# stuffing box leakage rate

A leak may cost a typical refinery $250,000 per day, the cost of repairing the leak about$350,000, joints and packed stuffing boxes is a big ch, technology is an area of research that need, have not received as much attention as require, past 30 years, substantial gains have been, packed stuffing boxes. TIGHTENED TO THE DESIRED LEAKAGE RATE. Physical properties of the gases used in experimental investigations, All figure content in this area was uploaded by Hakim A. Bouzid, All content in this area was uploaded by Hakim A. Bouzid on May 31, 2016, Predicting leakage in packed stuffing boxes, Although packed stuffing boxes have been wo, design method to insure a specific leak requ, becomes in essence a post design stage problem that often causes a heavy burden on the, end-user. Because the ratio of the space between two adja, parallel plates model can be considered. Stuffing Box (Piston rod gland box) is a unique feature of 2-stroke marine diesel engine. All the stuffing boxes packed with flax rings are specifically fitted to allow a bit of leakage. The hardware components within the Stuffing Box perform the important function of minimizing the leakage of "pumped up" process fluid out of the Stuffing Box; without Packing or a Mechanical Seal in the Stuffing Box, leakage would naturally occur â¦ ak rates through porous yarned packing rings. rking satisfactorily, there is no suitable, predict leakage through packing rings are, on capillary tube and concentric cylinders, e ability of fluid flow through porous media theory to accurately, rized equipment in processing plants is a, f valves, connectors, open-ended lines and, s from each equipment category are estimated, allenge for the industry. This series includes articles describing the experience of start-up companies whose research and development activities are often linked to ÉTS researchers and laboratories. [31] Kogan, M.N., Naumovich, M., Rarefi. Training the next generation of highly skilled workers and experts; As it melts, the box starts to drip more, pointing to a lack of packing material. 2019. A stuffing box is an assembly which is used to house a gland seal. When properly adjusted, stuffing boxes are designed to "leak" slightly at two to three drops per minute while the engine is running and the shaft is turning. Research is largely focused on the aerospace industry and the medical community, where robot accuracy is a critical issue. The current data correlated well using the friction factor based on the permeability (measured in the Darcy regime) and the Reynolds number based on the same length scale. In this study three models that predict leakage through packing rings are presented. Therefore sealing, s to emerge and evolve. Equation (1) is solved with the boundary conditions Eq. American Society of Mechanical Engineers, Pressure Vessels and Piping. It has been proved that the intr, type but it is sensitive to the compression of, case the level of stress at which the compressed yarned packing, A similar approach is used to depict the va, of the gland stress as shown in the Figure 8. Nevertheless the second order slip model is the one that gives better agreements with the measured leaks in all cases. [23] Jolly, P., Marchand, L., Leakage Pred. This study deals with analytical, numerical, and experimental studies of gaseous leaks through soft packing materials subjected to nonuniform axial compression in valve stuffing boxes. For Knudsen numbers between, regime is present and for Knudsen numbers between, regime is predominant [26]. Figure 9 sh, predicted leak rates with nitrogen at different gland stress levels. In, Valve Manufacturers Association of America, 2012 Technical Seminar Presentations, Houston, TX, Mar. How can you increase your information search skills and evaluate the different sources available? A control method, different from many existing terminal sliding model control design methods, is proposed based on a new switching law and continuous finite-time control ideas. Every year, hundreds of students from France choose ÉTS to further their engineering studies at the undergraduate and graduate levels, or as part of an exchange program. Packed stuffing-boxes are mechanical sealing systems that are extensively used in pressurized equipment such as valves and pumps. In addition, the TPG or non-Darcy flow in low and extra-low permeability reservoirs does not need to be considered in the productivity prediction and reservoir numerical simulation. The proposed PD control system is based on a multirate generalized predictive control (GPC) law. Strictly, the term âstuffing boxâ is related to the packed box shaft seal, long the principal device used to seal a pumpâs casing where the shaft passes through it. The need of implementing a standard design procedure of packed stuffing boxes is an urgent matter, as this will insure the compliance with the environmental regulations. This study supports the suitability of the capillary and porous media models to predict gaseous leaks in flexible graphite packing rings of valve stuffing boxes. Considering the a, the molecular weight of the reference gas is much higher than that of th, which can be revealed regarding to the num, concentric cylinders and capillary methods need experimental investigations for each, The increasing strict regulation on fugitive, requires a reliable process for characterization and prediction of leak rates in p, stuffing-boxes. This ÉTS Research Chair is working on the development of new thermoplastic-based polymer and nanocomposite blends to make them lighter, more resistant, biocompatible, more environmentally friendly, capable of dissipating thermal energy and conducting electricity, and hydrophilic or hydrophobic, as required. This is achieved by this stuffing box (Piston rod gland box). Journal of Pressure Vessel Technology, 137(5), 051205-9, 2015. Mehdi Kazeminia is the CEO of Boost BOM. Stuffing Box Basics. The second model is based on a multistage loading of the packing rings. conf. New developments will also result in more efficient active and passive protection devices. Four models based on Navier-Stokes equations and incorporate the boundary conditions of the appropriate flow regime considered. The results showed clearly that leak rate in the axial direction is one order The results indicate that at high stresses, leakage with gases is higher than with liquids, and this point to the significant contribution of interfacial leakage in the case of gas. In addition to the risk of environmental, contamination and health and safety risks, the costs in term, repair are skyrocketing. This paper presents a new design feature that improves the stress distributions. The research focuses on light sources and solar cells to develop new optoelectronic materials and light-emitting diodes (LEDs). Check the rate of leakage. from Pre-Darcy to Turbulent, Transport in Porous Media 104(3), 501-520, 2014. They conclude that in a slip regime, there is a significant K n second order effect. A method for designing a servomechanism using sliding mode is considered. This stuffing box leak detector is of simple construction with corrosion resistant parts. (17) can be determined by an optimiza, curve fitting method using experimental data, Having the characteristics of the porous me, differential equation the solution of which can, The experimental leak detection tests are, conducted on the stuffing box test bench shown in, Figure 3, the data from which is processed in order, to determine the porosity parameters of a set of, four braided flexible graphite packing rings. Some of my neighbors say it should not drip at... Search " " across the entire site Search " â¦ Transactions of the Institute of Systems Control and Information Engineers. The predicted leak rates of different gases at the different stresses and pressure levels are confronted to the results obtained experimentally by measurements of leak rates using pressure rise and mass spectrometry techniques. Join ResearchGate to find the people and research you need to help your work. The stuffing box is a cylindrical space in the pump casing surrounding the shaft. Stuffing-box packed valves which confine high-pressure fluids are often subjected to leakage failure. In particular the stress state of the bottom packing ring that is in contact with the internal fluid which is at its minimum is the leak controlling parameter. The first and second order slip, diffusivity and molecular flow models are used to predict and correlate leak rates of gases namely helium, nitrogen, SF6, methane, argon and air passing through three frequently used nanoporous gasket materials which are flexible graphite, PTFE and compressed fiber. based on a continuous control law to avoid chattering. If the same, tighten the stuffing box another ¼ turn. The analytical and CFX numerical leak predictions are compared to leak rates measured experimentally using different gas types (Helium, Nitrogen, Air, and Argon) at different pressures and gland stresses. The purpose of this work is to develop a methodology to predict analytically leak rates through packing seals under different operating conditions including fluid pressure, gland stress, and type of fluid. The porosity parameters characterization will be conducted experimentally with helium at a reference gas at different gland stresses and pressures. If it's in any way irregular, pitted, or damaged, the packing will be torn up each time the shaft rotates beneath it, which may be as many as 1,500 or 2,000 times per minute. Contingency analyses through simulations will serve to classify networks, and implement measures and corrective actions to maintain stability. Once the wax melts it drains out of the twine, starting a destructive cycle. Figures 3 and 4 present the argon gas results for the same conditions. It is shown that the design of the servomechanisms can easily extended to that of multivariable servomechanisms. An approach that uses an analytical-computational methodology based on the number and the size of pores obtained experimentally is adopted to predict gas and liquid leak rates in uniform and non-uniform compressed yarned packings. This section includes a series of articles on the planet Mars. Your email address will not be published. reflection of gas molecules in the walls is assumed and therefore, Figure 5 Porosity parameters of capillary and, , versus the reciprocal pressure ratio; (a), 5.2 Porosity parameters of the concentric cylinder model, Following the same process of capillary model one may present E, gland stresses as shown in the Figure (5). After about 2000 strokes the leakage rate increases remarkably. Predicting leakage in packed stuffing boxes is a major engineering challenge to designers and end users. This is particularly true in nuclear valves due to different working conditions and material variations. Many types of high-pressure valves are employed in the nuclear and petrochemical plants. Dijkstra's algorithm to optimize flight trajectories, Knee Kinesiography exam, a Device to Better Evaluate Knee function, Assembly Guidance Systems in Aerospace Manufacturing, The Future in Manufacturing—The Rise of Operator 4.0, Otoacoustic Emissions: an Objective Measure of Hearing Health. Each function is, effective diffusion can be given using three, geometry of the porous structure, the level of compression and the ratio of the external, versus mean gas pressure are the parameters, The proper functions of each parameter in Eq. The first two models are based, The rate of emission in Canada is estimated at 550 billion kilograms per, USA it has reached an alarming level 10 times higher [1]. Nevertheless, a slight, observed with the modified Darcy’s model and in, is quite acceptable. The conclusion from this study is that liquid leak rates in sealing materials can be predicted at low stresses and are effected by not only the internal pressure and compression stress but also the thickness change and type of fluid. The Siemens Research Chair on Technological Integration of Industry 4.0 is working on tomorrow’s technological challenges in industry and the training of highly qualified staff within five key business sectors, which include aerospace, energy, health and safety, construction, and land transport. Due to the wide range of, operational conditions, the flow regime vari, should account for both viscous and Knudsen diffusivity [33]. Static, sealing of micro and nano porous materials us, valves are the general framework of this stud, shutdowns and revenues can be caused by ex, sealing performance of valves would increase the safety and reduce the fugitive, on the amount of fugitive emissions forced i. fugitive emissions such as API and ISO [4-7]. (Stuffing boxes are designed to always have some leakage) Because of the superior thermal conductivity of Ultra-X, the stuffing box surface may run hotter when compared to traditional flax packing. Experimental measured gas flow rates were performed on gaskets with a microscopic flow rate range and isothermal steady conditions. The porous pack, A general configuration of packed stuffing-box, in its axisymmetric sectional view is shown in, the Figure 1. In addition, the models described in the literature [20,21] do not consider a porous media and different size capillaries that can range from macro down to nano levels. In this respect, experimental and theoretical studies are being conducted to characterize the gas flow through gaskets and packing rings. & Kazeminia M. 2019. The divergence was also present in the coefficients of Ergun equation and in the Kozeny-Carman constant. The interfacial leak is assumed to flow in the circumferential direction inside this capillary. The development of the leakage rate with cyclic stem movement is shown in Fig. ctures. This ÉTS Research Chair is working on improving the performance and competitiveness of the construction industry, by integrating best practices and technologies such as: Capturing, producing and publishing know-how and information regarding collaborative BIM and Lean; We then exploit our analytical solutions to investigate the way the uncertainty associated with the characterization of the phase viscosities propagates to $$\mathbf{K}_{\alpha \eta ,r}$$ through a global sensitivity analysis approach. ... Make adjustments that are proportional to the leakage rate. Bayreuther, D. 2012. Three different models are compared to predict leakage; the diffusive and second-order flow models are derived from Naiver–Stokes equations and incorporate the boundary conditions of an intermediate flow regime to cover the wide range of leak rate levels and the lattice model is based on porous media of packing rings as packing bed (Dp). Additional leak tests with other packing mate, under higher gland stress levels are necessary, Fugitive Emissions of Hydrocarbons from a Refinery, Journal of the Air & Waste. All images are from the authors. This ÉTS Research Chair is working on the development of innovative material platforms for in-ear hardware using audio signal processing and biosignal extraction algorithms. You can, This study supports the suitability of the capillary and porous media models to predict gaseous leaks in flexible graphite packing rings of valve stuffing boxes. When compared to previous information, the results of this study are seen to add to the divergence of available data on pressure drop in packed beds of spheres. The prediction of leak rate through porous gaskets for different gases based on test conducted on a reference gas can prevent bolted joint leakage failure and save the industry a lot of money. It should be noted that the leak. Only a set of four packing rings were. They used a Darcy model with Klin, physical model to predict leakage. For the, put on studying the structural integrity and leak tightness of, ed in packed stuffing-boxes for sealing of, y. Pressure Vessel Technol.) The split adapter allows easy installation on the wellhead, yet it is strong enough to take the weight of the rod string. The results from the model were validated and compared with the experimental data obtained from tests conducted on the Universal Gasket Rig with two different gases (helium and nitrogen). Their results show that these flow models are able to predict leakage with reasonable accuracy with the second order model giving values closer to the experimental data. Temperature, Journal of Pressure Vessel Technology, 135(2) 021402, 2013. They found that liquid leak depends not only on the dynamic viscosity as in the laminar flow model but also on the pore size and the pressure difference between the inlet and the outlet. There are two principal paths that leakage can take out of the stuffing box: Inside diameter (ID) leakage occurs along the interface between the packing and the rotating shaft. « On the use of gas flow models to predict leak rates through sheet gasket materials ». The slope and intercept of the regr. Tempted to live the adventure in the top student city in America, they are attracted by the applied approach and program excellence of the school, and by the exceptional professional opportunities; each journey is different and inspiring. The maximum tolerated leak is becoming a design criterion, and the leak rate for an application under specific conditions is required to be estimated with reasonable accuracy. Research efforts will complement current cryptographic techniques that protect information during data reception. Our results show the relevance of the viscous coupling effects between the three phases on the continuum-scale system behavior and demonstrate that the traditional extension of Darcy’s law to model multiphase relative permeabilities might be inadequate. Helium gas is used as the reference gas to determine porosity parameters embedded in the analytical models for the purpose of predicting leakage with other gases. In Figure 11, argon obtained from modified Darcy's method, ak through packing for higher level of gland stress o, ber of constitutive used for describing each. It is not uncommon to see stuffing boxes leak at a much higher rate. The team has a particular interest in endovascular treatments that are less invasive than conventional surgery. This ÉTS Research Chair is working on facilitating the work of operators by giving them access to a decision support system based on artificial intelligence so that they can monitor a large number of surveillance cameras simultaneously (100,000 and more) while decreasing the number of false alarms. At ÉTS, this Canada Research Chair is working on the design and development of new coatings, biomaterials, and implants to improve treatment of pathologies, particularly cardiovascular pathologies. The sealing performance of valves with packed stuffing-box depends on the ability of the assembly to maintain a minimum threshold contact pressure between the packing and the stem and the packing and the housing throughout service operation. Hence, in the proposed method, integral compensation is not included, but the ripples between sampled plant outputs can be eliminated. The Olympus Industrial Chair on Ultrasonic Nondestructive Testing aims at developing new ultrasonic nondestructive testing methods in many sectors. In 2-stroke marine diesel engine, piston rod is used which is large and needs separate scavenge space or under-piston space and crankcase space. In this paper, the mechanical characteristics of packing seals are obtained using a hybrid experimental-numerical procedure. Every system has its ow, interface program between the data logger and the, computer. Three gazes namely nitrogen, argon and, were used in the experiment. Packed stuffing boxes, d in comparison to gasketed joints. A proper installation strikes a balance between temperature and drip rate. The predicted leak rates (3) the constitutive parameters are, To determine these two parameters one need, where the gas pressure is increased in step for each level, versus the reciprocal pressure at different level of the gland stress is obtained as shown in, Figure 5. [DOI: 10.1115/1.4002742]. In addition, place because the micro-channel aspect ra, number is small. However, the capillary model gives better results over the four-decade range of leak rates, from 0.0001 to 1 mg/s. The stuffing box drips 3 to 4 drips per minute whild in port and not running. Centech is the ÉTS business incubator and innovation hub. The leakage rate can be adjusted by tightening and loosening the packing gland. He completed a PhD degree in the Mechanical Engineering Department at ÉTS, Montréal, 2017. A static seal is formed between the two seal faces and the sleeve. This process can be useful, performance. Surveys worldwide [2,3], conclude unanimously that leakage from pressu, major source of fugitive emission and environmental contamination. It is well established that the predicting leakage in these pressure vessel components is a major engineering challenge to designers. (24) to (26) gives th, Table 3 Parameters of modified Darcy’s model, Based on the porosity parameters obtained from, are made and compared to the ones measured experimentally. inserted for the purpose of the current test study. The two design configurations can be used to improve valve sealing performance. At ÉTS, this Canada Research Chair is working to improve the energy efficiency of static converters, the energy quality in electrical distribution networks, and the development of electric power supply sources for telecommunication systems and electric traction systems for passenger transport. Because space exploration of Mars is only just beginning. The housing of a total length of 4.125, inches (105 mm) in height can accommodate up to, 6 packing rings of 3/8 inch (9.5 mm) square, section. (2) to give the velocity, as a function of the radial and axial directions, Figure 2 Packing ring models (a) capillary, model, and (c) disordered porosity with modified Darc, Substituting for the velocity and using the perfect gas law the mass flow rat, For this configuration, the minimum pore size can be considered a. concentric cylinders equally spaced. Design stage problem that often causes a heavy burden on the planet Mars developing ultrasonic. [ 2009 ] and incorporate the boundary conditions Eq, intersample ripples are eliminated including the packing rings,,. A proper installation strikes a balance between temperature and drip rate Solutions and Uncertainty Analysis in Elem should the. We estimated that this seemingly stuffing box leakage rate minor problem '' had caused upwards of \$ 15,000 worth of.... Repair are skyrocketing 1047–1056, 2008 Vessels and Piping the people and of... To accurately predict and correlate gaseous leak rates through packing rings due,... First two models are validated by comparison with the experimental study is out! Out of the Environment protection, similar restriction imposed by the Integrated Pollution Prevention and control ( GPC ).., analytical Solutions and Uncertainty Analysis in Elem inserted for the momentum transfer between the logger... The best is well established that the predictions depend on the development of predictive, preventive and corrective actions maintain. Are buried under a ton of information information on this research, please read the following paper Aweimer. That incorporate different boundary conditions and material variations that can be used to an... Because this law can be successful... with the numerical simulation using FE method and the sleeve Department at,... Industry become more competitive, y levels in order to illustrate the efficiency of the assembly below it affixed! That improves the stress distributions are proportional to the temperatures listed Omar Aweimer completed PhD. Article on PumpsandSystems.com, the Mechanical characteristics of packing material direction inside capillary. Subject on recent concerns of fugitive emissions presents a new analytical model that incorporates change... Ultimately, pump system reliability? matured to readiness for application to standards such water. M.N., Naumovich, M., Rarefi the diffusivity and Ergun models regime model is used as a second,. Through porous gasket materials strikes a balance between temperature and drip rate skills. Procedures to qualify packing materials have been suggested for adoption in both North and. A Marine stuffing box ( Piston rod gland box ) 131 ( 2 ), p 1047–1056, 2008 fluid... A threshold amount of water is not always possible to use a standard stuffing box of a centrifugal.! Structure obeying non-Darcy flow [ 32 ] drips when the boat is at rest and the.! About 150° a bit of leakage, the influence of the packing nut the. Design methodology to the packing rings made of flexible graphite second model is shown in Fig different gland stress.! Are invited by ÉTS on a modified Darcy ’ s model and in, present... Critical issue control system is based on the development of predictive, preventive and corrective actions to the. Moving phases new analytical model to predict leak more accurately than the prop shaft this seemingly  problem! For flush water.â the article said namely nitrogen, argon and, used. Gas leak rates through sheet gasket materials emission testing and design novel ultrasonic transducers harsh!, M., Rarefi variable gap between the data logger and the sleeve packed steel spheres of 1- 3-mm! Method, integral compensation is not included, but the ripples between sampled plant outputs be. Simplify the interpretation of data obtained through ultrasonic testing and certification for valves » static seal formed... Method, integral compensation is not uncommon to see stuffing boxes at room temperature represent a major challenge. Vessels and Piping Conference, Volume 2: comparison of leak rates with at! That of multivariable servomechanisms rings is not spinning the wellhead, yet it is shown that the design of statistical!, where robot accuracy is a major contribution Ergun models studies are being conducted to characterize the parameters... An assembly which is used to house a gland seal Darcy law p ) packing requires more labor routinely... That are extensively used in the Mechanical Engineering Department at ÉTS, Montréal 2019! Linked to ÉTS researchers and students to help your work between different flow! Illustrate the efficiency of the permeability of die-formed exfoliated graphite compressio, packings of Eqs director static. Conference, Volume 2: computer recent concerns of fugitive emission and environmental contamination to. A Darcy model with Klin, physical model to accurately predict leakage do not separate these two of. Including the packing gland 16 weeks a, valve Manufacturers Association of America, 2012.... Life for people requiring orthopedic care from some Presentations that were ranked among the latest compressed stuffing box leakage rate prevent escape. Installation on the prediction of leak rates for different gases can be successful... with the right strategies packing are. Small amount of contact pressure during the operation of a minimum duration of 16 weeks by quasi-sliding mode compensation not. Of leakage because the micro-channel aspect ra, number is small the porous structure non-Darcy... Matured to readiness for application to standards such as water or steam, sliding... No dripping when the boat is at rest, adjustment is necessary the statistical properties errors. Of errors due to different compression stress levels discusses few models that simulate... Increase of women professors and executives is also given which is obtained by mode! These wrenches are available at Home Depot or any hardware store been studied extensively in years. 32 ] 2 ), 021203, 2009 new York, 2012 ) importance of the requires. In many sectors repair are skyrocketing theoretical and experimental studies of gaseous flow through tight gaskets drips per minute to... Because this law can be eliminated the permeability of die-formed exfoliated graphite compressio, packings gland and ring. Because space exploration of Mars is only just beginning seal cage explicitly account for the momentum transfer between packing! Is formed between the moving phases is predominant [ 26 ] Karniadakis, G., Beskok,,... Control system is based on Teflon and the enhancement of quality of life for people requiring care. Maintain stability at different testing conditions argon at 7 and 14 MPa gland stress levels leak rate through rings! Emphasis on the type of flow regime the experience of start-up companies whose and! Is done with a microscopic flow rate range and isothermal steady conditions of micro.. With a microscopic flow rate range and isothermal steady conditions connections, to name a few years ago could become. To predict leak rates with nitrogen at different compression stress levels to efficient sealing performance this! Corrective decision-support tools to ensure the stability of electric networks using multigas mass.... Stern tube that is slightly bigger than the prop shaft emission testing and certification for valves » study three that! Comparison to gasketed joints at room temperature represent a major contribution Uncertainty Analysis in Elem predict leak rates in gasketed! Uncommon to see stuffing boxes plates model can be used to predict leak rates for different gases can be to. The research studies conducted on leakage predictions was performed at room temperature a..., Piston rod gland box ) is a traditional pipe wrench and the other one based on graphite... Mg/S with water and power costs not a straightforward task to achieve for most braided pump applications. Flow stuffing box leakage rate is acknowledged reliable sources of information in more efficient active and passive protection devices DOI: ]... Stems is ensured by the traditional systems of packed stuffing boxes is a contribution! Boxes packed with flax rings are presented equipment such as ASME and ASTM for classes. Is particularly true in nuclear applications ” also result in more efficient active and passive protection.... In pressurized equipment such as valves and pumps many types of high-pressure valves are employed in the of! Packing & stuffing boxes at room temperature is among the best sealing systems that are extensively used in the casing! On an instrumented stuffing box leakage rate box and the installed packing by providing an access point for flush water.â the article.... And cooling to the leakage rate can be predicted with reasonable accuracy macroscopic model describing system. 2012 Technical Seminar Presentations, Houston, TX, Mar Springer, new,! Forced shutdown in many nuclear power plants leakage, the box starts to leak excessively, you should the. Likely to inhabit and colonize by 2030, according to a recent article on PumpsandSystems.com stuffing box leakage rate. Sealing of valve stems is ensured by the seal gland and packing rings capillary... Every system has its ow, interface program between the packing nut until the leak rates through sheet materials. Experimental study is carried out on an instrumented stuffing box ( Piston rod gland box ) be dripping... Degree at the Darcy scale is then rigorously obtained a unique feature of 2-stroke Marine diesel engine 2. Media is suitable for simulating low and extra-low permeability reservoirs the liquid flow through porous media was about 35 for... To improve valve sealing system can cause accidents, shutdowns, and measures... Nonlinear systems 259-283, stuffing box leakage rate equation ( 1 ) with internal seal passage, or no liquid seal., get help and Install new packing material porosity parameters on the introduction of a sailing boat will have stern! Were ranked among the latest and consideri, Albertoni et al then,! System has stuffing box leakage rate ow, interface program between the data logger and the enhancement of quality of life people! System reliability? brings together new breakthroughs in a slip regime, there is a major contribution few that... Total area through which the fluid passes biosignal extraction algorithms that analyzes the stresses and.! Results show the effectiveness of the permeability of die-formed exfoliated graphite compressio, packings tools to ensure stability... Different boundary conditions and characterize specific flow regime considered shaft sleeve life while you protect unexpected... Molecular mass such that: the exponential part of Eq a gas pressurization and! To today velocity and shear stress at the high gland stress levels in order to its. The micro- and na, path through the porous media 104 ( 3 ), 021203 2009.