Estimating pressure drop in vertical wells using a group data processing method (GMDH) approach; A comparative study. Reliable estimation of wellbore pressure drop is essential to solving many important production engineering and reservoir analysis problems. The purpose of this project is to create a tool that can estimate the pressure drop in a vertical well using the smallest possible variables.
This project group uses the Method of Data Handling (GMDH) approach to build the model. And for the optimization of the model, Trend Analysis is also used to arrive at a physically sound model. The analysis of the results was also confirmed with the test set that has not yet been seen by the GMDH during the development of the model and which still allowed an accurate estimation of the pressure drop to be achieved.
In addition, the model's simplicity and good functionality made it a better choice when it comes to predicting a pressure drop in any multi-stage vertical well. Mohammed Abdalla Ayoub, helping me complete this project with his full support, guidance and knowledge sharing. Working on this project has given me a very good experience on how to gain knowledge and work as engineers work.
- Project Background
- Group method of data handling (GMDH) Algorithms
- Selection of Independent variables
- Problem statement
- Objectives
- Feasibility of the study
The main problem with estimating the pressure drop in a vertical well is the number and type of independent variables that can affect the pressure drop. It can be used in simple hand calculations where it is easier to calculate the pressure drop than the Aziz et al model. Many methods have been proposed to estimate the pressure drop in vertical wells producing a mixture of oil and gas.
Accurate prediction of pressure drop in vertical wells can be very useful in cost management when it comes to well completion and production optimization. The accuracy of estimating the pressure drop in vertical wells has been discussed frequently in the last decades. Since measuring the pressure drop in vertical wells is not a practical option due to its high cost.
The aim of this project is to create a model capable of estimating pressure drop in vertical wells using the smallest possible number of parameters and to compare its performance with the best current methods. In addition, this new model can be generally considered for pressure drop estimation in vertical wells in the oil and gas industry due to its simplicity and high accuracy.
- Overview
- Empirical Correlations
- Mechanistic Models
- Artificial Neural Networks
Takacs (2001) collected and summarized the findings of many previous investigations on the accuracy of the various pressure drop calculation models. It applies a modeling approach to solving the pressure drop calculation and is based on a comprehensive description of the basic mechanisms that occur in multiphase flow. None of the available vertical multiphase pressure drop calculation models are generally applicable because their prediction errors can vary significantly in the different ranges of the flow parameters.
Most early pressure drop calculation was based on these correlations because of their direct applicability and fair accuracy over the range of data used in model generation. Hagedorn & Brown Correlation (1965): The Hagedorn & Brown correlation is one of the most common correlations used in industry. Prior knowledge of fluid retention is needed to calculate the pressure drop using the Mukherjee & Brill (1985) correlation.
This model was developed as part of the Tulsa University Fluid Flow Project (TUFFP) research program. Ayoub Model (2004): Ayoub presented an Artificial Neural Networks (ANNs) model for predicting the bottom hole flow pressure and consequently the pressure drop in vertical multiphase flow.
- Overview
- Data Gathering & Processing
- Partitioning
- Building GMDH Model
- Software Used
- Trend analysis
- Statistical Error Analysis
- Graphical Error Analysis
- Cross-plots
- Error Distribution
- Limitations of the Model
An optimization study also used the trend analysis that confirmed the physical feasibility of the proposed model. The most important and critical step in the project is the data collection, which has the biggest impact on creating a successful model. During the data collection and gathering, the quantity and quality of the collected data are taken into account to ensure sufficient information that helps to build the model.
Besides that, some of these parameters may not be available in the data collection process due to some technical problems. Although this inadequacy in the data may reduce the accuracy of the model, it may not have significant effects either, as will be discussed later. These input variables are oil rate, water rate, gas rate, diameter of the pipe, length of pipe “depth”, wellhead pressure, surface temperature and oil gravity “API”.
By definition, the training set is used to build and develop the model, the validation set is used to ensure the optimal generalization of the developed model, and the test set, which is not seen by the network during training, is used to examine the final performance of the model. Although all the input parameters had been used to generate the model, only a few are used in the final equation to estimate the pressure drop. This software provides a good way to monitor the performance of the three data sets (training, validation and test data) simultaneously, facilitating the optimization process and sensitivity analysis.
The connectivity and number of network layers is controlled by an evaluation criterion. The code algorithm also includes other parameters such as the maximum number of inputs for each neuron, the degree of polynomials in the neurons, whether neurons should be allowed to have inputs not only from the immediately preceding layer but also from the original input variables, the number of neurons in the layer, or decrease the number of neurons in each successive layer. To test the developed model, the effects of various input parameters are well known such as; oil volume, gas level, water level, "API" oil gravity, pipe length (depth) will be studied.
This type of error analysis has been used to check the accuracy of the proposed models and also of the other models under investigation. The first in the limitation of the data collected; as discussed earlier and this will certainly have a direct impact on the accuracy of the results. Each parameter has a specific range that works well, but accuracy can be slightly or severely affected if the parameters are not within the suggested range.
- Development of the GMDH model
- Introduction
- Summary of the Model’s Equation
- GMDH Model Optimization
- Trend Analysis for the Proposed GMDH Mode
- Statistical Error Analysis for the Proposed GMDH Model against Other
- Graphical Error Analysis for the Proposed GMDH Model against Other
- Cross Plots of GMDH Model against Investigated Models
- Error Distribution of GMDH Model against Investigated Models
- Discussion of the Results
They were selected based on their mapping influence within the data set on the pressure drop values. The final output layer "pressure drop" is formed from five variables of the input layer which are oil rate, depth "pipe length", water rate, oil gravity and gas rate. To test the developed model, the effects of gas rate, oil rate, water rate and depth "pipe length" on pressure drop were determined and plotted on Figure (4.2) to Figure (4.6).
The pressure drop increases as the gas, water and oil increase, as justified by the general energy equation. The increase in pressure drop when the gravity of the oil increases is simply justified by the equation of specific gravity, where specific gravity is directionally proportional to pressure. Figure (4.7) through Figure (4.9) show cross-graphs of estimated pressure drop versus measured pressure drop for the proposed GMDH model datasets; Training, validation and testing.
In addition, Figure (4.10) to Figure (4.18) show crossplots of estimated pressure drop versus measured pressure drop for other models examined, including the coefficient of determination for each model. Figure (4.19), Figure (4.20) and Figure (4.21) show the error distribution histograms for the GMDH model dataset, training, validation and test sets. And Figure (4.22) shows the error distribution histograms for the GMDH model and other investigated models.
According to the obtained results, the training set has a normal distribution with no noticeable shift towards the negative or positive side of the graph, which indicates a good estimate, the validation set has a slight shift towards the positive side of the graph, which means that the pressure drop was slightly underestimated, and the test set it also has a slight shift towards the positive side of the graph, which means that the pressure drop was slightly underestimated. A similar result can be extracted if the root mean square errors (RMSE) of each model were plotted against the standard deviation (STD) of the errors as shown in Figure (4.25). In addition, the average absolute relative errors (AAPE) of each model were plotted against the reliability of determination (R2) as shown in Figure (4.26).
Conclusions
Recommendations
Society of Petroleum Engineers 63rd Annual Professional Conference and Exhibition, 2-5 October. Houston, TX: U. of Texas.
