## 5 Cutter Spacing Optimization and Bit Rock Breaking Simulation
### Field Applications  
In order to validate the findings of the study, empirical fieldwork was conducted at the Tahe oilfield in China, utilizing a bit equipped with a triangular prism Polycrystalline Diamond Composite (PDC) cutter as well as a PDC bit with a mixed cutter configuration. The performance of both the bit with a triangular prism cutter and the one featuring mixed cutters was compared in terms of efficacy while keeping the drilling parameters, formation characteristics, and other conditions largely uniform.  
Figure 23 shows a comparative analysis between the pre-usage and post-usage stages of a bit outfitted with a triangular prism PDC cutter, while Figure 24 shows the same for a bit featuring a mixed cutter arrangement. Notably, subsequent to the completion of drilling, both categories of bits maintained an impressive freshness rate exceeding 85%, with no evidence of chipping or any instances of incorrect cutter usage reported.  
In the practical usage comparison between the two types of bits in terms of their respective drilling depth and rate of penetration (ROP), as shown in Figure 25, the PDC bit augmented with a mixed cutter arrangement manifests an ROP of 2.1 m/h, signifying an impressive enhancement of approximately 23.5% when juxtaposed against the 1.7 m/h ROP of the PDC bit complemented with triangular prism cutters. This ROP improvement is notably congruent with the resultant data procured from numerical simulations. In the context of drilling depth, the PDC bit with a triangular prism cutter records a level of 275.1 m, whereas the bit equipped with a mixed cutter arrangement registers a substantially higher drilling depth of 370.1 m, indicating a remarkable increase of 34.5% in comparison to the alternative PDC bit.  
Figure 23: Effect of using a bit: (**a**) Before using the triangular prism bit; (**b**) After using the triangular prism bit.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Bit Type** & \begin{tabular}{c} **Minimum Value of** \\ **ROP/mm\(\cdot\)s\({}^{-1}\)** \\ \end{tabular} & \begin{tabular}{c} **Maximum Value of** \\ **ROP/mm\(\cdot\)s\({}^{-1}\)** \\ \end{tabular} & \
\begin{tabular}{c} **ROP** \\ **Variance** \\ \end{tabular} &
\begin{tabular}{c} **ROP Standard** \\ **Deviation** \\ \end{tabular} \\ \hline Bit with an axe cutter & \(-\)52.87 & 69.24 & 388.11 & 19.7 \\ Bit with a triangular cutter & \(-\)38.39 & 55.15 & 258.09 & 16.06 \\ Bit with a mixed set of cutters & \(-\)19.95 & 26.77 & 83.59 & 9.14 \\ \hline \end{tabular}
\end{table}
Table 3: The data for the ROP calculation.  
The experimental results were compared with the simulation results. The data demonstrates that the ROP of the cutters arranged in a mixed layout improved by approximately 23.5% compared to the bit with a triangular prism cutter. However, under simulation conditions, the ROP for the drill bit using the mixed cutter arrangement increased by about 21.1% compared to the bit with a triangular prism cutter. The variation between the two ROP improvements is around 10.5%, exemplifying the reliability of the numerical simulation results. Similarly, the comparison of rock-breaking effects of drill bits pre- and post-optimization of cutter arrangement schemes by numerical simulation using the Box-Behnken method is also reliable. This signifies that optimizing relevant parameters of the cutter arrangement scheme with the Box-Behnken method could effectively provide design parameters for field drilling operations.