New Applications of the Pressure Derivative in Well-Test Analysis

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.

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

Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles ◽

10.2516/ogst/2020092 ◽

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.

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A Method for Reducing Model Error When Interpreting Pressure Derivative in Well Test Analysis. Application to Hassi Messaoud Oil Field

10.2118/2003-078 ◽

2003 ◽

Author(s):

S. Bachar ◽

A.H. Mills ◽

D. Tiab

Keyword(s):

Model Error ◽

Oil Field ◽

Well Test ◽

Well Test Analysis ◽

Pressure Derivative ◽

Test Analysis ◽

Analysis Application

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Linearly Supported Radial Flow-A Flow Regime in Layered Reservoirs

SPE Reservoir Evaluation & Engineering ◽

10.2118/77269-pa ◽

2002 ◽

Vol 5 (02) ◽

pp. 103-110 ◽

Cited By ~ 1

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

10.2118/36659-ms ◽

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

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Well Test Analysis Using Pressure Derivative Method at Gas Well X-1

Journal of Earth Energy Science, Engineering, and Technology ◽

10.25105/jeeset.v1i1.3036 ◽

2018 ◽

Vol 1 (1) ◽

Cited By ~ 2

Author(s):

Muhammad Handis Maulana ◽

Muhammad Taufiq Fathaddin ◽

Hari Karyadi Oetomo

Keyword(s):

Point Method ◽

Formation Damage ◽

Well Test ◽

Well Test Analysis ◽

Pressure Derivative ◽

Test Analysis ◽

Positive Skin ◽

Gas Well ◽

Plot Analysis ◽

Derivative Method

Wells X-1 is a gas condensate well which located in lapangan X, Sulawesi Island. At well X-1 well test was conducted using pressure build up, where the analysis was conducted with objective to determine the reservoir characteristic of X-1 wells such as permeability, skin, flow efficiency and investigation radius. In the pressure build up test, the horner plot and derivation analysis using pseudo pressure and P2 approaches were applied with the gas well X-1 has a reservoir pressure of 2555 psia. The analysis is done using saphir 3.20 and Ms.Excel software where the results of the counsel to see if there is any possibility of formation damage. X-1 is also known as homogeneous with a fault boundary present in the fault located at a certain distance from the well X-1 in which the fault is only one direction from the reservoir. The pressure derivative plot analysis was conducted with two methods such as two-point method and three-point method, where the result of the overlay of the derivative curve corresponds to the deviation of the calculation result method which is less than 10%. The horner plot analysis is also done with the ψ(P) pseudo pressure and P2 approach which is the result of horner plot analysis using pseudo pressure ψ(P) pseudo pressure in saphir 3.20 obtained the slope (m), permeability, and skin values respectively were 3.22432E + 5 psi2/cp, 132 mD, and 21.6, whereas Ms.Excel results obtained the price of slope (m), permeability, and skin respectively were 320890.61 psi2/cp, 134.83 mD, and 21.1. To analyze the horner plot using the P2 approach at saphir 3.20 the value of slope (m), permeability, and skins values respectively were 5495.07 psi2/cp, 125 mD, and 21.3 and for the results of Ms. Excel the price of slope (m), permeability, and skin respectively were 5451.66 psi2/cp, 147,29 mD, and 20,1. Positive skin results in both methods of horner plot and derivative plot indicate the well is damaged and need to be stimulated.

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