# Examining Pipe-Borehole Wall Contact and Pullback Loads for Horizontal Directional Drilling
## 4 Case Studies  
The analytical model proposed in the previous section was used to analyze two pipeline crossing projects (1) HD3-3, HDPE pipe; 2) Pull 9, steel pipe). Borehole geometries were obtained from the profiles recorded for each project. The coefficient of friction applicable at the surface before the pipe enters borehole \(\mu_{a}\) was inversely obtained from the measured pipe pullback loads. The values of the other parameters used for the analyses were either obtained from field measurements or were approximately based on typical values published in the literature [5, 45]. The pullback loads of the two crossing projects were measured by using a load unit attached to the pullback head. Further details can be found in references [5, 45]. Figure 11 compares the theoretical results (including the proposed model, ASTM method, and PRCI method), field-measured results, and the linear trend line of the field-measured results for projects HD3-3 (Figure 11a) and Pull-9 (Figure 11b). Considering the applicability of existing methods, the ASTM method was used to calculate the pullback loads of project HD3-3 (HDPE pipe), and the PRCI method was used to calculate the pullback loads of project Pull 9 (steel pipe). The results are shown in Figures 11a and 11b, respectively. As depicted in Figure 11, the spikes in the field-measured results reflected the pullback process, which consisted of a series of pullback and stopping (disassembly of drill rods) operations. Because the analysis assumed a continuous pullback process, the trend lines of the measured results were better suited for comparison with the theoretical results [5]. It can be seen that compared to existing methods, the calculation results of the proposed model are closer to the measured results. Moreover, the rates of change of the trend lines and calculated curves were similar. The minimum and maximum relative errors between the trend line of the measured results and the proposed model for project HD3-3 (HDPE pipe) are 0.54% and 13.01%, respectively. For project Pull-9 (steel pipe), the minimum and maximum relative errors between the trend line of the measured results and the proposed  
Figure 11: Comparison between the predicted and measured values of the pipe pullback loads: (**a**) HD3-3, HDPE pipe; (**b**) Pull 9, steel pipe. model are 0.26% and 1.24%, respectively. The calculation results of the proposed model for the HDPE and steel pipes indicate that the proposed model has broader applicability. This is because the pipe-borehole wall friction force in the proposed model is based on the pipe-borehole wall contact model rather than the prescribed friction coefficient, which is not limited by the type of pipe used. Several factors may have contributed to the differences between the theoretical and field-measured results. The first condition was that the resistance resulted from the pressure difference force at the front of the reamer. A lack of sufficient data makes it challenging to implement reasonable values in the model [46]. In the second condition, a series of recording points approximated the borehole used for the calculation. An approximate may differ from an actual borepath. The third condition was that specific material parameters used for the analysis (such as the elastic modulus, cohesion, and pressure distribution exponent \(n\)) were approximate, and even small changes in their values could affect the calculation results. Otherwise, the model provides a reasonable and widely applicable method for calculating pullback loads. The rheological parameters \(\tau_{0}\) and \(\mu\) have a considerable influence on drilling fluid drag force. To illustrate the influence of the rheological parameters, an analysis was conducted using the HD3-3 condition. The results are shown in Figure 12. It can be seen that as \(\tau_{0}\) and \(\mu\) increase, the drilling fluid drag force also increases. However, compared to that of the yield point, the influence of viscosity on the drilling fluid drag force is minimal.