Learning characteristic parameters and dynamics of centrifugal pumps under multiphase flow using physics-informed neural networks

TL;DR

This paper addresses the challenge of monitoring centrifugal ESPs under multiphase flow by developing a physics-informed neural network (PINN) that estimates fluid properties, dynamic states, and key pump parameters from inlet and outlet pressures. A lumped-element ESP model is integrated with a PINN, and comprehensive identifiability analyses (structural and practical) guide which parameters can be reliably estimated. The method is validated with simulated and experimental data, showing PINN generally achieves accurate state estimation and competitive parameter estimation compared to a particle filter, while offering a cost-effective alternative to traditional multiphase flow meters. The results support the potential of PINN-based virtual flow metering for improved ESP operation, with insights on identifiability and data requirements for robust deployment in field-like conditions.

Abstract

Electrical submersible pumps (ESPs) are prevalently utilized as artificial lift systems in the oil and gas industry. These pumps frequently encounter multiphase flows comprising a complex mixture of hydrocarbons, water, and sediments. Such mixtures lead to the formation of emulsions, characterized by an effective viscosity distinct from that of the individual phases. Traditional multiphase flow meters, employed to assess these conditions, are burdened by high operational costs and susceptibility to degradation. To this end, this study introduces a physics-informed neural network (PINN) model designed to indirectly estimate the fluid properties, dynamic states, and crucial parameters of an ESP system. A comprehensive structural and practical identifiability analysis was performed to delineate the subset of parameters that can be reliably estimated through the use of intake and discharge pressure measurements from the pump. The efficacy of the PINN model was validated by estimating the unknown states and parameters using these pressure measurements as input data. Furthermore, the performance of the PINN model was benchmarked against the particle filter method utilizing both simulated and experimental data across varying water content scenarios. The comparative analysis suggests that the PINN model holds significant potential as a viable alternative to conventional multiphase flow meters, offering a promising avenue for enhancing operational efficiency and reducing costs in ESP applications.

Figures (16)

• Figure 1: Schematic diagram of the experimental setup: A schematic diagram of the experimental setup indicates all the piping system's components and dimensions. It has four distinct flow lines, an oil flow line, a water flow line, a two-phase flow line carrying the oil-water mixture, and a closed loop of water used in the heat exchanger (HE). The separation tank is open to the atmosphere and separates the oil and water phases from the emulsion by gravity. It also stores the oil and water phases. The fluids are pumped independently from the separator tank and operate in a closed loop. The twin-screw pump pumps the oil phase from the separator tank. Then, the oil phase flows through a shell and tube heat exchanger, a water fraction meter (measures the water fraction inside the oil phase), and a Coriolis meter (measures the mass flow rate and density). A single-stage centrifugal pump pumps the water phase from the separator tank that flows through a Coriolis meter and a remotely controlled valve. Then, the oil and water phases mix in a "T" joint, forming an emulsion. Then, the emulsion is pumped by the ESP, flows through a remotely controlled valve, and returns to the separation tank.
• Figure 2: Schematic representation of the Physics-informed neural network for the ESP system: The deep neural network, shown in the red dashed-dotted rectangle on the left, is considered to approximate the solution of the ODEs system described in \ref{['subsec:esp-model']} (eq:esp-model1eq:esp-model6). The input to the neural network is time, denoted by $t$, and the output is the ESP system states, highlighted in the green dotted rectangle of the figure. Each differential equation of the ESP system has residues at certain collocation points that must be minimized. We indicate them in the black dotted region on the right. The time derivative of each state (DNN output) is computed using automatic differentiation. The total loss, denoted as $\mathcal{L}(\bm{\theta})$, includes data loss, physics (ODE) loss, and initial condition loss. The data loss ($\mathcal{L}^{data}(\hat{y}-y))$ is the loss between the DNN output and measured data, the physics (ODE) loss is the loss of the residue of the equations at the collocation points, and the initial condition loss is a loss between the initial condition and the DNN output at $t=0$. $\bm{\lambda}_d$, $\bm{\lambda}_r$, and $\bm{\lambda}_{ic}$ are the weights to the data loss, physics loss, and initial condition loss, respectively, while calculating the total loss. These may be fixed or adaptive. $\bm{\Lambda}$ are the unknown parameters in the ODE system. The activation function of the DNN is represented by $\sigma$.
• Figure 3: Absolute values of the estimated correlation matrices for ESP system model parameters. The matrices are derived based on the FIM. The matrix indicates whether parameters are identifiable or not. Parameters with absolute correlation values near 1 are practically unidentifiable. The \ref{['fig:practical_corr_12']} represents twelve structurally locally identifiable parameters, while the \ref{['fig:practical_corr_8']} focuses on eight parameters, particularly keeping fluid properties and pipeline resistances unknown.
• Figure 4: Cases and scenarios evaluated. As presented in \ref{['subsec:ps-var']}, two experimental investigations (blue) are performed, considering different water fractions and initial angular velocities. Each experimental investigation is analyzed using three different data sources (scenarios): simulation data, simulation data with added Gaussian noise, and experimental data collected from the instruments (green). For each scenario, three sets of unknown parameters, denoted as cases, are evaluated (red). Thus, we have 9.0 different results for each experimental investigation.
• Figure 5: Comparison of predicted and true states for the simulated scenario of the first experimental investigation with unknown parameters. The blue line indicates the true values, while the $\times$ markers denote the data points used for training the PINN. The red, black, and green lines represent the mean values of the predicted states calculated at each time instant across the 30.0 trained PINNs for Cases 1 to 3, as defined earlier in this section (\ref{['sec:results_pinn']}). Across all cases, the training dataset consists of 30.0 data points for the data loss in $P_1$ and $P_2$ and 100.0 collocation points for the physics loss. For brevity, the results for $Q_1$ and $Q_2$ are presented in \ref{['apdx:pinn_results']}, as they are similar to $Q_p$.