## 3 Results
### Rheological Properties with Temperature Response Characteristics of SFPDF  
3.1 KL, PAM, and XC Drilling Fluid and Rheological Properties with Temperature Response Characteristics of SFPDF  
Based on previous research and on the analysis given above, formulae were developed for the three types of SFPDF:  
Sample 1: 1L H\({}_{2}\)O + 15% NaCl + 0.5% NaOH + 0.8% KL;  
Sample 2: 1L H\({}_{2}\)O + 15% NaCl + 0.5% NaOH +0.4% PAM;  
Sample 3: 1L H\({}_{2}\)O + 15% NaCl + 0.5% NaOH +0.8% XC;  
The rheological parameters of the three samples were tested using a series of decreasing temperatures, and Figure 2 shows the curves of shear stress with the shear rate. Figure 2 shows the fitting curve and Table 4 shows the goodness-of-fit (\(R^{2}\)) and the sum of square errors (SSE) of four kinds of rheological models for the three kinds of drilling fluids. Figure 2: Shear stress with shear rate curves of three types of polymer drilling fluid at different temperatures. (**a**) Shear stress with shear rate curve of KL polymer drilling fluid shear stress with the shear rate curve; (**b**) Shear stress with the shear rate curve of PAM polymer drilling fluid; and (**c**) shear stress with the shear rate curve of XC polymer drilling fluid. Regression analysis of the rheological curves for drilling fluid with three kinds of polymers at different temperature was carried out using linear regression. The Herschel-Bulkley model was still the most ideal rheological model for all of the types of polymer systems and at all of the temperatures studied here (Table 4) by comparing the \(R^{2}\) and the SSE. This explains that the change in temperature did not change the rheological model of the drilling fluid system for SFPDF. For this reason, the Herschel-Bulkley model of the parameters was used to characterize the viscosity-temperature response law of solid-free polymer drilling fluid. Figure 3 shows the response curve that connects the data points based on this data. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Temperature (\({}^{\circ}\)C)** & & **10** & **7** & **4** & **1** & **-2** & **-5** & **-8** & **-11** \\ \hline \multirow{4}{*}{Sample 1 ** & 0.9383 & 0.9163 & 0.9351 & 0.9269 & 0.9125 & 0.9171 & 0.9145 & 0.9176 \\  & \multirow{2}{*}{BP model  & 0.9176 \\  & \multirow{2}{*}{SPE  & 0.9176 \\  & \multirow{2}{*}{SPE  & 0.9965 & 0.9965 \\  & \multirow{2}{*}{SPE [FOOTNOTE:6]Footnote 6: \(\mathrm{H_{2}O}\) + 15\(\mathrm{NaCl}\) + 0.5\(\mathrm{\%}\) NaOH + 0.8\(\mathrm{\%}\) KL\({}_{2}\)\({}^{2}\) H\({}_{2}O\) + 15\(\mathrm{NaCl}\) + 0.5\(\mathrm{\%}\) NaOH + 0.4\(\mathrm{\%}\) PAMM; \({}^{3}\) H\({}_{2}O\) + 15\(\mathrm{NaCl}\) + 0.5\(\mathrm{\%}\) NaOH + 0.8\(\mathrm{\%}\) XC; \({}^{4}\) the Bingham plastic model; \({}^{5}\) the Power Law model; \({}^A residual figure was produced using different functions of curve fitting (Figure 3). By comparison of the curve of apparent viscosity, yield stress, and consistency coefficient, the linear fitting of the residual distribution, as well as the trinary polynomial residual distribution of flow behavior indices, were both close to a normal distribution. In this way, a linear function curve fitting of apparent viscosity, yield stress, and consistency coefficient was drawn (Figure 3). A trinary polynomial function fitting the flow behavior indices was used and Table 5 shows the fitting equation. Figure 3 and Table 5 shows the following:  
(1) The apparent viscosities of the three polymer drilling fluids analyzed here were found to increase with decreasing temperature. In addition, the volume required for the PAM drilling fluid was found to increase slightly less than that of the KL drilling fluid and the XC drilling fluid. The apparent viscosity of the PAM drilling fluid was lower than that of the KL drilling fluid and the XC drilling fluid. The analysis above is completely consistent with the actual phenomenon that viscosity of the drilling fluids increased with temperature reduction.