# A Nodal Analysis Based Monitoring of an Electric Submersible Pump Operation in Multiphase Flow
## 4 Materials and Methods
### Model Validation and Interpretation  
To evaluate the model's utility, we used Delaware Basin oil well data to validate and calibrate the model under field conditions. We used the Schlumberger PIPESIM software (version 2017.01) to build a horizontal well model, then calibrated the model using field data, as shown in Figure 7. A horizontal oil well was considered as a test example. Table 2 summarizes the well, reservoir, fluid, and production data used in this model. The IPR curve was developed using the pseudo-steady state gas equation established by [PERSON] and [PERSON] (2018). The pressure drop in the tubing was estimated by employing the Hagedorn and Brown correlation for vertical sections and the Beggs and Brill correlation for horizontal sections ([PERSON] et al., 2019; [PERSON] et al., 2020). Thereby, the model estimated an approximate oil production rate of 430.3 STB/d. Less than 0.07% relative error was calculated compared to the field production rate. Figure 5: Variations in TPR curves as ESP performance varies. (**a**) Multiphase flow (dead well), (**b**) single-phase flow (dead well), (**c**) multiphase flow (naturally flowing well), (**d**) single-phase flow (naturally flowing well). The TPR-ESP curve reflects the TPR of a well with an ESP when the nodal analysis is performed at the intake (nodal point A of Figure 1). After that, ESP equipment optimized for wells of various types was selected during nodal analysis. Then, the GVFs were increased from 0.03 to 0.99 at a fixed gas-oil ratio (GOR) and water cut (W\({}_{\text{cut}}\)); the model was tested under multiphase conditions when GOR = 2218 SCF/STB and WC = 92.9% (real well data) and under single-phase conditions when GOR = 100 SCF/STB and W\({}_{\text{cut}}\) = 0 (artificial data). We used the homogenous model to calculate the corresponding heads and PIP/Pd differential pressures at specified GVFs. Thus, we performed a sensitivity analysis of ESP behavior at the intake and discharge nodes using the calculated differential pressures when the GVF varied. The Pd and PIP values at various GVFs were compared with the values of the specified, normal operating ranges (within \(\pm\)5% of the design conditions). We developed a method predictive of ESP operation conditions, from normal to shutdown (Table 3). The PIPs calculated at nodes were used to predict the critical gas fractions (\(\lambda_{\text{c}}\) values) at which an ESP abnormality (surging) commenced. For example, Ref. [15] showed that abnormal ESP operation commenced when the Turpin correlation \(\mathcal{O}_{\text{Turpin}}\geq 1\) (Table 1). Using this correlation, the PIPs appropriate for all pump conditions studied during nodal analysis were used to compute the corresponding critical gas fractions. We also employed the correlations established by [PERSON], [PERSON], and [PERSON] (Table 1). Figure 6: IPR curve variations at various ESP performances. (**a**) Multiphase flow (a dead well); (**b**) single-phase flow (a dead well); (**c**) multiphase flow (a naturally flowing well); (**d**) single-phase flow (a naturally flowing well). The IPR + ESP curve adequately reproduces the IPR + ESP curve when the nodal analysis is focused on the discharge node (nodal point B of Figure 1). \begin{table}
\begin{tabular}{l c} \hline \hline
**Parameter** & \\ \hline Reservoir pressure (psia) & 3378.93 \\ Reservoir temperature (F) & 206 \\ Payzone thickness (ft) & 68 \\ Horizontal distance (ft) & 3901 \\ Well permeability, (kx, ky, kz, respectively) (md) & 0.05, 0.05, 0.05 \\ Water cut (\%) & 92.9 \\ Gas oil ratio, GOR (SCF/STB) & 2218 \\ Gas SG & 0.65 \\ API & 42.98 \\ Well measured depth (MD) (ft) & 12,216 \\ Tubing measured depth (MD) (ft) & 7021 \\ Tubing ID (in) & 2.785 \\ Oil production rate (STB/d) & 430 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Input data sets, field example oil well.