# A Nodal Analysis Based Monitoring of an Electric Submersible Pump Operation in Multiphase Flow
## 4 Materials and Methods
### Nodal Analysis Simulation  
Nodal analysis can be used to increase oil and gas well production by determining an optimal flow rate, identifying problems, and optimizing artificial lifting. A point of interest in the production system serves as a node; this is an intersection point of the inflow and outflow performance curves. [PERSON] [33] found that a combination of pump intake and discharge node data, as well as downhole pressure information, could be used to analyze ESP performance. The inflow and outflow curves are governed by Equations (9) and (10), respectively, when the intake pressure node serves as the nodal point (A in Figure 1). \[\mathrm{I_{IPR}}=\mathrm{PIP} \tag{9}\]  
\[\mathrm{V_{VLP}}-\mathrm{E_{ESP}}=\mathrm{PIP} \tag{10}\]  
The inflow and outflow curves are governed by Equations (11) and (12), respectively, when the discharge node serves as the nodal point (B in Figure 1). \[\mathrm{I_{IPR}}+\mathrm{E_{ESP}}=\mathrm{P_{d}} \tag{11}\]  
\[\mathrm{V_{VLP}}=\mathrm{P_{d}} \tag{12}\]  
where \(\mathrm{I_{IPR}}\) is the inflow performance relationship, \(\mathrm{E_{ESP}}\) is the ESP performance, \(\mathrm{V_{VLP}}\) is the vertical (tubing) lift performance, and PIP and Pd are defined above. We simulated this approach using Schlumberger PIPESIM software (version 2017.01); we employed nodal points A and B as defined above. To generalize the model, we evaluated different types of wells. For example, an ESP deployed in a dead well was used to stimulate production; an ESP installed in a naturally flowing well served to increase production. We considered both single-phase and multiphase conditions inside the pump. Using the homogenous model, we calculated the \(\Delta\mathrm{P_{pump}}\) at various GVF conditions. The PIP was estimated using nodal point A. The Pd was evaluated at nodal point B. Again, we set threshold ranges for normal operation by reference to field data; any point outside a range reflected an abnormality. For example, ESP operation was considered abnormal when the PIP deviation caused by gas slugging exceeded 5% in the Mangala oil field [27]. [PERSON] [34] reported that a PIP deviation \(>\) 3% indicated gas locking. Thus, we considered that PIP deviations \(\pm\) 5% were normal, implying that the ESP operated under maximum production conditions (Q\({}_{\mathrm{max}}\)) when PIP fell by 5% from the design value; conversely, the ESP worked under the minimum operating conditions when the PIP increased by 5% of the design value--any greater deviation indicated an abnormality. In detail:  
Step 1 (nodal analysis in the absence of the ESP): Nodal analysis proceeded under natural flow conditions prior to ESP installation; we estimated the bottomhole pressure (BHP) and production rate (Q\({}_{\mathrm{N}}\)) for a well exhibiting natural flow (Figure 2a) and the BHP for a dead well (Figure 2b). Step 2 (nodal analysis in the presence of an ESP): The ESP was installed, and nodal analysis proceeded at the intake node (nodal point A, Figure 1). We recorded the operating ESP PIP\({}_{a}\) and production rate (Q\({}_{a}\)) under the design conditions (Figure 3a). Step 3: We calculated the PIP\({}_{\mathrm{min}}\) (PIP\({}_{\mathrm{min}}\) = PIP\({}_{a}\) + 0.05 PIP\({}_{a}\)) and PIP\({}_{\mathrm{max}}\) (PIP\({}_{\mathrm{max}}\) = PIP\({}_{a}\) \(-\) 0.05 PIP\({}_{a}\)) and projected these onto Figure 3a to compute Q\({}_{\mathrm{min}}\) and Q\({}_{\mathrm{max}}\) (Figure 3b). Step 4: We performed nodal analysis at the ESP discharge point (nodal point B, Figure 1) and estimated the discharge pressure of the operating pump (Pda) (Figure 4a). Step 5: We plotted Q\({}_{\mathrm{min}}\) and Q\({}_{\mathrm{max}}\) (estimated in step 3) to compute Pd\({}_{\mathrm{min}}\) and Pd\({}_{\mathrm{max}}\) for the ESP discharge point (Figure 4b). Moreover, based on Equations (9) and (10), a conceptual graph showing the variation in the tubing performance (TPR) curve was developed by reference to the ESP operating conditions. In Figure 5a-d, the TPR-ESP curve adequately represents the ESP tubing performance.