Simulation of Pressure- and Temperature-Dependent Fracturing Fluid Loss in Multi-Porosity Multi-Permeability Formations

2021 ◽  
Author(s):  
Chao Liu ◽  
Dung Phan ◽  
Younane Abousleiman

Abstract In this paper, the multi-porosity multi-permeability porothermoelastic theory is used to derive the analytical solution to calculate the pressure- and temperature-dependent fracturing fluid loss. A triple-porosity triple-permeability source rock formation is selected as an example to illustrate the model. The effects of fracturing fluid temperature and natural fractures on the fluid loss rate are systematically illustrated. The model successfully accounts for the varying leak-off rates in the multi-permeability channels through the hydraulic fracture faces. Furthermore, thermal diffusion near the hydraulic fracture faces contributes to a variation of pore pressure whose gradient at hydraulic fracture faces directly controls the fracturing fluid leak-off rate. The model shows that thermal effects bring almost 27% variation in the leak-off rate. Comparison study indicates that the single porosity model without considering multi-permeability systems or thermal effects significantly underestimates the rate of fracturing fluid loss and predicts nearly 84% and 87% lower leak-off rate, compared to the dual-porosity dual-permeability and triple-porosity triple-permeability models, respectively. Two case studies using published laboratory measurements on naturally fractured Blue Ohio sandstone samples are conducted to show the performances of the model. It is shown that the model presented in this paper well captures the total leak-off volume during the pressure-dependent fluid loss measured from laboratory tests. Matching the analytical solution to the laboratory data also allows rocks’ double permeabilities to be estimated.

1993 ◽  
Vol 115 (2) ◽  
pp. 267-276 ◽  
Author(s):  
Zhou Yang ◽  
Luis San Andres ◽  
Dara W. Childs

A thermohydrodynamic (THD) analysis is introduced for calculation of the performance characteristics of cryogenic liquid annular seals in the turbulent flow regime. A full-inertial bulk-flow model is advanced for momentum conservation and energy transport. The liquid material properties depend on the local absolute pressure and temperature. Heat flow to the rotor and stator is modeled by bulk-flow heat transfer coefficients. An approximate analytical solution is obtained to the governing equations when the seal operates at a steady-state and concentric condition. The temperature-rise in the fluid film of a cryogenic liquid seal is found to be composed of four sources due to viscous dissipation, pressure extrusion work, surface heat transfer and kinetic energy variation. For incompressible adiabatic flows, the fluid temperature rises linearly along the axial direction. The approximate analytical solution provides a useful tool for preliminary design and a better understanding of seal performance. Full numerical predictions of load, leakage, temperature, and rotordynamic coefficients for a high speed liquid oxygen seal are given in Part II to show the importance of thermal effects on seal performance. The accuracy of the approximate concentric seal analysis is then demonstrated by comparison to the results from the full numerical solution.


Author(s):  
Ramya Yeluri ◽  
Ravishankar Thirugnanasambandam ◽  
Cameron Wagner ◽  
Jonathan Urtecho ◽  
Jan M. Neirynck

Abstract Laser voltage probing (LVP) has been extensively used for fault isolation over the last decade; however fault isolation in practice primarily relies on good-to-bad comparisons. In the case of complex logic failures at advanced technology nodes, understanding the components of the measured data can improve accuracy and speed of fault isolation. This work demonstrates the use of second harmonic and thermal effects of LVP to improve fault isolation with specific examples. In the first case, second harmonic frequency is used to identify duty cycle degradation. Monitoring the relative amplitude of the second harmonic helps identify minute deviations in the duty cycle with a scan over a region, as opposed to collecting multiple high resolution waveforms at each node. This can be used to identify timing degradation such as signal slope variation as well. In the second example, identifying abnormal data at the failing device as temperature dependent effect helps refine the fault isolation further.


2017 ◽  
Vol 12 (1) ◽  
pp. 126-134
Author(s):  
A.M. Ilyasov

Based on the generalized Perkins-Kern-Nordgren model (PKN) for the development of a hyperbolic type vertical hydraulic fracture, an exact solution is obtained for the hydraulic fracture self-oscillations after terminating the fracturing fluid injection. These oscillations are excited by a rarefaction wave that occurs after the injection is stopped. The obtained solution was used to estimate the height, width and half-length of the hydraulic fracture at the time of stopping the hydraulic fracturing fluid injection based on the bottomhole pressure gauge data.


Materials ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 112
Author(s):  
Carlos Emiliano Buelna-Garcia ◽  
José Luis Cabellos ◽  
Jesus Manuel Quiroz-Castillo ◽  
Gerardo Martinez-Guajardo ◽  
Cesar Castillo-Quevedo ◽  
...  

The starting point to understanding cluster properties is the putative global minimum and all the nearby local energy minima; however, locating them is computationally expensive and difficult. The relative populations and spectroscopic properties that are a function of temperature can be approximately computed by employing statistical thermodynamics. Here, we investigate entropy-driven isomers distribution on Be6B11− clusters and the effect of temperature on their infrared spectroscopy and relative populations. We identify the vibration modes possessed by the cluster that significantly contribute to the zero-point energy. A couple of steps are considered for computing the temperature-dependent relative population: First, using a genetic algorithm coupled to density functional theory, we performed an extensive and systematic exploration of the potential/free energy surface of Be6B11− clusters to locate the putative global minimum and elucidate the low-energy structures. Second, the relative populations’ temperature effects are determined by considering the thermodynamic properties and Boltzmann factors. The temperature-dependent relative populations show that the entropies and temperature are essential for determining the global minimum. We compute the temperature-dependent total infrared spectra employing the Boltzmann factor weighted sums of each isomer’s infrared spectrum and find that at finite temperature, the total infrared spectrum is composed of an admixture of infrared spectra that corresponds to the spectra of the lowest-energy structure and its isomers located at higher energies. The methodology and results describe the thermal effects in the relative population and the infrared spectra.


Author(s):  
Yoann Launay ◽  
Jean-Michel Gillet

This article retraces different methods that have been explored to account for the atomic thermal motion in the reconstruction of one-electron reduced density matrices from experimental X-ray structure factors (XSF) and directional Compton profiles (DCP). Attention has been paid to propose the simplest possible model, which obeys the necessary N-representability conditions, while accurately reproducing all available experimental data. The deconvolution of thermal effects makes it possible to obtain an experimental static density matrix, which can directly be compared with theoretical 1-RDM (reduced density matrix). It is found that above a 1% statistical noise level, the role played by Compton scattering data becomes negligible and no accurate 1-RDM is reachable. Since no thermal 1-RDM is available as a reference, the quality of an experimentally derived temperature-dependent matrix is difficult to assess. However, the accuracy of the obtained static 1-RDM, through the performance of the refined observables, is strong evidence that the Semi-Definite Programming method is robust and well adapted to the reconstruction of an experimental dynamical 1-RDM.


2017 ◽  
Vol 09 (05) ◽  
pp. 1750076 ◽  
Author(s):  
Şeref Doğuşcan Akbaş

The purpose of this study is to investigate the thermal effects on the free vibration of functionally graded (FG) porous deep beams. Mechanical properties of the FG deep beam are temperature-dependent and vary across the height direction with different porosity models. The governing equations problem is obtained by using the Hamilton’s principle. In the solution of the problem, plane piecewise solid continua model and finite element method are used. The effects of porosity parameters, material distribution, porosity models and temperature rising on the vibration characteristics are presented and discussed with porosity effects for FG deep beams.


2021 ◽  
Vol 246 ◽  
pp. 09001
Author(s):  
Marwan Abugabbara ◽  
Jonas Lindhe

District heating and cooling systems have been undergoing continuous development and have now reached the fifth-generation. In this innovative technology, connected buildings share local excess energy that otherwise would be wasted, which consequently reduces primary energy demands and carbon emissions. To date, the issue of implementing fifth-generation district systems on existing buildings has received scant attention, and our research addresses this challenging gap by proposing a novel method for designing these systems. We first explain the possible thermal interactions between connected buildings, and then present an analytical solution for the network energy balance, pipe design, and the prediction of fluid temperature under a fixed temperature difference control strategy. The analytical solution was validated against numerical simulations performed on 11 existing buildings located in Lund, Sweden using Modelica models. A diversity index metric between heating and cooling demands was also included in these models to assess the efficiency of the district system in the building cluster. The results from the analytical and numerical solutions were in complete agreement since Modelica is an equation-based modelling language. The developed models pave the way towards future investigations of different temperature control strategies and new business models that arise from the shift to the fifth-generation.


Energies ◽  
2020 ◽  
Vol 13 (3) ◽  
pp. 633
Author(s):  
Guangzhi Yang ◽  
Shicheng Zhang ◽  
Jia Wang ◽  
Ning Li ◽  
Xinfang Ma ◽  
...  

Exploring engineering methods for increasing fracture network complexity is important for the development of unconventional oil and gas reservoirs. In this study, we conducted a series of fracturing experiments on naturally fractured volcanic samples. An injection method, multiple flow pulses, is proposed to increase fracture complexity. The results show that fluid leaked into the natural fracture network (NFN) when the injection rate was low (0.2 mL/min); hydraulic-fracture-dominant fracture geometry was created with an injection rate of 2 and 5 mL/min. Under the 2 mL/min-injection scheme with 3 pulses, the injection pressure during the intermittent stage was low (<5 MPa), resulting in a limited increase in fracture complexity. When the number of the flow pulses increased to 5, the pressure drop rate in the fourth and fifth intermittent stage significantly increased, indicating an increase in the aperture of natural fractures (NFs) and in the fluid leak-off effect. Under the 5 mL/min injection scheme containing 5 pulses, besides the enhanced fluid leak-off, a sharp injection pressure drop was observed, indicating the activation of NFs. The complexity and the aperture of the ultimate fracture network further increased. The injection method, multiple flow pulses, can be used to create complex fracture networks effectively.


1985 ◽  
Vol 25 (04) ◽  
pp. 482-490 ◽  
Author(s):  
Robert Ray McDaniel ◽  
Asoke Kumar Deysarkar ◽  
Michael Joseph Callanan ◽  
Charles A. Kohlhaas

Abstract A test apparatus is designed to carry out dynamic and static fluid-loss tests of fracturing fluids. This test apparatus simulates the pressure difference, temperature, rate of shear, duration of shear, and fluid-flow pattern expected under fracture conditions. For a typical crosslinked fracturing fluid, experimental results indicate that fluid loss values can be a function of temperature, pressure differential, rate of shear, and degree of non-Newtonian behavior of the fracturing fluid. A mathematical development demonstrates that the fracturing-fluid coefficient and filter-cake coefficient can be obtained only if the individual pressure drops can be measured during a typical fluid-loss test. Introduction In a hydraulic fracturing treatment, the development of fracture length and width is strongly dependent on a number of key fluid and formation parameters. One of the most important of these parameters is the rate at which the fracturing fluid leaks, off into the created fracture faces. This parameter, identified as fluid loss, also influences the time required for the fracture to heal after the stimulation treatment has been terminated. This in turn will influence the final distribution of proppant in the fracture and will dictate when the well can be reopened and the cleanup process started. Historically, tests to measure fluid loss have been carried out primarily under what is characterized as static conditions. In such tests, the fracturing fluid is forced through filter paper or through a thin core wafer under a pressure gradient, and the flow rate at the effluent side is determined. Of course, the use of filter paper cannot account for reservoir formation permeability and porosity; therefore, the fluid-loss characteristics derived from such tests should be viewed as only gross approximations. The static core-wafer test on the other hand, reflects to some extent the interaction of the formation and fracturing-fluid properties. However, one important fluid property is altogether ignored in such static core-wafer tests. This is the effect of shear rate in the fracture on the rheology (viscosity) of fracturing fluid and subsequent effects of viscosity on the fluid loss through the formation rock. In the past, several attempts were made to overcome the drawbacks of static core-wafer tests by adopting dynamic fluid-loss tests. Although these dynamic tests were a definite improvement over the static versions, each had drawbacks or limitations that could influence test results. In some of the studies, the shearing area was annular rather than planar as encountered in the fracture. In other cases, the fluid being tested did not experience a representative shear rate for a sufficiently long period of time. An additional problem arose because most studies were performed at moderate differential pressures and temperatures. The final drawback in several of the studies was that the fluid flow and leakoff patterns did not realistically simulate those occurring in the field. In the first part of this paper, we emphasize the design of a dynamic fluid-loss test apparatus that possesses none of these drawbacks. In the second part of the paper, test results with this apparatus are presented for three different fluid systems. These systems areglycerol, a non-wall-building Newtonian fluid,a polymer gel solution that is slightly wall-building and non-Newtonian, anda crosslinked fracturing system that is highly non-Newtonian in nature and possesses the ability to build a wall (filter cake) on the fracture face (see Table 1). The fluids were subjected to both static and dynamic test procedures. In the third part of the paper, results of experiments carried out with crosslinked fracturing fluid for different core lengths, pressure differences, temperatures, and shear rates are compared and the significance of the difference of fluid loss is emphasized. Experimental Equipment and Procedure The major components of the experimental apparatus shown in Fig. 1 are a fluid-loss cell, circulation pump, heat exchanger, system pressurization accumulators, and a fluid-loss recording device. The construction material throughout most of the system is 316 stainless steel. The fluid loss is measured through a cylindrical core sample, 1.5 in. [3.81 cm] in diameter, mounted in the fluid-loss cell. Heat-shrink tubing is fitted around the circumference of the core and a confining pressure is maintained to prevent channeling. Fracturing fluid is circulated through a rectangular channel across one end of the core. SPEJ P. 482^


Sign in / Sign up

Export Citation Format

Share Document