# Examining Pipe-Borehole Wall Contact and Pullback Loads for Horizontal Directional Drilling
###### Abstract  
Pipeline pullback load is a crucial basis for drill rig selection and pipeline strength design. This paper presents a new pullback load calculation model from the perspective of pipe-borehole wall contact. The pipe-borehole wall contact analysis includes the distribution of contact pressure and the relationship between the external load and compressive displacement. The friction force between the pipe and the borehole wall was calculated based on the pipe-borehole wall contact analysis and adhesion theory without depending on the empirical friction coefficient. The effects of the eccentricity were also considered when calculating the fluid drag force. Through case studies, we verified the applicability of the model and discussed the possible reasons for the errors between the theoretical and field-measured results. This study can provide a helpful tool for analyzing the pipe-borehole wall contact and pullback loads for horizontal directional drilling. horizontal directional drilling; pullback loads; pipe-borehole wall contact; friction force; fluid drag force +
Footnote †: journal: Applied Sciences  
pipeline during the pullback process. The resultant of these forces in the pullback direction constitutes the pullback load. To calculate pullback loads in HDD, scholars have conducted extensive research and proposed practical methods that promote the advancement of HDD technology [8; 9; 10; 11; 12; 13; 14]. The Phillips Discopipe model [9] considers the pipe-borehole wall friction caused by the net weight of the pipeline. This friction force is considered to be the pullback load required for pipeline installation. To maintain the stability of the borehole wall, the HDD borehole was filled with a drilling fluid. Previous studies have found that drilling fluid drag force is an essential component of pullback loads. The CNPC method [12] further considers the drilling fluid drag force, which is calculated by multiplying the outer surface area of the pipeline in the borehole by the viscosity coefficient \(k_{\mathrm{s}}\). The calculation of pipe-borehole wall friction force in the CNPC method aligns with that of the Phillips Discopipe model. The HDD borepath generally comprises straight and curved segments. When the pipeline crosses the curved segment, owing to the change in the direction of the pilot borehole, the external load applied to the borehole wall increases, known as the capstan effect. The increased external load resulted in additional pullback loads. The PRCI model [14] and ASTM model [11] consider the impact of the capstan effect. In addition, the drilling fluid drag force in the ASTM model is calculated by considering a balance of the forces acting on the fluid annulus in the borehole due to the pressure difference and the lateral shear forces acting on the pipe and borehole walls. The pressure difference is estimated to be 70 kPa. [PERSON] et al. [13], [PERSON] et al. [8], and [PERSON] et al. [15] further improved the calculation of drilling fluid drag force. The pressure difference is no longer estimated as a specific value. The drilling fluid was assumed as a non-Newtonian fluid. Formulas for the pressure difference and pipe wall shear stress in a concentric annulus were derived based on fluid mechanics [8; 13; 15]. The rheological characteristics have a considerable influence on drilling fluid drag force. [PERSON] et al. [16] investigated the rheological characteristics of drilling fluids with varying bentonite concentrations. Their findings indicate that both the Bingham and Herschel-Bulkley models can describe the behavior of drilling fluids used in HDD. [PERSON] et al. [17] conducted a parameter sensitivity analysis on the effect of rheological parameters on the drilling fluid drag force. The results showed that the ratio of borehole to pipe radius and rheological characteristics significantly affect the drilling fluid drag force. At present, there is a lack of research on the pipe-borehole wall contact in HDD.