A New Analytical Method for Analyzing Linear Flow in Tight/Shale Gas Reservoirs: Constant-Flowing-Pressure Boundary Condition

2012 ◽  
Vol 15 (03) ◽  
pp. 370-384 ◽  
Author(s):  
Morteza Nobakht ◽  
C.R.. R. Clarkson
Keyword(s):  
Shale Gas ◽  
Analytical Method ◽  
Flow Analysis ◽  
Initial Pressure ◽  
Reliable Estimate ◽  
Square Root ◽  
Linear Flow ◽  
Straight Line ◽  
Half Length ◽  
Time Plot

Summary Many tight/shale gas wells exhibit linear flow, which can last for several years. Linear flow can be analyzed using a square-root-of-time plot, a plot of rate-normalized pressure vs. the square root of time. Linear flow appears as a straight line on this plot, and the slope of this line can be used to calculate the product of fracture half-length and the square root of permeability. In this paper, linear flow from a fractured well in a tight/shale gas reservoir under a constant-flowing-pressure constraint is studied. It is shown that the slope of the square-root-of-time plot results in an overestimation of fracture half-length, if permeability is known. The degree of this overestimation is influenced by initial pressure, flowing pressure, and formation compressibility. An analytical method is presented to correct the slope of the square-root-of-time plot to improve the overestimation of fracture halflength. The method is validated using a number of numerically simulated cases. As expected, the square-root-of-time plots for these simulated cases appear as a straight line during linear flow for constant flowing pressure. It is found that the newly developed analytical method results in a more reliable estimate of fracture half-length, if permeability is known. Our approach, which is fully analytical, results in an improvement in linear-flow analysis over previously presented methods. Finally, the application of this method to multifractured horizontal wells is discussed and the method is applied to three field examples.

A New Analytical Method for Analyzing Linear Flow in Tight/Shale Gas Reservoirs: Constant-Rate Boundary Condition

2012 ◽  
Vol 15 (01) ◽  
pp. 51-59 ◽  
Author(s):  
Morteza Nobakht ◽  
C.R.. R. Clarkson
Keyword(s):  
Production Rate ◽  
Shale Gas ◽  
Analytical Method ◽  
Gas Production ◽  
Square Root ◽  
Gas Reservoirs ◽  
Linear Flow ◽  
Shale Gas Reservoirs ◽  
Straight Line ◽  
Time Plot

Summary Hydraulically fractured vertical and horizontal wells completed in shale gas and some tight gas plays are known to exhibit long periods of linear flow. Recently, techniques for analyzing this flow period using (normalized) production data have been put forth, but there are known errors associated with the analysis. In this paper, linear flow from fractured wells completed in tight/shale gas reservoirs subject to a constant-production-rate constraint is studied. We show analytically that the square-root-of-time plot (a plot of rate-normalized pressure vs. square root of time that is commonly used to interpret linear flow) depends on the production rate. We also show that depending on production rate, the square-root-of-time plot may not be a straight line during linear flow; the higher the production rate, the earlier in time the plot deviates from the expected straight line. This deviation creates error in the analysis, especially for flow-regime identification. To address this issue, a new analytical method is developed for analyzing linear-flow data for the constant-gas-rate production constraint. The method is then validated using a number of numerically simulated cases. As expected, on the basis of the analytical derivation, the square-root-of-time plots for these cases depend on gas-production rate and, for some cases, the plot does not appear as a straight line during linear flow. Finally, we found that there is excellent agreement between the fracture half-lengths obtained using this method and the input fracture half-lengths entered in to numerical simulation.

Analysis of Transient Linear Flow Associated with Hydraulically-Fractured Tight Oil Wells Exhibiting Multi-Phase Flow

2015 ◽  
Author(s):  
H.. Behmanesh ◽  
H.. Hamdi ◽  
C. R. Clarkson
Keyword(s):  
Analytical Method ◽  
Flow Parameter ◽  
Saturation Pressure ◽  
Parameter Estimates ◽  
Phase Flow ◽  
Square Root ◽  
Linear Flow ◽  
Multi Phase Flow ◽  
Multi Phase ◽  
Time Plot

Abstract Hydraulically-fractured vertical and horizontal wells completed in the tight formations typically exhibit long periods of transient linear flow that may last many years or decades. From this transient linear flow period, the linear flow parameter (xf√k) may be extracted. However, changes in effective permeability to the oil phase during production, caused by wellbore pressure falling below the saturation pressure, affect the flow dynamics in tight oil reservoirs and complicate the analysis. The use of methods that assume single-phase flow properties, such as the square-root of time plot, can lead to significant errors in linear flow parameter estimates. In this study, an analytical method is introduced to mathematically correct the slope of the square-root-of-time plot for the effects of multi-phase flow through the use of modified pseudovariables. Although the correction was derived for wells producing at constant flowing pressure during transient linear flow, the method is extended for wells producing at variable rate/flowing pressures. In order to evaluate pseudovariables used in the correction, the saturation-pressure relationship must be known. In this work, an analytical method for evaluating the saturation-pressure relationship is also developed. The results of our new analytical method for linear flow analysis are validated against numerical simulation. The new method yields linear flow parameter estimates that are within 10% of those input into the numerical simulator.

A quantitative measure of nonlinearity

1993 ◽  
Vol 39 (5) ◽  
pp. 766-772 ◽  
Author(s):  
K Emancipator ◽  
M H Kroll
Keyword(s):  
Analytical Method ◽  
Response Curve ◽  
Polynomial Regression ◽  
Quantitative Measure ◽  
Square Root ◽  
Straight Line ◽  
The Mean ◽  
The Difference ◽  
Definition Of ◽  
Fitting In

Abstract Quantitative measures of the nonlinearity of an analytical method are defined as follows: the "(dimensional) nonlinearity" of a method is the square root of the mean of the square of the deviation of the response curve from a straight line, where the straight line is chosen to minimize the nonlinearity. The "relative nonlinearity" is defined as the dimensional nonlinearity divided by the difference between the maximum and minimum assayed values. These definitions may be used to develop practical criteria for linearity that are still objective. Calculation of the nonlinearity requires a method of curve-fitting. In this article, we use polynomial regression to demonstrate calculations, but the definition of nonlinearity also accommodates alternative nonlinear regression procedures.

Application of Linear Flow Analysis to Shale Gas Wells - Field Cases

2010 ◽  
Author(s):  
Hasan A. Al Ahmadi ◽  
Anas M. Almarzooq ◽  
Robert A. Wattenbarger
Keyword(s):  
Shale Gas ◽  
Flow Analysis ◽  
Gas Wells ◽  
Linear Flow

scholarly journals Investigation of the Main Factors During Shale-gas Production Using Grey Relational Analysis

2016 ◽  
Vol 9 (1) ◽  
pp. 207-215 ◽  
Author(s):  
Hongling Zhang ◽  
Jing Wang ◽  
Haiyong Zhang
Keyword(s):  
Shale Gas ◽  
Gas Production ◽  
Gas Reservoirs ◽  
Fracture Conductivity ◽  
Matrix Permeability ◽  
Shale Gas Reservoirs ◽  
Main Factors ◽  
Grey Relational ◽  
The Impact ◽  
Half Length

Shale gas is one of the primary types of unconventional reservoirs to be exploited in search for long-lasting resources. Production from shale gas reservoirs requires horizontal drilling with hydraulic fracturing to achieve the most economic production. However, plenty of parameters (e.g., fracture conductivity, fracture spacing, half-length, matrix permeability, and porosity,etc) have high uncertainty that may cause unexpected high cost. Therefore, to develop an efficient and practical method for quantifying uncertainty and optimizing shale-gas production is highly desirable. This paper focuses on analyzing the main factors during gas production, including petro-physical parameters, hydraulic fracture parameters, and work conditions on shale-gas production performances. Firstly, numerous key parameters of shale-gas production from the fourteen best-known shale gas reservoirs in the United States are selected through the correlation analysis. Secondly, a grey relational grade method is used to quantitatively estimate the potential of developing target shale gas reservoirs as well as the impact ranking of these factors. Analyses on production data of many shale-gas reservoirs indicate that the recovery efficiencies are highly correlated with the major parameters predicted by the new method. Among all main factors, the impact ranking of major factors, from more important to less important, is matrix permeability, fracture conductivity, fracture density of hydraulic fracturing, reservoir pressure, total organic content (TOC), fracture half-length, adsorbed gas, reservoir thickness, reservoir depth, and clay content. This work can provide significant insights into quantifying the evaluation of the development potential of shale gas reservoirs, the influence degree of main factors, and optimization of shale gas production.

scholarly journals An Analytical Method for Parameter Interpretation of Fracture Networks in Shale Gas Reservoirs considering Uneven Support of Fractures

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Shijun Huang ◽  
Jiaojiao Zhang ◽  
Sidong Fang ◽  
Xifeng Wang
Keyword(s):  
Data Analysis ◽  
Shale Gas ◽  
Analytical Method ◽  
Material Balance ◽  
Gas Production ◽  
Production Data ◽  
Analysis Method ◽  
Gas Reservoirs ◽  
Data Analysis Method ◽  
Parameter Interpretation

In shale gas reservoirs, the production data analysis method is widely used to invert reservoir and fracture parameter, and productivity prediction. Compared with numerical models and semianalytical models, which have high computational cost, the analytical model is mostly used in the production data analysis method to characterize the complex fracture network formed after fracturing. However, most of the current calculation models ignore the uneven support of fractures, and most of them use a single supported fracture model to describe the flow characteristics, which magnifies the role of supported fracture to a certain extent. Therefore, in this study, firstly, the fractures are divided into supported fractures and unsupported fractures. According to the near-well supported fractures and far-well unsupported fractures, the SRV zone is divided into outer SRV and inner SRV. The four areas are characterized by different seepage models, and the analytical solutions of the models are obtained by Laplace transform and inverse transform. Secondly, the material balance pseudotime is introduced to process the production data under the conditions of variable production and variable pressure. The double logarithmic curves of normalized production rate, rate integration, the derivative of the integration, and material balance pseudotime are established, and the parameters are interpreted by fitting the theoretical curve to the measured data. Then, the accuracy of the method is verified by comparison the parameter interpretation results with well test results, and the influence of parameters such as the half-length and permeability of supported and unsupported fractures on gas production is analyzed. Finally, the proposed method is applied to four field cases in southwest China. This paper mainly establishes an analytical method for parameter interpretation after hydraulic fracturing based on the production data analysis method considering the uneven support of fractures, which is of great significance for understanding the mechanism of fracturing stimulation, optimization of fracturing parameters, and gas production forecast.

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