Hvac Filtration

William A. Greco 2007

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Particle and Fiber Mechanics as related to HEPA Filtation Introduction Filters are a critically important component in Pharmaceutical HVAC systems. The majority of the following has been researched and compiled from many sources. The intent is to bring together useful information to form one uniform article relating to HEPA filtration with respect to particulate interaction with filter fibers. Although Ashrae has partially covered some of the mechanics of particulate capture, a more complete definition of these processes and concepts will be found within these pages. This report is not a repetition nor an explanation of ASHRAE 52.1 or 52.2. It does not identify or explain the usual dust-spot procedures for testing air filters. The reader will not find any reference to MERV (minimum efficiency reporting values). What will be found is the mechanics of filter fiber and particulate interaction, which will provide new insight to filtration operational concepts. General Considerations A captured particle becomes part of the filter structure, increasing the pressure drop while at the same time increasing the filter efficiency. A new filter will be less efficient than one that has been in service for a while. Filters are changed because of reduced airflow due to increased pressure drop, they are not replaced because of loss of capture efficiency unless they have been punctured and leak. It should therefore be expected that recently replaced filters will pass more particles than filters that have been in use for a while. A time period of settling in or running of the system should be a standardized procedure after filter replacement. Filter manufacturer’s charts indicate the pressure drop at a specified CFM, filter charts never indicate the interception efficiency versus length of filter service or interception efficiency versus loading capacity. The rate at which a filter will become clogged is related to particle size, the finer (smaller) the particle size the higher the rate of clogging.

Particulate Branched Structures During the early part of filter life, particles attach themselves to filter fibers. During the middle and late stage of filter life particles attach themselves to other particles and begin to build branched structures, see figure-1. Particles furthest away from the filter fiber on these branched structures cause a high velocity gradient which interrupts normal flow patterns causing considerable local turbulence. Particulates caught in this increased turbulence tend to be quickly captured by the larger branched particle structures, which also speeds up local structure growth rate.

William A. Greco 2007

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Particle and Fiber Mechanics as related to HEPA Filtation

Filter Fiber Vortex A vortex forms on the downstream flow side of filter fibers. This vortex promotes particle capture. The size of the vortex increases with local velocity. The flow pattern surrounding a filter fiber lacks upstream-downstream symmetry. See figure-2.

Filter Structure Filters should be considered as layers of fibers in an open three dimensional network. Points of fiber to fiber contact are infrequent. If each layer of a (100) layer filter only captured 5% of the particles passing through it, the filter as a whole would capture 99.4% of the particles, if there were (138) layers it would capture 99.9% of the particles, if the filter captured 7% with each layer of the particles passing through it, the filter as a whole would capture 99.9% of the particles with (96) layers, this same filter would capture 97.5% of the particles at it’s 51st layer. Particle size not withstanding. Thick fibrous filters are more efficient than thin filters. Layers are sparsely populated with fibers. Packing Fraction The “Packing Fraction” ( the fraction of the volume of filter media in relation to the overall volume of the filter) is only a few percent. This could be readily seen by compacting the filter media and comparing the filter volume to the media volume. Particle capture throughout a HEPA filter is defense in depth or “Depth Filtration”. All packing fractions are less than unity (1<). A packing fraction of one would simply be a solid mass which no air could pass through. The lower the packing fraction the higher the dust holding capacity and the lower the filter efficiency and initial pressure drop. Testing versus Operation In actual operation filters are subjected to “polydisperse” particulates which range in differing sizes, if filters are tested using “monodisperse” particles of uniform size, serious misconceptions or errors could result.

Macroscopic Theory Versus Single Fiber Theory Fibers should not be considered as isolated or independent closed systems because fiber to fiber distances in a filter are only tens of micrometers apart and have a collective influence on the flow pattern. Any attempt to mathematically account for filter flow patterns should be worked out with empirical data based on a macroscopic closed system. Predicting filter performance based on “single fiber theory” and “Cell Theory” are the presently accepted methods of filter calculation. Some calculations are by necessity statistically based.

William A. Greco 2007

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Particle and Fiber Mechanics as related to HEPA Filtation “Example of Statistical Description of Filter Fiber Structure” If fiber thickness is assumed to have zero width, a typical pore shape (a pore as defined here is a cross section of intersecting filter fibers that are normal to the airflow direction and form a closed geometric shape) could be predicted, the probability of more than two lines intersecting at the same point approaches zero. When two lines intersect, four angles are formed, each of which is the vertex angle of a polygon forming a pore. The average sides of a pore is four, triangles and polygons of higher order are also formed, but are probably less frequent. The probability of intersection (Int) of two fibers of length (L) drawn at random in a square element with side (L) is:

If there are (Nf) fibers per unit area of filter the likely number of pores produced by intersections, Np , is:

Which for very large values of Np approaches:

It would be difficult to measure the number of fibers (Nf) per unit area. Predicting the number of intersections would not be useful unless the pore size could be calculated. It is possible by statistical means to identify the pore size, but the accuracy of the procedures may lie in statistical methods. Page 6 of 12 indicates a “Cell Theory” method of determining cell area. The dimensional random fragmentation of the inside of a filter combined with particle distribution and particle flow action can be treated with statistical theory. Predicting the pore size does not lend itself to simple analytical procedures, pore areas will be “skewed” and “unimodal”. Note: Skewed = Probabilities which the median and the mean are not coincident. Unimodal = If x < y y > c then f (y) > f (x) or vice versa. Function (f) possesses a single maximum or minimum in the interval. It would be required to approximate pore size by one of the standard distributions, gamma, weibull or lognormal. Constants for these distributions would have to be assumed. Because of the nature of flow through a filter the influence of pores on airflow is governed more by hydraulic radius than by cross-sectional area. Characteristics and Forces affecting Airflow, Particulates and Fibers with respect to Air Filtration The forces affecting fibers and particulates are: Local Gravitational forces Mass or inertia of the particulate Viscosity of the air, particle and fiber Elasticity of the particulate and fiber Molecular action of the particulate and fiber Ionization potential of the particulate Surface tension (capillary) forces between particulate and filter fiber Thermal energy Transfer Between Transport Medium (air) and the Particulate Vibration and sound transferred to the filter fiber from the local environment Velocity Pressure acting on captured particulates

William A. Greco 2007

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Particle and Fiber Mechanics as related to HEPA Filtation Shape of the Particulate and Filter Fiber Non-spherical particulates and non-circular filter fibers should be considered. Particulate Theory deals with spherical shapes because these are easier to work with, however particulates come in elaborate shapes. Aspect ratio of the particulate should also be considered. A particle with a large aspect ratio could easily pass through a filter by considering it’s width as below 1 micron and be huge with respect to it’s length.

Mechanisms Governing Particulate Capture Filter Theory usually classifies particulate capture by Diffusion, Interception, Inertial Impaction (see figure-3) or Gravitation, and each mechanism is dealt with separately. In actual fact more than one particulate capture mechanism acts on the particle at any given time. Deciding which one is the predominant capture mechanism is difficult to identify at any given moment. Ashrae includes straining as a particulate filtration capture mechanism, however HEPA filtration and straining have very little in common. Capture by Diffusion Small particulates are transported in the air stream. Particulates that are relatively small and have low amounts of mass quickly achieve thermal equilibrium with the transport medium (air) with which they have been entrained. Particulates suspended in a gas receive thermal energy from that gas. A constant exchange of thermal energy between the transport medium (air) and particulate results in microscopic motion of the particulate. This additional motion or wobble of the particulate prevents it from traveling in a straight streamline course resulting in a diffused trajectory, which aids in their capture. Capture by diffusional thermal motion (known in physics as Brownian Motion) has a greater effect on very small particulates than on large ones. Particulates captured by diffusion are often found on the back part of the filter fiber with respect to airflow Capture by Interception Particles captured by pure interception depend strictly on the airflow velocity and generally have a low inertia caused by a low mass and / or low velocity, Interception depends on conditions close to the filter fiber surface. Air velocity at the fiber surface is close to zero and contact by interception is a gentle process. A radial and tangential air component exists close to the filter fiber, both of these components vanish at the fiber surface. Capture by Inertial Impaction Inertial Impaction usually occurs with the particulate flowing practically in a straight line and striking the filter fiber head on. Particulates with a high inertia break free from the streamlines which surround the filter fiber and head straight into the fiber. Particulates captured by inertial impact will usually be found on the front side of the filter fiber with respect to airflow. The energy spent during the head on collision of the particle and fiber results in plastic deformation of the filter fiber and particulate.

William A. Greco 2007

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Particle and Fiber Mechanics as related to HEPA Filtation

Particulate Capture by Gravitation Particulates in still or stagnant air settle out under gravitational influence. The effect of gravity during filtration will depend on the direction of airflow, with the result that gravitational settling may either augment or diminish the transport of the particles toward the fibers. Local dead zones within the filter can cause air stagnation allowing gravity to become the predominant force within the filter. Humidity effects on Particulate Capture Increasing relative humidity will tend to improve particle adhesion to filter fibers. Two situations occur simultaneously at higher relative humidity levels. Capillary forces are significantly higher at elevated relative humidity ranges increasing fiber to particulate adhesion. Filter fibers at raised humidity levels are softer, influencing the impact dynamics. Unfortunately Pharmaceutical production areas require low humidity values to be present in the transport medium (air). Particulate Shredding and Filter Fiber Shedding Particulates should not be thought of as singular entities but as a number of fragments held together by various forces, if a particle undergoes enough stress it may dislodge some of it’s fragments into the air stream. Filters sometimes lose or “shed” fibers when the system is first activated. Transfer of Static Electric Charge The transfer of electric charge on contact between filter fibers and particulates by frictional electrification (static electricity) is a process that results in higher adhesion energy for particles approaching fibers than those leaving the fiber surface, the effect however compared to the number of particles captured by strictly mechanical process is very small. Particulate Escape There must exist an energy level in which the fiber and the particulate contribute the same adhesion energies and where the approach velocity becomes critical causing sufficient energy for the particulate to escape capture or bounce off of the first fiber it encounters. Particulates which either completely escape the filter or are captured deep within the filter probably exhibit high mass relative to their size and are aerodynamically well suited to high velocity and a low drag coefficient. Vibration by sources outside of the filter media could cause loss of particulate adhesion from the filter fiber, such vibrational forces can easily be found in most Pharmaceutical production areas and processes, equipment vibration can be transmitted to the filter housing through the building structure and ductwork system. The size of particulates which either evade capture or are found buried deep within the filter will have an increased diameter when the diameter of the filter fiber is increased and the packing fraction and velocity are decreased. Airflow around a captured particle provides an additional force which helps to encapsulate the particulate within the surrounding flow streamlines. When airflow is shut down this encapsulating force is deactivated, thereby allowing some of the previously captured particles to become detached. Those particulates that have been captured by inertial impact will be more difficult to detach than those captured by other means. Velocity increases in filters that have become clogged past their recommended replacement pressure drop. A substantial increase in velocity may cause particulate shredding or total detachment to occur. Temperature change can cause the filter fiber to expand and actually release a captured particle. Some particulates are caught in the room by heat stratification or points of room airflow stagnation which never reach the HVAC system and are a subject of space airflow and not associated with filter dynamics. Pin hole leaks are not as big a problem as might at first be expected. A pin hole leak will exhibit a measure of size selection the same way that a filter does. Since air passes through the leak faster than the air passing through the filter, there will be a convergence of streamlines into the leak, this increased convergence increases diffusional movement and particulate inertial impaction.

William A. Greco 2007

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Particle and Fiber Mechanics as related to HEPA Filtation Filter Cell Area Calculated by Cell Theory

A filter fiber cell area calculated in accordance with “Cell Theory” defines a reference surface concentric with the fiber surface as shown in figure-4. The cell surface distance is such that the packing fraction of the fiber within this cylinder is identical to that of the fibers within the filter. The cell surface radius is equal to the fiber radius divided by the square root of the filter packing fraction. See page 3 of 12 for example of statistical description of filter fiber structure.

Where: R = Fiber Radius c = packing fraction Example-1: For a 20 mm fiber radius and a filter packing fraction of 0.011 or 1.1%, the calculated cell radius in accordance with Filter Cell Theory is:

Where: 20 = microns Note: Micron = symbol m A former name for the micrometer; 0.000001 meters

Sometimes written as mm. 25400 = microns per inch

Note: For packing fraction definition see page 2 of 12.

William A. Greco 2007

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Particle and Fiber Mechanics as related to HEPA Filtation Theoretical Method of Pressure Drop Calculation Through a Filter The flow equation for filter pressure drop as solved for a limited region, is assumed to be typical of the filter as a whole. The theory results in a simple analytical expression for an airflow stream function based on moderate velocities. The filter fiber radius, depth of the filter and the packing fraction are required to solve the equation, these three variables can be obtained from the filter manufacturer. The following equation for pressure drop is from Happel, J. “Viscous flow relative to arrays of cylinders”, American Institute of Chemical Engineers Journal, 1959 pp. 174-177.

Where: DP = Pressure drop, pounds per square foot R = Radius of the filter fibers, feet c = Packing Fraction h= Coefficient of viscosity of air at normal conditions (0.000004 lbs/square foot/sec.) U = Average Velocity of airflow through filter media, feet per second h = Filter Depth, feet Note: Coefficient of viscosity of air as given by Baumeister, T. Marks Standard Handbook for Mechanical Engineers, McGraw-Hill sixth edition, 1967 Pg. 3-50..fig. 2. Example – 2: Assume a packing fraction (c) of 0.011, an airflow of 100 feet per minute ( 1.67 feet per second) and a filter depth of 6 inches (h = 0.5 feet) and a filter fiber radius of 40m microns . The theoretical pressure drop for this filter is:

Canceling units:

144 square inches per square foot A water column of 27.72 inches is the equivalent to 1 pound of pressure Therefore:

William A. Greco 2007

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Particle and Fiber Mechanics as related to HEPA Filtation Example – 3: Assume the same filter as in example-2 with a clean packing fraction (c) of 0.011, an airflow of 100 feet per minute ( 1.67 feet per second) and a filter depth of 6 inches (h = 0.5 feet) and a filter fiber radius of 40m microns. As the filter gets dirty the packing fraction will increase, and the filter pressure drop can be recalculated. Assume a 20% particulate loading : The new packing fraction will be: 0.011 + (0.20 x 0.011) = 0.011 + 0.0022 = 0.0132 The new velocity through the filter will be: (100 feet per minute x 0.20) + 100 feet per minute = 120 feet per minute or 2 feet per second

Pressure drop of 7.37 pounds per square foot or

On this particular filter an increase of 20% loading increases the packing fraction to 0.0132 and causes the velocity to climb to 120 fpm which equals a pressure drop of 1.42 inwg. Most HEPA filters are changed at a 2 inches water gage pressure drop. This particular filter would require a 39% increase in the packing fraction prior to being changed. A 39% increase in the packing fraction would increase the velocity to 2.31 feet per second and the packing fraction to 0.0153, the pressure loss would now equal 2 inwg thus:

Pressure drop of 10.32 pounds per square foot or

or roughly 2 inwg Please note that the packing fraction increase is by volume not by weight, an equal volume of captured particulate will weigh considerably more than an equal volume of filter packing media.

William A. Greco 2007

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Particle and Fiber Mechanics as related to HEPA Filtation Loading Loading or clogging rate is very low for the inertial impact capture mechanism. Diffusional capture has a very high clogging rate, while the capture rate by interception falls somewhere between inertial and diffusional. The rate of clogging in HEPA filters is independent of velocity. The major capture mechanism for HEPA filter particulate loading is interception. With high particulate inertia the likelihood of particle to fiber contact without capture is higher for a clean filter than it is for a loaded filter. Towards the end of life of a high efficiency filter there is a tendency to convert from depth filtration to surface filtration where the leading surface forms a dust cake. This is usually the final behavioral mode of a clogged filter. A relationship exists between clogging rate and filtration efficiency. The best means of controlling the loading rate is to use layered structures. A layered filter can be made from composite materials such that the lowest efficient layer is first to capture the entering particulates. The entire filter would be made of the same size fibers but the packing fraction made to vary with depth. This would promote depth filtration and reduce the filter tendency to form a dust cake at the surface. Calculation of Mean Thermal Diffusional Energy as it relates to Coagulation and filter clogging is given by the theory of “Equipartation of Energy”. The theory states that the average energy of the molecules of a gas are equally divided among the various degrees of freedom of the molecules and the degree of freedom is equal to: ½ kT, where k is the Boltzmann constant and T is the absolute temperature. Extending this to include mass and velocity gives: ½ mV2 = ½ kT where m = mass of the particle and V = velocity. The thermal velocity then equals:

k = Boltzmann constant where J/K = Joules per degree of absolute temperature Where the (IP) Inch Pound system is to be used as opposed to (SI) System International units (metric), 1 joule = 1 watt/sec = 0.7376 ft/lbs/sec. And Absolute temperature = degrees C + 273.15 and degrees F + 459.67 k (Bolzmann constant in Inch Pound system) =

Canceling units:

William A. Greco 2007

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Particle and Fiber Mechanics as related to HEPA Filtation Calculation of Mean Thermal Diffusional Energy (continued from page 9 of 12) Example-4: Consider a spherical particle of dry soil (dirt) with a one micron diameter in an air mass of 70 degrees F. = Volume of a sphere =

Where: D = diameter of sphere 1 inch = 25,400 microns therefore a one micron diameter has a volume of:

Architectural Graphic Standards _John Wiley & Sons –6th Edition – 1970 gives the weight of dry soil as 76 pounds per cubic foot. one spherical micron of dry soil weighs:

where:

m = mass, pounds ; T = Degrees F. Absolute ; k = foot-pounds/sec/degree F Absolute

Velocity of a spherical particle of dry soil (dirt) with a one micron diameter in an air mass of 70 degrees F. due to diffusional thermal movement (Brownian motion) = 0.00151 feet per second This velocity represents the contorted vector movement which keeps the particle from moving along the same path as the airflow streamlines. The thermal energy which the particulate comes in contact with any surface which it encounters is represented by:

9.16 foot pounds per second = 1 horsepower

William A. Greco 2007

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Particle and Fiber Mechanics as related to HEPA Filtation Agglomeration An indiscriminately formed cluster of particles can coagulate forming larger particles if they have high adhesion properties. Certain forces could prevail in a space in which particles that are below the minimum capture size pass through HEPA filtration, invade the protected space and then proceed to join together and form larger particulates which could remain active in the space if not captured by the HVAC system. A build up of such a process could cause the space to eventually fail it’s classification rating. Another term for agglomeration is flocculation. Particles below 0.1 microns in size exhibit violent diffusional thermal movement as shown on pages 9 and 10, the mass of the particle is divided into the Bolzmann constant, hence the smaller the mass the more violent the particulate vector movement (Brownian Motion). This increases their collision frequency with consequent formation of agglomerated masses or aggregate structures. Suspensions of such particulates eventually achieve sufficient mass to succumb to gravity and settle. Settled particulate masses tend to stick to vertical walls and surfaces with which they collide. The time course of particulate agglomeration in a homogenous gas cannot be measured by the decrease in the number of separate particles in the suspension because some of the particles would have settled to vertical or horizontal surfaces. A theoretical method exists to measure the time course of particulate agglomeration, however the theory and calculation is only useful for an infinite space that is not bounded by surfaces and has no practical engineering value. Aerodynamic Slip Air molecules move by pushing against adjacent molecules. Air molecules travel a free path distance at STP (standard temperature and pressure) of 0.065 microns before colliding with the next air molecule. The effect of this free path is that the velocity of air at the fiber surface does not vanish in the tangential direction, but approaches a minimum limit. If the air molecule waves travel in a definite direction and the direction of the approaching molecules and reflected molecules make equal angles with a line perpendicular to the filter fiber surface, the tangential velocity will equal the approach velocity, causing the particulate to slip past the filter fiber. This process is termed “Aerodynamic Slip”. Particulate to Particulate Impact Often particulates impact and collide with one another without coagulation or agglomeration and simply bounce off of each other. Consider the case of a large particle with mass m1, with velocity v1 making a perfectly elastic impact with a smaller mass m2 with a velocity of v2. Conservation of energy by the first law of thermodynamics would conclude that: (m1)(v1)+(m2)(v2) = (m1)(V1)+(m2)(V2) Where: v1 and v2 are velocity before impact V1 and V2 are velocity after impact A slight loss of energy is given off to friction. Neglecting any losses due to coagulation forces, frictional or aerodynamic drag forces and taking into account the coefficient of elasticity’s, the equation becomes: (m1)(v1)(e1)+(m2)(v2)(e2) = (m1)(V1)(e1)+(m2)(V2)(e2) and to calculate the velocity of the particulates after impact:

William A. Greco 2007

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Particle and Fiber Mechanics as related to HEPA Filtation Conclusion The information contained within these pages was an attempt to present the mechanics of filter fiber and particulate interaction in a simple manner. Many intricate equations and concepts pertaining to filtration mechanics exist, however individuals actively engaged in HVAC system design would find this theoretical information’s usefulness inversely proportional to it’s complexity.

References:

Baumeister, T. Marks Standard Handbook for Mechanical Engineers, McGraw-Hill sixth edition, 1967 Den Hartog, J.P. Mechanics, Dover, 1948 Dorman, R.G. Dust Control and Air Cleaning, Pergamon Press, Oxford, 1974 Happel, J. Viscous flow relative to arrays of cylinders. American Institute of Chemical Engineers Journal, 1959 pp. 174-177 Hudson, R.G. The Engineers Manual, John Wiley & Sons, 1917 Illingworth, V. Dictionary of Physics, Penguin Books, 1991 Kanagawa, A. Advances in Filtration and Separation Technology, American Filtration Society 1991 pp. 341-345 Kaye, B.H. Describing filtration dynamics from the perspective of fractal geometry. KONA Powder and Particle 1991, pp 218-236 Kolmogorov, A.N. The logrithmically normal distribution of dimensions of particles when broken into small parts. English Translation from Russian N69-29262 (NASA-TT-F-12287). Piekaar, H.W. and Clarenburg L.A. Aerosol Filters- pore size distribution in fibrous filtration Chemical Engineering Science, 1967 1399-1408 Stafford, R.G. and Ettinger, H.J. Filter efficiency as a function of particle size and air velocity. Atmospheric Environment, 1972 pp 353-362 Wake, D. And Brown, R.C. Filtration of monodisperse aerosols and polydisperse dusts by porous foam filters. Journal of Aerosol Science, 1991 pp. 693-706