the influence radius of surrounding rock under different maximum internal pressures. The variation law of surrounding rock radial stress with radial distance within the range of (75m) (such as Figure 3 ). Figure 3 It can be seen that in The radial stress in the range drops rapidly, from the maximum gas storage internal pressure to about 4MPa. The radial stress decreases slowly within the range. The stress at the site (3.05MPa~3.24MPa) is basically close to the ground stress (3MPa). The surrounding rock at the location is basically not affected by the internal pressure of the gas storage. The influence radius of the surrounding rock is reasonable.

[0092] Based on the above determined influence radius and parameter values, the maximum gas storage internal pressure of 12MPa is selected, and the stress and displacement of the liner gas storage and the load sharing ratio of each structure are calculated according to the formula derived by this method. The results are as follows: Figures 4 to 6 shown.

[0093] Figure 4 is the radial stress of the liner gas storage obtained by the formula derived according to this method. Figure 4 It can be seen that the gas storage reservoir is under radial pressure, and the compressive stress gradually decreases with the increase of radial distance; although the moduli of the steel lining, concrete lining and surrounding rock are quite different, the radial compressive stress gradually decreases from the maximum gas storage internal pressure (12MPa) at the inner wall of the steel lining to the ground stress (3MPa) at the outer interface of the surrounding rock, indicating that the difference in modulus of the steel lining, concrete lining and surrounding rock will not cause sudden changes in radial stress.

[0094] Figure 5 is the hoop stress of the lined gas storage obtained by the formula derived according to this method. Figure 5 It can be seen that the gas storage is under circumferential tension, and the tensile stress decreases with the increase of radial distance. The difference in modulus of each structure has a significant effect on its circumferential stress. Stress mutation occurs at the junction of steel lining and concrete lining, and concrete lining and surrounding rock. The circumferential stress in the steel lining is basically unchanged. The circumferential stresses of the inner and outer interfaces are 119.43MPa and 119.10MPa, respectively, which are lower than the tensile strength of Q235 steel 205MPa. The steel lining will not yield. At the junction of the steel lining and the concrete lining, the circumferential stress drops sharply from 119.10MPa at the outer interface of the steel lining to 15.64MPa at the inner interface of the concrete lining. With the increase of radial distance, it drops to 14MPa at the outer interface of the concrete lining. The circumferential stress in the concrete lining changes little and is higher than the tensile strength of C40 concrete 1.71MPa (without considering reinforcement); the concrete lining will be torn. The hoop stress of the inner boundary of the surrounding rock is 4.46MPa, and the hoop stress of the outer boundary is -2.54MPa, indicating that with the increase of radial distance, the surrounding rock changes from being under tension to being under compression in the hoop direction. At the same time, the surrounding rock bearing tensile stress may deteriorate or even be cracked due to hoop tension.

[0095] Figure 6 is the radial displacement of the lined gas storage obtained by the formula derived from this method. Figure 6 It can be seen that the difference in modulus of each structure has little effect on the radial displacement, the deformation is within a few millimeters, and the displacement at the steel lining is the largest. The radial displacement gradually decreases with the increase of radial distance. The range changes greatly, from 6.65mm to 2.53mm; The range becomes flat and gradually converges to 1.68mm.

[0096] In the figure of this embodiment: r0-gas storage reservoir radius, steel lining inner radius; r1-steel lining outer radius, concrete lining inner radius; r2-concrete lining outer radius, surrounding rock inner radius; r3-influence radius; p0-gas storage internal pressure; p1-radial stress at the junction of steel lining and concrete lining; p2-radial stress at the junction of concrete lining and surrounding rock; p3-ground stress; σ r - radial stress; σ θ - Hoop stress; u r - Radial displacement.

[0097] According to the load proportion of each structure of the lined gas storage obtained by the formula derived in this embodiment, the surrounding rock of the gas storage bears about 77.8% of the load, the concrete lining bears about 18.3%, and the steel lining bears the least load, accounting for only 3.9%.

[0098] The above is only a preferred specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A method for calculating the force of a gas storage structure, characterized in that: include: Construct the stress model of lined gas storage under high internal pressure load; The stress model of the lined gas storage under high internal pressure load includes: a stress model of the steel lining, a stress model of the concrete lining and a stress model of the surrounding rock; The stress model of the lined gas storage under high internal pressure load is: Among them, A1, A2, A3, C1, C2, C3 are all unknown coefficients, which are determined by boundary conditions. The coefficient A represents the degree to which the radial / circumferential stress changes with the radial distance, the coefficient C represents the degree to which the radial / circumferential stress remains unchanged with the radial distance, and r is the radial distance. is the stress function of the steel lining, is the stress function of the concrete lining, is the stress function of surrounding rock; Based on the force model of the lined gas storage under high internal pressure load, the stress field function and radial displacement function of the lined gas storage are obtained; wherein the stress field function and radial displacement function both include undetermined coefficients; the undetermined coefficients are used to characterize the magnitude of the stress field and radial displacement field; The stress field function of the lined gas storage is: Among them, σ r1 is the radial stress of the steel lining, σ θ1 is the hoop stress of the steel lining, σ r2 is the radial stress of the concrete lining, σ θ2 is the hoop stress of the concrete lining, σ r3 is the radial stress of the surrounding rock, σ θ3 is the hoop stress of the surrounding rock, A1, A2, A3, C1, C2, C3 are all unknown coefficients, which are determined by the boundary conditions, among which the coefficient A represents the degree of change of radial / hoop stress with radial distance, the coefficient C represents the degree of invariance of radial / hoop stress with radial distance, and r is the radial distance; The radial displacement function of the lined gas storage is: Among them, u r1 、u r2 、u r3 are the radial displacements of the steel lining, concrete lining and surrounding rock respectively; E1′, E2′, E3′ are the elastic moduli of the steel lining, concrete lining and surrounding rock respectively required for analyzing the plane strain problem; v1′, v2′, v3′ are the Poisson’s ratios of the steel lining, concrete lining and surrounding rock respectively required for analyzing the plane strain problem; Based on the preset boundary conditions of the lined gas storage reservoir, the undetermined coefficients in the stress field function and radial displacement function of the lined gas storage reservoir are solved to obtain the radial stress of the lined gas storage reservoir, and based on the radial stress of the lined gas storage reservoir, the load sharing ratio of the lined gas storage reservoir is obtained to complete the force calculation of the lined gas storage reservoir under high internal pressure load; The preset boundary conditions of the lined gas storage include: internal stress boundary conditions of the gas storage, external stress boundary conditions of the gas storage, boundary conditions at the junction of the steel lining and the concrete lining, and boundary conditions at the junction of the concrete lining and the surrounding rock; The internal stress boundary conditions of the gas storage reservoir and the external stress boundary conditions of the gas storage reservoir are: Among them, σ r1 is the radial stress of the steel lining, σ r3 is the radial stress of the surrounding rock, r0 is the inner radius of the steel lining, r3 is the influence radius, p0 is the internal pressure of the gas storage, and p3 is the in-situ stress simplified to a uniform stress field; The stress boundary conditions at the junction of the steel lining and the concrete lining, and at the junction of the concrete lining and the surrounding rock are: Among them, σ r2 is the radial stress of the concrete lining, r1 is the outer radius of the steel lining and the inner radius of the concrete lining, and r2 is the outer radius of the concrete lining and the inner radius of the surrounding rock; The displacement boundary conditions at the junction of the steel lining and the concrete lining, and at the junction of the concrete lining and the surrounding rock are: Among them, u r1 is the radial displacement of the steel lining, u r2 is the radial displacement of the concrete lining, u r3 is the radial displacement of the surrounding rock.

2. The method for calculating the force of a gas storage structure according to claim 1 is characterized in that: Construct a stress model of a lined gas storage facility under high internal pressure load, including: Based on the stress model of a single-layer thick-walled cylinder under high internal pressure load, the stress model of a multi-layer thick-walled cylinder under high internal pressure load is obtained; The stress model of the multi-layer thick-walled cylinder under high internal pressure load is regarded as the stress model of the lined gas storage under high internal pressure load.

3. The method for calculating the force of a gas storage structure according to claim 1, characterized in that: The method for solving the undetermined coefficients is:

4. The method for calculating the force of a gas storage structure according to claim 1, characterized in that: The load sharing ratio of the lined gas storage is: Among them, α i is the load sharing ratio of each structure, Δp i is the radial stress p on the interface of each structure i-1 The radial stress p i Δp is the difference between the internal pressure of the gas storage p0 and the ground stress p3.

Images