COMPARATIVE ANALYSIS OF THE ANALYTICAL AND NUMERICAL METHODS FOR CALCULATING THE STRESS-STRAIN STATE OF THE NEAR-WELLBORE ZONE BASED ON THE ELASTIC MODEL TAKING INTO ACCOUNT THE MAIN STRUCTURAL ELEMENTS OF THE WELL

Abstract

Link for citation: Popov S.N., Chernyshov S.E., Krivoshchekov S.N. Comparative analysis of the analytical and numerical methods for calculating the stress-strain state of the near-wellbore zone based on the elastic model taking into account the main structural elements of the well. Bulletin of the Tomsk Polytechnic University. Geo Аssets Engineering, 2023, vol. 334, no. 5, рр.94-102. In Rus. The relevance of the research is caused by the scientific interest in calculating the near-wellbore zone stress-strain state to improve the development of oil and gas fields, to predict the casing stability and the safety of the cement stone. The main aim: based on a comparative analysis of the methods of analytical and numerical simulation of stress calculation near a vertical well using an elastic model, determine the distribution of radial and tangential stresses, compare the accuracy of their calculation by different methods and identify the advantages and disadvantages of each of them. Objects: near-wellbore zone of the terrigenous reservoir of the Achimov deposits of one of the fields of the Khanty-Mansiysk autonomous region. Methods: analytical and numerical finite element methods for stress-strain state calculating of the near-wellbore zone, taking into account the main structural elements of the well and using a linear elastic model. Results. The paper considers the analytical relationships used to calculate the radial and tangential stresses in the casing, cement stone and reservoir rock, as well as the equations used in numerical finite element modeling of stresses near a vertical well. The authors have developed a finite element scheme of the near-wellbore zone, including its main structural elements. The paper introduces the results of calculation of the main components of the stress tensor in the structural elements of the well depending on the radial coordinate for the bottom hole pressure of 20, 40 and 60 MPa. The authors carried out the comparative analysis of the stress calculations results by the methods used. It is shown that the largest discrepancy between the analytical and numerical methods was 2 % that corresponds to radial stresses for the calculation option with a bottom hole pressure of 20 MPa. On average, the discrepancies were: for radial stresses – 0,04 %, for tangential stresses – 0,72 %. It is concluded that when using the model of a linearly elastic medium and under boundary conditions in the form of fixing the model in the upper and lower parts along the normal to the surface, and also without taking into account the pressure distribution in the depression funnel of the model, it is sufficient to use the analytical method of calculation. If it is supposed to use combined boundary conditions, a poroelastic model, taking into account viscoplastic deformations, then it is most preferable to use the numerical simulation method.

Keywords

• radial and tangential stresses
• analytical method
• numerical method
• finite element method
• bottomhole pressure
• well