Use of Second Pressure Derivative for Automatic Model Identification in Well Test Analysis

1996 ◽  
Author(s):  
Marcel J. Bourgeois ◽  
Jean-Luc Boutaud de la Combe ◽  
Mohamed Ajjoul
Keyword(s):  
Model Identification ◽  
Well Test ◽  
Well Test Analysis ◽  
Pressure Derivative ◽  
Test Analysis

Automatic reservoir model identification method based on convolutional neural network

2021 ◽  
pp. 1-11
Author(s):  
Xuliang Liu ◽  
Wenshu Zha ◽  
Zhankui Qi ◽  
Daolun Li ◽  
Yan Xing ◽  
...  
Keyword(s):  
Classification Accuracy ◽  
Field Data ◽  
Model Identification ◽  
Well Test ◽  
Reservoir Model ◽  
Well Test Analysis ◽  
Test Analysis ◽  
Reservoir Models ◽  
Actual Field ◽  
Model Recognition

Abstract Well test analysis is a crucial technique to monitor reservoir performance, which is based on the theory of seepage mechanics, through the study of well test data, to identify reservoir models and estimate reservoir parameters. Reservoir model recognition is the first and essential step of well test analysis. It is usually judged by professionals' experience, which results in low efficiency and accuracy. This paper is devoted to applying convolutional neural network (CNN) to well test analysis and proposes a new intelligent reservoir model identification method. Eight reservoir models studied in this paper include homogenous reservoirs with different outer boundaries such as infinite acting boundary, circular, single, angular, channel, U-shaped and rectangular sealing fault boundaries and a radial composite reservoir with infinite acting boundary. Well testing data used in this paper, including actual field data and theoretical data generated by analytical solutions. To improve the classification accuracy of actual field data, noise processing was carried out on the data before training. The CNN that is most suitable for model recognition has been obtained through trial-and-error procedures. The availability of proposed CNN is proved with actual field cases of Daqing oil field, China. The method realizes the automatic identification of reservoir model with the total classification accuracy (TCA) of test data set of 98.68% and 95.18% for original data and noisy data respectively.

New Applications of the Pressure Derivative in Well-Test Analysis

1989 ◽  
Vol 4 (03) ◽  
pp. 429-437 ◽  
Author(s):  
M. Onur ◽  
N. Yeh ◽  
A.C. Reynolds
Keyword(s):  
Well Test ◽  
Well Test Analysis ◽  
Pressure Derivative ◽  
Test Analysis ◽  
New Applications

Evaluation of Pressure Derivative Algorithms for Well-Test Analysis

2004 ◽  
Author(s):  
Freddy Humberto Escobar ◽  
Juan Miguel Navarrete ◽  
Hernãn Dario Losada
Keyword(s):  
Well Test ◽  
Well Test Analysis ◽  
Pressure Derivative ◽  
Test Analysis

scholarly journals The Similar Structure Method for Solving the Model of Fractal Dual-Porosity Reservoir

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Li Xu ◽  
Xiangjun Liu ◽  
Lixi Liang ◽  
Shunchu Li ◽  
Longtao Zhou
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Dual Porosity ◽  
Well Test ◽  
Well Test Analysis ◽  
Pressure Derivative ◽  
Test Analysis ◽  
Type Curves ◽  
Bessel Equation ◽  
Wellbore Pressure

This paper proposes a similar structure method (SSM) to solve the boundary value problem of the extended modified Bessel equation. The method could efficiently solve a second-order linear homogeneous differential equation’s boundary value problem and obtain its solutions’ similar structure. A mathematics model is set up on the dual-porosity media, in which the influence of fractal dimension, spherical flow, wellbore storage, and skin factor is taken into cosideration. Researches in the model found that it was a special type of the extended modified Bessel equation in Laplace space. Then, the formation pressure and wellbore pressure under three types of outer boundaries (infinite, constant pressure, and closed) are obtained via SSM in Laplace space. Combining SSM with the Stehfest algorithm, we propose the similar structure method algorithm (SSMA) which can be used to calculate wellbore pressure and pressure derivative of reservoir seepage models clearly. Type curves of fractal dual-porosity spherical flow are plotted by SSMA. The presented algorithm promotes the development of well test analysis software.

scholarly journals Analysis of well testing results for single phase flow in reservoirs with percolation structure

2021 ◽  
Vol 76 ◽  
pp. 15
Author(s):  
Elahe Shahrian ◽  
Mohsen Masihi
Keyword(s):  
Alternative Methods ◽  
Model Parameters ◽  
Well Testing ◽  
Well Test ◽  
Well Test Analysis ◽  
Apparent Permeability ◽  
Pressure Derivative ◽  
Test Analysis ◽  
Heterogeneous Reservoirs ◽  
Occupancy Probability

Constructing an accurate geological model of the reservoir is a preliminary to make any reliable prediction of a reservoir’s performance. Afterward, one needs to simulate the flow to predict the reservoir’s dynamic behaviour. This process usually is associated with high computational costs. Therefore, alternative methods such as the percolation approach for rapid estimation of reservoir efficiency are quite desirable. This study tries to address the Well Testing (WT) interpretation of heterogeneous reservoirs, constructed from two extreme permeabilities, 0 and K. In particular, we simulated a drawdown test on typical site percolation mediums, occupied to fraction “p” at a constant rate Q/h, to compute the well-known pressure derivative (dP/dlnt). This derivative provides us with “apparent” permeability values, a significant property to move forward with flow prediction. It is good to mention that the hypothetical wellbore locates in the middle of the reservoir with assumed conditions. Commercial software utilized to perform flow simulations and well test analysis. Next, the pressure recorded against time at different realizations and values of p. With that information provided, the permeability of the medium is obtained. Finally, the permeability change of this reservoir is compared to the permeability alteration of a homogeneous one and following that, its dependency on the model parameters has been analysed. The result shows a power-law relation between average permeability (considering all realizations) and the occupancy probability “p”. This conclusion helps to improve the analysis of well testing for heterogeneous reservoirs with percolation structures.

Linearly Supported Radial Flow-A Flow Regime in Layered Reservoirs

2002 ◽  
Vol 5 (02) ◽  
pp. 103-110 ◽  
Author(s):  
Boyun Guo ◽  
George Stewart ◽  
Mario Toro
Keyword(s):  
Radial Flow ◽  
Constant Pressure ◽  
Low Permeability ◽  
Well Test ◽  
High Permeability ◽  
Reservoir Model ◽  
Well Test Analysis ◽  
Pressure Derivative ◽  
Test Analysis ◽  
Diagnostic Plot

Summary This paper discusses pressure responses from a formation with two communicating layers in which a fully penetrated high permeability layer is adjacent to a low-permeability layer. An analytical reservoir model is presented for well-test analysis of the layered systems, with the bottom of the low-permeability layer being a constant-pressure boundary. The strength of the support from the low-permeability layer is characterized with two parameters: layer bond constant and storage capacity. Introduction The log-log plot of pressure derivative vs. time is called a diagnostic plot in well-test analysis. Special slope values of the derivative curve usually are used for identification of reservoir and boundary models. These slopes include 0-slope, 1/4-slope, 1/2-slope, and unity slope. In many cases, however, the derivative curves do not exhibit slopes of these special values, and it is believed that some nonspecial slopes also reflect certain flow patterns in the reservoirs. Layered, thick reservoirs are one such example.1 In a layered reservoir, it is common practice to perforate a high-permeability section intentionally (adjacent sections are known to be less permeable) or unintentionally (adjacent sections are believed to be impermeable). It is expected that the flow in the perforated high-permeability layer will be partially fed by fluids in the adjacent layers. Warren and Root2 classified this type of layered reservoir as one of the dual-porosity systems in which the storage effect of the low-permeability layer is considered while the crossflow between layers is neglected. They presented a model based on the mathematical concept of superposition of the two media, as introduced previously by Barenblatt et al.3 This paper discusses the pressure response from a formation with two communicating layers. The flow in the two-layer system is referred to as Linearly Supported Radial Flow (LSRF) in this study. The reservoir model is depicted in Fig. 1. The LSRF may exist in the drainage area of a vertical well where radial (normally horizontal) flow prevails in a high-permeability layer and linear (normally vertical) flow into the high-permeability layer dominates in a low-permeability layer. The LSRF also may exist in the drainage area of a horizontal well after pseudoradial flow in the high-permeability layer is reached. Two LSRF systems were investigated:an LSRF system with a no-flow boundary at the opposite side of (not adjacent to) the high-permeability layer, andan LSRF system with a constant boundary pressure at the opposite side of (not adjacent to) the high-permeability layer. Model Description LSRF With No-Flow Boundary at Bottom. An LSRF system with a no-flow boundary at the bottom of the low-permeability layer was investigated with a finite-element-based numerical simulator. The simulator was fully tested and commercially available in the market. Model configuration and input data are summarized in Table 1. The model well flowed 1,000 hours at a constant flow rate of 1,000 STB/D. A diagnostic plot of the generated response is shown in Fig. 2. It is seen from the figure that the radial-flow derivative is V-shaped in a certain time period. This is an expected signature of dual-porosity systems. It is concluded that the radial-flow derivative curve is similar to the derivative curve of single-layer double-porosity reservoirs. The signature of the pressure-derivative responses cannot be used for further diagnostic purposes. Other information from fracture/void detections is required. LSRF With Constant-Pressure Boundary at Bottom. Pressure response from an LSRF system with a constant-pressure boundary at the bottom of the low-permeability layer was also investigated with the numerical simulator. Model configuration and input data were kept the same as those in Table 1. The model well flowed 300 hours. A diagnostic plot of the generated response is shown in Fig. 3. It is seen from the figure that pressure derivative drops sharply in the later time. This is an expected signature of reservoirs with bottomwater or gas-cap gas drive. One may use a bottomwater- drive reservoir model to determine horizontal and vertical permeabilities in the perforated layer. However, one cannot be sure whether the derived vertical permeability is the permeability of the perforated layer or the low-permeability layer. Also, one cannot characterize the strength of the waterdrive based on the pressure-transient data. To retrieve true reservoir properties and characterize the strength of the waterdrive based on pressure-transient data, an analytical reservoir model was derived in this study. The mathematical formulation of the model is shown in the Appendix. When U.S. field units are used, the resultant constant-rate solution for oil takes the following form:Equation 1 where pd = p-pwf. The constants B and C are defined asEquations 2 and 3 Noticing that the derivative of Ei (t) is given byEquation 4 the diagnostic derivative of pressure for radial flow becomesEquation 5 Taking the 10-based logarithm of this equation givesEquation 6 This equation indicates that the diagnostic derivative currently used in well-test-analysis practice for radial-flow identification is not a constant during the LSRF (i.e., the radial-flow pressure derivative curve will not have a plateau but will decrease with time). This rate of increase depends on B and C if no other boundary effect exists. Therefore, constants B and C can be used to characterize the strength of the supporting layer.

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