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Analytical modeling on the geo-stress and casing damage prevention with the thermo-hydro-mechanical (THM) coupling of multi-field physics

  • Youjun Ji
  • Huijin XuEmail author
  • Junwei Zhang
  • Liang Guo
Article
  • 13 Downloads

Abstract

Understanding the rule of squeezing force on casing changing with the working parameters of wells, such as steam injection pressure, steam injection temperature and bottom hole pressure, is very important to prevent casing damage in the complex thermal recovery process involving the interaction of temperature, stress and seepage field. According to the theory of heat transferring, seepage mechanics and elastic–plastic mechanics, the mathematical model considering seepage-stress-heat transferring coupling of thermal recovery was established. The numerical model of the thermal recovery for a block in GuTong oil field was built, and the stress sensitivity of the rock was tested. The research work indicates that the permeability is more sensible to the stress when the maximum stress is less than 35 MPa. The calculation results of the temperature, pressure and vertical displacement fit well with the monitoring data, and the error is less than 20%. The stress and displacement of well wall achieve peak value in the 7th–9th cycles. In the ninth cycle, the maximum horizontal displacement of the well wall occurs and reaches about 13 cm, and the casing damage is most likely to happen in the 7th–9th production cycles. The equivalent element method was used to calculate the extrusion force on the casing pipe. The pressure on casing under different steam injection rate, temperature of steam and bottom hole pressure was obtained and used for prevention of casing damage during the thermal recovery of heavy oil.

Keywords

Thermal recovery of heavy oil Geo-stress Numerical simulation THM coupling 

List of symbols

\(\sigma_{\text{ij}}\)

The total stress tensor, MPa

\(x_{\text{j}}\)

The coordinate at \(j\) direction, m

\(f_{{{\text{x}}_{\text{i}} }}\)

The volume force of direction \(x_{\text{i}}\), N m−3

\(\sigma_{\text{ij}}^{'}\)

Effective stress tensor

\(p\)

Pore pressure, MPa

\(\varepsilon_{\text{ij}}\)

The strain tensor

\(u\)

Displacement, cm

\(G\,{\text{and}}\,\lambda\)

Lame constants

\(\varepsilon_{\text{v}}\)

Volume strain

\(u_{\text{i}}\)

The displacement at \(x_{\text{i}}\) direction, cm

\(K_{\text{ij}}\)

Permeability tensor of the reservoir, μm2

\(K_{\text{ij}} {}^{0}\)

Initial permeability, μm2

\(Q_{\text{h}}\)

Energy input and output in unit time and unit volume of the reservoir, kJ m−3 day−1

\(\lambda_{\text{R}}\)

Thermal conductivity of the reservoir rock, kJ m−1 day−1 °C−1

\(C\)

Constant volume specific heat, kJ K−1 m−3

\((\rho C)_{\text{R}}\)

Rock heat capacity, kJ m−3 °C−1

\(\phi\)

Porosity of the reservoir

\(\mu\)

Fluid viscosity, mPa s

\(L_{\text{V}}\)

The latent heat of steam vaporization, kJ m−3

\(T_{0}\)

Initial reservoir temperature, °C

\(\Delta T\)

The difference between saturated steam temperature and the reservoir temperature, °C

\(e_{\text{in}}\)

The heat injected into the reservoir, kJ day−1

\(x_{\text{q}}\)

Steam quality at the well bottom

\(\lambda_{\text{c}}\)

Rock thermal conductivity of the top and bottom, kJ day−1 m−1 °C−1

\(E\)

Elastic modulus, MPa

\(v\)

Poison ratio

\(\alpha\)

Thermal expansion coefficient, m2 s−1

\({\text{d}}\sigma_{\text{ij}}^{'}\)

The effective stress increment, Mpa

\(D_{\text{ep}}\)

Elastic–plastic matrix, Mpa

\({\text{d}}\varepsilon_{\text{ij}}\)

The strain increment

\(I_{1}^{'}\)

The first non-variable for effective stress

\(J_{2}^{'}\)

The second effective deviation stress invariant

\(\sigma_{\text{x}}^{'} ,\,\sigma_{\text{y}}^{'} ,\,\sigma_{\text{z}}^{'}\)

Effective stress components at x, y, z direction, MPa

\(\tau_{\text{xy}}^{'} ,\,\tau_{\text{yz}}^{'} ,\tau_{\text{zx}}^{'}\)

Effective shear stress components on the surfaces where the normal lines are x, y, z

\(\beta \,{\text{and}}\,k_{\text{f}}\)

Shear strength parameters, Eq. (15)

\(c\)

Cohesion, MPa

\(\phi\)

Internal friction angle of rock

\(L_{\text{j}}\)

The directional derivative of the boundary

\(s_{\text{i}}\)

Distribution function for surface force, MPa

\(g_{\text{i}}\)

Distribution function for the surface displacement, Eq. (17)

\(\frac{\partial p}{\partial n}\)

Pressure derivative on the direction of outside the normal

\(f_{1} (x,y,z,t)\)

A known function set artificially to represent the flow rate

\(p(x,y,z,0)\)

Initial pore pressure of the reservoir, MPa

\(S_{\text{w}}\)

Water saturation of the reservoir

\(S_{\text{o}}\)

Oil saturation of the reservoir

\([K]\)

The stiffness matrix

\(\{ u\}\)

Node displacements matrix

\(\{ F_{\text{v}} \}\)

Volume load matrix

\(\{ F_{\text{s}} \}\)

Surface load matrix

\(\{ F_{\text{p}} \}\)

Equivalent load matrix derived from pore pressure

\(\{ F_{\text{T}} \}\)

The thermal load matrix caused by temperature changes

\(\{ F_{{\upsigma_{0} }} \}\)

The initial stress matrix in situ

\(\sigma_{\text{v}}\)

The vertical stress, MPa

\(\sigma_{\text{H}}\)

The larger horizontal stress component, MPa

\(\sigma_{\text{h}}\)

The smaller horizontal stress component, MPa

\(p_{\text{wf}}\)

Fluid pressure in well, MPa

\(p_{\text{co}}\)

The equivalent extrusion force on the casing pipe, Mpa

\(r_{\text{ci}}^{{}}\)

The inner radius of the casing pipe, m

\(r_{\text{co}}^{{}}\)

The equivalent outer radius of the thick wall cylinder, m

\(\sigma_{\text{r}}\)

Radial extrusion force on the casing pipe, MPa

Subscript \(1,2,3\)

The coordinate axis x, y and z, respectively

Notes

Acknowledgements

This work was financially supported by National Natural Science Foundation of China (Grant Nos. 41702340 and 41602290), the youth scientific and technological innovation team of southwest petroleum university under (Grant No. 2018CXTD02), the major projects of national science and technology (Grant No. 2017ZX05013006-005). All the parameters of the rock and fluid and some monitoring data of casing pipe in this manuscript were provided by GuTong oil field, which is greatly appreciated.

References

  1. 1.
    Wang Z, Lu W, Hu J. Mechanism and prevention of casing damage of well in oilfield. 1st ed. Beijing: Petroleum Industrial Press; 1991.Google Scholar
  2. 2.
    Diao S, Yang C, Liu J. Mechanism of seepage induced casing damage and numerical simulation. Rock Soil Mech. 2008;29(2):327–32.Google Scholar
  3. 3.
    Wei Z, Gu S-q. Casing mechanism of engineering hazards in a oil field in central China. Environ Earth Sci. 2013;70:869–75.CrossRefGoogle Scholar
  4. 4.
    Raoof G, Vamegh R, Bernt A. Geomechanical and numerical studies of casing damages in a reservoir with solid production. Rock Mech Rock Eng. 2016;49:1441–60.CrossRefGoogle Scholar
  5. 5.
    Liu J, Feng X. Advance of studies on thermo-hydro-mechanical interaction in oil reservoir in China. Rock Soil Mech. 2003;24:645–50.Google Scholar
  6. 6.
    Zhang Y. Thermal recovery for enhancing recovery ratio. 2nd ed. Beijing: Petroleum Industrial Press; 2006.Google Scholar
  7. 7.
    Huang X, Liu J, Yang C, He X. The fluid-structure coupling bet well sidewall stability studies. Oil Drill Prod Technol. 2008;30(6):83–7.Google Scholar
  8. 8.
    Lei H, Jin G, Shi Y. Numerical simulation of subsurface coupled thermo-hydro-mechanical(THM) processes: application to CO2 geological sequestration. Rock Soil Mech. 2014;35(8):2415–25.Google Scholar
  9. 9.
    Yin Y, Liu Y-l, Jiang P, Zhu Q-j. Finite element analysis about high pressure water injection formation of fluid- structure interaction. J Hebei United Univ (Nat Sci Ed). 2012;34(4):8–12.Google Scholar
  10. 10.
    Han X, Liang G, Wu E, Qian H, Zhou Y. Oil field numerical simulation for the casing damage of software development and application. Dig Pet Chem Ind. 2006;4(1):32–6.Google Scholar
  11. 11.
    Ren L, Wang F, Liu J. Analysis of effect of sand production on casing damage in dagang Gangxi oilfield. Oil Field Equip. 2010;39(6):28–31.Google Scholar
  12. 12.
    Zhu Q, Chen Y. Analysis of strata deformation and casing failure under fluid–solid interaction. J Liaoning Tech Univ(Nat Sci). 2018;37(2):272–8.  https://doi.org/10.11956/j.issn.1008-0562.2018.02.008.CrossRefGoogle Scholar
  13. 13.
    Cheng L, Luo Y, Ding Z. Fuzzy comprehensive evaluation model for estimating casing damage in heavy oil reservoir. Pet Sci Technol. 2013;31(10):1092–8.CrossRefGoogle Scholar
  14. 14.
    Rahmat E, Sait SM, Shehzad N, Mobin N. Numerical simulation and mathematical modeling of electroosmotic Couette–Poiseuille flow of MHD power-law nanofluid with entropy generation. Symmetry. 2019;11(8):1038–63.CrossRefGoogle Scholar
  15. 15.
    Shen X. Abaqus fem analysis for elasto-plasticity of casing used in ultra deep well. Nat Gas Ind. 2007;27(2):54–6.Google Scholar
  16. 16.
    Xu B, Liu X. Applied elastic and plastic mechanics. 3rd ed. Beijing: Tsinghua University Press; 2003.Google Scholar
  17. 17.
    Wang T, Yang S, Zhu W. Law and countermeasures for the casing damage of oil production wells and water injection wells in Tarim Oilfield. Pet Explor Dev. 2011;38(3):352–61.CrossRefGoogle Scholar
  18. 18.
    Shangyu Y, Lihong H, Chun F. Mechanical performance of casing in in situ combustion thermal recovery. J Pet Sci Eng. 2018;168:32–8.CrossRefGoogle Scholar
  19. 19.
    Xu B, Zhang Y, Wang H. Application of numerical simulation in the solid expandable tubular repair for casing damaged wells. Pet Explor Dev. 2009;36(5):651–7.CrossRefGoogle Scholar
  20. 20.
    Fei Y, Lihong H, Shangyu Y. Casing deformation from fracture slip in hydraulic fracturing. J Pet Sci Eng. 2018;166:235–41.CrossRefGoogle Scholar
  21. 21.
    Xiong Z, Shiming H, Ming T. Mechanism of collapse failure and analysis of yield collapse resistance of casing under combined load. Eng Struct. 2019;191:12–22.CrossRefGoogle Scholar
  22. 22.
    Yin Y, Liu Y. Numerical simulation of stratum deformation based on fluid-structure interaction. Chin J Undergr Sp Eng. 2015;11(1):98-7.Google Scholar
  23. 23.
    Shen D-h, Zhang Y-t, Zhang X. Study on cyclic carbon dioxide injection after steam soak in heavy oil reservoir. Acta Pet Sin. 2005;26(1):83–6.Google Scholar
  24. 24.
    Song C, Cao L, Cao L. Determination of reasonable well spacing for low-permeability heavy-oil reservoirs by steam huff and puff: taking O oilfield in Syria for example. Fault Block Oil Gas Field. 2019;26(2):210–4.Google Scholar
  25. 25.
    Yang J, Li X, Chen Z. Aproductivity prediction model for cyclic steam stimulation in consideration of non-Newtonian characteristics of heavy oil. Acta Pet Sin. 2017;38(1):84–90.Google Scholar
  26. 26.
    Fu J, Dianfa D, Zheng Y. Dynamic prediction model of steam flooding in extra heavy oil reservoirs. Oil Gas Geol. 2018;39(1):192–7.Google Scholar
  27. 27.
    Liu H, Cheng L, Huang S. A mathematical model for steam frontier prediction in solvent enhanced steam flooding process. J China Univ Pet. 2017;41(1):110–7.Google Scholar
  28. 28.
    Han J, John Yilin W, Virendra P. A fully coupled geomechanics and fluid flow model for proppant pack failure and fracture conductivity damage analysis. J Nat Gas Sci Eng. 2016;31:546–54.CrossRefGoogle Scholar
  29. 29.
    Liu T, Liu Y, Guo L. Field test on air-assisted steam flooding of heavy oil field. Oil Drill Prod Technol. 2018;40(6):800–4.Google Scholar
  30. 30.
    Hossein N, Jamalabadi MYA, Sadeghi R, Safaei MR, Nguyen TK, Shadloo MS. A smoothed particle hydrodynamics approach for numerical simulation of nano-fluid flows. J Therm Anal Calorim. 2019;135(3):1733–41.  https://doi.org/10.1007/s10973-018-7022-4.CrossRefGoogle Scholar
  31. 31.
    Wang J, Li G, Zhao H. Stability analysis of a borehole wall during horizontal directional drilling in fluid–solid coupling condition. Chin J Undergr Sp Eng. 2012;8(4):796–800.Google Scholar
  32. 32.
    Qu H-L, Hao L, Hu H-G. Dynamic response of anchored sheet pile wall under ground motion: analytical model with experimental validation. Soil Dyn Earthq Eng. 2018;115:896-6.CrossRefGoogle Scholar
  33. 33.
    Zhao J, Wang M. Elasticity and finite element. 2nd ed. Wuhan: Petroleum Industry Press; 2008.Google Scholar
  34. 34.
    Xu Z. Elasticity. 4th ed. Beijing: Higher Education Press; 2016.Google Scholar
  35. 35.
    Yin Z, Liu Z. Changes of rock structure after water flooding in ansai oil field. Sci Geol Sin. 1999;8(3):321–30.Google Scholar
  36. 36.
    Sharma S, Shadloo MS, Hadjadj A. Effect of thermo-mechanical non-equilibrium on the onset of transition in supersonic boundary layers. Heat Mass Transf. 2019;55(7):1849–61.  https://doi.org/10.1007/s00231-018-2429-9.CrossRefGoogle Scholar
  37. 37.
    Kong X. Higher seepage mechanics. 3rd ed. Beijing: China Science and Technology Publishing House; 2010.Google Scholar
  38. 38.
    Asadollahi A, Rashidi S, Esfahani JA, Ellahi R. Simulating phase change during the droplet deformation and impact on a wet surface in a square microchannel: an application of oil drops collision. Eur Phys J Plus. 2018;133:306–22.CrossRefGoogle Scholar
  39. 39.
    Yousif MA, Ismael HF, Abbas T, Ellahi R. Numerical study of momentum and heat transfer of MHD Carreau nanofluid over exponentially stretched plate with internal heat source/sink and radiation. Heat Transf Res. 2019;50(7):649–58.CrossRefGoogle Scholar
  40. 40.
    Ellahi R, Zeeshan A, Shehzad N, Alamri Sultan Z. Structural impact of Kerosene-Al2O3 nanoliquid on MHD Poiseuille flow with variable thermal conductivity: application of cooling process. J Mol Liq. 2018;264:607–15.  https://doi.org/10.1016/j.molliq.2018.05.103.CrossRefGoogle Scholar
  41. 41.
    Sadeghia R, Shadloob MS. Three-dimensional numerical investigation of film boiling by the lattice Boltzmann method. Numer Heat Transf Part A Appl. 2017;71(5):560–74.CrossRefGoogle Scholar
  42. 42.
    Nguyen TS. Thermo-hydro-mechanical-chemical processes in geological disposal of radioactive waste—an example of regulatory research. Adv Geo Energy Res. 2018;2(2):173–89.CrossRefGoogle Scholar
  43. 43.
    Wang Y, Yang W, Li M, Liu X. Risk assessment of floor water inrush in coal mines based on secondary fuzzy comprehensive evaluation. Int J Rock Mech Min Sci. 2012;52:50–5.CrossRefGoogle Scholar
  44. 44.
    Ma D, Xx Miao, Zq Chen, Xb Mao. Experimental investigation of seepage properties of fractured rocks under different confining pressures. Rock Mech Rock Eng. 2013;46:1135–44.CrossRefGoogle Scholar
  45. 45.
    Bhatti MM, Zeeshan A, Ellahi R, Shit GC. Mathematical modeling of heat and mass transfer effects on MHD peristaltic propulsion of two-phase flow through a Darcy–Brinkman–Forchheimer Porous medium. Adv Powder Technol. 2018;29:1189–97.CrossRefGoogle Scholar
  46. 46.
    Oparin VN, Usol’Tseva OM, Semenov VN. Evolution of stress-strain state in structured rock specimens under uniaxial loading. J Min Sci. 2013;49(5):677–90.CrossRefGoogle Scholar
  47. 47.
    Schutjens PMTM, Hanssen TH, Hettema MHH. Compaction-induced porosity/permeability reduction in sandstone reservoirs: data and model for elasticity-dominated deformation. SPE Reservoir Eval Eng. 2004;7(3):202–14.CrossRefGoogle Scholar
  48. 48.
    Thomas LK, Chin LY, Pierson RG. Coupled geomechanics and reservoir simulation. SPE J. 2003;8(4):350–8.CrossRefGoogle Scholar
  49. 49.
    Settari A. Physics and modeling of thermal flow and soil mechanics in unconsolidated porous media. SPE Prod Eng. 1992;7(1):47–55.CrossRefGoogle Scholar
  50. 50.
    Chin LY, Raghavan R, Thomas LK. Fully coupled analysis of well responses in stress-sensitive reservoirs. SPE Reserv Eval Eng. 2000;3(5):435–43.CrossRefGoogle Scholar
  51. 51.
    Kong X-y, Li D-l, Xu X-z, Lu D-t. Study on the mathematical models of coupled thermal-hydrological-mechanical (THM) processes. J Hydrodyn. 2005;20(2):269–75.Google Scholar
  52. 52.
    Akin JE. Application and realization of finite element method. 3rd ed. Beijing: Science Press; 1992.Google Scholar
  53. 53.
    Yang H-l, Chen M, Jin Y. Analysis of casing equivalent collapse resistance in creep formations. J China Univ Pet. 2006;30(4):94–7.Google Scholar
  54. 54.
    Lin Y, Deng K, Sun Y. Through-wall yield collapse pressure of casing based on unified strength theory. Pet Explor Dev. 2016;43(3):462–8.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.School of Geoscience and TechnologySouthwest Petroleum UniversityChengduChina
  2. 2.China-UK Low Carbon CollegeShanghai Jiao Tong UniversityShanghaiChina

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