Research On Constitutive Equations And Evaluation Models Of Mechanical Integrity Of Cement Stone

Cement sheath integrity, which associated with the safety production of oil and gas well, gas storage injection-production wells and so on, is an important part of the wellbore integrity and is key to the daily production operations. The key to build the appraisal model of cement sheath integrity is how to describe the constitutive equations of cement stone, and now there is no mature theories can be used to do it at home and abroad. Started with understanding the material foundation of constitutive equations—the cement stone mechanical property, this article has tested the mechanical properties of typical cement stone with the following methods:uniaxial compression testing, tensile strength testing, bond strength testing, triaxial stress testing and cyclic loading testing. Meanwhile, the main way of cement sheath failure has been tested directly by the cement annular isolating simulation test. Based on the cement mechanical properties, this paper has described the constitutive equations of cement stone with the two paths of the elastic constitutive equations and elastoplastic constitutive equation by referencing the concrete constitutive theory of research methods and ideas. Based on the research, two kinds of analysis models for cement sheath integrity has been built. These models have been applied in Longgang gas field, and some results have been achieved.The main results formed from this article as follows:(1) Experiments found that the stress and strain evolution process of cement stone, under the condition of uniaxial compression, can be divided into four stages:compaction stages, linear elastic stage, nonlinear deformation stage and break stage. Young’s modulus and Poisson’s ratio of cement stone is interval value, and young’s modulus distribution is relatively concentrated while Poisson’s ratio distribution is scattered.(2) This paper has designed tensile strength measuring method, measuring the typical cement tensile strength, and tensile strength of cement stone found in the range of 1.5～3.5 MPa, is about 7%～13% of the compressive strength, conforming to the inference of 1/8～ 1/12 from the Griffith theory of fracture mechanics.(3) Proposed the cementing strength of the cement bonding strength should be divided into longitudinal and transverse bonding strength. The longitudinal bonding strength test method, which simulated the way of casing moving, was designed, testing the low density cement longitudinal bonding strength is about 0.7～1.5 MPa, and the normal density cement system is roughly 1.5～2.5 MPa. Estimating the horizontal bonding strength by about 50% of the longitudinal cementation strength, low density cement’s transverse bonding strength is about 0～0.5 MPa, normal density system is about 0.5～1 MPa. Comparing cement stone supporting casing weight and resisting casing transverse separation movement, it was found that cement dangerous working conditions is not on the vertically instead of horizontally.(4) The triaxial stress testing and load cycling testing of cement stone shows that the cement is a kind of pressure-sensitive materials, its material properties is highly affected by the confining pressure. Simulation test of cement annular isolating show that the main failure of cement stone is:tensile crack damage and plastic yielding micro-annulus.(5) As with concrete, this article has demonstrated that different cement stones have the uniform functional relation between bulk modulus and octahedral normal strain, or between shear modulus and octahedral shear strain:the functional form of bulk modulus is y=axm, the functional form of shear modulus is y=b(x-c)n, and the cement stone non linear elastic constitutive equation, being used to describe the nonlinear deformation of cement stone, was established upon the two functional relations.(6) Though analyzing the development law of interaction relationship between sheath and casing or between sheath and formation rock in the changing process of cement from liquid state to plastic state and plastic state to solid state, the interface force in the first and second interface in the initial state was thought to be close to hydrostatic force. Subsequent work pressure changes can be seen as the result of casing pressure in the initial state superimposing a pressure increase. Based on knowing the initial state and subsequent state of interaction relationship among casing, cement sheath and formation rock, a cement sheath mechanical integrity analysis model was established, which contains the nonlinear elastic constitutive equations of cement stone.(7) The cement sheath mechanical integrity damage indicators that based on the theory of continuum damage mechanics has been proposed. It can quantitatively depict the mechanical integrity of the cement sheath.(8) Based on the elastoplastic constitutive equation and the finite element method, the analytical method of cement sheath mechanical integrity under cycling loads in gas storage wells was explored. This method was testified to be a effective way to deal with gas storage cement sheath, and was worth of intensive study.