# Development of an expert system for selection of multiphase flow correlations

## Abstract

Our target was to develop an expert system to help petroleum engineers in selecting the most suitable multiphase flow correlation in the absence of measured flowing pressure. A large database of pressure points was collected and analyzed using many multiphase flow correlations. The expert system was developed with a set of rules to identify the best correlation for variety of well, flow, and PVT conditions. The expert system is based on the idea of clustering the data and finding the best multiphase flow correlation(s) for each cluster. The error associated with the selected correlation is also quantified for every correlation in each data sub-cluster so the engineer would expect the accuracy of pressure drop prediction when utilizing this approach. Over the entire database, if one multiphase flow correlation is selected, the overall mean absolute percent error ranges between 12.7 and 57.5%, while the range of errors for best correlation(s) in different data sub-clusters range from 0.01 to 3% for most cases with accurate PVT. The expert system was validated by a new set of data. It succeeded in identifying the best correlation(s) 70% of the times, and the calculated pressure was more accurate than using one correlation by a factor of 2. Use of the expert system in the validation database gave a mean absolute percent error of 8.8%. This represents approximately one-third of the error value when any single correlation is used over the entire validation dataset. (Error for using single correlation ranges from more than 21 to 29%.)

## Keywords

Multiphase flow Out flow performance Multiphase correlations Production engineering Nodal analysis## List of symbols

- API
American Petroleum Institute (density measurement)

*A*_{t}Actual flowing pressure data

- bbl
Barrel

- Begg
Beggs and Brill correlation

- BHT
Bottom-hole temperature

*d*Diameter

- D
Day

- DRM
Duns and Ros modified correlation

- DRO
Duns and Ros original correlation

- ESP
Electrical submersible pump

- FB
Fancher and Brown correlation

- FT
Foot

*F*_{t}Forecasted flowing pressure data from different 14 correlations

- °F
Degree Fahrenheit

- GOR
Gas/oil ratio

- GRE
GRE correlation

- HB
Hagedorn and Brown correlation

- HYDRO
HYDRO correlation

- in
Inch

- ID
Inner diameter

- MAPE
Mean absolute percent error

- MPE
Mean percent error

- MB
Mukherjee and Brill correlation

*n*Number of data points

- OD
Outer diameter

- ORK
Orkiszewski correlation

- PET
Petroleum experts correlation

- PET 2
Petroleum experts 2 correlation

- PET 3
Petroleum experts 3 correlation

- PET 4
Petroleum experts 4 correlation

- PET 5
Petroleum experts 5 correlation

*q*_{L}Liquid flow rate

*q*_{o}Oil flow rate

- scf
Standard cubic feet

- T.S.
Tubing size

- W.C.
Water cut

- Ɣg
Gas specific gravity

*ε*Pipe roughness

- %
Percentage

## Introduction

Multiphase flow correlations are routinely used to calculate pressure (and temperature) drop in the tubing and flow lines for production and injection wells. The pressure drop calculations have many applications in artificial lift design and optimization, well deliverability forecasting, and flow assurance applications. Over several decades, many investigators developed multiphase flow correlations to calculate pressure drop in tubing at variety of conditions. Each correlation was derived for certain conditions. Several comparison studies between different correlations for specific sets of data are also available in the literature. Predicting multiphase flow pressure drop can sometimes present a challenge for practicing engineers.

Multiphase flow occurs due to the variations of phases that flow through one pipe. These phases may be oil, water, and gas. Due to the different properties of gas compared with oil and water for viscosities and other properties, the gas tends to flow faster than oil and past the liquid in the upward flow (gas slippage). The in situ liquid volume in the pipe is defined as the liquid holdup.

The pressure drop calculations depend on the properties of the mixture of liquid including oil and water in addition to the gas. The total pressure drop is equal to the summation of the hydrostatic, friction, and acceleration pressure drops. The hydrostatic term depends on the mixture density, which is a function of the liquid holdup. The friction term depends on the friction factor for the mixture. The acceleration term appears due to the change in velocity resulting from the change in pressure. The friction calculations depend on the flow regime, which in turn depends on the superficial velocity of liquid and gas phases.

The most common flow regimes for vertical wells include single liquid flow, bubble, slug, churn, annular, and mist flow. The possible flow regimes for horizontal wells usually include dispersed bubble, annular, slug, stratified wavy, and stratified smooth.

- 1.
Correlations that assume no slip and do not consider flow patterns. Examples include Poettmann and Carpenter (1952) and Fancher and Brown (1963).

- 2.
Correlations that consider the slip but not the flow patterns. Examples include Gray (1978) and Hagedorn and Brown (1964 and 1965), etc.

- 3.
Correlations that consider both the slip and the flow patterns. Examples include correlations by Duns and Ros (1963) and Beggs and Brill (1973).

The mechanistic models, however, usually include some physical phenomena with analytical relations to predict the flow patterns. In these models, mostly analytical expressions are used to calculate the different parameters for each flow regime. Examples for mechanistic models include Aziz et al. (1972) and Ansari et al. (1990).

Although many correlations to calculate the pressure drop in pipes are available, clear rules on how to select appropriate correlations do not exist in the absence of actual pressure measurements. In this work, an expert system is developed to select the best correlation(s) for specific well and flow conditions.

## Expert system development

The first step in developing the expert system was to collect a large database of pressure drop points covering a wide variety of well and flow conditions.

Range of data used in developing and validating the expert system

Data for development of the expert system (2730 points) | Data for validation of the expert system (144 points) | ||
---|---|---|---|

Property | Range | Property | Range |

qo, bbl/D | 5–36,800 | qo, bbl/D | 15–31,427 |

GOR, scf/bbl | 0–40,000 | GOR, scf/bbl | 223–6081 |

W.C., % | 0–98 | W.C., % | 0–76 |

BHT, °F | 82–370 | BHT, °F | 121–264 |

API, ° | 8–60 | API, ° | 13–46.5 |

ɣg | 0.57–1.81 | ɣg | 0.57–0.93 |

Depth, ft. | 250–14,358 | Depth, ft. | 650–12,862 |

To cover all the points in the database, more than 560 well models were developed using a commercial pipe modeling software. We performed around 1042 simulation runs and calculated the predicted bottom-hole flowing pressure using 14 different correlations for each point. We, then, calculated the error from each correlation for each point.

Average error and average absolute error of the different fourteen correlations for the entire database

Correlation Prosper Software Help Manual, Petroleum Experts (2013) | Database for development of the expert system (2730 points) | |||
---|---|---|---|---|

Mean percent error % | Mean absolute percent error % | Minimum absolute error % | Maximum absolute error % | |

Duns and Ros modified | 11.09 | 19.42 | 0.02 | 729.68 |

Hagedorn and Brown | − 4.74 | 13.68 | 0.00 | 466.54 |

Fancher and Brown | − 10.38 | 16.53 | 0.01 | 408.25 |

Mukherjee and Brill (1983) | 3.85 | 14.54 | 0.02 | 481.03 |

Beggs and Brill | 8.38 | 13.93 | 0.00 | 712.03 |

Petroleum experts | − 1.61 | 13.31 | 0.01 | 605.45 |

Orkiszewski (1967) | − 5.53 | 15.23 | 0.00 | 737.27 |

Petroleum experts 2 | − 0.80 | 12.88 | 0.00 | 568.50 |

Duns and Ros original | 2.82 | 12.81 | 0.00 | 321.14 |

Petroleum experts 3 | − 4.82 | 13.46 | 0.00 | 511.42 |

GRE | − 0.75 | 12.69 | 0.00 | 582.91 |

Petroleum experts 4 | − 2.73 | 13.34 | 0.00 | 320.65 |

Hydro 3P | 49.16 | 57.52 | 0.00 | 954.75 |

Petroleum experts 5 | − 0.75 | 12.67 | 0.00 | 586.94 |

Shallow depth is for points that are less than 2000 ft. TVD, deep is for pressure points that are more than 9000 ft. in depth, and the moderate depth is between.

Sub-clusters production criteria for oil wells [after Abd El-Moniem and El-Banbi (2015)]

qo, bbl/D | W.C., % | GOR, scf/bbl |
---|---|---|

< 2500 | < 5 | < 1000 |

2500–10,000 | 5–30 | 1000–5000 |

> 10,000 | 30–70 | > 5000 |

> 70 |

Sub-clusters reference number and data points for oil wells

A Microsoft Access program was developed for the entire dataset to store the actual values of pressure, calculated values from all 14 correlations, and the error for every point. The Access Database was then used to extract a total of 131 sub-clusters for tubular flow and identify the best correlation(s) in each sub-cluster.

The clusters (13) are divided based on geometry (well depth, well deviation, and ID). The sub-clusters division is based on flow conditions (oil rate, WC, and GOR). According to these divisions, we should theoretically have 13 × 36 sub-cluster. However, many sub-clusters did not contain data (e.g., it is not possible to have high oil rate wells with small ID, and it is not possible to have high GOR wells with high oil rate and high WC). The sub-clusters that contained enough data points to draw conclusions were 131.

- 1.
Strong sub-cluster containing more than 20 points.

- 2.
Moderate sub-cluster containing between 5 and 20 points.

- 3.
Weak sub-cluster containing less than 5 points.

The identification of different levels of correlation strength was covered by defining a correlation “strength factor” and covered in Abd El-Moniem and El-Banbi (2015). They also reported the error for every correlation in every sub-cluster.

## Results

Sample of complete results for one sub-cluster [after Abd El-Moniem and El-Banbi (2015)]

### Application of the expert system

The use of the expert system is based on selecting the appropriate cluster as shown in Fig. 3. The selection of the cluster is based on (1) well type (vertical, deviated, or horizontal), (2) tubing size, and (3) depth. The following step is to select the sub-cluster based on (4) oil production rate, (5) gas/oil ratio (GOR), and (6) water cut as listed in Table 4. The sub-cluster is determined from Fig. 3 and Table 4. The detailed sub-cluster tables to determine the best correlation, its strength, and expected error range are given in “Appendix A.” An example on how to use the expert system is also given in “Appendix B.”

We also developed a VBA (Visual Basic code) for Microsoft Excel to facilitate the selection of the appropriate correlation. The user can input the six inputs required by the expert system, and the VBA code will automatically find the following information: (1) the cluster and sub-cluster where the user data point is located, (2) the multiphase correlation(s) that should be used to predict the pressure drop for this particular data point, (3) the expected error of this best correlation(s) in the database, and (4) the strength factor for the selected correlation(s) within the sub-cluster. The authors can share the VBA code with interested readers.

### Validation of the expert system

Expert system validated points status

Performance results of the expert system versus all correlations for validation dataset

Correlation | Mean percent error % | Mean absolute percent error % |
---|---|---|

Expert system | − 0.22 | 8.82 |

Duns and Ros modified | 17.16 | 28.06 |

Hagedorn and Brown | 5.81 | 24.14 |

Fancher and Brown | − 2.04 | 29.18 |

Mukherjee and Brill | 14.55 | 21.20 |

Beggs and Brill | 17.53 | 22.16 |

Petroleum experts | 8.55 | 23.16 |

Orkiszewski | 2.83 | 25.79 |

Petroleum experts 2 | 9.47 | 23.30 |

Duns and Ros original | 13.77 | 21.59 |

Petroleum experts 3 | 5.18 | 24.88 |

GRE | 8.70 | 22.65 |

Petroleum experts 4 | 9.76 | 21.96 |

Hydro 3P | 11.07 | 21.74 |

Petroleum experts 5 | 9.27 | 22.33 |

### Sensitivity of the expert system to uncertain input parameters

In this section, we wanted to test the strength of the expert system and how it reacts to inaccurate input data. The measured GOR is usually among the most uncertain parameters in oil well operations. Other parameters that may carry some uncertainty include API gravity of the oil, specific gravity of the gas, and tubing roughness. In each one of these four parameters, a random subset of the database was used to test the effect of the parameter sensitivity on the expert system accuracy. In the sensitivity analysis study, we used a randomly selected dataset out of the database. We made sure the selected dataset covered points from most sub-clusters. The sensitivity analysis work involves changing a parameter (e.g., GOR or API) and running all correlations again with the new value for GOR or API, then extracting the data, calculating errors, and comparing correlations with actual data. Enough points were tested to validate and generalize the conclusions regarding the effect of these parameters.

For each point within the subset of the database, the parameter was perturbed by 10–20% and the expert system was run to predict the best correlation(s). The suggested correlation by the expert system was also used (with the perturbed input parameter) to predict the pressure drop and compared with the actual value of the pressure. The following paragraphs summarize our findings from the sensitivity study.

### GOR sensitivity

GOR affects both the input to the expert system and the input to correlation calculations. Four groups of wells were selected: (1) low GOR and high oil rate wells, (2) high GOR and high oil rate wells, (3) low GOR and low oil rate wells, and (4) high GOR and low oil rate wells.

For low GOR and high rate wells, the expert system could predict the best correlation with a success rate of 56%, when the GOR input (one of the sensitive input parameters) was changed by ± 20%. This reflects that changing GOR for low GOR high rate wells has a moderate effect in changing the order of the best correlation.

For high GOR and high rate wells, the expert system could predict the best correlation by 75%. It reflects that changing GOR for high GOR high rate wells by a percentage of ± 20% has a slight effect in changing the order of the best correlation.

For low GOR and low rate wells, the expert system could predict the best correlation by 37.5%. It reflects that changing GOR for low GOR low rate wells by a percentage of ± 20% has a significant effect in changing the order of the best correlation.

For high GOR and low rate wells, the expert system could predict the best correlation 95% of the cases. We can safely conclude that a ± 20% error in GOR for those wells had minor effect in changing the order of the best correlation.

Effect of different sensitive parameters on correlation prediction

Well flow condition | GOR effect | API effect | Gas specific gravity effect | Tubing roughness effect |
---|---|---|---|---|

Low GOR and high production rate | Medium | Low | Low | Low |

Low GOR and low production rate | High | Low | High | Low |

High GOR and high production rate | Low | Low | Medium | Medium |

High GOR and low production rate | Low | Low | Low | Low |

### Other parameters sensitivity

Other parameters were investigated to check their uncertainty on the expert system and the error of the calculated pressure by the selected correlation(s). These parameters include API, gas specific gravity and tubing roughness.

Changing the API of the oil by ± 10% had slight effect on both the expert system selection and the calculated pressure drop by the selected correlation. In more than 90% of the cases, the expert system was successful in picking up the best correlation even with the ± 10% error in API.

For gas specific gravity, changing gas specific gravity with ± 10% had minor effect on changing the order of the best correlation as the expert system predicted the best correlation with 90%. The exception was for low GOR low rate wells, as the expert system could obtain the best correlation with only 37.5%.

For tubing roughness, the expert system could obtain the best correlations 95% of the time. The exception was for high GOR high rate wells, where the expert system could predict the best correlation with only 37.5%.

The selection of the range of sensitivity analysis parameters was mainly based on measurement errors in operations of oil fields. GOR measurement error may reach ± 20%, while API and specific gravity of gas are usually estimated with much more certainty. Table 8 summarizes the results of the sensitivity analysis of these parameters and their effect on changing the order of the best correlation and consequently the capability of the expert system to predict the best correlation even with some measurements errors.

## Conclusions

- 1.
The overall mean absolute percent error is around 12.7% for the best multiphase flow correlation in the entire dataset, while the range of errors for the best correlation(s) in different data sub-clusters is from 0.01 to 3% for most cases with accurate PVT.

- 2.
In the validation dataset, the mean absolute percent error was 8.8% when the expert system was used. This represents approximately one-third of the error value when any single correlation is used over the entire dataset. (Error for using single correlation ranges from more than 21 to 29%.)

- 3.
From the sensitivity runs, we found that GOR, API, and gas specific gravity may have different degrees of effectiveness on the correlation selection. PVT data are probably one of the most important multiphase flow correlations input data affecting the accuracy of the correlation.

- 4.
In practice, an accurate gas rate should be determined through production test separator especially for low rate oil wells as GOR has important effect on pressure drop results. GOR was found to have impact on changing the best correlations for different clusters of oil data in case of low GOR wells. However, GOR has minor effect on selection of best correlations for high GOR wells.

- 5.
Tubing roughness was found to have small impact on changing the best correlations for different clusters of oil well data (except for high GOR and high oil rate wells).

## Notes

## Supplementary material

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