2024 August 20

Mahdi Salimmehr, Reservoir Engineering Lead, South Azadegan Project

**Introduction **

Well-Testing is a one of the usual methods in petroleum engineering for evaluating reservoir and well parameters. This method is based on measuring downhole pressure verses time in different production conditions and then drawing these data in different pressure-time graphs and evaluating reservoir characteristics and calculating reservoir parameters.

This article describes the development of techniques for the automation of the model identification and parameter estimation of a well test interpretation, using Artificial Intelligence. The computer programs which are written in MATLAB software use Neutral Network toolbox to detect a model that is based on the pressure derivative curve, and simulates the visual diagnosis performed by a human expert. Most of the reasoning involved in such a diagnosis uses a symbolic representation of the pressure derivative curve, which in the case of a human expert is built almost unconsciously. Techniques were developed to replicate this perception step. A major difficulty in the analysis of real data, particularly using the pressure derivative, is the separation of the true reservoir response from signal or differentiation noise. Again, this is relatively simple for a human observer, but difficult to implement in a computer program.

This article describes an algorithm developed to overcome this problem. The algorithm was able to distinguish response from noise correctly, therefore permitting correct model identification.

**Summary**

An artificial neural network is a data processing system which has the same performance of biological neural network. In this study, the neural network has been employed for identification of components of the pressure derivative curves. The signal that comes from neural network are translated to an explanation for identification of the flow regimes in porous media and then the reservoir parameters belongs to this specific flow regimes are estimated, using common equations.

In a manner analogous to a human expert, the technique constructs an interpretation model by combining the features of the different flow periods of the pressure response, for the entire duration of a test. The adequacy of a model is determined by qualitative as well as quantitative information. Once a model is chosen, its parameters are estimated using correlations. The software developed in this work can perform model identification on analytical as well as real data.

We used the neural network to try one logarithmic cycle called Test Cycle at a time. By moving a window one logarithmic cycle wide from each point to the next, we can identify the appropriate pattern for each point in the test.

Training data for all patterns are randomly generated and normalized. Wide range of skin coefficients have been used to generate hump pattern data. Different storativity ratios have been used in the double porosity model with stable interporosity flow to generate data for the valley pattern.

Data for other patterns were generated using simple mathematical relationships. One hundred sets were used as sample data for each pattern as training data and another hundred sets of data were used as test data. Figures (1 and 2) show the data used for training the neural network.

Figure 1: Training data for neural network for hump pattern

Figure 2: Training data for neural network for line with slope -1/2 pattern

Training a neural network usually takes a large amount of computer memory and CPU time. This amount depends on factors such as the number of training and test data, the number of processor units in each layer and the complexity of the problem.

In this study, the number of repetitions in the neural network training was around 2000 to 3000 times. When more repetitions do not improve the results, training was stopped. Then the performance of the network was measured with the test data. Among the networks that were trained, many were successful. However, these trained neural networks still have some weaknesses. A particular neural network sometimes performs very poorly in identifying certain patterns. Therefore, it is necessary to be very careful in predicting the results of neural network for flow regimes. Although the neural network has been trained to recognize 8 patterns, 5 patterns of straight line, a line with unit slope, hump and valley are of great importance.

The description of the characteristic components of the pressure derivative curve in order of occurrence for each reservoir model can be summarized as follows:

**1- Infinite acting radial flow function:** line with unit slope, hump, smooth line.

**2-** **Closed fault boundary:** a line with unit slope, hump, zero slope straight line, a second straight line with a double value for pressure derivative

**3-** **No flow boundary:** a line with unit slope, hump, zero slope straight line, a line with unit slope

**4- Constant pressure boundary:** line with unit slope, hump, zero slope straight line, downward trend

**5-Pseudo steady state dual porosity with interporosity flow: **a line with unit slope, hump , zero slope straight line, smooth line, valley, second straight line or line with unit slope, hump, valley, zero slope straight line

**6-Closed fault boundary-pseudo steady state dual porosity with interporosity flow:** a line with unit slope, hump, zero slope straight line, valley, second straight line or line with a single slope, hump, valley, zero slope straight line, transient state, second zero slope line with double derivative value, transient state, third straight line with double derivative value or line with unit slope, hump, valley, zero slope line, transient state, second smooth line with double derivative value

**7- No flow boundary pseudo steady state dual porosity with interporosity flow: **line with unit slope, hump, zero slope straight line, valley, second straight line, line with unit slope, hump, valley, zero slope line, line with unit slope

**8- Constant pressure boundary pseudo steady state dual porosity with interporosity flow:** line with unit slope, hump, zero slope straight line, valley, second straight line downward trend or line with unit slope, hump, valley, zero slope line, downward trend

Eight reservoir models have been selected for this study and according to the nominated reservoir models, the estimable reservoir parameters were recommended. The candidate reservoir models beside estimable reservoir parameters are shown in Table 1.

*Table **1**: Estimable parameters for different reservoir and boundary models*

*boundary models*

The sample well test data has been used for this study was extracted from SPE paper number 13054 which belongs to an oil well located in

west of Venezuela. Figure 3 shows the activation level of neural network outputs and Figure 4 shows the interpolated reservoir pressure drop in same intervals from logarithmic time and pressure derivative. Results of estimation of reservoir parameters for fractured reservoir are also available in Table 2.

Figure 3: Activation level of neural network outputs

Figure 4: Interpolated pressure drop and pressure derivative

Table 2: Estimated values for reservoir parameter of fractured reservoir

Reservoir parameter |
Estimated value |

K(md) |
40.39 |

S |
-2.43 |

C(psi |
0.01 |

r |
4450 |

λ |
7.88E-08 |

ω |
0.1
- Neural network is resistant to data noises. This can be an advantage and also disadvantage at same time. The advantage is that the using of neural network is applicable for identification of noisy data and no data smoothing is required. But the disadvantage is that using neural network may results in wrong regime classifications for noisy data. This is while is it possible to remove this kind of issues, using experiences from welltest analysis in model identification algorithm.
- This approach is a novel method which can accelerate the welltest analysis process and considering the improvements in measurements, can be easily used to analysis massive amount of data at wellsite location, and consequently take proper and timely manner action during operation.
- The performance of trained neural network that has been used in this study was not good for cases which the flow regimes was less than one logarithmic cycle. To overcome this issue, an auxiliary program was used.
- As a recommendation and in order to have more reliable and comprehensive interpretation of data, the data from geology, coring and well logging can be used. Also using more reservoir models may be of interest for automatization of data interpretation process.
I would like to declare my special thanks to Dr.Shadizadeh for his support and advises during execution of this study.
[1] Al-Raabi, A.TZ and Lee, W.J.: “Using Artificial Neural Networks to Identify the Well Test Interpretation Model, paper SPE 20332 [2] Allain, O.F. and Houzé, O.P.: A Practical Artificial Intelligence Application in Well Test Interpretation, paper SPE 21287 [3] Anraku, T.: Discrimination between Reservoir Models in well Test Analysis, PhD dissertation, Stanford University (December 1993). [4] G.Da Prat, J.Mannucci: Use of pressure transient testing to evaluate fractured reservoirs in west Venezuela, SPE 13054, (September 1984). |