*Modeling and Analysis Techniques for Solving Mechanical Pipe Sticking Problems… DOI: http://dx.doi.org/10.5772/intechopen.107307*

mechanical behavior and interaction between the drilling system parts during the actual condition will lead to a better understanding and solution as well as support the decision-making. Consequently, modeling and analyzing this complex process which consists of many interaction parts with different boundary conditions like pressure, forces, stress, and others is a significant challenge in predicting and preventing or mitigating the sticking problem during drilling. Based on the foregoing information, the physical model is created to simulate the actual case with similar operating conditions. The main parts consist of the drill pipe, mud cake, wellbore housing, and the surrounding formation. **Figure 2A** and **B** illustrates these model components in (2D) and (3D).

**Figure 3.** *Contact behavior between the interaction parts.*

#### **Figure 4.**

*The boundary condition includes constraining the wellbore from any movements and applying downward pressure on the drill pipe.*

The interaction and constrain between these parts were defined according to their function. The drill pipe is modeled as a rigid body (non-deformable part), while the mud in contact with the outer surface of the pipe is modeled as a deformable region. Also, the wellbore sleeve is considered as a rigid body and reacts as a non-deformable part.

**Figure 3** is an illustration of the contact behavior between these parts and the direction of the applied loads.

The boundary condition is built according to the main function of this process. The wellbore sleeve is restricted and constrained in all directions to prevent any possible movements. While the boundary condition (move down) will apply on the upper surface of the drill pipe in order to allow the pipe to move downward direction. **Figure 4** shows the constraints on the wellbore, and applied pressure on the drill pipe to move down.

## **3. Main calculations**

For a quick approximation, here below introduced some mathematical formulas for calculating the required force to free the stuck string and the depth of the stuck pipe [15].

$$\text{Depth of stack pipe(feet)} = \text{Pipe stress} (\text{inch}) \tag{1}$$

$$\times \text{Free point constant} (\text{FPC}) / \text{Pull force} (\text{k} - \text{lbs})$$

$$\text{FPC} = \text{As} \times 2500 \tag{2}$$

*As* is the pipe wall cross-sectional area (sq. inch).

$$\mathbf{As} = \left(\mathbf{0.5}\right)^{2} \left(\mathbf{OD^{2}} - \mathbf{ID^{2}}\right) \times \boldsymbol{\pi} = \left(\mathbf{OD^{2}} - \mathbf{ID^{2}}\right) \times \mathbf{0.7854} \tag{3}$$

Where;

ID is the inner diameter of the drill pipe in inches. OD is the outer diameter of the drill pipe in inches. Alternatively, the stuck depth can also be calculated using this approach;

$$\text{Stuck depth} = 735.294 \times E \times \text{Drill Price Weight} / \text{Differential Pull} \tag{4}$$

735.294 is a constant.

$$\text{Differential } pull = higher \text{ } pull \text{ } on \text{ } (lb)\text{-}lower \text{ } pull \text{ } of \text{ } (lb)\text{-} \tag{5}$$

$$\mathbf{E} = \text{Higher pull pipe stretching } (in) \text{-lower pull pipe stretching } (in) \tag{6}$$

$$\text{Axial force required to free pipe} = \mu \times \text{Pull force} / 1000 \tag{7}$$

## **4. Finite element analysis**

The Commercial software (ANSYS/2019 R3) has been adopted for the analysis and simulation of this process.

### *Modeling and Analysis Techniques for Solving Mechanical Pipe Sticking Problems… DOI: http://dx.doi.org/10.5772/intechopen.107307*

ANSYS is a finite-element modeling package normally used for numerically solving mechanical problems such as structural analysis. There are two methods used in (ANSYS) namely; graphical user interface (GUI) and the command line interface (CLI). Factors, such as the interaction type between the contact parts, material properties, and element type according to the mesh method are the main input variables. The Mapped Face Meshing method has been used to facilitate and extracted the element size. The method-based analysis is the failure criteria that have been incorporated to predict the problems of stuck pipes. It depends on estimating the mechanical properties of formations and the state of stresses. It also depends on the effect of the intermediate principal stress component in the failure analysis. The type of contact between the interacting parts is categorized and defined according to their functions. Bonded and non-separation contact is the suitable contact type for defining the nature of contact between these parts during drilling, and the adaptive meshing technique is also used to enhance the results and findings of this analysis. **Figure 5** illustrates the contact and mesh types.

**Figure 5.** *The contact and mesh type.*

**Figure 6** illustrates the nature of interaction and the applied load during the total deformation option. This type of deformation is defining the elements of the part that are subjected to deformation to be classified as (Slaves), while the non-deformable elements are classified as (Masters).

The drill pipe displacement is assumed to be a small value at the beginning of the drilling process due to the high resistance and high frictional forces between the contact surfaces. However, displacement of the drill pipe will increase rapidly and in proportion with the applied pressure due to an increase in contact surface area between the parts.

In this analysis model, many failure criteria have been incorporated to predict the problems of stuck pipes and estimate the mechanical stability of drilling string.

During the drilling process, the total deformation interaction will impose on the contact between the formation rock and drill pipe. Consequently, a large deformation (elastic-plastic type), and a high amount of material flow will result due to severe contact and high frictional forces between these surfaces.

**Figure 6.** *The fixed support constraints and applied load.*
