Method for determining equivalent hydraulic fracture width of CO2 injection well cement ring interface

Abstract

The application provides a method for determining equivalent hydraulic fracture width of CO2 injection well cement ring interface. The method comprises the following steps: S1, preparing a cement ring test piece; S2, pressurizing the cement ring; S3, monitoring the gas flow at the top of the cement ring, adjusting the injected CO2 flow, recording the pressure of the gas passing through the cement ring under different CO2 gas flows, and recording the gas flow passing through the cement ring under different injection pressure conditions by using a flow meter; S4, calculating the supercritical CO 2 density; S5, obtaining the gas flow at the top of the cement ring under different CO2 viscosity and cementing qualities; and S6, calculating the equivalent hydraulic fracture width of supercritical CO2 in the cement ring interface. The method obtains the equivalent fracture width of the cement ring interface by processing and analyzing experimental data, and is used for evaluating the influence of the viscosity and flow of supercritical CO2 and different cementing qualities on the annular gap of the cement ring interface, and evaluating the anti-channeling capacity of the cement ring under different CO2 injection conditions.

Description

Technical Field

[0001] This invention relates to the field of oil production engineering technology, and in particular to a method for determining the equivalent hydraulic fracture width at the cement sheath interface of a CO2 injection well. Background Technology

[0002] As many oil wells in my country enter the mid-to-late stages of their lifespan, oil recovery rates have significantly decreased. To improve the recovery rate and production of low-permeability oilfields, there is an urgent need to research new oil displacement technologies. Numerous studies both domestically and internationally have shown that CO2 flooding can significantly improve oil and gas recovery rates and bury CO2 underground, thus demonstrating its promising potential for developing low-permeability oilfields. However, wells converted to CO2 injection are generally completed early, and their wellbore safety status is currently unclear. Furthermore, the downhole conditions become more complex after conversion, and the casing-cement sheath interface faces the risk of sealing failure under harsh operating conditions such as high-pressure injection, alternating temperature and pressure loads, and supercritical CO2 corrosion. This can lead to injected gas channeling or even gas reaching the surface, affecting CO2 injection effectiveness and creating safety hazards. Therefore, it is necessary to analyze the annular gap size of the casing-cement sheath interface under different injection conditions in CO2 injection wells and evaluate the anti-channeling capability of the cement sheath interface to ensure safe and efficient production from CO2 injection wells.

[0003] Although domestic research has been conducted on the evaluation of cement sheath interface anti-channeling capability, there are still shortcomings in the evaluation of cement sheath interface anti-channeling capability under CO2 injection conditions. Current research methods for evaluating cement sheath interface anti-channeling capability mainly include two types: experimental and numerical simulation.

[0004] (1) Regarding experimental methods, the high-temperature and high-pressure gas well cement sheath sealing integrity evaluation system (CN 109681190 A) mainly uses N2 as the fluid medium to pressure the cement sheath interface and obtain the pressure of the cement sheath to evaluate the sealing capacity of the cement sheath. However, this method cannot simulate CO2 injection under supercritical conditions, nor can it obtain the size of the annular gap at the casing-cement sheath interface. A method for measuring the size of the micro-annular gap at the first interface of cementing (CN 110424947B) introduces gas into the bottom of the cement sheath and calculates the cement sheath interface gap by detecting parameters such as pressure and flow rate at the upper and lower ends of the cement sheath. However, this device does not have a supercritical CO2 generator and cannot simulate the supercritical CO2 injection condition. Therefore, it cannot accurately characterize the cement sheath's sealing capacity against supercritical CO2. At the same time, this device does not have a cementing quality detection device and cannot analyze the influence law of the cement sheath interface under different cementing quality conditions. Moreover, the cementing quality of old wells in the field varies greatly. Therefore, the application of this evaluation method in CO2 injection wells still has limitations. A non-contact high-temperature and high-pressure well cement sheath micro-annulus generation device (CN CN115680621A) analyzes the cement sheath annulus size by cyclically loading and unloading the cement sheath into the casing until the cement sheath seal fails, and then using image acquisition equipment to capture digital images and track the movement of image points. While this device can monitor annulus changes after cement sheath interface failure, it lacks a supercritical CO2 generator, making it unable to analyze the annulus size under different CO2 injection conditions. Furthermore, the device lacks built-in cementing quality testing instruments, preventing analysis of cement sheath interface changes under different cementing indices during CO2 injection. Therefore, this method has limitations in field application in CO2 injection wells.

[0005] (2) In terms of numerical simulation, there is a numerical simulation method, system and storage medium for oil and gas flow in the cementing annulus of deep-water high-temperature and high-pressure wells (CN113898312A) and a numerical simulation method for sealing failure of the casing-cement sheath-formation system in deep-water high-temperature and high-pressure wells (CN113756744A). The above methods mainly use Cohesive elements to simulate the cement sheath interface, set two injection units and one injection point, and use the interface stiffness degradation coefficient SDEG to evaluate the state of cement sheath breakthrough. When SDEG=1, the injection pressure is used as an indicator to evaluate the sealing capacity of cement sheath. This numerical simulation method mainly simulates the complete destruction of the cement sheath interface, which is significantly different from the situation where partial destruction of the cement sheath in the field may lead to sealing failure. Therefore, it cannot correspond to the actual situation in the field.

[0006] In summary, current technologies are not yet able to accurately quantify and evaluate the annular gap at the casing-cement sheath interface under different CO2 injection conditions, thus failing to guide the feasibility analysis of conversion wells to gas injection. Summary of the Invention

[0007] The technical problem to be solved by this invention is to overcome the limitation of existing technologies in which the variation law of anti-channeling capability of the casing-cement sheath interface under different CO2 injection conditions cannot be precisely quantified. This invention provides a method for determining the equivalent hydraulic gap width of the cement sheath interface in CO2 injection wells. This method obtains the equivalent gap width of the cement sheath interface by processing and analyzing experimental data; it then evaluates the influence of supercritical CO2 viscosity, flow rate, and different cementing qualities on the annular gap of the cement sheath interface using the equivalent gap width, thereby evaluating the anti-channeling capability of the cement sheath under different CO2 injection conditions.

[0008] The present invention solves its problem through the following technical solution: a method for determining the equivalent hydraulic fracture width at the cement sheath interface of a CO2 injection well, comprising the following steps:

[0009] S1. Fabricate the cement ring test piece required for the experiment, wherein the cement ring test piece comprises:

[0010] Cement ring test piece A is used to test the gas flow rate Q at the top of the cement ring under different CO2 viscosity conditions;

[0011] Cement sheath test piece B is used to test the gas flow rate Q at the top of the cement sheath under different cementing quality conditions;

[0012] S2. Inject supercritical CO2 generated under certain working conditions into the bottom of the cement ring at the casing to compress and channel the cement ring.

[0013] S3. After gas leakage through the cement ring, monitor the gas flow rate Q at the top of the cement ring. By adjusting the injected CO2 flow rate, record the pressure of the gas passing through the cement ring under different CO2 gas flow rates. And use a flow meter to record the gas flow rate passing through the cement ring under different injection pressure conditions.

[0014] S4. Calculate the density of supercritical CO2;

[0015] S5. For cement ring test piece A, by adjusting the temperature and pressure of the supercritical CO2 generator, obtain supercritical CO2 with different viscosities, calculate the supercritical CO2 viscosity, and record the pressure of gas passing through the cement ring under different CO2 viscosities; repeat step 3 under different CO2 viscosity conditions, adjust the gas injection pressure at the bottom of the cement ring, and record the gas flow rate Q at the top of the cement ring under different CO2 viscosity conditions.

[0016] For cement sheath test piece B, after obtaining the cement sheath test piece with the cementing quality required for the experiment, repeat steps 2 to 3 and record the gas flow rate Q at the top of the cement sheath under the different cementing quality conditions.

[0017] S6. Based on the gas flow rate Q at the top of the cement sheath under different CO2 viscosity conditions in step S5, and the gas flow rate Q at the top of the cement sheath under different cementing quality conditions; and the experimental data of cement sheath sealing performance evaluation, the equivalent hydraulic gap width of supercritical CO2 at the cement sheath interface is calculated using the nonlinear Darcy flow formula and the gas state equation.

[0018] Preferably, in step S1, the cement ring test piece A is the original test piece after curing, and the cement ring amplitude is tested on the original test piece after curing, and the initial bonding index and bonding strength of the cement ring after curing are calculated.

[0019] The cement sheath test piece B is the cement sheath acoustic amplitude tested after the test piece has been cured; after calculating the initial cementing index and cementing strength of the cured cement sheath, a certain internal pressure load is applied inside the casing, and after unloading, the cementing index is measured again. This operation is repeated until the cement sheath test piece with the cementing quality required for the experiment is obtained.

[0020] And / or,

[0021] The method for preparing the cement ring of the test specimen and completing the curing of the cement ring of the test specimen in step S1 is as follows:

[0022] Experiments were conducted using a full-size cement ring seal integrity evaluation device. Based on the inner diameter of the device and the outer diameter of the casing at the site, a formation rock ring of the corresponding size was prepared and placed inside the device.

[0023] Cement slurry is prepared by mixing cement with cement on site and filling the annulus between the casing and the formation annulus with the prepared cement slurry. The cementing quality testing instrument is then placed inside the casing.

[0024] The poured cement ring is cured for 48 hours, depending on the on-site temperature and pressure.

[0025] Preferably, the method for calculating the initial bonding index and bonding strength of the cement ring after curing in step S1 is as follows:

[0026] The cementing quality testing instrument is used to collect acoustic logging data to test the acoustic amplitude; the cement sheath cementing index BI is calculated according to the cementing index formula; the cement sheath cementing strength S is calculated according to the cement sheath cementing strength formula to evaluate the cementing quality of the initial cement sheath.

[0027] The formula for the cementation index is:

[0028]

[0029] In the formula: BI is the cementation index; A Max The maximum amplitude of the first wave obtained from high-resolution imaging; A E A represents the amplitude of the first wave at the measurement point. minThe amplitude value of the first wave obtained at the low gradation point; all the above parameters were measured by a cementing quality testing instrument;

[0030] The formula for the cement ring bond strength is:

[0031]

[0032] in:

[0033] p = -0.00434T 2 -0.0622T+4.44 (3)

[0034] α=-21.8723×logU-0.0137×d+49.62 (4)

[0035] Where: S is the cement bond strength, MPa; T is the sleeve wall thickness, mm; p is the dimensionless exponent; α is the sound wave attenuation rate, dB / m;

[0036] d is the outer diameter of the casing, mm; U is the relative acoustic amplitude, %, which is measured by the cementing quality tester; k is a coefficient related to the source distance l, the value of which is given by the source distance, which is the distance between the transmitting transducer and the receiving transducer in the cementing quality tester.

[0037] Preferably, the method for step S2, which involves pressurizing the cement ring, is as follows: using a full-size cement ring sealing evaluation device and a supercritical CO2 generator, supercritical CO2 generated under certain working conditions is injected into the bottom of the casing cement ring, and the pressure is continuously increased to pressurize and push the cement ring until gas leakage occurs in the cement ring.

[0038] Preferably, the method for obtaining the supercritical CO2 density in step S4 is as follows:

[0039] Based on the Peng-Robinson theory, the density ρ of supercritical CO2 under certain temperature and pressure conditions is obtained using the supercritical CO2 equation of state and density formula:

[0040] The equation of state for supercritical CO2 is:

[0041]

[0042] The density formula is:

[0043]

[0044] Where: P is the fluid pressure under equilibrium conditions; T is the fluid temperature under equilibrium conditions;

[0045]

[0046] V mThe molar volume of supercritical CO2 under these temperature and pressure conditions can be calculated using formula (5).

[0047] Preferably, the method for calculating the supercritical CO2 viscosity under certain temperature and pressure conditions in step S5 is as follows:

[0048] The viscosity μ of supercritical CO2 under certain temperature and pressure conditions is calculated using the Chung viscosity calculation method. The Chung viscosity calculation formula is as follows:

[0049]

[0050] in:

[0051]

[0052] T * =1.2593T r (9)

[0053]

[0054]

[0055]

[0056]

[0057]

[0058] In the formula: A1 = 1.16145; B1 = 0.14874; C1 = 0.52487; D1 = 0.7732; E = 2.16178; F1 = 2.43787; F c =1-0.2756ω;

[0059] The critical parameter for CO2 to transition from the gas phase to the supercritical state is: T c =304.13K, P c =7.38MPa, V c = 93.8cm 3 / mol, for CO2, ω=0.2249, M=44g / mol, E1~E 10 The values ​​are as follows: E1 = 17.662, E2 = 9.5 × 10⁻⁴, E3 = 62.455, E4 = 15.200, E5 = 21.461, E6 = -4.720, E7 = 25.051, E8 = 1.048, E9 = -0.223, E 10 =0.147.

[0060] Preferably, the method for calculating the equivalent hydraulic joint width of supercritical CO2 at the cement ring interface in step S6 specifically includes:

[0061] 1) The seepage of supercritical CO2 gas in the cement ring interface satisfies the supercritical CO2 equation of state (5) and the nonlinear Darcy flow formula (15);

[0062] 2) Obtain the permeability k of supercritical CO2 gas at the cement ring interface;

[0063] 3) Based on the permeability k, the expression for the equivalent slit width h can be determined according to the cubic law formula; based on the determined equivalent slit width expression, the value of the equivalent slit width is obtained.

[0064] Preferably, the method for obtaining the permeability k of supercritical CO2 gas at the cement ring interface includes:

[0065] The seepage of supercritical CO2 gas in the cement ring interface satisfies the supercritical CO2 state equation (5) and the nonlinear Darcy seepage formula (15), and formula (5) is transformed according to the isothermal steady-state flow condition to obtain formula (16).

[0066] Establish the average pressure formula (17), and substitute the formula (17) into the formula (16) to obtain the average pressure conversion formula (18);

[0067] Then, by substituting formula (18) into the nonlinear Darcy formula (15), we obtain the pressure gradient transformation formula (19).

[0068] Finally, by transforming the above formula (19), we can obtain the CO2 gas seepage formula (20);

[0069] Among them, the nonlinear Darcy flow formula (15) is:

[0070]

[0071] In the formula: ΔP is the pressure gradient, Q is the annular supercritical CO2 volumetric flow rate, μ is the supercritical CO2 viscosity, and k is the permeability. ρ is the cross-sectional area of ​​the annular supercritical CO2 flow, D is the diameter of the cement ring, d is the diameter of the casing, β is the inertia coefficient, and ρ is the supercritical CO2 density.

[0072] The gas state equation (5) is transformed according to the isothermal steady-state flow condition of the gas to obtain formula (16):

[0073]

[0074] In the formula: V is the average pressure; mLet T be the molar volume of supercritical CO2 under these temperature and pressure conditions, and T be the supercritical CO2 temperature.

[0075] And the average pressure The expression can also be represented as:

[0076]

[0077] In the formula: P u P d These represent the CO2 injection and discharge pressures of the cement sheath, respectively; the cementing bond strength S = P in step 2. u -P d If P d =0, then S and the injection end pressure P u If they are the same, then:

[0078]

[0079]

[0080]

[0081] In the formula: L is the length of the cement ring interface;

[0082] Equation (20) can be rewritten as:

[0083]

[0084] In the formula:

[0085] The data obtained from the experiment and the results calculated based on the experimental data are substituted into equation (21) to obtain the coordinates (x, y) of different points. The coordinates (x, y) of the points are plotted as a straight line with a slope that is a function of the inertia coefficient β and an intercept that is inversely proportional to the permeability k. The permeability k can be obtained by plotting the line.

[0086] Preferably, the method for obtaining the equivalent seam width specifically includes:

[0087] Based on the permeability k, the expression for the equivalent slit width h can be determined according to the following cubic law formula, as shown in equation (22):

[0088]

[0089] In the formula, ω=πd is the hydraulic circumference; A=πdL is the surface area of ​​the cement ring interface; h is the equivalent hydraulic joint width; and k is the permeability.

[0090] Preferably, the equivalent hydraulic fracture width of supercritical CO2 at the cement sheath interface obtained through steps S1-S6 can be used to evaluate the influence of different CO2 viscosities and gas flow rates on the hydraulic fracture width at the cement sheath interface; or to evaluate the influence of different cementing qualities on the hydraulic fracture width at the cement sheath interface.

[0091] Compared with the above-mentioned background technology, the present invention has the following beneficial effects:

[0092] This invention proposes a method for determining the equivalent hydraulic fracture width at the cement sheath interface in CO2 injection wells. The experimental method described in this invention can realistically simulate CO2 injection viscosity, injection gas volume, different cement sheath bonding strengths, and the CO2 channeling process under different injection conditions in CO2 injection wells. Simultaneously, a method for calculating the equivalent fracture width at the cement sheath interface is proposed, which can accurately characterize the influence of different CO2 viscosities, gas flow rates, and different cementing qualities on the anti-channeling capability of the cement sheath interface, thereby enabling a quantitative evaluation of the anti-channeling capability of the cement sheath interface under different injection conditions in CO2 injection wells. Attached Figure Description

[0093] Figure 1 This is a flowchart illustrating the method for determining the equivalent hydraulic fracture width at the cement sheath interface in a CO2 injection well according to the present invention.

[0094] Figure 2 This is a curve showing the effect of CO2 viscosity on the equivalent hydraulic joint width of the cement ring interface in an embodiment of the present invention.

[0095] Figure 3 This is a curve showing the effect of gas flow rate on the equivalent hydraulic joint width of the cement ring interface in an embodiment of the present invention.

[0096] Figure 4 This is a curve showing the influence of cementing quality on the equivalent hydraulic fracture width of the cement sheath interface in an embodiment of the present invention. Detailed Implementation

[0097] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0098] To more clearly illustrate the implementation of this method, the technical solution of the present invention will be described with reference to the accompanying drawings. Figure 1 As shown, a method for determining the equivalent hydraulic fracture width at the cement sheath interface in a CO2 injection well includes the following steps:

[0099] Step 1: Conduct experiments based on the full-size cement sheath seal integrity evaluation device. Prepare a formation rock sheath of the appropriate size according to the inner diameter of the device and the outer diameter of the casing at the site, and place it inside the device. Use cement slurry prepared with the cementing cement at the site, and fill the annulus between the casing and the formation sheath with the prepared cement slurry. Place the cementing quality testing instrument inside the casing.

[0100] Step 2: After the cement sheath is poured and cured, it is cured for 48 hours according to the on-site temperature and pressure. The cement sheath bonding index BI is calculated according to formula (1) and the cement sheath bonding strength S is calculated according to formula (2) to evaluate the bonding quality of the initial cement sheath.

[0101]

[0102] In the formula: BI is the cementation index; A Max The maximum amplitude of the first wave obtained from high-resolution imaging; A E A represents the amplitude of the first wave at the measurement point. min This is the amplitude value of the first wave obtained at the lower digit.

[0103]

[0104] Where: S is the cement bonding strength, MPa; T is the sleeve wall thickness, mm; p is the dimensionless exponent, given by equation (3); α is the sound wave attenuation rate, dB / m, given by equation (4):

[0105] p = -0.00434T 2 -0.0622T+4.44 (3)

[0106] α=-21.8723×logU-0.0137×d+49.62 (4)

[0107] In the formula: d is the outer diameter of the casing, mm; U is the relative acoustic amplitude value, %, which is measured by the cementing quality tester; k is a coefficient related to the source distance l, and the value of k is given by the source distance, which is the distance between the transmitting transducer and the receiving transducer in the cementing quality tester. Table 1 shows the applicable range of the selected k value, the source distance, and the corresponding k value.

[0108] Table 1

[0109]

[0110] Step 3: Using a full-size cement ring sealing evaluation device, supercritical CO2 generated under certain working conditions is injected into the bottom of the cement ring, and the pressure is continuously increased until gas leakage occurs in the cement ring.

[0111] Step 4: After gas leakage through the cement ring, monitor the gas flow rate Q at the upper surface of the cement ring using a soap film flow meter. The gas flow rate Q is measured according to standard GB / T 22133-2008 using a soap film flow meter. After gas leakage, adjust the gas injection pressure at the bottom of the cement ring according to experimental requirements, and record the gas flow rate through the cement ring under different injection pressure conditions using a flow meter.

[0112] Step 5: Calculate the supercritical CO2 density. Based on the Peng-Robinson theory, the density ρ of supercritical CO2 under the given temperature and pressure conditions is obtained using the supercritical CO2 equation of state (5) and equation (6):

[0113] Equation of state for supercritical CO2 (5):

[0114]

[0115]

[0116] In the formula: V m The molar volume of supercritical CO2 under these temperature and pressure conditions can be calculated using formula (6).

[0117] Step 6: By changing the temperature and pressure of the supercritical CO2 generator, different viscosities of CO2 are obtained. Step 4 is repeated under different CO2 viscosity conditions. The gas injection pressure at the bottom of the cement ring is adjusted, and the leakage gas flow rate Q at the top of the cement ring is recorded under different injection pressures.

[0118] The specific method for calculating the viscosity of supercritical CO2 is as follows: The viscosity μ of supercritical CO2 under the given temperature and pressure conditions is calculated using the Chung method, as shown in equations (7) to (14):

[0119]

[0120] in:

[0121]

[0122] T * =1.25 r 9 (9)

[0123]

[0124] In the formula: A1 = 1.16145, B1 = 0.14874, C1 = 0.52487, D1 = 0.7732, E = 2.16178, F1 = 2.43787, F c =1-0.2756ω

[0125]

[0126]

[0127]

[0128]

[0129] For CO2, ω = 0.2249, M = 44 g / mol, E1~E 10 The values ​​are as follows:

[0130] E1=17.662, E2=9.5×10-4, E3=62.455, E4=15.200, E5=21.461, E6=-4.720, E7=25.051, E8=1.048, E9=-0.223, E 10 =0.147.

[0131] T c =304.13K, P c =7.38MPa, V c = 93.8cm 3 / mol is the critical parameter for CO2 to transition from the gas phase to the supercritical state. By substituting the temperature T and the supercritical CO2 density ρ into equations (7) to (14), the supercritical CO2 viscosity under the given temperature and pressure conditions can be obtained.

[0132] Step 7: Calculate the hydraulic joint width h of supercritical CO2 at the cement ring interface based on the supercritical CO2 gas seepage formula and the cubic formula.

[0133] The seepage of supercritical CO2 gas in the cement ring interface satisfies the supercritical CO2 equation of state (5) and the nonlinear Darcy flow formula (15). Formula (5) is then transformed according to the isothermal steady-state flow condition to obtain formula (16). Formula (17) is then substituted into formula (16) to obtain formula (18). Formula (18) is then substituted into the nonlinear Darcy formula (15) to obtain formula (19). Finally, formula (19) is transformed to obtain the CO2 gas seepage formula (20), as shown below:

[0134] Nonlinear Darcy flow formula (15):

[0135]

[0136] In the formula, ΔP is the pressure gradient, Q is the annular supercritical CO2 volumetric flow rate, μ is the supercritical CO2 viscosity, and k is the permeability. ρ is the cross-sectional area of ​​the annular supercritical CO2 flow, β is the inertia coefficient, and ρ is the supercritical CO2 density.

[0137] The gas state equation (5) is transformed according to the isothermal steady-state flow condition of the gas to obtain formula (16):

[0138]

[0139] In the formula, The average pressure, and the average pressure The expression is:

[0140]

[0141] In the formula, P u P d These represent the CO2 injection and discharge pressures of the cement sheath, respectively. The cementing bond strength S = P in step 2 is... u -P d If P d =0, then S and the injection end pressure P u same.

[0142]

[0143]

[0144]

[0145] In the formula, L is the length of the cement ring interface.

[0146] Equation (20) can be rewritten as:

[0147]

[0148] In the formula,

[0149] The data obtained from the above experiments and the results calculated based on the experimental data are substituted into equation (21) to obtain the coordinates (x, y) of different points. The coordinates (x, y) of the points are plotted as a straight line, the slope of which is a function of the inertia coefficient β, and the intercept is inversely proportional to the permeability k. The permeability k can be obtained by plotting the line.

[0150] The permeability k calculation method, based on the following cubic law formula, can determine the expression for the equivalent slit width h, as shown in equation (22):

[0151]

[0152] In the formula, ω=πd is the hydraulic circumference, A=πdL is the surface area of ​​the cement ring interface, h is the equivalent hydraulic joint width, and k is the permeability.

[0153] Step 8: Repeat steps 1 and 2, then apply the required internal pressure load inside the casing, stabilize the pressure for 5 minutes, and then unload. After unloading, perform sonic logging again and calculate the corresponding cement bond strength. After multiple repetitions of loading, the required cement sheath bond strength is obtained and used for simulation experiments under different cementing quality conditions. After completing one round of experiments, repeat the cement sheath test piece, then destroy the cementing quality, and then conduct the experiment again.

[0154] Step 9, as described in steps 3 to 8, reveals the influence of different CO2 viscosities, gas flow rates, and cementing strengths on the equivalent fracture width h. This allows for a quantitative evaluation of the anti-channeling capability of the cement sheath interface in CO2 injection wells under different injection conditions and cementing quality.

[0155] Example 1

[0156] This invention provides a method for calculating the equivalent hydraulic fracture width at the cement sheath interface in CO2 injection wells. It proposes a formula for calculating the equivalent hydraulic fracture width and uses experimental data to obtain the effects of different CO2 viscosities, gas flow rates, and cementing bond strengths on the sealing capacity of the cement sheath. The specific method is as follows:

[0157] Step 1, taking a gas injection drive site casing with an outer diameter of 139.7 mm, a cement sheath thickness of 38.1 mm, and a full-size cement sheath seal integrity evaluation device with an inner diameter of 400 mm as an example; prepare a formation rock sheath with an outer diameter of 400 mm and an inner diameter of 215.9 mm and place it inside the device. Use field-grade G cementing cement to prepare cement slurry, pour the cement slurry into the annulus formed by the casing and the formation, and pre-install an 8-sector cementing quality logging tool inside the casing.

[0158] Step 2: Based on the downhole temperature and pressure of the CO2 injection well, the cement sheath was cured for 48 hours. Then, the acoustic amplitude curve was detected using a cementing quality logging tool. The maximum acoustic amplitude value was 159.872 mV; the minimum acoustic amplitude value was 14.763 mV; and the ratio of the first wave acoustic amplitude value to the acoustic amplitude value of the free casing section was 38.39%. The cement sheath bonding index was calculated to be 0.402 using formula (1). The bonding strength was calculated using formula (2) based on the casing outer diameter of 5.5 in, the casing wall thickness of 0.304 in, and the source distance of 1.5 m.

[0159] p = -0.00434 × 7.72 2 -0.0622 × 7.72 + 4.44 = 3.7

[0160] α=-21.8723×log38.39-0.0137×139.7+49.62=13.06dB / m

[0161]

[0162] Step 3: Using a full-size cement ring sealing evaluation device and a supercritical CO2 generator, supercritical CO2 is injected into the bottom of the cement ring and continuously pressurized until gas leakage occurs in the cement ring.

[0163] Step 4: After gas leakage through the cement ring, the gas flow rate Q at the upper surface of the cement ring is monitored using a soap film flow meter. The test method for the gas flow rate Q is based on standard GB / T 22133-2008, using a soap film flow meter. After gas leakage, the injection pressure at the bottom of the cement ring is adjusted according to experimental requirements, and the gas flow rate through the cement ring under different injection pressure conditions is recorded using a flow meter. The experimental results for evaluating the sealing performance of the cement ring are shown in Table 2. This example uses the experimental results corresponding to experiment number 3 in Table 2 as an example, with injection pressures ranging from 1.34 to 2.73 MPa, corresponding to CO2 flow rates of 37 to 111 cm³. 3 / s.

[0164] Step 5: Calculate the CO2 density under different temperature and pressure conditions using formulas (5) and (6). This example uses the experimental results corresponding to experiment number 1 in Table 2, where the injected CO2 density ranges from 0.08 to 0.96 g / cm³. 3 .

[0165] Step 6: By changing the temperature and pressure of the supercritical CO2 generator, different viscosities of CO2 are obtained. Step 4 is repeated under different CO2 viscosity conditions. The gas injection pressure at the bottom of the cement ring is adjusted, and the gas flow rate Q at the top of the cement ring is recorded under different injection pressures. The experimental results of this cement ring sealing performance evaluation are shown in serial number 1 in Table 2. This example uses the experimental results corresponding to experimental serial number 1 in Table 2. The injected CO2 viscosity is 0.02~0.1 mPa·s, and the corresponding pressures are 1.68~3.37 MPa.

[0166] Step 7: Use formula (20) to calculate the injection end pressure corresponding to different viscosity CO2 and different CO2 flow rates to obtain the permeability of the specimens under different experimental conditions, and calculate the equivalent hydraulic gap width of each specimen according to formula (22).

[0167] Step 8: Repeat steps 1 and 2, then apply the required internal pressure load inside the casing. In this example, an internal pressure of 40 MPa is applied. After stabilizing the pressure for 5 minutes, the pressure is unloaded. After unloading, sonic logging is performed again to calculate the corresponding cement sheath cementing index and cementing strength. Using a cementing index of 0.4 as an example, the injection end pressure is 1.39 MPa under this condition. The equivalent hydraulic fracture width is 17.518 μm. Repeat the above steps, but with different loads and repetitions inside the casing each time to obtain different cement sheath cementing indices for different experiments. This example uses the experimental results corresponding to experiment number 2 in Table 2, where the cement sheath cementing indices range from 0.2 to 0.8, and the corresponding injection pressures range from 0.59 to 2.73 MPa.

[0168] Step 9: Repeat steps 3 to 8, recording experimental data such as CO2 gas flow rate, CO2 injection end pressure, CO2 discharge end pressure, and CO2 injection end pressure and CO2 discharge end pressure under different CO2 viscosities and different cementing strengths. The experimental results of the cement sheath sealing performance evaluation are shown in Table 2. Based on Table 2, calculate the equivalent hydraulic fracture width of the cement sheath interface under different experimental conditions, and analyze the influence of CO2 viscosity, injection volume, and cementing quality on the equivalent hydraulic fracture width. (See...) Figure 2 , Figure 3 , Figure 4 By combining the downhole temperature, pressure, and cementing quality of the CO2 injection well, and calculating the hydraulic fracture width h using the above method, a quantitative evaluation of the cement sheath sealing capacity of the CO2 injection well under different injection conditions and cementing quality conditions can be achieved.

[0169] Table 2. Experimental results for evaluating the performance of cement ring seals

[0170]

[0171] Based on the experimental data in Table 2, and the following baseline parameter: β = 3.09 × 10⁻⁶ 4 Given D = 139.7 mm, L = 1000 mm, M = 44 g / mol, and R = 8.314 J / (mol·K), the effects of CO2 viscosity, gas flow rate, and cementing strength on the equivalent hydraulic fracture width h were calculated using the permeability k and the formula for calculating the equivalent hydraulic fracture width h. Figures 2-4 As shown below, the calculation process of the equivalent hydraulic joint width under experimental conditions of 360K temperature, 40MPa pressure, and a cementation index of 0.4 will be used as an example for illustration:

[0172] Substituting the parameters T = 360K and P = 40MPa into formula (13), we obtain the CO2 density ρ:

[0173]

[0174]

[0175]

[0176] V m =55cm 3 / mol

[0177] ρ=44 / V m =0.8g / cm 3

[0178] With parameters T = 360 K, P = 40 MPa, and ρ = 0.8 g / cm³, 3Substituting into equations (5) to (12), we obtain the result for the CO2 viscosity μ:

[0179]

[0180] y = ρV c / 6=0.893.8 / 6 / =12.5

[0181]

[0182]

[0183]

[0184] Ω V = 1.16145 × (1.49) (-0.14874) +0.52487e (-0.77320×1.49) +2.16178e (-2.43787×1.49) =1.318

[0185]

[0186]

[0187] Set parameters T = 360K, P u =1.39MPa, P d =0, Q=111cm 3 / s、V m =55cm 3 / mol, β=3.09×10 4 , D=139.7mm, L=1000mm, ρ=0.8g / cm 3 Substituting μ = 72 μPa·s and a = 348444.82 into formula (20), we obtain the permeability k:

[0188]

[0189]

[0190] k = 4.48 × 10 -10 mm 2

[0191] Set the parameter k = 4.48 × 10 -10 Substituting into equation (22), we obtain the result for the hydraulic joint width h:

[0192]

[0193] Repeat the above steps to obtain the hydraulic gap width under different experimental conditions.

[0194] By evaluating the effects of different CO2 viscosities and gas flow rates on the hydraulic joint width at the cement sheath interface, the specific patterns observed are as follows: as the CO2 viscosity and gas flow rate increase, the hydraulic joint width at the cement sheath interface exhibits a pattern of rapid initial decrease followed by a gradual decrease in the rate of decrease. The influence of changes in gas flow rate is far less than that of CO2 viscosity.

[0195] Cement sheath test specimens were repeatedly fabricated, and a certain internal pressure load was applied inside the casing. After unloading, the cementing index was measured again. This operation was repeated until cement sheath test specimens with the required cementing quality for the experiment were obtained. The experiment and calculations were then repeated to evaluate the effect of different cementing qualities on the hydraulic fracture width at the cement sheath interface. The evaluation results were as follows: as the cementing quality of the cement sheath increased, the hydraulic fracture width at the cement sheath interface decreased rapidly in the initial stage, and then the rate of decrease gradually slowed down. After the cementing index was greater than 0.8, increasing the cementing quality had little effect on the hydraulic fracture width at the interface.

[0196] It should be noted that the embodiments described above are only for explaining the present invention and do not constitute any limitation on the present invention. The present invention has been described with reference to typical embodiments, but it should be understood that the terms used therein are descriptive and explanatory terms, not limiting terms. Modifications can be made to the present invention within the scope of the claims, and revisions can be made to the present invention without departing from the scope and spirit of the present invention. Therefore, the content of the present invention is not limited to the embodiments listed, and any equivalent modifications made to the technical solutions of the present invention by those skilled in the art through reading the present invention specification are covered by the claims of the present invention.

Claims

1. A method for determining the equivalent hydraulic fracture width at the cement sheath interface of a CO2 injection well, characterized in that: Including the following step: S1. Fabricate the cement ring test piece required for the experiment, wherein the cement ring test piece comprises: Cement ring test piece A is used to test the gas flow rate Q at the top of the cement ring under different CO2 viscosity conditions; Cement sheath test piece B is used to test the gas flow rate Q at the top of the cement sheath under different cementing quality conditions; S2. Inject supercritical CO2 generated under certain working conditions into the bottom of the cement ring at the casing to compress and channel the cement ring. S3. After gas leakage through the cement ring, monitor the gas flow rate Q at the top of the cement ring. By adjusting the injected CO2 flow rate, record the pressure of the gas passing through the cement ring under different CO2 gas flow rates. And use a flow meter to record the gas flow rate passing through the cement ring under different injection pressure conditions. S4. Calculate the density of supercritical CO2; S5. For cement ring test piece A, by adjusting the temperature and pressure of the supercritical CO2 generator, obtain supercritical CO2 with different viscosities, calculate the supercritical CO2 viscosity, and record the pressure of gas passing through the cement ring under different CO2 viscosities; repeat step 3 under different CO2 viscosity conditions, adjust the gas injection pressure at the bottom of the cement ring, and record the gas flow rate Q at the top of the cement ring under different CO2 viscosity conditions. For cement sheath test piece B, after obtaining the cement sheath test piece with the cementing quality required for the experiment, repeat steps 2 to 3 and record the gas flow rate Q at the top of the cement sheath under the different cementing quality conditions. S6. Based on the gas flow rate Q at the top of the cement sheath under different CO2 viscosity conditions in step S5, and the gas flow rate Q at the top of the cement sheath under different cementing quality conditions; and the experimental data of cement sheath sealing performance evaluation, the equivalent hydraulic gap width of supercritical CO2 at the cement sheath interface is calculated using the nonlinear Darcy flow formula and combined with the gas state equation. The method for calculating the equivalent hydraulic joint width of supercritical CO2 at the cement ring interface specifically includes: 1) The seepage of supercritical CO2 gas in the cement ring interface satisfies the supercritical CO2 equation of state and the nonlinear Darcy flow formula. 2) Obtain the permeability k of supercritical CO2 gas at the cement ring interface; 3) Based on the permeability k, the expression for the equivalent slit width h can be determined according to the cubic law formula; based on the determined equivalent slit width expression, the value of the equivalent slit width is obtained; The method for obtaining the equivalent seam width specifically includes: Based on the permeability k, the expression for the equivalent slit width h can be determined according to the following cubic law formula, as shown in equation (22): In the formula, ω=πd is the hydraulic circumference; A=πdL is the surface area of ​​the cement ring interface; L is the length of the cement ring interface; h is the equivalent hydraulic joint width; and k is the permeability.

2. The method for determining the equivalent hydraulic fracture width at the cement sheath interface of a CO2 injection well according to claim 1, characterized in that: The cement ring test piece A in step S1 is the original test piece after curing. The acoustic amplitude of the cement ring is tested on the original test piece after curing, and the initial bonding index and bonding strength of the cement ring after curing are calculated. The cement sheath test piece B is the cement sheath acoustic amplitude tested after the test piece has been cured; after calculating the initial cementing index and cementing strength of the cured cement sheath, a certain internal pressure load is applied inside the casing, and after unloading, the cementing index is measured again. This operation is repeated until the cement sheath test piece with the cementing quality required for the experiment is obtained. And / or, The method for preparing the cement ring of the test specimen and completing the curing of the cement ring of the test specimen in step S1 is as follows: Experiments were conducted using a full-size cement ring seal integrity evaluation device. Based on the inner diameter of the device and the outer diameter of the casing at the site, a formation rock ring of the corresponding size was prepared and placed inside the device. Cement slurry is prepared by mixing cement with cement on site and filling the annulus between the casing and the formation annulus with the prepared cement slurry. The cementing quality testing instrument is then placed inside the casing. The poured cement ring is cured for 48 hours, depending on the on-site temperature and pressure.

3. The method for determining the equivalent hydraulic fracture width at the cement sheath interface of a CO2 injection well according to claim 2, characterized in that: The calculation method for the initial bonding index and bonding strength of the cement ring after curing is as follows: The cementing quality testing instrument is used to collect acoustic logging data for testing acoustic amplitude; The cement ring cementing index BI is calculated based on the cementing index formula; the cement ring cementing strength S is calculated based on the cement ring cementing strength formula, which is used to evaluate the cementing quality of the initial cement ring. The formula for the cementation index is: In the formula: BI is the cementation index; A Max The maximum amplitude of the first wave obtained from high-resolution imaging; A E A represents the amplitude of the first wave at the measurement point. min The amplitude value of the first wave obtained at the low gradation point; all the above parameters were measured by a cementing quality testing instrument; The formula for the cement ring bond strength is: in: p=-0.00434T 2 -0.0622T+4.44 (3) α=-21.8723×logU-0.0137×d+49.62 (4) Where: S is the cement bonding strength, MPa; T represents the casing wall thickness, in mm; p is the dimensionless exponent; α is the sound wave attenuation rate, dB / m; d is the outer diameter of the sleeve, in mm; U represents the relative acoustic amplitude value, expressed as a percentage, which is measured by a cementing quality testing instrument. k is a coefficient related to the source distance l. The value of k is given by the source distance, which is the distance between the transmitting transducer and the receiving transducer in the cementing quality tester.

4. The method for determining the equivalent hydraulic fracture width at the cement sheath interface of a CO2 injection well according to claim 1, characterized in that: The method for pressurizing the cement ring in step S2 is as follows: using a full-size cement ring sealing evaluation device and a supercritical CO2 generator, supercritical CO2 generated under certain working conditions is injected into the bottom of the casing cement ring, and the pressure is continuously increased to pressurize the cement ring until gas leakage occurs in the cement ring.

5. The method for determining the equivalent hydraulic fracture width at the cement sheath interface of a CO2 injection well according to claim 1, characterized in that: The method for obtaining the supercritical CO2 density in step S4 is as follows: Based on the Peng-Robinson theory, the density ρ of supercritical CO2 under certain temperature and pressure conditions is obtained using the supercritical CO2 equation of state and density formula: The equation of state for supercritical CO2 is: The density formula is: Where: P is the fluid pressure under equilibrium conditions; T is the fluid temperature under equilibrium conditions; V m The molar volume of supercritical CO2 under these temperature and pressure conditions can be calculated using the supercritical CO2 equation of state (5).

6. The method for determining the equivalent hydraulic fracture width at the cement sheath interface of a CO2 injection well according to claim 1, characterized in that: The method for calculating the supercritical CO2 viscosity under certain temperature and pressure conditions in step S5 is as follows: The viscosity μ of supercritical CO2 under certain temperature and pressure conditions is calculated using the Chung viscosity calculation method. The Chung viscosity calculation formula is as follows: in: T * =1.2593T r (9) In the formula: A1 = 1.16145; B1 = 0.14874; C1 = 0.52487; D1 = 0.7732; E = 2.16178; F1 = 2.43787; F c =1-0.2756ω; The critical parameter for CO2 to transition from the gas phase to the supercritical state is: T c =304.13K P c =7.38MPa, V c = 93.8cm 3 / mol, for CO2, ω=0.2249, M=44g / mol, ρ is the density of supercritical CO2; E1~E 10 The values ​​are as follows: E1=17.662,E2=9.5×10-4,E3=62.455,E4=15.200,E5=21.461,E6=-4.720,E7=25.051,E8=1.048,E9=-0.223,E 10 = 0.

147.

7. The method for determining the equivalent hydraulic fracture width at the cement sheath interface of a CO2 injection well according to claim 1, characterized in that: The method for obtaining the permeability k of supercritical CO2 gas at the cement ring interface includes: The seepage of supercritical CO2 gas in the cement ring interface satisfies the supercritical CO2 equation of state (5) and the nonlinear Darcy flow formula (15), and the supercritical CO2 equation of state (5) is transformed according to the isothermal steady-state flow condition to obtain formula (16). Establish the average pressure formula (17), and substitute the formula (17) into the formula (16) to obtain the average pressure conversion formula (18); Then, by substituting formula (18) into the nonlinear Darcy formula (15), we obtain the pressure gradient transformation formula (19). Finally, by transforming the above formula (19), we can obtain the CO2 gas seepage formula (20); Furthermore, the nonlinear Darcy flow formula (15) is as follows: In the formula: ΔP is the pressure gradient, Q is the annular supercritical CO2 volumetric flow rate, μ is the supercritical CO2 viscosity, and k is the permeability. ρ is the cross-sectional area of ​​the annular supercritical CO2 flow, D is the diameter of the cement ring, d is the diameter of the casing, β is the inertia coefficient, and ρ is the supercritical CO2 density. The supercritical CO2 equation of state (5) is transformed according to the isothermal steady-state flow condition of the gas to obtain the following formula (16): In the formula: V is the average pressure; m Let T be the molar volume of supercritical CO2 under the given temperature and pressure conditions, and T be the supercritical CO2 temperature. And the average pressure The expression can also be represented as: In the formula: P u P d These represent the CO2 injection and discharge pressures of the cement sheath, respectively; the cementing bond strength S = P in step 2. u -P d If P d =0, then S and the injection end pressure P u If they are the same, then: In the formula: L is the length of the cement ring interface; Equation (20) can be rewritten as: In the formula: The data obtained from the experiment and the results calculated based on the experimental data are substituted into equation (21) to obtain the coordinates (x, y) of different points. The coordinates (x, y) of the different points are plotted as a straight line with a slope that is a function of the inertia coefficient β and an intercept that is inversely proportional to the permeability k. The permeability k can be obtained by plotting the line.

8. The method for determining the equivalent hydraulic fracture width at the cement sheath interface of a CO2 injection well according to claim 1, characterized in that: The equivalent hydraulic fracture width of supercritical CO2 at the cement sheath interface obtained through steps S1-S6 can be used to evaluate the influence of different CO2 viscosities and gas flow rates on the hydraulic fracture width at the cement sheath interface; or to evaluate the influence of different cementing qualities on the hydraulic fracture width at the cement sheath interface.

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