A Neural-Network Approach for Modeling a Water-Distribution System

Fig. 1—Crossplot of results of the third neural-network-model run: predicted vs. actual flow-rate data. The outliers are highlighted by the yellow circle in the graph.

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The authors present a new data-driven approach to estimate the injection rate in all noninstrumented wells in a large waterflooding operation accurately. The paper outlines the methodology and procedures used to analyze a branch of the water-network system and the modeling of accurate estimation of injection rates. The model performance is distinctive in its use of only field and wellhead measured data and considering the natural uncertainty inherited in these values.


Lost Hills is a relatively large oil field located in western California. The field contains a significant amount of remaining producible reserves. There are six oil pools in five producing units of varying geologic age. The permeability of one of these units, the Monterey formation, is very low on the scale of millidarcies, which leads to lower production rates and even a very low recovery factor for the field. To address this challenge, a new expansion of the field was undertaken, with the introduction of waterflood development and close infill drilling.

Lost Hills operations follow a basic ­injection-system setup of a typical water­flood. Produced water is transported to the water strain. After the filtration steps are complete, the polished water is pumped into a 20-in. trunk line to the main tank battery. From the main trunk line, the line is reduced to 16 in. and is dedicated to the northernmost portions of the fields. It then is further reduced to an 8-in. line to the western portion, where Header 43 (the subject of this study) is located. This type of system with two separate strings, more formally known as a dual-string injection system, has the advantage of being able to inject water into specific depths of the reservoir. Basic terminology for this type of system classifies the short string as surface casing and the long string as production tubing. Such a system might have the ability to inject at shallow depths by use of the short string, while producing from a deeper interval by use of the long string.

Technology Overview

Artificial Neural Networks (ANNs). An ANN is a computational method based on a large collection of neural units, or artificial neurons, that loosely imitates how a biological brain would solve problems. Each neuron is connected and may have a different function to estimate the overall function of the data set. The system is self-trained, rather than explicitly programmed. A number of inputs are provided into the system, and the hidden layers use the various neurons to derive the relationship between the inputs to reach the output.

Pressure-Drop-Simulation Software. A process-engineering software was used that allows state-of-the-art modeling and simulation of flow in oil-and-gas-­gathering networks and pipeline systems. The platform offers the flexibility to model applications ranging from ­single-well sensitivity analyses of key parameters to a multiyear planning study for an entire producing field. The tool covers a range of fluids encountered in the industry, including single-phase oil and various compositional mixtures.

For the purposes of this study, the software was used to model the pressure drops expected along the main branch line and validate them with the measured values collected from the pressure-­indicator transmitter (PIT). Once validated, the pressure drops were computed through analogy for the branches where pressure measuring instruments were not available and from estimation of upstream pressure of the manual-injection wellheads.


Header 43 and its corresponding pipeline branch were selected for the initial model for three major reasons:

  1. Continuous data gathered from the automated wells are readily available.
  2. A significant number of wells (eight) on the branch correspond to this header, with a good mixture of wells having both a long and a short string.
  3. A PIT is located exactly at the header.

The location of the PIT at the header inlet allows for pressure to be measured at this location and significantly strengthens the development and validation of the model. In addition to having a significant number of active automated wells on this branch, the mixture of both dual and single completions was welcomed into the system.

Data Collection. The sources of data collection in the study include automated control valves, PITs, flowmeters, and pressure losses in pipelines. For the current pilot, a full year of data (30 June 2015 to 30 June 2016) was queried from the system.

Software Modeling. Pressure-drop and flow-rate simulation for the entire water-distribution network was modeled with the software. Consequently, a representation of Header 43 was built in order to understand the pressure drop through the pipeline at each of the wells. The shortcoming that had to be addressed during this modeling process was the inability of the software to create separate strings for each well that had a dual-string setup. However, because the pressure reading for each of the wells is measured after the choke, these pressures will not have any relationship with any other pressures on the branch at a given PIT inlet pressure.

Software Model Inputs and Outputs. Ten randomly selected samples within the 5 months of operations were used to estimate and validate the pressure drop for the entire length of the pipeline. These pressures at the header and the flow-rate values at each node were entered into the software program. Each sampled timestep included values of flow rates for each node and the corresponding header pressure for that same time stamp. For all 10 selected samples, an estimated pressure drop was obtained through the software’s simulation function. The total pressure drops were then averaged, and the resulting values were used to derive an empirical relationship between pressure and length of pipe for this system. This pressure drop calculated from each length of pipe to the wells was then subtracted from the PIT inlet pressure at Header 43. The resulting value, which the authors refer to as pressure upstream of choke, could then be used to calculate a pressure drop across the choke for each time stamp. This resulting value was introduced into a neural-network model, resulting in a much higher degree of accuracy in neural-network modeling.

Results: Neural-Network Model

First Run. The first neural-network run concerned one well, 3-11 WCL, and was used as a test to determine whether the neural network had the capability to derive a relationship with the inputs. The model trained surprisingly well, especially considering the randomness seen during the data-visualization steps, in scatter plots, and in histogram distributions. However, the achieved relationship is specific to this particular well and might not be a good indicator of the entire branch or (to a greater extent) the field. This initial result provided confidence that the developed neural-network model can perform accurately. Thus, the authors expanded the method to include all eight wells on the Header 43 branch.

Second Run. The next run used all eight wells on Header 43. The entire data set consisted of 40,630 training cases, out of which 28,430 were used as the training set and 12,200 were used to validate the model’s accuracy. The system performance, however, showed a coefficient of determination (R2) of .667 for the training set and R2=.67 for the validation set. This performance suggests that the model is not as accurate as intended and is not a good enough fit.

Third Run. In this run, the cases with injection rates lower than 150 BWPD and higher than 300 BWPD were removed. Thus, the total number of compiled cases decreased to less than 23,000. The results of the third run improved, with the model showing a performance of R2=.766 for the training set and R2=.784 for the validation set. Interestingly, the endpoints still contained the most error associated with the model. The lowest error seemed to be achieved at an injection rate of approximately 200 BWPD. Fig. 1 above consists of a crossplot of the actual flow rates and the predicted flow rates given by the validation set. Note the cluster of data points within the yellow circle; these can be considered outliers that do not correlate well. However, it was calculated that 83.63% of the data in the crossplot was between a ±20-BWPD margin from an ideal 1:1 predictor. For approximately 4,500 data cases, this result indicates a high level of correlation.

Fourth Run. During the fourth run, discussions on improving the accuracy of the model resulted in the decision to add a new variable to the input set and capture the relative variation of pressure between upstream of choke and downstream of choke. The addition of this new input attribute yielded improved results vs. the previous run. The R2 values increased significantly to .931 for the training set and .899 for the validation set. The process illustrates that the model’s accuracy improved significantly for each respective model’s training sets.

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 185678, “A Neural-Network Approach for Modeling a Water-Distribution System,” by Andrei S. Popa, Chevron; Conor O’Toole, University of Southern California; Juan Munoz, Steve Cassidy, and Dallas Tubbs, Chevron; and Iraj Ershaghi, University of Southern California, prepared for the 2017 SPE Western Regional Meeting, Bakersfield, California, USA, 23–27 April. The paper has not been peer reviewed.

A Neural-Network Approach for Modeling a Water-Distribution System

01 May 2018

Volume: 70 | Issue: 5


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