A calculation method for interlayer gas channeling based on the heat release of cement slurry hydration

Abstract

The present invention discloses a calculation method for interlayer gas channeling based on the hydration heat release of cement slurry, which relates to the field of well cementing in oil exploitation. The present invention considers the influence of the hydration heat effect during the waiting period of the cement slurry on the gas seepage mechanism, and then establishes an interlayer gas channeling model, determines the boundary conditions and initial conditions of the model, obtains the pore pressure in the cement slurry matrix, so as to estimate the gas migration speed and the critical distance of gas channeling in the early stage of cement slurry solidification, and can accurately judge the gas channeling prevention ability of the cement slurry.

Description

Technical Field

[0001] The present invention relates to the field of well cementing in oil exploitation, and particularly to a calculation method for interlayer gas channeling based on the heat release of cement slurry hydration. Background Art

[0002] Well cementing has the characteristics of large investment, high risk, short operation time, one-time operation, and strong systematicness. Its main purpose is to conduct effective interlayer isolation, consolidate the achievements of drilling technology, and ensure the safe exploitation of oil and gas resources. However, during the setting period of the well cementing slurry, due to the weight loss caused by the heat release of the cement slurry hydration, the pore pressure decreases. When the weight loss of the pore pressure is lower than the gas layer pressure, the gas in the formation will channel into the annulus, and then interlayer cross-channeling will occur. Seriously, it will contaminate the oil and gas layers and reduce the recovery rate of oil and gas. Therefore, the gas channeling prevention ability under the condition of the heat release of the cement slurry during the setting period is an important factor affecting the evaluation of well cementing in oil and gas wells.

[0003] The essence of gas channeling in the cement slurry body is a physical process in which gas flows from a high-pressure formation to a low-pressure formation under the driving action of a pressure difference. Whether gas interlayer channeling occurs depends on whether the critical gas channeling distance exceeds the interlayer distance of the formation. It is generally believed that the characteristics of the cement slurry during the setting period are important factors affecting gas channeling, and the heat release of the cement slurry hydration is the key factor affecting the performance of the cement slurry during the setting period. The temperature rise during the heat release of the cement slurry hydration affects the permeability, porosity, and static gel strength of the slurry body performance, and thus affects the gas channeling distance of the cement slurry.

[0004] Currently, there is little research on the influence of the heat release of cement slurry hydration on interlayer gas channeling. The existing research mainly focuses on the analysis of the influence of the characteristics of the cement slurry during the setting period of well cementing on interlayer gas channeling. The article "Research on the Mechanism of Annular Pressure Build-up Based on the Performance of Cement Slurry System" mainly established a gas interlayer channeling model and effectively evaluated the gas channeling prevention ability of the cement slurry. However, during the setting period of the cement slurry, the matrix temperature of the cement slurry continuously changes under the action of hydration, affecting parameters such as the permeability, porosity, and static gel strength of the cement slurry; at the same time, the temperature change also affects the gas compressibility factor, viscosity, etc. And the existing method is to analyze the influence of the heat release on the slurry matrix, and at the same time, it does not analyze the influence of the wellbore temperature on the gas properties, which makes it difficult to accurately and effectively apply this calculation method to practice. Summary of the Invention

[0005] Aiming at the above deficiencies in the prior art, a calculation method for interlayer gas channeling based on the heat release of cement slurry hydration provided by the present invention solves the problem that the existing calculation methods for interlayer gas channeling are difficult to obtain accurate and effective calculation results.

[0006] In order to achieve the above invention purpose, the technical solution adopted by the present invention is as follows:

[0007] Provided is a calculation method for interlayer gas channeling based on the heat release of cement slurry hydration, which includes the following steps:

[0008] S1. Construct an annulus cement slurry heat conduction model according to the cementing design parameters and geological design parameters, and perform discrete processing on the annulus cement slurry heat conduction model to obtain a discrete heat conduction model;

[0009] S2. According to the initial conditions and the initial temperature of the cement slurry during the waiting-for-hardening period, use the finite difference method to solve the discrete heat conduction model to obtain the temperature of each region of the cement slurry at each time node during the waiting-for-hardening period;

[0010] S3. Construct a pore pressure calculation model in the cement slurry matrix and perform discrete processing to obtain a discrete pore pressure calculation model;

[0011] S4. According to the initial conditions and boundary conditions, use the finite difference method to solve the discrete pore pressure calculation model to obtain the pore pressure of each region of the cement slurry at each time node during the waiting-for-hardening period;

[0012] S5. Obtain the pore pressure at the next moment according to the pore pressure of each region of the cement slurry at each time node during the waiting-for-hardening period, and judge whether the difference between the pore pressure at the next moment and the preset pore pressure in the cement slurry matrix is less than or equal to the preset accuracy. If so, enter step S7; otherwise, enter step S6;

[0013] S6. Update the preset pore pressure in the cement slurry matrix with the average value of the preset pore pressure in the cement slurry matrix and the pore pressure at the next moment, and return to step S5;

[0014] S7. Update the pore pressure in the cement slurry matrix with the pore pressure at the next moment, and combine with the one-dimensional Darcy seepage equation to calculate and obtain the gas channeling distance;

[0015] S8. Judge whether the gas channeling distance is greater than or equal to the average interlayer distance of the formation. If so, it is determined that the possibility of interlayer gas channeling is relatively large; otherwise, it is determined that the possibility of interlayer gas channeling is relatively small.

[0016] Further, the expression of the annulus cement slurry heat conduction model in step S1 is:

[0017]

[0018] Where T c is the annulus cement slurry temperature; T a is the casing wall temperature during waiting for hardening; λ m is the casing heat conduction coefficient; λ c is the heat conduction coefficient of the cement slurry in the annulus; ρ m is the cement slurry density; r1 is the inner diameter of the casing; r2 is the inner diameter of the cement sheath; r3 is the inner diameter of the wellbore wall; T wis the wellbore temperature during setting; Q ∞ is the final heat of hydration of the cement slurry; c c is the specific heat capacity of the cement; α is the heat of hydration of the cement slurry; λ w is the heat conduction coefficient of the wellbore; t represents time.

[0019] Furthermore, the expression of the pore pressure calculation model in the cement slurry matrix in step S3 is:

[0020]

[0021] where p is the pore pressure; Z is the cement slurry compression factor; C(p) is the isothermal compressibility; φ(x,t) is the porosity; t represents time; x is the axial distance of the cement slurry; k(t) is the permeability at time t; μ(p) is the gas viscosity.

[0022] Furthermore, the initial conditions in step S4 are:

[0023] When the critical static gel strength is less than or equal to 48 Pa:

[0024]

[0025] When the critical static gel strength is greater than 48 Pa:

[0026]

[0027] where p d is the pressure at the top of the cement slurry column; ρ m is the density of the cement slurry; g is the acceleration due to gravity; L is the height of the cement slurry column; SGS c is the critical static gel strength; x is the axial distance of the cement slurry; d w is the wellbore diameter; d c is the casing diameter; p(x,t1) is the transient pore pressure of the cement slurry at the beginning of gas channeling.

[0028] Furthermore, the preset precision value in step S5 is 1×10 -3 .

[0029] Furthermore, the expression of the one-dimensional Darcy seepage equation in step S7 is:

[0030]

[0031]

[0032] where u(x,t) is the gas channeling velocity at time t; k(t) is the permeability at time t; μ(p) is the gas viscosity; φ(x,t) is the porosity; p(x,t) is the transient pore pressure of the cement slurry; t represents time; S(t) is the gas channeling distance; k(τ) is the permeability at time τ; and t1 is the start time of gas channeling.

[0033] The beneficial effects of the present invention are as follows:

[0034] 1. The present invention fully considers the influence of the heat of hydration during the setting period on the porosity and static gel strength of the cement slurry; at the same time, it considers the influence of the annulus temperature on the gas physical property parameters during the hydration of the cement slurry. Based on these as the calculation conditions, the simulation process is closer to the actual conditions, and the simulation results have better feasibility.

[0035] 2. The present invention linearizes and discretizes the complex cement slurry pore pressure equation and then uses the iterative method to solve it. It has the characteristics of high calculation efficiency and good convergence effect, can quickly obtain the cement slurry pore pressure distribution, and then judge the gas channeling distance of the cement slurry. Description of the Drawings

[0036] Figure 1 is a schematic flow diagram of this method;

[0037] Figure 2 is a schematic diagram of the wellbore structure of the present invention and a schematic diagram of the fluid distribution in the annulus;

[0038] Figure 3 is a diagram showing the distribution of the gas channeling distance over time under the conditions of considering and not considering the heat release during hydration of the present invention. Detailed Embodiments

[0039] The following describes the detailed embodiments of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the detailed embodiments. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

[0040] As Figure 1 shown, the calculation method for interlayer gas channeling based on the heat release during the hydration of the cement slurry includes the following steps:

[0041] S1. Construct an annulus cement slurry heat conduction model according to the cementing design parameters and geological design parameters, and perform discrete processing on the annulus cement slurry heat conduction model to obtain the discrete heat conduction model;

[0042] S2. According to the initial conditions and the initial temperature of the cement slurry during the waiting-on-set period, use the finite difference method to solve the discretized heat conduction model to obtain the temperature at each time node in each region of the cement slurry during the waiting-on-set period;

[0043] S3. Construct a pore pressure calculation model in the cement slurry matrix and perform discretization to obtain the discretized pore pressure calculation model;

[0044] S4. According to the initial conditions and boundary conditions, use the finite difference method to solve the discretized pore pressure calculation model to obtain the pore pressure at each time node in each region of the cement slurry during the waiting-on-set period;

[0045] S5. Obtain the pore pressure at the next moment based on the pore pressure at each time node in each region of the cement slurry during the waiting-on-set period, and determine whether the difference between the pore pressure at the next moment and the pre-set pore pressure in the cement slurry matrix is less than or equal to the preset accuracy. If so, go to step S7; otherwise, go to step S6;

[0046] S6. Update the pre-set pore pressure in the cement slurry matrix with the average value of the pre-set pore pressure in the cement slurry matrix and the pore pressure at the next moment, and return to step S5;

[0047] S7. Update the pore pressure in the cement slurry matrix with the pore pressure at the next moment, and combine with the one-dimensional Darcy seepage equation to calculate the gas channeling distance;

[0048] S8. Determine whether the gas channeling distance is greater than or equal to the average interlayer distance of the formation. If so, it is determined that the possibility of interlayer gas channeling is relatively large; otherwise, it is determined that the possibility of interlayer gas channeling is relatively small.

[0049] The expression of the heat conduction model of the annulus cement slurry in step S1 is:

[0050]

[0051] where T c is the temperature of the annulus cement slurry; T a is the temperature of the casing wall during the waiting-on-set period; λ m is the thermal conductivity of the casing; λ c is the thermal conductivity of the cement slurry in the annulus; ρ m is the density of the cement slurry; r1 is the inner diameter of the casing; r2 is the inner diameter of the cement sheath; r3 is the inner diameter of the wellbore wall; T w is the temperature of the wellbore wall during the waiting-on-set period; Q ∞ is the final heat of hydration of the cement slurry; c c is the specific heat capacity of the cement; α is the heat of hydration of the cement slurry; λ w is the thermal conductivity of the wellbore wall; t represents time.

[0052] In step S2, the finite difference method is used to solve the discretized heat conduction model, and the expression for the temperature of each region of the cement slurry at each time node during the waiting for setting period is as follows:

[0053]

[0054] Where is the transient temperature of the cement slurry at the n+1th moment and the jth position; is the transient temperature of the cement slurry at the nth moment and the jth position; Δt is the time step; is the temperature of the casing wall at the nth moment and the jth position; is the temperature of the wellbore wall at the nth moment and the jth position; is the degree of hydration at the n+1th moment and the jth position; is the degree of hydration at the nth moment and the jth position.

[0055] The expression of the pore pressure calculation model in the cement slurry matrix in step S3 is:

[0056]

[0057] Where p is the pore pressure; Z is the cement slurry compression factor; C(p) is the isothermal compressibility; φ(x,t) is the porosity; t represents time; x is the axial distance of the cement slurry; k(t) is the permeability at the tth moment; μ(p) is the gas viscosity.

[0058] The initial conditions in step S4 are:

[0059] When the critical static gel strength is less than or equal to 48 Pa:

[0060]

[0061] When the critical static gel strength is greater than 48 Pa:

[0062]

[0063] Where p d is the pressure at the top of the cement slurry column; ρ m is the density of the cement slurry; g is the acceleration due to gravity; L is the height of the cement slurry column; SGS c is the critical static gel strength; x is the axial distance of the cement slurry; d w is the wellbore diameter; d c is the casing diameter; p(x,t1) is the transient pore pressure of the cement slurry at the beginning of gas channeling.

[0064] The specific method of step S4 is:

[0065] The pore pressure calculation model is simplified to:

[0066]

[0067] Among them

[0068] The discretized pore pressure calculation model is solved using the finite difference method:

[0069]

[0070] Among them is the pore pressure of the cement slurry at the position j - 1 at the (n + 1)-th moment; is the pore pressure of the cement slurry at the position j at the (n + 1)-th moment; is the pore pressure of the cement slurry at the position j + 1 at the (n + 1)-th moment; k is the permeability; m is an intermediate parameter, is the average value of the m value at the position j + 1 and the m value at the position j at the (n + 1)-th moment; is the average value of the m value at the position j and the m value at the position j - 1 at the (n + 1)-th moment; is the pore pressure of the cement slurry at the position j at the n-th moment; is the pore pressure of the cement slurry at the position j + 1 at the n-th moment; is the pore pressure of the cement slurry at the position j - 1 at the n-th moment.

[0071] The preset precision value in step S5 is 1×10 -3 .

[0072] In step S6, when actually presetting the pore pressure, the pore pressure of the previous moment is selected. Considering the change trend of the pore pressure in the cement slurry matrix, the average value of the preset value and the calculated value is gradually calculated, that is, the update operation is completed.

[0073] In step S7, the pore pressure of the next moment calculated in step S5 is used as the pore pressure in the cement slurry matrix. The expression of the one-dimensional Darcy seepage equation in step S7 is:

[0074]

[0075]

[0076] where u(x, t) is the gas channeling velocity at time t; k(t) is the permeability at time t; μ(p) is the gas viscosity; φ(x, t) is the porosity; p(x, t) is the transient pore pressure of the cement slurry; t represents time; S(t) is the gas channeling distance; k(τ) is the permeability at time τ; t1 is the start time of gas channeling.

[0077] In an embodiment of the present invention, the initial conditions of this solution are preferably:

[0078] ①Wellbore conditions: actual wellbore structure, casing size, well diameter;

[0079] ②Fluid properties: densities and rheological parameters of drilling fluid, spacer fluid, and cement slurry, as well as cement slurry permeability, static gel strength, porosity, and degree of hydration, etc.;

[0080] ③Formation conditions: surface temperature, geothermal gradient, formation pressure, gas production volume under different pressure differences, etc.

[0081] In an embodiment of the present invention, the axial step Δh and the time step Δt of the wellbore can be obtained, and the axial grid number and the time grid number of the wellbore can be determined respectively based on their steps. Among them, the axial step is less than 5% of the well depth; the time step is 1 min.

[0082] In an embodiment of the present invention, the cement slurry temperature distribution obtained according to the transient heat transfer model of the cement slurry is used to obtain the gas compressibility factor and the gas viscosity

[0083] The calculation model of gas physical property parameters is:

[0084] Viscosity:

[0085]

[0086] where M g is the molar mass;

[0087] The gas compressibility factor is obtained by solving the following two equations simultaneously:

[0088]

[0089]

[0090] where p d is the formation pressure, MPa; p l is the gas critical pressure, MPa; ρ r is the apparent density of the gas, Kg / m 3 ; T l is the gas critical temperature, °C.

[0091] In an embodiment of the present invention, as Figure 2 shown, taking a high-pressure gas well in a certain block as an example, it successively includes the following steps:

[0092] (1) According to the cementing design and geological design, obtain the properties of the cement slurry and the annulus working fluid, surface temperature, formation temperature, and wellbore structure. The well depth is 4403 m, the main gas layer is at 4277 - 4396 m, and the density of the drilling fluid is 2210 Kg / m3 , the density of the spacer fluid is 2220 Kg / m 3 , the density of the cement slurry is 2240 Kg / m 3 , when the thickening time is 202 min, the static gel strength is 48 Pa, the permeability of the cement slurry is 134.16 mD, the degree of hydration is 0.1, when the static gel strength is 240 Pa, the permeability of the cement slurry is 72.91 mD, the degree of hydration is 0.505, the transition time of the static gel strength is 89 min, the formation pressure and temperature are 95 MPa and 116 °C respectively, the wellhead and the temperature at the top of the cement slurry column are 23.4 °C and 108 °C respectively, the wellbore diameter is 0.2159 m, the casing diameter is 0.1778 m, the casing wall thickness is 12.7 mm, the drilling depth is 4403 m, the cemented interval is 4000 m - 4403 m, and the length of the cemented section is 403 m;

[0093] (2) Determine the axial and time step lengths. The axial step length is 20 m, and the time step length is 60 s;

[0094] (3) According to the established model above, set the transient temperature change value of the cement slurry and the pore pressure change value within the cement slurry matrix

[0095] (4) Take the axial node j as the outer loop condition and the time node n as the inner loop condition, and discretize the degree of hydration, transient temperature, and pore pressure of each part of the cement slurry;

[0096] (5) Obtain the degree of hydration at the time node n and the spatial node j according to the hydration kinetics model Combine with the cement slurry heat transfer model to obtain the temperature distribution of the cement slurry and obtain the gas compressibility and viscosity According to the pre-set pore pressure Obtain the pore pressure at the (n + 1)th moment If is less than the set accuracy range (δ = 1×10 -3 ), that is then stop the calculation, otherwise continue to go back to (5) for iterative calculation.

[0097] (6) Obtain the pore pressure distribution characteristics within the cement slurry matrix;

[0098] (7) Calculate the gas channeling velocity according to the one-dimensional Darcy seepage equation, and then obtain the gas channeling distance, and compare it with the average formation layer spacing to judge whether interlayer channeling will occur in this well.

[0099] Using this method, the interlayer gas channeling distance under the condition of considering heat release during hydration is obtained, as shown in Figure 3As shown in the figure, by comparing the interlayer gas channeling distance obtained by considering the hydration heat release condition in this solution with the interlayer gas channeling distance without considering the hydration heat release condition, it can be seen that the starting time of gas channeling under the hydration heat release of the cement slurry in this solution is earlier than that without considering the hydration condition, and the interlayer gas channeling distance is smaller than that without considering the hydration condition. Therefore, if the original formation temperature is used as the condition to judge whether interlayer gas channeling occurs, this temperature is lower than the actual downhole environment, which has an adverse effect on judging whether interlayer gas channeling occurs. If the occurrence of interlayer gas channeling is judged considering the hydration heat release of the cement slurry, this temperature condition meets the downhole working conditions, and the interlayer gas channeling distance under the actual working conditions can be obtained, thereby improving the accuracy of the evaluation of the gas channeling prevention ability of the cement slurry.

[0100] In summary, the present invention considers the influence of the hydration heat effect during the setting period of the cement slurry on the gas seepage mechanism, thereby establishing an interlayer gas channeling model, determining the boundary conditions and initial conditions of the model, obtaining the pore pressure in the cement slurry matrix, so as to estimate the gas migration speed and the critical gas channeling distance in the early stage of cement slurry solidification, and can accurately judge the gas channeling prevention ability of the cement slurry.

Claims

1. A calculation method for interlayer gas channeling based on the heat release of cement slurry hydration, characterized in that, It includes the following steps: S1. Construct an annulus cement slurry heat conduction model according to the cementing design parameters and geological design parameters, and discretize the annulus cement slurry heat conduction model to obtain the discretized heat conduction model; S2. Solve the discretized heat conduction model by using the finite difference method according to the initial conditions and the initial temperature of the cement slurry during the waiting-for-cementing period to obtain the temperature of each region of the cement slurry at each time node during the waiting-for-cementing period; obtain the gas viscosity according to the temperature of each region of the cement slurry at each time node during the waiting-for-cementing period; wherein the gas viscosity is used to solve the one-dimensional Darcy seepage equation and the pore pressure calculation model in the cement slurry matrix; S3. Construct a pore pressure calculation model in the cement slurry matrix and perform discretization to obtain the discretized pore pressure calculation model; S4. Solve the discretized pore pressure calculation model by using the finite difference method according to the initial conditions and boundary conditions to obtain the pore pressure of each region of the cement slurry at each time node during the waiting-for-cementing period; S5. Obtain the pore pressure at the next moment according to the pore pressure of each region of the cement slurry at each time node during the waiting-for-cementing period, and judge whether the difference between the pore pressure at the next moment and the pre-set pore pressure in the cement slurry matrix is less than or equal to the pre-set accuracy. If so, go to step S7; otherwise, go to step S6; S6. Update the pre-set pore pressure in the cement slurry matrix with the average value of the pre-set pore pressure in the cement slurry matrix and the pore pressure at the next moment, and return to step S5; S7. Update the pore pressure in the cement slurry matrix with the pore pressure at the next moment, and combine with the one-dimensional Darcy seepage equation to calculate and obtain the gas channeling distance; S8. Judge whether the gas channeling distance is greater than or equal to the average interlayer distance of the formation. If so, it is determined that the possibility of interlayer gas channeling is relatively large; otherwise, it is determined that the possibility of interlayer gas channeling is relatively small.

2. The calculation method for interlayer gas channeling based on the heat release of cement slurry hydration according to claim 1, wherein The expression of the annulus cement slurry heat conduction model in step S1 is: ； wherein is the temperature of the annulus cement slurry; is the temperature of the casing wall during setting; is the thermal conductivity of the casing; is the thermal conductivity of the cement slurry in the annulus; is the density of the cement slurry; is the inner diameter of the casing; is the inner diameter of the cement sheath; is the inner diameter of the wellbore wall; is the temperature of the wellbore wall during setting; is the final heat of hydration of the cement; is the specific heat capacity of the cement; is the heat of hydration of the cement slurry; is the thermal conductivity of the wellbore wall; t represents time.

3. The interlayer gas channeling calculation method based on the heat release of cement slurry hydration according to claim 1, wherein The expression of the pore pressure calculation model in the cement slurry matrix in step S3 is: ； wherein is the pore pressure; is the cement slurry compression factor; is the isothermal compressibility; is the porosity; t represents time; is the axial distance of the cement slurry; is the permeability at time t; is the gas viscosity.

4. A calculation method for interlayer gas channeling based on the heat release of cement slurry hydration according to claim 1, characterized in that The initial conditions in step S4 are: When the critical static gel strength is less than or equal to 48 Pa: ； When the critical static gel strength is greater than 48 Pa: ； wherein is the pressure at the top of the cement slurry column; is the density of the cement slurry; g is the acceleration due to gravity; is the height of the cement slurry column; is the critical static gel strength; is the axial distance of the cement slurry; is the wellbore diameter; is the casing diameter; is the transient pore pressure at the start of gas channeling of the cement slurry.

5. A calculation method for interlayer gas channeling based on the heat release of cement slurry hydration according to claim 1, characterized in that, The preset precision value in step S5 is .

6. The interlayer gas channeling calculation method based on the heat release of cement slurry hydration according to claim 1, characterized in that, The expression of the one-dimensional Darcy seepage equation in step S7 is: ； ； Among them is the gas channeling velocity at time t; is the permeability at time t; is the gas viscosity; is the porosity; is the transient pore pressure of the cement slurry; t represents time; is the gas channeling distance; is the permeability at time is the gas channeling start time.

Images