Analytical Solution for Determining Fracture Attenuation

2021 ◽  
Author(s):  
Vadim Andreevich Rubailo ◽  
Kirill Dmitrievich Isakov ◽  
Anton Vyacheslavovich Shirobokov
Keyword(s):  
Analytical Solution ◽  
Hydraulic Fracturing ◽  
Analytical Model ◽  
Crack Width ◽  
Laboratory Studies ◽  
Crack Geometry

Abstract This work is devoted to the analytical solution of the damping of the fracture of the hydraulic fracturing. A solution is obtained for changing the dimensionless conductivity of the crack due to a decrease in the conductivity of the proppant and its removal from the crack. The considered crack geometry corresponds to the Perkins-Kern analytical model, which allows us to take into account the change in the crack width depending on its length. To calculate the proppant conductivity, laboratory studies were used, the data of which were extrapolated in order to predict the destruction of proppant balls during the operation of a well with a fractured hydraulic fracturing.

AN ANALYTICAL MODEL OF A NON-STATIONARY TEMPERATURE FIELD IN A RESERVOIR WITH A HYDRAULIC FRACTURING

2021 ◽  
Vol 7 (2) ◽  
pp. 75-94
Author(s):  
Ramil F. SHARAFUTDINOV ◽  
Filyus F. Davletshin
Keyword(s):  
Temperature Field ◽  
Hydraulic Fracturing ◽  
Analytical Model ◽  
Oil Recovery ◽  
Temperature Anomaly ◽  
Nonstationary Temperature ◽  
Initial Moment ◽  
Positive Temperature ◽  
Fluid Filtration ◽  
Stage Of Development

At the present stage of development of the oil and gas industry, considerable attention is paid to methods of increasing oil recovery of productive reservoirs. One of the most popular methods of intensifying oil production today is hydraulic fracturing. The efficiency and success of hydraulic fracturing largely depends on the parameters of the formed fracture; in this regard, the development of methods for evaluating the parameters of hydraulic fracturing fractures is an urgent task. Non-stationary thermometry is a promising area for monitoring the quality of hydraulic fracturing. To date, thermometry is used to localize the locations of multiple fractures in horizontal wells. In this paper, we study the application of non-stationary thermometry for estimating the parameters of a vertical hydraulic fracturing fracture. An analytical model of non-isothermal single-phase fluid filtration in a reservoir with a vertical fracture is developed. To calculate the temperature field in the formation and the fracture, the convective heat transfer equation is used, taking into account the thermodynamic effects (Joule — Thomson and adibatic), for the fracture, the heat and mass transfer between the fracture and the formation area is also taken into account. To assess the correctness of the model, the analytical solution is compared with the results of numerical modeling in the Ansys Fluent software package. The nonstationary temperature field is calculated for the constant sampling mode. It is established that at the initial moment of time after the well start-up, a negative temperature anomaly is formed due to the adiabatic effect, the value of which increases with a decrease in the fracture width. Over time, the temperature of the fluid flowing into the well increases due to the Joule — Thomson effect, and the value of the positive temperature anomaly increases as the width and permeability of the fracture decreases due to an increase in the pressure gradient in it. The developed analytical model can be used to solve inverse problems for estimating hydraulic fracturing parameters based on non-stationary temperature measurements in the wellbore of producing wells.

Modeling and electromechanical performance analysis of frequency-variable piezoelectric stack transducers

2020 ◽  
Vol 31 (6) ◽  
pp. 897-910
Author(s):  
Jianjun Wang ◽  
Shuyuan Cai ◽  
Lei Qin ◽  
Donghuan Liu ◽  
Peijun Wei ◽  
...  
Keyword(s):  
Experimental Study ◽  
Performance Analysis ◽  
Analytical Solution ◽  
Resonance Frequency ◽  
Analytical Model ◽  
Dynamic Characteristics ◽  
Active Element ◽  
Underwater Sound ◽  
Layer Number ◽  
Electromechanical Performance

An exact analytical model of frequency-variable piezoelectric stack transducers is proposed, and their dynamic characteristics are studied in this article. Based on the linear piezoelasticity theory, the dynamic analytical solution is first derived, and then its correctness is validated by comparing it with the results of a special example in the previous literature and the ones of the experimental study. The effects of the tuning resistance and the layer number of the active element on the dynamic characteristics are discussed. Numerical results show that tuning the resistance and the layer number of the active element can enable the multi-frequency characteristics of the piezoelectric stack transducers. A proper layer number of the active element can minimize the short-circuited resonance frequency and the open-circuited anti-resonance frequency. These findings provide guidelines to design and optimize the piezoelectric stack transducers, which have promising potential in developing the multi-frequency Langevin transducers for some underwater sound and ultrasonic applications, such as ultrasonic cleaning, ultrasonic chemistry, and sonar radiators.

Use of Mathematical Model to Predict the Maximum Permissible Stage Injection Time for Mitigating Frac-Driven Interactions in Hydraulic-Fracturing Shale Gas/Oil Wells

2020 ◽  
Vol 143 (8) ◽  
Author(s):  
Nan Zhang ◽  
Boyun Guo
Keyword(s):  
Hydraulic Fracturing ◽  
Analytical Model ◽  
Shale Gas ◽  
General Model ◽  
High Rate ◽  
Fluid Injection ◽  
Injection Time ◽  
Gas Oil ◽  
Fracturing Fluid ◽  
Multiple Fractures

Abstract Frac-driven interactions (FDIs) often lead to sharp decline in gas and oil production rates of wells in shale gas/oil reservoirs. How to minimize the FDI is an open problem in the oil and gas industry. Xiao et al.’s (2019, “An Analytical Model for Describing Sequential Initiation and Simultaneous Propagation of Multiple Fractures in Hydraulic Fracturing Shale Oil/Gas Formations,” Energy Sci Eng., 7(5), pp. 1514–1526.) analytical model for two-fracture systems was extended in this study to obtain a general model for handling multiple fractures. The general model was used to identify engineering factors affecting the maximum permissible stage fluid injection time for minimizing FDI. On the basis of model results obtained, we found that increasing fluid injection rate can create more short fractures and thus increase the maximum permissible stage injection time before FDI occurs. Use of dilatant type of fracturing fluid (n > 1) can reduce the growth of long fractures, promote the creation of more short fractures, and thus increase the maximum permissible stage injection time before FDI occurs. It is also expected that injecting dilatant type of fracturing fluid at high rate will allow for longer injection time and thus larger injection volume, resulting in larger stimulated reservoir volume (SRV) with higher fracture intensity and thus higher well productivity and hydrocarbon recovery factor.

scholarly journals Laboratory Studies on Hydraulic Fracturing Criteria in Soil

1989 ◽  
Vol 29 (4) ◽  
pp. 14-22 ◽  
Author(s):  
Ali Komak Panah ◽  
Eui Yanagisawa
Keyword(s):  
Hydraulic Fracturing ◽  
Laboratory Studies

Computation of Stress Intensity Factor for Multiple Cracks Using Singular Finite Element

2011 ◽  
Vol 214 ◽  
pp. 75-79 ◽  
Author(s):  
Ruslizam Daud ◽  
Ahmad Kamal Ariffin ◽  
Shahrum Abdullah ◽  
Al Emran Ismail ◽  
A. Zulkifli
Keyword(s):  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Analytical Solution ◽  
Crack Width ◽  
Width Ratio ◽  
Multiple Cracks ◽  
Two Dimensional ◽  
Interval Ratio

The simplification of two dimensional approaches in singular finite elements has promoted the method to be used in the formulation of stress intensity factor (SIF) of multiple cracks in finite body. The effect of shielding and amplification are considered in defining the SIF. As been observed, the current available analytical approximations are more restricted to several assumptions. The more accurate and less restricted method has motivated this study. This paper presents the investigation of singular finite elements applied in two dimensional finite element models subjected to different crack-width ratio and cracks interval ratio. The newly finite element formulations are resulted with good agreement with theoretical statement compared to analytical solution. The weak points of presented analytical solution are discussed regards to the influence of crack width ratio and cracks interval ratio.

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