Mathematical Problems in Engineering

Volume 2015 (2015), Article ID 575492, 9 pages

http://dx.doi.org/10.1155/2015/575492

## Application of Multiphysics Coupling FEM on Open Wellbore Shrinkage and Casing Remaining Strength in an Incomplete Borehole in Deep Salt Formation

College of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China

Received 10 September 2014; Revised 2 December 2014; Accepted 12 December 2014

Academic Editor: Chenfeng Li

Copyright © 2015 Hua Tong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Drilling and completing wells in deep salt stratum are technically challenging and costing, as when serving in an incomplete borehole in deep salt formation, well casing runs a high risk of collapse. To quantitatively calculate casing remaining strength under this harsh condition, a three-dimensional mechanical model is developed; then a computational model coupled with interbed salt rock-defective cement-casing and HPHT (high pressure and high temperature) is established and analyzed using multiphysics coupling FEM (finite element method); furthermore, open wellbore shrinkage and casing remaining strength under varying differential conditions in deep salt formation are discussed. The result demonstrates that the most serious shrinkage occurs at the middle of salt rock, and the combination action of salt rock creep, cement defect, and HPHT substantially lessens casing remaining strength; meanwhile, cement defect level should be taken into consideration when designing casing strength in deep salt formation, and apart from the consideration of temperature on casing the effect of temperature on cement properties also cannot be ignored. This study not only provides a theoretical basis for revealing the failure mechanism of well casing in deep complicated salt formation, but also acts as a new perspective of novel engineering applications of the multiphysics coupling FEM.

#### 1. Introduction

With the deep complicated regions becoming the major battlefield of oil and gas exploitation on land, increasing exploration and production around the world require drilling through and completing wells in deep salt formation, which are technically challenging and costing. The introduction of a borehole in deep salt formation changes the existing stress field and displacement field, resulting in open wellbore shrinkage and time-dependent loading on the casing, which leads to severe well casing damage [1]. The statistical data shows that the well having casing damage in the Zhongyuan oil field is 1123, while the number of casing damage incidents in the salt strata contributed by 68.03% of the total number [2]. At greater depths, both stress and temperature increase; well cementing also faces great technical challenges. Statistical data collected in an oil region in western China shows that five out of seven wells are poorly cementing at the depths of 2990~3460 m [3]. Partial cementing and deboning at the casing/cement or cement/rock interfaces are potential causes of cement sheath failure [4]. Lacking the intact support of cement sheath, when well casings serve in deep salt formation, their security will drop significantly.

In recent years, severe casing damage in deep salt strata has been carefully followed and comprehensively studied by many scholars. Salt rock creep leads to open wellbore shrinkage and casing collapse [5–8], the well condition and casing performance are getting worse under high pressure and high temperature [1, 9], and another cause of casing damage is cement sheath failures [4, 10, 11]. However, to simplify the calculation, prior work on casing damage in deep salt formation only considered the impact of a single factor, ignoring interaction between salt rock creep, defective cement, and HPHT, which has great deviations from actual situation. To quantitatively assess the service applicability of well casing in deep salt formation, we propose to use multiphysics coupling FEM to solve this problem.

#### 2. Basic Theory of Multiphysics Coupling FEM on Casing Remaining Strength Calculation

##### 2.1. Temperature Field Model

Considering the particularity of the wellbore, to simplify the calculation, the following assumptions are made in this paper: (1) the formation temperatures at initial moment and at infinity are uniform, which are kept as the in situ temperature, and there is no internal heat source inside the formation; (2) wellbore thermal conductivity is constant, and the thermal stress is considered to be in a single-valued function relation with the elastic modulus and temperature increment; (3) the influence of the drilling mud radial temperature gradient and axial thermal conduction on wellbore temperature distribution is ignored. The three-dimensional thermal conduction equation of wellbore under cylindrical coordinate system is shown as follows [12]: where is casing temperature, ; is casing density, kg/m^{3}; is specific heat capacity, J/(kg·K); is casing heat transfer coefficient, W/(m·K); and is heat transfer time, s.

In the process of heat conduction between salt rock and cement, the interior wall of borehole is considered as the first boundary condition; that is, where is bottom hole standard temperature, K, and is boundary.

For heat convection between drilling mud and casing, the interior wall of casing is considered as the third boundary condition: where is bottom hole circulating temperature, K; is convective heat transfer coefficient, W/(m^{2}·K); is outside the normal direction on the boundary; and is boundary.

According to incremental theory, temperature strain increment of well casing can be written as follows:where is transient temperature; is initial temperature; is thermal expansion coefficient.

##### 2.2. Salt Rock Creep Model

As a viscous, slowly flowing material, due to its sealing and low permeability, salt rock may easily develop to become the covering layer of the deep reservoir. Salt rock behaves in a visco-elastic manner is called creep, which changes the existing stress field and displacement field, resulting open wellbore shrinkage and time-dependent loading on well casing [13]. Creep behavior is used to describe as a creep curve, Figure 1 shows an example of typical creep behavior, as it sequentially undergoes the initial creep (), steady creep () and accelerated creep (). However, salt rocks surround the wellbore mainly experience the steady creep stage during the service life of the oil and gas wells. Temperature, time and stress field are closely related to salt creep rate, creep strain increment is described as follows:where is equivalent stress; is equivalent creep strain; is temperature; is time.