Research on the influence of heat release from cement hydration on the mechanical properties of casing

In order to study the influence of cement hydration heat release on the mechanical properties of casing, this paper calculates the wellbore temperature and pressure field based on the mathematical model of steady-state heat conduction of casing-cement ring-formation rock, establishes a mathematical model for the mechanical evaluation of cement hydration heat release and casing interaction, and performs finite element calculation and experimental simulation of the effect of cement hydration heat release on casing loss, and the results show that the results show: Along the axial direction of the wellbore, the maximum stress on the entire cement ring occurs in the lower position of the cement ring, and the maximum deformation on the casing occurs in the middle position. The axial stress variation range of the middle part of the casing is 50MPa, and the strain is 0.12%; The axial stress variation range of the outer ring is 235MPa, and the strain is 0.09%; The circumferential stress of the middle part varies from 500MPa to 0.255%. It is found that the stress and strain in the middle part of cement sheath are large, and yield is prone to occur. Under the action of cement hydration heat release, the long-axis elliptical deformation of (7.15∼31.8) mm occurs in the casing, that is, a large ovality is produced, which weakens the collapse strength of the casing. Two repeated tests showed that under the cement hydration heat release condition at the casing loss position, the temperature change of 60°C caused the increase of axial force of casing column and the increase of annular air pressure, which caused the non-uniform deformation of casing under the composite load of external extrusion and compression axial force.


Introduction
In recent years, with the development of high temperature and high pressure wells, the influence of temperature on the performance of casing has attracted more and more attention, studies have shown that compared with normal temperature, the decrease in tensile strength of casing is within 5% at 200 °C, the decline of yield strength is within 10%, with the reduction of yield strength, the bearing capacity of casing will inevitably change, if still designed with rated strength, the safety factor will be reduced.At present, there are many studies on the influence of mechanical properties of casing under high temperature conditions, Lu Y.H et al. [1][2][3] conducted a triaxial test on cement samples under high temperature and high pressure conditions, and scanned the cement samples with scanning electron microscopy to analyze their microscopic damage mechanism.The fracturing process of casing wells was simulated with finite elements, and the integrity of the casing-cement-formation system was analyzed.Agofack N et al. [4][5][6][7][8] used an improved discrete element method (MDEM) to study isotropic and anisotropic boundary stresses using real cement and formation properties for the effect of thermal loading on casing.The results show that in addition to casing pressure difference, other parameters such as casing pressure, boundary stress, cement and rock properties also affect the

Mathematical and mechanical model of casing under non-uniform load
During the cementing process, after the cement slurry is in place, a large amount of heat is released instantaneously after the cement is hydrated, and when the quality of the on-site cementing is not good, there is a trap space in the annular space, and the temperature increase causes the annular liquid between the closed casings to expand, forming the annular trap pressure.Under the condition of heat release, local high pressure is formed in the trapping space position, the force of the casing changes, and the strength of the casing is low, which is bound to cause problems in the casing.In addition, the cement hydration temperature rises, resulting in an increase in the trapping pressure and an increase in the compression load of the fixed casing at both ends, resulting in the collapse failure and buckling failure of the casing, as shown in Fig. 1.Fig. 1   (1) The heat transfer of the upper and lower surfaces of the analyzed layer is not considered, and only the radial heat transfer of the wellbore is considered; (2) The steam is directly injected into the oil pipe, and the heat exchange is evenly carried out with the oil pipe, and the temperature of the inner surface of the oil pipe is consistent; (3) There is no eccentricity in the tubing and casing, and it is centered in the well; (4) The sealing between the casing, cement ring and the formation is good, and there is no channeling phenomenon.Based on the mathematical model of steady-state heat conduction of casingcement ring-formation rock, the wellbore temperature and pressure field was calculated, and the casing heat conduction temperature model was shown in Fig. 3 and Fig.

Mathematical model of temperature field and stress
The temperature field control equation of circulating medium in the wellbore is considered as an axisymmetric transient convection-conduction equation [18]: Boundary conditions: T T = Boundaries of a given temperature value, such as circulating medium inlet, distant boundaries, etc.
Exchange boundary conditions, such as initial media outlet, initial conditions The temperature value at the initial moment at any point in the wellbore (t=0) is the ground temperature value.

Thermal stress generated on the casing
Casing thermoelastic strain differential equation [18]: For axisymmetric and plane strain problems, there are: For definite solution problems: For general solutions: Complete solution: ( ) For good cementing quality, and when the casing pressure increases to zero, there are: 0, 0 The thermal yield of the casing under triaxial stress is calculated by the Von Mises equiforce (i.e. the fourth strength theory in materials mechanics) with the expression: When vm σ the yield limit of the material is exceeded y σ , plastic deformation occurs in the casing.
During hydration and heat release, the yield strength of the casing material also changes due to a change in temperature, its expression: In the formula, Φthermoelastic displacement potential energy; ∇2-Laplace operator; µ-Poisson's ratio; a-casing inner diameter; As -casing cross-sectional area; b-casing outer diameter; E-casing material Yang touch; F-axial load of casing before hydration heat release; Pa-casing pressure during hydration and heat release; Pb-the external pressure of the casing during hydration and heat release; ∆Pa-the increase value of casing internal pressure during hydration heat release; ∆Pb-the growth value of the external pressure of the casing during hydration and heat release; T-casing temperature; ∆T-casing temperature change value; αcoefficient of thermal expansion of the casing; ε-Thermal strain; σa-casing axial stress; σr-casing radial stress; σθcasing circumferential stress; ∆σcasing thermal stress; ∆σa-The value of the increase in axial stress of casing during hydration and heat release.

Local stress changes under temperature load
Due to the change of local temperature field caused by the hydration and exothermic process, high shear and radial stresses are generated in the formation, and this stress change will cause shear or tensile failure of the rock around the borehole, thereby damaging the casing.When the temperature of the casing changes, its strain consists of two parts, one is caused by the in-situ stress and the other is caused by the temperature change.According to Generalized Hooke's Law, there are: ) Assuming that the rock is isotropic, when the temperature changes, the formation can quickly transfer and consume the vertical stress change caused by temperature, so that the vertical principal stress remains in balance with the gravity of the overlying rock layer.Since the reservoir boundary can be regarded as infinity, its lateral deformation is constrained, the lateral strain caused by temperature change can be regarded as zero, and the horizontal in-situ stress caused by temperature can be changed to: 1

Determination of test boundary conditions
Based on the transient heat transfer theory and the experimental value of cement hydration heat release (according to the recommended parameter of cement hydration heat of cement 274,468J/kg), the transient temperature field change of the wellbore in the process of graded cementing was calculated, so as to determine the boundary conditions of the test: The simulated well depth is 4594m, and the 244.48*11.99mm*HS110-BCcasing is produced by Henggang, and the initial force is applied: -898kN, and the final force: -1918k; Initial temperature: 80°C, final temperature: 140°C; Initial external pressure applied: 2.8 MPa, final pressure: 43.15 MPa.

Analysis of sleeve loss finite element calculation results for non-uniform load 3.2.1. Test process and results.
The main instrument of the test is the casing-cement ring system test device of oil and gas well, and its schematic diagram is shown in Fig. 5, which can realize the service performance simulation of casing-cement ring in non-uniform external extrusion, shearing, axial tension, bending, internal pressure, high temperature and other composite load conditions, and the mechanical load data can be monitored and stored in real time.
The main parameters of the test device are shown in Fig. 5 This experimental specimen involves 4 welds (sealing tube, casing and flange, casing + plug), all of which are carried out by argon arc welding, arc welding and heat treatment to ensure the integrity of the pressure seal, as shown in Fig. 6, the total length of the specimen is 4.3m, the total weight is 910kg, this experiment also involves a pressure control system, a dynamic stress-strain detection system, and a temperature control system for the recording of key data during the experiment.

Test system establishment.
The sample is mounted to the test bench (oil and gas well casingcement ring system test device) -connected pressure device (pressure control system) -connected heating device (temperature control system), as shown in Fig. 7. Grind the casing body, clean and paste the position of the strain gauge tube body, the strain gauge is resistant to high temperature, and connect the stress and strain monitoring device (dynamic stress strain detection system).In order to observe the inner and outer deformation of the casing more intuitively, the section 3, section 4 and section 5 are cut, and the deformation photos of the casing before and after cutting are shown in Fig. 9 and Fig. 10, after cutting the sealed tube, it is found that the casing has obvious non-uniform radial necking deformation, and the deformation of the casing is detected and the deformation data is measured, and the data of the measurement position is shown in Table 1.Referring to the data in Table 1, compared with the casing before denaturation, under the action of cement hydration heat release, the long-axis ellipse deformation of (7.15~31.8)mm occurred in the casing, that is, a large ovality was produced, which weakened the collapse strength of the casing.As shown in Fig. 11, nine strain gauges are installed in three cross-sections, two axial and two radial, with a sampling frequency of 10 / s, and a total of 360,000 data are collected.From the stress-strain curve of Fig. 12, the axial stress change range of the middle part is 50MPa, and the strain is 0.12%; the axial stress variation range of the outer ring is 235MPa, and the strain is 0.09%; the circumferential stress of the middle part varies from 500MPa to 0.255%.From the graph, it is found that the stress and strain in the middle part are large, and yield is prone to occur.By finite element calculation, the rock stress distribution in the near well area is shown in Fig. 13, the wellbore at the end of cement hydration heat release-Stratigraphic temperature distribution cloud.Along the axial direction of the wellbore, the maximum stress generated on the entire cement ring is 18.57MPa, and the maximum stress occurs in the lower position of the cement ring, and the upper stress in the cement ring is small, especially the middle stress is 1.558MPa.Due to the hydration and heat release of cement, the temperature in the wellbore rises, so that the casing instantaneous temperature rises, so that the casing has a variety of possible forms of failure, such as thermal stress failure or buckling failure.The peak equivalent force on the casing is 788.1MPa, and the maximum deformation on the casing occurs in the middle position, with small upper and lower stresses and few areas of high stress.

Summary
(1) Along the axial direction of the wellbore, the maximum stress on the entire cement ring occurs in the lower position of the cement ring, the upper stress in the cement ring is small, the maximum deformation on the casing occurs in the middle position, the upper and lower stresses are small and there are few high stress areas.
(2) From the stress-strain curve of casing after the test, the axial stress change range of the middle part is 50MPa, the strain is 0.12%; the axial stress change range of the outer ring part is 235MPa, the strain is 0.09%; the circumferential stress change range of the middle part is 500MPa, and the strain is 0.255%.From the graph, it is found that the stress and strain in the middle part are large, and yield is prone to occur.
(3) After the completion of the test, the deformation of the casing in the cement hydration heat release casing was analyzed, and under the action of cement hydration heat release, the long-axis elliptical deformation of (7.15 mm ~31.8 mm) occurred in the casing, that is, a large ovality was produced, which weakened the collapse strength of the casing.
(4) Two repeated tests show that under the cement hydration heat release condition at the casing loss position, the temperature change of 60°C causes the increase of the axial force of the casing column and the increase of the annular air pressure, which causes the non-uniform deformation of the casing under the composite load of external extrusion and compression axial force.

Figure 1 .
Figure 1.Logging and fault location resultsThe most serious diameter reduction of the abnormal casing well section: depth 4594.86m(as shown in Fig.2a), depth 4770m (as shown in Fig.2b), maximum diameter 224mm, minimum diameter 217.4mm, average 219.5mm.The casing temperature changes with well depth at different times, as shown in Fig.2.

Figure 2 .
Figure 2. Temperature of the set of damage points over time In the process of coupled transient analysis of wellbore thermal stress, the following basic assumptions are based:(1) The heat transfer of the upper and lower surfaces of the analyzed layer is not considered, and only the radial heat transfer of the wellbore is considered;(2) The steam is directly injected into the oil pipe, and the heat exchange is evenly carried out with the oil pipe, and the temperature of the inner surface of the oil pipe is consistent;(3) There is no eccentricity in the tubing and casing, and it is centered in the well;(4) The sealing between the casing, cement ring and the formation is good, and there is no channeling phenomenon.Based on the mathematical model of steady-state heat conduction of casingcement ring-formation rock, the wellbore temperature and pressure field was calculated, and the casing heat conduction temperature model was shown in Fig.3and Fig. 4. Fig. 4 (a) is the schematic diagram of annular air fluid unit control body, Fig. 4 (a) is the schematic diagram of casing unit control body.

4
Figure 2. Temperature of the set of damage points over time In the process of coupled transient analysis of wellbore thermal stress, the following basic assumptions are based:(1) The heat transfer of the upper and lower surfaces of the analyzed layer is not considered, and only the radial heat transfer of the wellbore is considered;(2) The steam is directly injected into the oil pipe, and the heat exchange is evenly carried out with the oil pipe, and the temperature of the inner surface of the oil pipe is consistent;(3) There is no eccentricity in the tubing and casing, and it is centered in the well;(4) The sealing between the casing, cement ring and the formation is good, and there is no channeling phenomenon.Based on the mathematical model of steady-state heat conduction of casingcement ring-formation rock, the wellbore temperature and pressure field was calculated, and the casing heat conduction temperature model was shown in Fig.3and Fig. 4. Fig. 4 (a) is the schematic diagram of annular air fluid unit control body, Fig. 4 (a) is the schematic diagram of casing unit control body.
Figure 2. Temperature of the set of damage points over time In the process of coupled transient analysis of wellbore thermal stress, the following basic assumptions are based:(1) The heat transfer of the upper and lower surfaces of the analyzed layer is not considered, and only the radial heat transfer of the wellbore is considered;(2) The steam is directly injected into the oil pipe, and the heat exchange is evenly carried out with the oil pipe, and the temperature of the inner surface of the oil pipe is consistent;(3) There is no eccentricity in the tubing and casing, and it is centered in the well;(4) The sealing between the casing, cement ring and the formation is good, and there is no channeling phenomenon.Based on the mathematical model of steady-state heat conduction of casingcement ring-formation rock, the wellbore temperature and pressure field was calculated, and the casing heat conduction temperature model was shown in Fig.3and Fig. 4. Fig. 4 (a) is the schematic diagram of annular air fluid unit control body, Fig. 4 (a) is the schematic diagram of casing unit control body.

Fig. 4 (
Figure 2. Temperature of the set of damage points over time In the process of coupled transient analysis of wellbore thermal stress, the following basic assumptions are based:(1) The heat transfer of the upper and lower surfaces of the analyzed layer is not considered, and only the radial heat transfer of the wellbore is considered;(2) The steam is directly injected into the oil pipe, and the heat exchange is evenly carried out with the oil pipe, and the temperature of the inner surface of the oil pipe is consistent;(3) There is no eccentricity in the tubing and casing, and it is centered in the well;(4) The sealing between the casing, cement ring and the formation is good, and there is no channeling phenomenon.Based on the mathematical model of steady-state heat conduction of casingcement ring-formation rock, the wellbore temperature and pressure field was calculated, and the casing heat conduction temperature model was shown in Fig.3and Fig. 4. Fig. 4 (a) is the schematic diagram of annular air fluid unit control body, Fig. 4 (a) is the schematic diagram of casing unit control body.

Figure 3 .Figure 4 .
Figure 3. Schematic diagram of heat exchange between wellbore and formation system

Fig. 7 (Figure 7 .Figure 8 .
Figure 7. Temperature and pressure control system3.2.3.Test Pass -Group IAs shown in Fig.8(a), the initial casing thermal load is guaranteed according to the actual downhole working conditions of Section 3.1, and then the loading temperature is carried out according to the transient change law of hydration and heat release.As shown in Fig.8 (b), with the increase of temperature, the pressure in the annular air gradually increases; the test value is closer to the predicted pressure value, and the prediction formula can be modified appropriately.

Fig. 9 (Figure 9 .Figure 10 .
Figure 9. Photograph of conduit deformation before and after cutting Fig. 12 (a) is the axial curve and Fig. 12 (b) is the circumferential stress-strain curves.

Figure 11 .Figure 12 .
Figure 11.Photo of the placement position of the strain gauge

Figure 13 .Figure 14 .Figure 15 .
Figure 13.Numerical simulation verification According to the measured deformation data, the shape and stress state of the casing are reconstructed, Fig. 14 (a) is the diagram of casing stress state is the stress of the first group of casing, Fig. 14 (b) is the diagram of casing deformation state of the first group of casing.Fig. 15 (a) is the diagram of casing stress state is the stress of the second group of casing, Fig. 15 (b) is the diagram of casing deformation state of the second group of casing.It can be seen from Fig.14 and Fig.15 that the two repeated tests show that the temperature change (80°C→140°C) under the cement hydration heat release condition at the casing depth of 4594m caused the increase of axial force of casing column (-898kN→-1918kN) and the increase of annular air pressure (2.8MPa→43.15MPa), which caused the non-uniform deformation of casing under the composite load of extrusion + compressive axial force.

Table 1 .
Casing deformation measurement data