A thermo-poroelastic model for dual steel casing−cement sheath−formation in deep earth environment
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摘要: 基于热孔弹性理论，并考虑水泥环热渗效应，论文研究了双钢套管−水泥环−围岩组合体在套管内压力和温度荷载作用下的孔弹性力学行为。通过模型验证重现了已有文献的试验数据。模型结果表明，组合体中不排水水泥环1比排水水泥环2更容易产生界面径向开裂和界面脱黏失效破坏；相比于50 MPa套管内压力的作用，−100 ℃温度荷载引发了不排水水泥环1界面1处最大负孔隙压力−26.4 MPa，负孔隙压力导致了界面1处的有效拉应力远大于水泥环的抗拉强度和黏结强度，引发了界面1的径向开裂和界面脱黏失效破坏；当水泥环的热渗系数大于1×10−12 m2/(℃∙s)时，水泥环的热渗效应导致水泥环1负孔隙水压力更大，使得界面1处的有效拉应力更大，水泥环界面1处更容易发生径向开裂和界面脱黏失效破坏。Abstract: Based on thermo-poroelastic theory and accounting for the thermo-osmotic effect, this work investigates the poroelastic behavior of dual steel casing−cement sheath−formation subject to inner casing pressure and thermal loading. According to the model validation, the model well reproduces the experimental data in the existing literature. The model results show that compared with the drained cement sheath 2, the undrained cement sheath 1 is more susceptible to radial cracking and interface debonding; compared with the application of 50 MPa inner casing pressure, −100 ℃ thermal loading induce higher negative pore pressure at interface 1 of cement sheath 1, whose pore water pressure reach as much as −26.4 MPa, the high negative pore water pressure leads to high effective tensile stress at interface 1, resulting in the radial cracking and debonding of interface 1; when the thermo-osmotic coefficient of cement sheath is higher than 1×10−12 m2/(℃∙s), the thermo-osmotic effect leads to higher negative pore water pressure and thus higher effective tensile stress at interface 1, resulting in radial cracking and interface debonding at interface 1.
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Key words:
- cement sheath /
- pore water pressure /
- thermo-osmosis effect /
- thermal loading /
- thermo-poroelastic model
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图 1 双钢套管−水泥环−围岩组合体示意图
Figure 1. Schematic diagram of dual steel casing-cement sheath-formation
图 3 水泥环/围岩剪切模量比Gfor/Gcem对不同界面处水泥环孔隙压力时变规律的影响，套管内压力pi=50 MPa
Figure 3. Effect of cement sheath/formation shear modulus ratio Gfor/Gcem on the time-dependent pore-pressure evolution in the cement sheath at different interfaces (casing internal pressure pi=50 MPa)
图 4 t=103 s时，围岩与水泥环剪切模量比Gfor/Gcem对水泥环有效应力的影响，套管内压力pi=50 MPa
Figure 4. Effect of the shear modulus ratio of surrounding rock Gfor/Gcem to cement sheath on the effective stress of the cement sheath at t=103 s (pi=50 MPa)
图 5 ΔT =−100 ℃，Gfor/Gcem =0.14时，水泥环不同界面处孔隙水压力增量，径向有效应力增量和环向有效应力增量时变规律
Figure 5. Time-dependent variations of pore water pressure increment, radial effective stress increment and circumferential effective stress increment at different interfaces of the cement sheath at ΔT = −100 ℃ and Gfor/Gcem =0.14
图 6 ΔT =−100 ℃，t=103 s时，围岩与水泥环不同剪切模量比Gfor/Gcem对水泥环环向有效应力增量和径向有效应力增量的影响规律
Figure 6. Effect of shear modulus ratio Gfor/Gcem between surrounding rock and cement sheath on circumferential and radial effective stress increments of the cement sheath at ΔT =−100 ℃ and t=103 s
图 7 ΔT =−100℃，Gfor/Gcem=0.14时，不同水泥环热传导系数对在界面1处环向有效应力增量和径向有效应力增量时变规律的影响
Figure 7. Effect of thermal conductivity of different cement sheaths on time-dependent variations of circumferential and radial effective stress increments at Interface 1 under ΔT = −100 ℃ and Gfor/Gcem=0.14
图 8 在ΔT =−100 ℃温度作用下，不同热渗流系数对界面1处孔隙水压力增量，环向有效应力增量和径向有效应力增量时变规律的影响， Gfor/Gcem =0.14
Figure 8. Effect of different thermo-osmotic coefficients on time-dependent variations of pore water pressure increment, circumferential effective stress increment and radial effective stress increment at Interface 1 under temperature condition ΔT = −100 ℃ with Gfor/Gcem = 0.14
图 9 在ΔT =−100 ℃和pi=50 MPa共同作用下, 水泥环界面1与界面4的环向有效应力增量和径向有效应力增量时变规律, Gfor/Gcem = 0.14
Figure 9. Time-dependent variations of circumferential and radial effective stress increments at Interface 1 and Interface 4 of the cement sheath under combined effects of ΔT = −100 ℃ and pi = 50 MPa, with Gfor/Gcem = 0.14
表 2 双钢套管−水泥环−地层组合体的力学性质、热学性质和几何参数
Table 2. Mechanical, thermal and geometric parameters of the dual steel casing–cement sheath–formation assembly
参数 数值 单位 来源 地层 $ {G}^{\rm{s,for}} $ 0.9 GPa [22] $ {K}^{\rm{s,for}} $ 3 GPa [22] $ {\kappa }^{\rm{for}} $ 0.5×10−18 m2 [22] $ \varphi^{\rm{for}} $ 0.1 [22] 水泥环 $ {G}^{\rm{s,cem}} $ 10 GPa [23] $ {E}^{\rm{s,cem}} $ 13.9 GPa [8] $ \varphi^{\rm{cem}} $ 0.3 [23] $ {k}^{\rm{cem}} $ 1×10−18 m2 [23] $ b $ 0.525 [8] $ k_{\rm{T}}^{\rm{cem}} $ 0.34 W/(m·℃) [6] $ {\beta }^{\rm{cem}} $ 3.00×10−5 1/℃ [23] $ {\kappa }^{\rm{cem}} $ 1.1x10−19 m2 [24] 孔隙水 $ \mu $ 1×10−3 Pa·s [22] $ {K}^{\rm{f}} $ 2.18 GPa [22] $ {\beta }_{\rm{f}} $ 1.98×10−4 1/℃ [22] 钢套管 $ {E}^{\rm{cas}} $ 200 GPa [6] $ {\upsilon }^{\rm{cas}} $ 0.27 [6] $ k_{\rm{T}}^{\rm{cas}} $ 15 W/(m·℃) [6] $ {\beta }^{\rm{cas}} $ 3.6×10−5 1/℃ [6] 几何参数 $ {r}_{1} $ 0.05715 m $ {r}_{2} $ 0.06985 m $ {r}_{3} $ 0.118745 m $ {r}_{4} $ 0.13 m $ {r}_{\text{5}} $ 0.18 m 
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