55
Determination of Rotary Filter Behavior Arthur Shih Malcolm Hegeman Brown Industries, Inc. November 5, 2012
Determination of Rotary Filter Behavior
Arthur Shih Malcolm Hegeman
Brown Industries, Inc.
November 5, 2012
Determination of Rotary Filter Behavior:
Evaluation of Rotary Filtration for Microalgae Concentration
Arthur Shih, Team Leader Malcolm Hegeman, Staff Engineer
Brown Industries, Inc.
Rotation 2 Report
Monday Lab
November 5, 2012
“We have neither given nor received aid on this project, nor have we concealed any violation of the Honor Code.”
___________________________ Arthur Shih
___________________________ Malcolm Hegeman
ABSTRACT
Brown Industries, Inc. is looking to study the use of microalgae to produce biodiesel. Rotary filtration has been introduced to deal with removal of excess water from the algae feedstock. Rotary filtration Rotation Team 1 investigated the operation limits and basic behaviors of the rotary filter utilizing both water and dilute algae feedstock.
Objectives included:
(a) Characterization of filter behavior and operating limits with water
(b) Definition of operating limits with algae
(c) Suggestion of a procedure for concentrate concentration estimation
(d) Characterization of filter behavior and fouling with algae feedstock
Investigation of the rotary filter was successful. With a water feed, filtrate flow increases with chamber pressure and decreases with rotational speed. With algae feed, low chamber pressure and high rotational speed is not recommended because of low filtrate flow rate. The algae concentrate concentration can be accurately predicted under certain operating conditions. Filter fouling decreases filtrate flow rate over time when filtering algae feedstock, but can be controlled by altering the chamber pressure and filter rotation speed. Rotary filter operation may be enhanced by investigating the effects of agitation through periodic reverse filtration.
TABLE OF CONTENTS
INTRODUCTION ............................................................................................................................... 4
Overview ..................................................................................................................................... 4
Goals and Objectives ................................................................................................................... 4
Summary of Key Results ............................................................................................................. 5
BACKGROUND AND THEORY ........................................................................................................... 5
Industrial background .................................................................................................................. 5
Oil Extraction Process .................................................................................................................. 5
Rotary Filter Transport ................................................................................................................. 5
Rotary Filter Model Development ............................................................................................... 5
Alternative Cell Harvesting Unit Operations ............................................................................... 5
MATERIAL AND METHODS .............................................................................................................. 7
Equipment ................................................................................................................................. 18
Materials ................................................................................................................................... 19
Experimental Design .................................................................... Error! Bookmark not defined.
Safety ........................................................................................................................................ 20
RESULTS AND DATA ANALYSIS ......................................................... Error! Bookmark not defined.
Collected Data ........................................................................................................................... 23
Design Space Validation ............................................................................................................ 23
Process Model Development .................................................................................................... 23
Back Flushing Procedure .............................................................. Error! Bookmark not defined.
Filtration Schedule Optimization ................................................. Error! Bookmark not defined.
UNCERTAINTY AND ERROR ........................................................................................................... 31
Sources of Error ........................................................................... Error! Bookmark not defined.
Error Analysis ............................................................................... Error! Bookmark not defined.
CONCLUSION AND RECOMMENDATIONS .................................................................................... 32
Conclusion .................................................................................... Error! Bookmark not defined.
Recommendations .................................................................................................................... 33
REFERENCES ..................................................................................... Error! Bookmark not defined.
NOMENCLATURE TABLE ................................................................................................................ 33
LIST OF APPENDICES ........................................................................ Error! Bookmark not defined.
INTRODUCTION
Overview
Brown Industries, Inc. is entering the biofuel market and is interested in designing and building a plant in Michigan to convert algae to biodiesel for commercial use. Biofuels is a safe, non-toxic, biodegradable, and renewable fuel that assists the environment by minimizing the release of greenhouse gases and toxic chemicals into the atmosphere. The biodiesel process layout in the USDA Haas study will be used as a basis to propose a plant layout, as shown in Appendix A.[1] Two years ago, a new and modified biodiesel production process that minimizes wastes was proposed by a previous BI research team, as shown in Appendix B. President Burns would like our research team to build up on this success and design an even better and more economical biodiesel production process since the overall goal of Brown Industries is to license additional new and relevant technologies for incorporation into a state-of-the-art biodiesel production plant. [2] Biofuels, and its byproduct glycerin, are produced by chemically reacting either methanol or ethanol with different sources of oil in the presence of sodium or potassium hydroxide as a catalyst.[3] In the past year, the option of creating oil from algae went under further study. The proposed plan for Brown Industries to create oil is to grow algae in lipid-enriching photobioreactors, harvest and dewater it using a rotary filter, and then finally extract the oil using a microalgae oil extractor at high temperature water and pressure.
Goals and Objectives
On September 7, 2012, you requested our team to conduct a study to characterize the rotary filter, proposed as a method of concentrating algae. See Appendix C for the schematic. [4] The following rotational objectives comprise the rotary filter project:
Rotation 1: Characterize process variables and recommend operating conditions
Rotation 2: Prepare a model and specify the ideal operating condition for maximum production
Rotation 3: Optimize and scale-up to the desired production scale. In short, our overall goal is to study the characteristics of the rotary filter, determine the conditions that maximize production, and finally to scale-up the rotary filter to the desired production scale. From September 7th to October 1st, BI staff engineers started preliminary characterization of the rotary filter. [5] Their results, which included effects of pressure and rotation speed to flux through the filter along with studies on fouling of the filter by algae, were insightful and useful, and will be confirmed and used in its full potential in rotations two and three.
The following objectives comprise rotation two:
Complete the rotary filter characterization from rotation one
Validate the design space proposed by rotation one
Establish a filtration schedule that optimizes cycle time for filtering, back-flushing, and cleaning operations to maximize cell harvesting and final cell concentration
Establish procedure to measure amount of algae collected in the filter media. Determine if it is a significant amount. Improve the washing process if necessary.
Develop a process model for the scale-up of the rotary filter process. After completing these objectives, rotation three will be able to optimize and scale the rotary filter up to the desired production state.
Summary of Key Results
The following key results were obtained:
Completed the rotary filter characterization from rotation one
Validated the design space proposed by rotation one:
Established a filtration schedule that optimizes cycle time for filtering, back-flushing, and cleaning operations to maximize cell harvesting and final cell concentration
Established procedure to measure amount of algae collected in the filter media:
Determined amount collected in filter media is not a significant amount.
+
Developed a process model for the scale-up of the rotary filter process:
(
(
)
(
))
where
(
)
(
)
BACKGROUND The background section will go over how the rotary filter fits within the oil extraction process, microfiltration theory, models for concentration algae, and alternative cell harvesting unit operations. Oil Extraction Process The purpose of the rotary filter in our process is to concentrate the algae solution from the lipid enrichment photobioreactor, or open ponds (such as runoff water or sewage) for use in the microalgae oil extraction process, as shown in Figure 1. The concentration of the algae solution entering the rotary filter from the photobioreactor or an open pond is approximately 0.2 to 0.6 galgae/L, as reported by BI Staff Engineers on that project and literature. [5][6] The concentration of the algae slurry desired for the micro algae oil extractor is not specified due to the lack of a team working on the equipment; literature values report 50 to 150 galgae/L as a rule of thumb for the desired concentration of algae slurry.[6] Harvesting algae from tanks and separating the oil are difficult and energy intensive processes, so optimizing the spinning filter to concentrate the algae will aid in reducing the energy costs associated with the oil extraction process.
Figure 1: Oil extraction process proposed for Brown Industries.
Algae Solution
(~0.2 to 0.6 g/L)
Algae Slurry
(~2.0 g/L)
Water Filtrate and
Growing Medium
Biomass and Water
Oil (Lipid) Lipid
Enrichment
Photobioreactor
Rotary Filter Microalgae
Oil Extractor
Rotary Filter Transport Theory behind the removal of solids from liquids with a membrane will be discussed in this section.
Figure 2: Spinning Filter Apparatus
Membrane filtration theory will be used in our study to characterize the behavior of algae in the spinning filter apparatus, which consists of a pressurized inner chamber, accumulated algae cake on the filter, and the membrane filter, as illustrated in Figure 2. A pressure driving force pushes the algae solution toward the membrane for algae filtration. The membrane allows the filtrate (i.e. particles/molecules < 5 microns in diameter such as water) to pass through, but not algae (> 5 microns in diameter). It is necessary to understand how the flux of the filtrate, as defined in equation (1), changes with deposition thickness.
(1)
Where J = flux of filtrate out of rotary filter (L/m^2/sec)
V = volume of filtrate removed by rotary filter (L) A = surface area of membrane filter (m^2) t = time elapsed (sec)
An increase of filtrate flow rate (V/t) would increase the flux, whereas an increase in membrane area decreases the flux. There are two well-known theories for filtration: film theory and cake filtration theory. Film theory is applicable for separation of particles ~ 5 microns in diameter from fluids. Cake filtration theory is applicable for separation of particles greater than 5 microns in diameter from fluids. Notice that cake filtration theory is mathematically easier to apply and is equivalent to film theory as the gradient between the concentration at the membrane (cm) and bulk concentration (cb) approaches infinity. Algae is typically ~2 to 10 microns in diameter, so our membrane is not applicable for all species of algae. Algae < 2 microns in diameter will not
be retained by the membrane. Since algae in our process is 5 microns in diameter, we will use cake filtration theory in our model. [7][8]
Figure 3: Membrane filtration theory. (Adapted from “Fundamentals of Particle Technology” by Richard Holdich) While maintaining constant pressure drop through the membrane, increasing resistance due to fouling of the membrane causes the liquid flux through the membrane to decrease with time, as seen in the decreasing filtrate volume rate. This effect of fouling is illustrated in Figure 4.
Figure 4: Left: Effect of fouling on cumulative filtrate volume. Right: Cross-sectional view of fouling on the filter medium. (Adapted from “Fundamentals of Particle Technology” by Richard Holdich) To combat the problem of decreasing flux rate, momentarily back flushing water to dislodge algae adhered to the surface of the membrane at regular time intervals will be implemented. As shown in Figure 5, we observe that after periodic back-flushing, the average flux rate is significantly higher than the flux rate with no back flushing. [7][8]
Figure 5: Back flushing the membrane to restore the flux of filtrate out of the rotary filter. (Adapted from “Fundamentals of Particle Technology” by Richard Holdich) The theory behind these processes will be derived in the following section. Later, parameters and constants will be extracted from experimental data. The final model will be used by Rotation 3 to optimize filter and back flushing cycles and for scale up. Rotary Filter Transport Model Development Three driving forces are present in our rotary filter system: (1) centripetal force exerted onto the fluid by the spinning filter, (2) pressure drop across the membrane and (3) pressure drop across the algae cake.
Figure 5: Three pressure driving forces.
A pressure balance combining the three driving forces above and fluid properties will be combined to produce an expression to model the deposition of algae onto the membrane filter. The expected effect of algae deposition onto the membrane filter on filtrate volume is shown in Figure 5. [7][8]
(2)
Where = pressure drop from chamber through the membrane (psi)
= pressure drop through filter (psi)
= pressure drop through algae cake (psi) = pressure drop through inner chamber (psi)
Since we are interested in modeling the effects of filter rotation speed and chamber pressure on the filter flow rate (which is a measure of the effectiveness of the spinning filter), our models will be designed to take the rotation speed and chamber pressure as inputs to determine the filtrate flow rate. In the next three sections, we will develop the design equations for each component of the total pressure drop through the rotary filter. Pressure Drop through Filter Modeling the filter as a packed bed, the Ergun equation, as shown in equation (3), will be used to describe water flow through a packed bed due to an applied pressure drop. [10]
(3)
Where ∆Pfilter = pressure drop through filter (psi) L = depth of the packed bed (m) ρ = fluid density (kg/m^3)
µ = fluid viscosity (Pa* sec or kg/m/s) dp = effective particle diameter (m) ε = interparticle void fraction (dimensionless) = superstitial fluid velocity (m/s)
The superstitial fluid velocity is defined as follows in equation (4).
(4)
Where = superstitial fluid velocity (m/sec) = filtrate volumetric flow rate (m^3/sec) A = surface area of membrane filter (m^2)
The Reynolds number for flow through a packed bed is shown in equation (5). [9]
Blake-
Kozeny
Equation for
laminar flow
Burke-Plummer
Equation for
turbulent flow
(5)
Where Re = Reynolds number (dimensionless) = superstitial fluid velocity (m/sec) = void fraction (dimensionless)
D = diameter of spherical bed particles (m) ρ = fluid density (kg/m^3)
µ = fluid viscosity (Pa* sec or kg/m/s) As shown in Appendix A, the filter was calculated to be laminar for all flows with Re < 10 for QF < 54,400 g/s. Since our operating range for QF is between 0 m^3/sec and 30 m^3/sec, flows in all our trials will be in the laminar regime. This allows us to ignore the turbulent part of the pressure equation above. Substituting equation (4) into equation (3) and combining constants into one term leads to equation (6). (6)
Where ∆Pfilter = pressure drop through filter (psi)
= filtrate volumetric flow rate (m^3/sec) C1 = constant resistance through filter (psi*sec/m^3)
Equation (6) is our design equation that describes how filtrate flow rate is related to the pressure drop through the filter when rotation rate is zero. Flux, as defined in equation (1), allows us to rewrite equation (6) in terms of flux, as shown in equation (7). (7)
Where ∆Pfilter = pressure drop through filter (psi)
J = filtrate flux (m^3/sec/m^2) R1 = constant resistance through filter (psi*sec/m)
Equation (7) is the general design equation for any pressure drop through a filter given a specified filtrate flux. Pressure Drop through Inner Chamber To determine the pressure drop through the chamber, we will use the continuity equation and the Navier-Stokes Equations, as shown as equation (8) and equation (9), respectively. [12]
(8)
Where ρ = fluid density (kg/m^3) t = time (sec) = fluid velocity (m/s)
(9) (
)
Where ρ = fluid density (kg/m^3) t = time (sec) v = fluid velocity (m/s) p = pressure (Pa)
µ = fluid viscosity (Pa* sec or kg/m/s) = fluid velocity (m/s) = external body forces (i.e. gravity) (N/m^3)
The continuity equation is a statement of the conservation of mass, whereas the Navier-Stokes equation is a statement of the conservation of momentum. These equations are useful in modeling fluid systems when appropriate assumptions and boundary conditions are made. The assumptions we will use in our model for tangential flow between two vertical coaxial cylinders, where the inner cylinder is rotating with an angular velocity, are as follows:
Laminar flow (Navier-Stokes equations is valid)
Steady State
Incompressible flow
No edge effects at top and bottom of cylinders (
No pressure gradients in the -direction and z-direction (
No external body forces
Applying these assumptions to equation (8), we obtain equation (10) which states that fluid velocity within the system is not a function of .
(10)
Where = velocity in the theta direction (m/s) = degrees in the azimuthal direction (radians) Applying equation (10) and the assumptions stated earlier to the Navier-Stokes equation (equation (9)) in cylindrical coordinates leads to equation (11) and equation (12).
(11)
Where ρ = fluid density (kg/m^3) p = pressure (Pa)
= velocity in the theta direction (m/s) = degrees in the azimuthal direction (radians) r = radial distance from z-axis (m)
(12)
Where = velocity in the theta direction (m/s) = degrees in the azimuthal direction (radians) r = radial distance from z-axis (m) Equation (11) is the design equation we will use to describe the radial pressure distribution. Equation (12) describes the velocity profile within the inner chamber, which can be simplified to equation (13).
(13)
Where = velocity in the theta direction (m/s) r = radial distance from z-axis (m) A1 = constant (1/s) B1 = constant (m^2/s) Setting two boundary conditions for the rotating filter and stationary outer wall, as shown in equation (14) and equation (15), respectively, allows us to solve for the constants in equation (13). Equation (16) is the laminar velocity profile for flow in the inner chamber. (14) (15) Where = velocity in the theta direction (m/s) = inner radius of the chamber (m) = outer radius of the chamber (m) = filter rotation rate (rad/s)
(16)
(
)
Where = velocity in the theta direction (m/s) = radius of filter cylinder (m) = outer radius of chamber (m) = filter rotation rate (rad/s)
Now, since the velocity distribution as a function of radius is known, we can solve for the pressure profile across the inner chamber by substituting equation (16) into equation (11) and integrating from to . The final derived equation is shown in equation (17).
(17) (
(
)
(
))
Where = pressure drop through inner chamber (psi)
ρ = fluid density (kg/m^3) A = constant, defined in equation (16) (1/s) B = constant, defined in equation (16) (m^2/s) = inner radius of the chamber (m) = outer radius of the chamber (m)
µ = fluid viscosity (Pa* sec or kg/m/s) Equation (17) can be explicitly solved using the fluid density, inner radius of the chamber, and outer radius of the chamber. This pressure drop model for the inner chamber will be used to determine the component of the total pressure drop through the spinning filter.
We must be aware that equation (17) is only valid for laminar flow, which is one of the crucial assumptions we made when developing this model. If the flow regime transitions from laminar to turbulent, equation (17) will be invalid from that point onward. However, once the turbulent regime has fully taken effect, the pressure drop will increase linearly with increasing rotation speed. The Reynolds number for flow in an annular gap between two rotating cylinders has been defined, as shown in equation (18). [11]
(18)
Where = Reynolds number (dimensionless) ρ = fluid density (kg/m^3)
µ = fluid viscosity (Pa* sec or kg/m/s) = inner radius of the chamber (m)
= outer radius of the chamber (m) = filter rotation rate (rad/s)
Appendix A will present the calculations executed to determine the critical rotation speed for a laminar to turbulent transition.
Pressure Drop through Algae Cake To determine the pressure drop through the algae cake, we will modify equation (7) to take into account an increasing resistance as shown in equation (19). (19)
Where ∆Pfilter = pressure drop through filter (psi)
J = filtrate flux (m^3/sec/m^2) R2 = transient resistance through algae cake (psi*sec/m)
When concentrating algae with the spinning filter, algae will begin to accumulate on the surface of the metal filter due to the applied pressure onto the chamber, however algae will also begin to detach from the filter as filter rotational speeds are increased. These two forces counteract each other. A model based off the models for pressure drop through the filter and chamber can be derived for the resistance through the cake, as shown in equation (20).
(20)
It should be noted that this model only describes the steady state resistance of the algae cake. The steady state model will have to have terms to transiently describe the two counteracting forces, as described in equation (21).
(21) [
] [
]
Models for these effects are currently unknown, so empirical models (though less robust than theoretical models) will have to be developed to describe how the algae cake resistance changes with time given specific operating conditions. Alternative Cell Harvesting Unit Operations There are several widely used unit operations, or basic steps in a process, used to harvest and dewater algae. The three major operations are: flocculation, floatation, centrifugation, and filtration. The mechanics behind each of the three methods are discussed below. In addition, Table 1 displays their advantages and disadvantages. The selection of a harvesting technique is crucial for the overall economics of the biodiesel production process since 20% to 40% of production costs. [6][13][14][15][16] Flocculation Flocculation uses the negative cell surface charges on algae to form clumps, or “flocs”, after their surfaces have been neutralized. These flocs can be induced in several ways:
Chemical flocculation using either inorganic chemicals or polyelectrolytes
Bioflocculation using natural environmental stimuli such as pH and oxygen levels
Electroflocculation using an external electric field.
The flocs can be collected by flotation and then sent to centrifugation or filtration processes for dewatering. Flotation Floatation is often used in conjunction with flocculation after the algae has already formed flocs. Flotation harvests algae by bubbling air through the water and gathering the froth that gathers on the surface. Centrifugation Centrifugation separates algae by using a centrifuge to accelerate the settling of algae to the bottom of a container. Filtration Filtration separates algae by using a membrane to filter out water in the presence of an applied pressure. Table 1: Advantages and Disadvantages of Algae Harvesting Techniques
Unit Operations Advantages Disadvantages
Flocculation and Flotation
Chemical flocculation physically link algae together
Electroflocculation works for all algae types, and has a high separation efficiency.
Difficult to remove added chemicals
Often too expensive for large operations
Bioflocculation is unreliable
Flotation is too costly for commercial use
Centrifugation Well established Energy intensive, high costs
Risks damaging algae
Filtration Can collect low density algae
Low costs
Limited to small volumes
Eventual clogging of filter
MATERIAL AND METHODS
Equipment
The following equipment is required for successful rotary filter operation.
Essential components of the rotary filter
Porous metal cylindrical filter 9-in. long and 2.3-in. diameter. Filter is rated at a 5-micron pore size made of type 316 stainless steel.
Polycarbonate plastic cylindrical pressure vessel with a 3.75 in. inside diameter equip with stainless steel end pieces.
Variable speed motor that can be adjusted between zero and 2000 RPM to rotate the filter inside the pressure vessel.
Peristaltic pump to feed algae solution into the pressure vessel. Pump speed is adjustable to match desired filtrate flow rate.
Back-pressure regulator used to regulate pressure outside the filter. Adjustable to any desired pressure between zero and 25 PSIG.
Three plastic collection buckets with volume capacities greater than 12-L
Magnetic stir bar and stir plate
LabView data collection software for measuring filtrate flow rate
Essential components for visual absorbance
Kimax 13 x 100 mm optical test tubes with screw on caps Some method of marking test tubes (marker, tape) Micro stir bar Syringe (10 mL) Thermo Scientific Genesys 20 Spectrophotometer KimWipes lint-free paper towel
Figure , below, depicts the rotary filter apparatus.
Figure 6: The rotary filtration apparatus.
Materials
Materials required for rotary filter operation include:
25-40 liters of dilute (~1g/L) algae (C. vulgaris) solution Tap water At least two liters of 3% hydrogen peroxide solution Pressurized air (available at least 25 psi)
EXPERIMENTAL DESIGN The following sections will explain the necessary experimental procedures to accomplish our objectives.
Validation of Design Space and Optimization of Operating Conditions In order to optimize the operating conditions, a design space must first be defined; that is, a range for which certain parameters can be run. Rotation one has established a preliminary design space for the rotary filter; we intend to validate and expand upon the previous rotation’s findings. We have determined that two criteria must be considered in establishing the bounds of rotary filter’s design space. The first is the physical limitation of equipment such as pumps, motors, and filter apparatus. We should not experimentally determine the physical limitations, because of risk of damaging laboratory equipment. Instead, we will use literature (i.e. equipment manuals) to help us define limits. The second criterion used to determine the design space is the overall process requirements. Since the spinning filter is only one unit operation in the entire proposed bio-refinery, its operation conditions will be dependent upon the algae input stream properties coming from our lipid enrichment photobioreactors or other sources, as well as the outlet stream specifications dictated by the oil extraction unit. The variables that need to be used for characterizing the rotary filter are: rpm, pressure, and inlet algae concentration. Because the purpose of the rotary filter apparatus is to concentrate the dilute algae stream, while producing a filtrate stream, we will be examining conditions the afore mentioned variables lead to negligible filtrate flow or negligible outlet algae concentration. The relationships we aim to characterize for the rotating filter are as follows:
Effect of pressure effects on filtrate flux through the filter
Effect of filter rotation rate on filtrate flux through the filter
Effect of pressure on algae fouling of the filter
Effect of filter rotation rate on algae fouling of the filter
Effect of filter rotation rate on improved filtrate flux for the back flushing cycle Table 2 below shows the trials that we anticipate to run during our three week rotation to generate the relationships listed above. Using the data we collect from our trials, we aim to validate the trials run by rotation one as well as collect more data to characterize the rotary filter since rotation one was not able to complete that part of their rotation.
Table 2: Anticipated Trials for validation of rotation one and characterizing rotary filter cycles.
Objective Chamber Pressure (psig)
Filter Rotation Speeds (rpm)
Water or Algae
Design Space Validation 2.5 0,500,1000,1500,2000 Both
5 (Control Run) 0,500,1000,1500,2000 Both
10 0,500,1000,1500,2000 Both
15 0,500,1000,1500,2000 Both
Back Flush Measurement
- 0,1000,2000 Algae only
Control Run In order to confirm we have reproducible and accurate data between weeks, a control run, as labeled in Table 2 will be run pure water with a chamber pressure of 5 psig and a filter rotation speed of 1000 rpm. The flux observed will be compared to repeated runs over the course of the rotation two. Expected Trends The expected trends for the relationships we aim to characterize for the rotating filter are as follows: Effect of pressure effects on filtrate flux through the filter It is expected that increased pressure will increase flux through the filter. Ideally, flux will increase linearly with increased pressure, but due to properties of the filter and pump such as pore size or maximum head, it is likely to increase slower and start leveling off. This trend has been shown by rotation one, but they adjusted the pressure during operation, giving them unreliable data. Effect of filter rotation rate on filtrate flux through the filter It is expected that filtrate flux will decrease as the filter rotation rate increases due to both centripetal forces expelling the water outward and the formation of a boundary layer on the surface of the filter. Effect pressure on algae fouling of the filter through the filter It is expected that algae will foul the filtrate faster, thus decreasing flux, with increased pressure since the pressure driving force will force more algae toward the filter.
Effect filter rotation rate on algae fouling of the filter It is expected that algae will foul the filtrate slower, thus increasing flux, with increases in filter rotation rate. The fluid shear and centripetal force from the rotating filter will force algae cells away from the filter. Effect of rotation rate on improved filtrate flux for the back flushing cycle It is expected that increases in the filter rotation rate will restore the filter more effectively than lower filter rotation rates. This is because the increased flux of water flowing through the membrane filter in the opposite direction will be able to agitate and remove algae more effectively. Standard Operating Procedures The next few sections will give a quick summary of the methods that will be used to operate the rotating filter. Preparation According to the SOP for Algae Filtration using a Rotary Filter and SOP for Visual Absorbance, we will first prepare the algae solution. We will measure the concentration of algae in the solution by extracting two 10-mL samples, transferring them in the optical test tubes, then placing them in the Thermo Scientific Genesys 20 Spectrophotometer to be measured, and recording the results. The algae will be diluted to a specified concentration to maintain constant concentrations throughout our trials. The algae feed tube and the back pressure regulator tubes in to the algae solution bucket. Finally, we will close the air supply valve, close the algae concentrate outlet valve, close the filtrate outlet valve, and open the feed ball valve. [13][14] Filtration We will start LabVIEW to start recording weight and flow of filtrate solution. Next we open the back pressure regulator valve and turn on the peristaltic pump to highest setting to fill the vessel with algae solution until full. Once full, we need to adjust the back pressure to the desired level, by rotating the valve. The filtrate outlet 3-way valve will then be turned to the filtrate out position. The trial is run until all the algae feed solution runs out, or when the filtrate flows is too low. At the end of the run, will turn off the feed pump, turn off the rotor motor, turn off the filtrate outlet valve, and reduce the pressure in the vessel by adjusting the back pressure regulator. [13] Concentrated and Filtrated Solution Collection To collect our concentrated solution, we first tare a 4 L bucket. We then drain the rotary filter apparatus to the bucket by opening the concentrate outlet valve to the bucket. Next we weight the concentrated solution and record the weight. Finally, we take two 10 mL samples using a syringe and determine the concentration by means of visual absorbance, as described in the preparation section. For our filtrated solution collection, we place all filtrate solution in a bucket, stir, and take two samples for visual absorbance. [13]
Procedure for Back flushing Algae During the operation of the rotary filter apparatus, some fouling occurs due to algae adhering to the filter. This fouling reduces the ability of water to flow across the membrane and needs to be periodically back flushed to remove accumulated algae. The back flush can be collected and sent to the lipid enrichment unit, provided that it is of suitable concentration. Though an SOP has already been written describing the process to back flush the filter, no procedure exists for measuring the algae concentration. We created a rudimentary procedure to determine the amount of algae accumulated on the filter. Throughout the rotation we will make corrections and improvements to the existing washing SOP. [15]
1. Close inlet outlet ball valves and open back pressure valve 2. Turn the three way valve to the upward position 3. Fill the chamber completely with water from the cold water supply 4. Run the filter at 2000 rpm for 10 seconds 5. Drain the chamber and repeat once more
Procedure for Cleaning the Rotary Filter According to the SOP for Cleaning the Rotary Filter, we must first drain the concentrated algae slurry, then remove the algae feed tube and back pressure regulator (BPR) and place them in a beaker with 100 mL of water. We will then fill the chamber with water, turn on the rotor motor for 5 seconds then off, and then open the outlet valve chamber. Repeat filling and draining the chamber until the water leaving is clear. We will now back flush and drain the rotary filter multiple times until the water is clear. We will now close the algae slurry valve and place the algae feed tube and BPR into 1.5 liters of 3% hydrogen peroxide. The rotary filter chamber will then be submerged in 3% hydrogen peroxide overnight. To remove the cleaning solution the next day, we will drain the solution, and flush the rotary filter with water twice. [16]
Safety
The rotary filter is a fast spinning pressure gradient dependent device that should be utilized carefully. Operators should wear the proper personal protection equipment (PPE), which includes goggles, lab coats, long pants, and closed-toe shoes at all times. Operators should be aware that there are fast moving parts associated with the spinning filter, and that friction may cause these parts to get extremely hot. Operators should not try to adjust anything associated with the rotary filter while the device is in operation, taking care to turn the apparatus off before putting extremities within close proximity to moving parts. Operators should also refrain from exceeding design parameters. For instance, do not allow the backpressure regulator to exceed 25 psig. Operators should also take care to ensure that all pressure has been vented before opening exit valves, to avoid any accidental forceful discharge due to pressure buildup.
RESULTS AND DATA ANALYSIS
The following sections describe the significance of our experimental results as well as how we managed to analyze our data.
Collected Data In the previous section, we outline our proposed trials to attain the appropriate data for our rotational objectives. As in any experimental setting, things do not always go smoothly; we were no exception to this case. Though we had proposed a set of experimental trials, we were not able to compete all of our anticipated runs due to time constraints. Table 3 below depicts the runs in which we were able to collect usable data with regards to our original proposed runs.
Table 3: Executed Experimental Trials.
Objective Chamber Pressure (psig)
Filter Rotation Speeds (rpm)
Water or Algae
Design Space Validation 5 (Control Run) 0,500,1000,1500 Both
Back Flush Measurement - 0 Algae only
Process Model Validation As described in the Background section, we have established a process model that is intended for scale up of the rotary filter. In this section, we will explain how we derived our model parameters.
Process Model As derived theoretically in the background section, the process model shown below:
(
(
)
(
))
where
(
)
(
)
Our experimental design was focused on collecting data to validate, modify, and determine parameters for the model above.
Determining Model for Pressure Drop through the Filter Experimental data was used to determine unknown parameters and to further develop our derived models for the rotating filter. The methods and sample calculations used to develop the process models are explained in Appendix F.
Below is the process model:
{
Where J is in units of (g/s)/m^2 is in units of rpm pressure drops are in units of psi.
will have to be determined empirically due to a lack of an accurate model to predict how a thickening algae cake over time affects resistance of flow. The user of the process model will have to estimate from Figure 8, after specifying a desired time, rotational speed, and pressure. If a steady-state is desired, then Figure 9 will the optimal chart to use to determine .
Figure 8: Resistance of Algae Cake vs. Time
Although we were not able to find or develop an accurate model to predict as a function of time, there are some interesting trends that were observed:
1. At 5psi, the steady state resistance of the algae cake reaches at minimum at a rotation
speed of ~1500 rpm, as shown in Figure 9. This minimum is likely due to centripetal
force and pressure effects cancelling out with each other.
2. At 5 psi, the time it takes to reach steady state decreases with increasing rotation
speed, as shown in Figure 10. This is likely due to centripetal forces preventing the
algae cake from getting too thick,
Future experimentation on the rotary filter should also determine whether these observations hold for pressures higher than 5psi and also develop a model to accurately determine R2.
0
0.1
0.2
0.3
0.4
0.5
0.6
0 100 200 300 400 500 600 700 800
Re
sist
ance
th
rou
gh A
lgae
Cak
e
(psi
/(g/
s)*m
^2)
time (seconds)
0 rpm, 5 psi
500 rpm, 5 psi
1000 rpm, 5 psi
1500 rpm, 5 psi
2000 rpm, 5 psi
1000 rpm, 10 psi
2000 rpm, 10 psi
Figure 9: Effect of rotation speed and pressure on steady state resistance through algae cake
Figure 10: Effect of time required to reach steady state as function of the rotation speed at 5 psi.
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0 500 1000 1500 2000 2500
Re
sist
ance
(p
si/(
g/s)
/m^2
Rotation Speed (rpm)
5 psi
10 psi
-100
0
100
200
300
400
500
600
700
0 500 1000 1500 2000 2500
Tim
e (
se
con
ds)
Rotational Speed (rpm)
Back Flushing Process
As the apparatus operates, algae accumulate on the rotary filter, resulting in a filter cake. This filter cake needs to be periodically removed to allow the filter to operate effectively as possible. In this section, we have established a procedure to measure the amount of algae collected on the filter media.
As shown in the figure below, as the rotary filter operated, filtrate flux decreases until some pseudo steady state value has been achieved. Though the rotary filter continues to concentrate the inlet stream while operating at steady state, the filtrate flux without back flushing is significantly less than if back flushing or some other mechanical cleaning of the membrane takes place. Figure 5, shown in the background section, compares filtrate flux for an operation with back flush to that without. One can observe that if no back flushing occurs once steady state filtrate flux is achieved, the area underneath the curve for the remainder of the process without back flushing is much less than the area under the curve with back flushing, indicating that this procedure is beneficial driving off more water, thus forcing the algae to higher concentration. It is important to note that different rotational speeds lead to different accumulation rates of algae on the filter, the operational time between back flushing will vary.
Rather than allowing the algae accumulated on the filter to be lost when back flushed, we have established a procedure to recover this algae to be recycled to the feed stream. The purpose of our rotary filter process is to concentrate dilute algae into a slurry; if the concentration of algae obtained from back flushing is less than the feed, then the back flush procedure can be deemed impractical. Filtrate flux is a function of algae accumulation on the filter, meaning that the amount of algae that will have accumulated on the filter will vary for rotational speeds.
Back Flushing Balance
Though we did not measure the concentration of the obtained back flush solution for each of the runs, we executed a mass balance on our system with known process parameters to solve for the mass of algae accumulated on the filter. This is shown in Figure 11 and equations 22 and 23 below.
Feed Tank
Filter
Feed Stream
CFeed
VFeed
VFiltrate
Filtrate Stream
Concentrated Slurry
CSlurry
VSlurry
Vent Stream
Vent CollectionCVent
VVent
Accumulated Algae
Figure 11: Block diagram of apparatus
(22) +
(23)
Where =Volume of feed solution filtered (L) = Volume of concentrated slurry product (L)
= Volume of filtrate removed by filter (L) = Volume of solution leaving system via vent (L) = Concentration of feed (g/L) = Concentration of concentrated slurry (g/L)
= Concentration of vent product (g/L) These equations can be used to determine the amount of algae that can be recovered from the filter.
We have provided a sample calculation in Appendix G, however, during the execution of our trials, we failed to take measurements for the concentration or volume that exited through the vent. Because of this, we have decided to approximate our “vent” term as zero in our calculations, though future rotations should be sure to measure and record these values and apply them in the mass balance.
Procedure After the chamber has been drained of the concentrated algae slurry, measure and record the concentration and volume of the concentrated slurry product and the vent product. Close both the inlet and outlet ball valves. Turn the 3-way valve to the upward position. Fill the chamber completely with the calculated amount of back flush water from the equation above, using the cold water supply. Spin the filter at 2500 rpm for 15 seconds to dislodge the accumulated algae from the filter. Collect back flushed solution in a 2 L beaker. Measure the concentration. If equal to or greater than the feed concentration, recycle the collected solution to the feed solution tank. If not, discard the collected backflush solution.
Follow this procedure with the existing back flushing Standard Operating Procedure to ensure the filter is completely clean for the next run.
Filtration Schedule Optimization To maximize the amount of algae slurry per unit time that can be obtained from this process, we have established a schedule that uses the most optimal operating conditions. We have broken the schedule down into two sections: filtration and back flush. We provide both the optimal operating conditions and the estimated time required for each section.
From our experimental trials, we have determined that filtration should occur at a rotational speed of 1500 rpm and a pressure of 5 psi. Figure 12 shows that a rotational speed of 1500 rpm yields the highest filtrate flowrate, implying that a more concentrated slurry can be produced.
Figure 12. Filtrate flowrate plotted against rotational speed at 100 seconds.
As mentioned in the previous section regarding back flushing, filtration should be run while the filtrate flux is in transient state. Once the filtrate flux reaches pseudo steady state, that is, the slope of the filtrate flux vs. time graph appears to be relativity constant, the filtration step should be halted. We observed this occurs at approximately 100 seconds. Drainage of the chamber should be no different than the instructions stated in the standard operating procedure. When using air to assist, the total drainage time is approximately 10 seconds.
Using the back flushing procedure above, coupled with the back flushing standard operating procedure equates to three fill/drain cycles. Each fill time is approximately 20 seconds, while each drain time is about 10 seconds, resulting in a total back flush procedure time of 90 seconds.
After summing all of the time values, we can see that the total cycle time is approximately 200 seconds.
UNCERTAINTY AND ERROR
This section will describe how we will perform our uncertainty and error calculations. We have tested for reproducibility and error propagation. Sources of error may have arisen from the limited accuracy of our pressure gauge, inaccuracies in the calibration of the filtrate flowrate, and other systematic inconsistencies for measurements. Significance Testing We implemented a Students t-test to test the repeatability of our control run and rotating filter. It is necessary to be able to confirm, with high confidence, that our trials and data is reproducible. We have selected our control run to be water at a pressure of 5 psig and rotational speed of 0 rpm. Using the experimental data found in Appendix D, we have found an average filtrate flowrate of 15.42 g/L and standard deviation of 0.566. We set our hypothesis to be filtrate flowrate =15 g/L and confidence of 90%. With these conditions, we found a t-value of 1.916, which is less than the t-value, two-sided at 90% of 2.35. From this we can conclude that the trials are in fact reproducible. Error Propagation Error propagation methods, as shown in Table 3, will be implemented through our calculations to keep track of the overall errors and pinpoint variables that contribute most to the uncertainty.
Table 3: Error propagation equations (Table from http://www.clemson.edu/ces/phoenix/tutorials/errorp/index.html)
Performing error of propagation calculations on filtrate flow rate based off our model yields propagated errors equations (#1) and (#2).
√
When
√
When
These equations show that error in the flow measurement for rotational speeds less than 500 rpm is dependent almost entirely upon the error in the pressure drop, rather than the error in the rotational speed. The error in the filtrate flowrate measurement due to the rotational speed error is more significant for rotational speeds greater than 500 rpm, though still not as important as the error from the pressure drop term. These equations suggest that one should repeat test pressures over a broad range appropriately determine filtrate flowrate.
CONCLUSION AND RECOMMENDATIONS
Conclusions
The design space for the rotary filter apparatus as proposed by Rotation 1 was validated.
The pressure drop is through the chamber is limited by the total head the peristaltic pump is able to apply, and the rotation speed is limited by the motor’s maximum rotation speed. A process model that describes the characteristics of the rotary filter was developed to aid in scale-up. The model was developed by breaking down the overall pressure drop into three separate components: pressure drop through the filter, cake, and chamber. Models were developed based off well-known filtration theory and flow theory, and fitted to data obtained from characterizing the rotary filter. Error analysis and propagation was implemented to determine errors in the calculated parameters.
Procedures for back flushing algae and measuring the amount of algae accumulated in the filter have been established. These are shown in the results section. Finally, we have proposed process conditions that would optimize filtration cycle time. These conditions are running the filter at a pressure of 5 psi, 0 rpm, and for 100 seconds. Coupled with the necessary backflushing time, this yields a total cycle time of approximately 200 seconds.
Recommendations
After working with the rotary filter for three weeks we have a few recommendations that could help make the most of each laboratory session. We suggest that future groups examine different back flushing techniques. We only considered one method, but there could be more effective ways to carry out this process. After performing the filtration operation, we recommend that the algae be recycled for subsequent trials. To carry this out, pour the filtrate, concentrated slurry, back flush product, and vent product back into the feed container to get back to the original feed concentration. Once this is done, be sure to take absorbance measurements to ensure feed concentration within operating limits (0.2-0.6 g/L). When taking setting the rotational speed of the rotary filter, we advise using the tachometer to measure rpm, rather than using dial. The markings on the dials do not have values that denote the rotational speeds, so using a tachometer is useful to determine the exact rotational speed for each run.
REFERENCES [1] Haas, M., McAloon, A. J., Yee, W. C., and Foglia, T. A. (2005). A process model to estimate biodiesel production costs. Bioresource Technology, 97 (2006), 671-678. [2]Burns, M. (2012). ChE 460: New Biodiesel Venture for Brown Industries. ChE 460 Coursepack. Ann Arbor, MI: University of Michigan, College of Engineering. [3] LaValle, P. (2012). Rotary filter for algae concentration. ChE 460 Coursepack. Ann Arbor, MI: University of Michigan, College of Engineering. [4] Wang, H. (2012). Evaluation of a Spinning Filter for cell Harvesting in Microalgae Cultivation. ChE 460 Coursepack. Ann Arbor, MI: University of Michigan, College of Engineering. [5] Donofrio, J., McMullen, C. (2012). Determination of Rotary Filter Behavior. Brown Industries. [6] Brennan, L., & Owende, P. (2009). Biofuels from microalgae—a review of technologies for production, processing, and extractions of biofuels and co-products. Renewable and Sustainable Energy Revie
[7] Holdich, R. (2002). Fundamentals of particle technology. Loughborough, UK: Midland Information Technology and Publishing. [8] Perry, R. H., & Green, D. W. (2008). Perry’s chemical engineers' handbook. (8 ed.). New York, NY: McGraw-Hill Professional. [9] Rhodes, M. (2008). Introduction to particle technology. (2nd ed.). The Atrium, UK: Wiley. [10] Thornhill, D. (n.d.). Flow through packed beds. Retrieved from http://faculty.washington.edu/finlayso/Fluidized_Bed/FBR_Fluid_Mech/packed_beds_fbr.htm [11] Avila, M., Grimes, M., Lopez, J., & Marques, F. (2008). Global endwall effects on centrifugally stable flows.Physics of Fluids, 20(10), Retrieved from http://pof.aip.org/resource/1/phfle6/v20/i10/p104104_s1 [12]Scott, C. (2001). Transport phenomena notebook. Retrieved from http://www.polymerprocessing.com/notes/ [13] Schenk, P. M., Thomas-Hall, S. R., Stephens, E., Marx, U. C., Mussgnug, J. H., Posten, C., Posten, C., & Posten, C. (2008). Second generation biofuels: high-efficiency microalgae for biodiesel production. Bioenerg Res, (Vol. 1, pp. 20-43). [14] Uduman, N., Qi, Y., Danquah, M. K., Forde, G.M., and Hoadley, A. (2010). Dewatering of microalgal cultures: A major bottleneck to algae-based fuels. J. Renewable Sustainable Energy, 2 (2010), 1-15. [15] Sreevatsan, S. (2007). Harvesting of micro algae. Retrieved from http://www.oilgae.com/algae/har/mia/mia.html [16] Alabi, A. O., & Tampier, M. (2009). Microalgae technologies & processes for biofuels/bioenergy production in British Columbia: current technology, suitability, & barriers to implementation. [17] Reodacha, M., and LaValle, P. (2012). SOP for algae filtration using a rotary filter. ChE 460 Coursepack. Ann Arbor, MI: University of Michigan, College of Engineering.. [18] Gonik, D. (2010). SOP for visual absorbance. ChE 460 Coursepack. Ann Arbor, MI: University of Michigan, College of Engineering. [19] Reodacha, M. (2012). SOP for backwashing the rotary filter. ChE 460 Coursepack. Ann Arbor, MI: University of Michigan, College of Engineering. [20] Reodacha, M. (2012). SOP for cleaning the rotary filter. ChE 460 Coursepack. Ann Arbor, MI: University of Michigan, College of Engineering.
NOMENCLATURE TABLE
Term Definition Units
ω angular velocity radians/sec
J flux of filtrate through filter L/m^3/sec
V volume of filtrate removed by filter L
A surface area of filter m^3
t time elapsed sec
∆P pressure drop psi
total pressure drop through system psi
pressure drop through filter psi
pressure drop through algae cake psi
pressure drop through inner chamber psi
L length of the packed bed m
ρ fluid density kg/m^3
µ fluid visosity Pa*sec or kg/m/s
dp effective particle diameter m
ε interparticle void fraction dimensionless
supertitial fluid velocity m/s
filtrate volumetric flow rate m^3/sec
C1constant resistance through filter psi/m^2
fluid velocity m/s
µ fluid viscosity Pa* sec or kg/m/s
external body forces (i.e. gravity) N/m^3
velocity in the theta direction m/s
degrees in the azimuthal direction radians
r radial distance from z-axis m
constant 1/s
constant m^2/s
inner radius of the chamber m
outer radius of the chamber m
Resistance through filter psi/(g/s/m^2)
Resistance through cake psi/(g/s/m^2)
Volume of feed solution filtered L
Volume of concentrated product L
Volume of filtrate removed by filter L
Volume of solution leaving system via vent L
Volume of backflush water required g/L
Concentration of feed g/L
Concentration of concentrated slurry g/L
Concentration of vent product g/L
Mass of algae accumulated on filter g
LIST OF APPENDICES
Appendix A: Reynold’s Number Calculations
Appendix B: Algae Specifications
Appendix C: Filter Element Specifications
Appendix D: Water Trials Experimental Data
Appendix E: Algae Trials Experimental Data
Appendix F: Sample Calculations for Determining Model Parameters
Appendix G: Sample Calculation for Mass of Algae Accumulated on Filter
Appenix H: Propagation of Error Calculation
Appendix A: Reynold’s Number Calculations
Reynolds Number through Filter
As defined in literature, the Reynolds number through a packed bed is shown in equation (A-1). The reported critical values of the Reynolds number is Re<10 for laminar flow and Re>2000 for turbulent flow.
(24)
Where Re = Reynolds number (dimensionless)
= superstitial fluid velocity (m/sec) = void fraction (dimensionless)
D = diameter of spherical bed particles (m) ρ = fluid density (kg/m^3)
µ = fluid viscosity (Pa* sec or kg/m/s)
Specifications of the Pall Filter (MBS100 S050 H13) are:
ρ = 1000 kg/m^3 µ = 1.002*10^-3 Pa*s = Qf/A = 2πr*h = 0.063m/2 = 0.2286 m = 0.4
D = 5 microns Determining the maximum flowrate of water through the filter that can sustain laminar flow, we will set Re = 10 and solve for Qf.
Solving, Qf = 0.0544021 m^3/sec = 54,402 g/sec
The transition between laminar and turbulent flow within the filter occurs at an extremely high filtrate flow, out of the range for our rotating filter apparatus. Thus, we can assume laminar flow for our models for the filter. For scale-up, we will need to calculate a new transition flow to confirm the assumption of laminar flow.
Reynolds Number of Inner Chamber
As defined in literature, the Reynolds number through a co-axial flow between two cylinders is shown in equation (A-2).
The reported critical value for the transition between laminar and turbulent flow is Re = 68.
(25)
Where = Reynolds number (dimensionless) ρ = fluid density (kg/m^3)
µ = fluid viscosity (Pa* sec or kg/m/s) = inner radius of the chamber (m)
= outer radius of the chamber (m) = filter rotation rate (rad/s)
Specifications of the system are:
ρ = 1000 kg/m^3 µ = 1.002*10^-3 Pa*s = 0.02921 m = 0.04763 m = filter rotation rate (rad/s)
Determining the maximum flowrate of water through the filter that can sustain laminar flow, we will set Re = 68 and solve for .
Solving,
Thus, the transition between laminar and turbulent flow in the inner chamber occurs at an extremely low filter rotation rate.
Appendix B: Algae Specifications
It was determined from Pablo (see email below) that the algae we use in Brown Industries is:
Chlorella Vulgaris (University of Texas Culture Collection of Algae #259)
ChE 460 - Algae species 4 messages
Arthur Shih <[email protected]> Tue, Oct 30, 2012 at 12:12 PM To: Pablo LaValle <[email protected]>, Kevin Dahlberg <[email protected]>
Dear Pablo and Kevin, Do either of you know what algae species (and other specifications) we're using for the photobioreactor/spinning filter? I was talking to the photobioreactor group and they said that they were able to get super high concentrations of algae using the photobioreactor, so something is different between the new algae and old algae. Thanks! -Arthur
Pablo Lavalle <[email protected]> Tue, Oct 30, 2012 at 3:52 PM To: Arthur Shih <[email protected]> Cc: Kevin Dahlberg <[email protected]>, CHE-460-super <[email protected]>
The only species of algae we use in Brown Industries is Chlorella Vulgaris (University of Texas Culture Collection of Algae #259) Of course there could be many differences between the algae growing in the MLE reactor and the algae growing in the new pilot-plant PBR. The most important could be the operator carrying out the analysis though. Pablo. ----------------------------------------------------- Pablo LaValle University of Michigan Department of Chemical Engineering Tel: (734) 763-1336 Fax: (734) 763-0459 e-mail: [email protected] ----------------------------------------------------
Henry Wang <[email protected]> Tue, Oct 30, 2012 at 5:59 PM To: Pablo Lavalle <[email protected]> Cc: Arthur Shih <[email protected]>, che-460-super <[email protected]>
Dear Arthur, We suppose to be using just one algae species in ChE 460. But, we can always be in a situation that it is contaminated with a different species since we do not practice sterile operations in ChE 460. But, it is highly unlikely because the competing one must be able to out grow the existing C. vulgaris. I love to isolate such such a species if it does exist and name it C. Michigaris. (just kidding). Please think about growing microalgae like growing trees. Besides nutrients, it also needs light and CO2 for growth. The light needs to penetrate through the dense culture to reach inside (light transport limited similar to mass transfer limited). I suspect the different cell concentrations of the 2 systems are more due to light intensities available to the culture. Pablo had shown me a plot of cell growth in the large scale photobioreactor system which turns out to be linear instead of log growth as in the smaller system. Thus, one may conclude the cell growth is limited by something, most likely by light. But, we have to do additional experimentation to prove that in order to confirm this hypothesis.
Appendix C: Filter Element Specifications
The following physical properties of the Pall Filter (MBS100 S050 H13) are summarized in the table below:
Specifications
Material 316L low carbon, stainless steel powder, bonded.
Diameter 2 3/8 inches
Filter thickness 1/16 inches
Height 9 inches
Void fraction ~0.4
Maximum pore size 5 microns
50% capture pore size 0.5 microns
If more information is needed, Element data sheets are available in the web link listed under sources below. Sources:
1. http://www.pall.com/main/Fuels-and-Chemicals/Product.page?id=26664 2. The email below:
Web Lead from Pall.com site / UMich 3 messages
[email protected] <[email protected]> Wed, Oct 31, 2012 at 2:14 PM To: [email protected]
Hi Arthur, Thank you for your inquiry. Do you have some of these filters in house and what is the part number? In general, the product has a 2 3/8 to 2 1/2" OD. It depends upon the part number that you have. The void volume is in the 40-70% range, again depending on the part number.
If you have a specific application (liquid or gas) that I can assist with, let me know details and I can review. Alternately, if you provide your phone number, I can have our local distributor make contact. Thank you. Regards, Margarita Luis Pall Corporation Energy / Fuels & Chemicals Group Cell Phone 516-924-1518 Fax 516-801-9762 Email [email protected] Website http://www.pall.com ----- Forwarded by Margarita Luis/PortWashington/Pall on 10/31/2012 02:07 PM ----- Pall.com Web Lead Customer has requested a response via : Email Name: Arthur Title: Email Address: [email protected] Phone Number: Company: Address: City: State or Province: Zip or Postal Code: Country: United States Application or Industry: Comments/Feedback: Hi I was wondering if you know the: (1) average diameter of the metal powder/filter elements (2) the void fraction of the filter of the product below: http://www.pall.com/main/Fuels-and-Chemicals/Product.page?id=26664 Thanks! -Arthur
Referring Web Page: Received at Pall.com at 10/31/2012 12:12 PM EDT -------------------------------------------------------------------------------- Attention: This communication may contain information that is confidential, privileged and/or exempt from disclosure under applicable law. If you are not the intended recipient, please notify the sender immediately and delete the original, all attachments, and all copies of this communication. --------------------------------------------------------------------------------
Arthur Shih <[email protected]> Wed, Oct 31, 2012 at 9:33 PM To: [email protected]
Dear Margarita, The part # is MBS100 S050 H13. We are using this filter to separate algae (~5 to 10 microns) from water. Also, I'm looking for the effective particle diameter of the metal filter, not the outer diameter. Sorry for the confusion Thanks! -Arthur
[email protected] <[email protected]> Thu, Nov 1, 2012 at 3:19 PM To: Arthur Shih <[email protected]>
Hi Arthur, Are you doing research for developmental objective or for a university project /paper? Grade S050 has a maximum pore size of 5 microns. This would be the largest pore and is generally found on the media surface. The media depth contains a tortuous path that helps to achieve finer removal down to 0.5 microns (about 50% capture at 0.5 micron). Void volume is estimated to be 40% for this product. Regards,
Margarita Luis Pall Corporation Energy / Fuels & Chemicals Group Cell Phone 516-924-1518 Fax 516-801-9762 Email [email protected] Website http://www.pall.com
Appendix D: Water Trials Experimental Data
TRIAL Pressure (psi) Rotation
(rpm) Flow (g/s) Flow Standard Deviation (g/s)
3 10.0 1010 20.00 0.25 4 10.0 1010 20.90 0.06 5 15.0 1010 26.70 0.12 6 13.0 1010 25.00 0.52 7 15.0 0 31.20 0.24 8 15.0 2100 18.50 0.22 9 20.0 2100 18.10 0.36 10 20.0 2100 17.50 0.20 11 5.0 1010 12.90 0.47 12 5.0 2100 6.45 0.09 13 5.0 0 15.20 0.18 CONTROL
14 2.5 0 8.50 0.04 15 2.5 1010 5.35 0.08 17 25.0 2100 21.70 0.35 201 2.5 2100 5.02 0.55 202 2.5 1010 6.04 0.06 203 2.5 0 9.09 0.07 205 5.0 1010 12.70 0.12 206 5.0 0 14.90 0.16 CONTROL
207 5.0 0 16.4 0.15 CONTROL
301 4.1 500 11.91 0.08 302 5.3 1000 12.15 0.05 303 6.8 1500 12.10 0.12 304 5.0 0 15.80 0.28 305 5.0 0 16.32 0.05 306 5.0 500 14.35 0.09 307 5.0 1000 12.27 0.07 308 3.6 0 11.90 0.05 309 5.0 0 15.67 0.12 CONTROL
400 8.0 2000 11.96 0.08
Appendix E: Algae Trials Experimental Data
0rpm, 5 psi
Time (sec)
Filtrate Flow (g/s)
Flux (g/s/m^2)
0 16 381.3575
10 7.342071 174.9971
20 4.443357 105.9067
30 2.856714 68.08934
40 2.275143 54.22768
50 2.008286 47.86719
60 1.697571 40.46134
70 1.514786 36.10469
80 1.330143 31.70375
90 1.196786 28.52521
100 1.109214 26.43794
110 1.048786 24.99765
120 0.963786 22.97169
130 0.906143 21.59778
140 0.851214 20.28855
150 0.756286 18.02596
160 0.782857 18.65928
170 0.7295 17.38752
180 0.713071 16.99594
190 0.679857 16.20429
200 0.647786 15.43988
210 0.626357 14.92912
220 0.602071 14.35027
230 0.586571 13.98083
240 0.569214 13.56713
250 0.559714 13.3407
260 0.537643 12.81464
270 0.519214 12.37539
280 0.509429 12.14216
290 0.5 11.91742
300 0.490571 11.69268
310 0.481142 11.46795
320 0.471713 11.24321
330 0.467 11.13087
340 0.462287 11.01854
Appendix F: Sample Calculations for Determining Model Parameters
Determining the Design Equation for Pressure Drop Through the Filter
From equation (7), we know that
.
Experimental data was collected with rotation speed = 0 rpm and with no algae so that the measured total pressure will simply be the pressure drop through the filter.
A series pressure drops were applied through the filter, and resulting fluxes through the filter were measured. R1 was calculated and averaged. The standard deviation of the averages was treated as the error for R1.
TRIAL Pressure
(psi) Rotation
(rpm) Mean
flow (g/s) Flow std
dev Flux (g/s/m^2) C1
(psi/(g/s/m^2) 14 2.5 0 8.500 0.040 202.6
0.0123398174
203 2.5 0 9.090 0.070 216.7
0.0115388832 308 3.6 0 11.896 0.047 283.5
0.0126968178
206 5.0 0 14.900 0.160 355.1
0.0140789863 13 5.0 0 15.200 0.180 362.3
0.0138011116
309 5.0 0 15.672 0.117 373.5
0.0133851570 304 5.0 0 15.805 0.279 376.7
0.0132729298
305 5.0 0 16.319 0.051 389.0
0.0128546721
Filter Surface Area:
AVG 0.0129960469
0.0419554 m^2
STDEV 0.000820492
TRIAL Pressure (psi)
Rotation (rpm)
Mean flow (g/s)
Flow std dev
Flux (g/s/m^2)
C1 (psi/(g/s/m^2)
14 2.5 0 8.500 0.040 =D2/$M$4
=B2/F2 203 2.5 0 9.090 0.070 =D3/$M$4
=B3/F3
308 3.6 0 11.896 0.047 =D4/$M$4
=B4/F4
206 5 0 14.900 0.160 =D5/$M$4
=B5/F5 13 5 0 15.200 0.180 =D6/$M$4
=B6/F6
309 5 0 15.672 0.117 =D7/$M$4
=B7/F7 304 5 0 15.805 0.279 =D8/$M$4
=B8/F8
305 5 0 16.319 0.051 =D9/$M$4
=B9/F9
Filter Surface Area:
AVG =AVERAGE(H2:H9)
0.0419553792692728 m^2
STDEV =STDEV(H2:H9)
Thus, R1 = 0.0129960469 psi/(g/s/m^2) +/- 0.00082 psi/(g/s/m^2) and
Note: This model is only valid for pressure drops between 2.5 psi and 5 psi. It was advised by Pablo that the backpressure air valve should not be on to increase the pressure while collecting data since air bubbles may force its way into the chamber and through the filter.
Error Propagation Below are the errors for each variable used for propagating.
(User error in flow from reading a set pressure drop)
Thus,
(
) . Errors for R1 was calculated for each trial run and then averaged
to obtain an overall error, giving us Determining the Design Equation for Pressure Drop Through the Inner Chamber
From equation (7), we know that (
(
)
(
))
where
(
)
(
)]
We are able to obtain the design equation for pressure drop through the inner chamber by plugging the values defined below into equation (7).
r1 (inner diameter) 0.02921 m r2 (outer diameter) 0.04763 m rho 1000 kg/m^3
This is the theoretical pressure drop through the chamber for laminar flow. The total pressure drop through the rotary filter can be expressed by adding and together as
shown below
Where J is the desired filtrate flux in g/s/m^2 and w is the rotational speed in rpm.
Experimental data was collected with filtrate flux = 0 g/s/m^2 and with no algae so that the pressure drop through the inner chamber due can be related to the rotation speed. This data was plotted with the theoretical model, as shown below.
Notice that the pressure drop required for a specified flow rate (in this case, 12 g/s) is lower than the predicted pressured drop. This may be due to the transition between laminar to turbulent, and calculated in Appendix B, however the exact reason is unknown.
More data points will have to be taken between 0 and 500 rpm at a filtrate flow of 12 g/s to explore where deviations start occurring.
Since the model’s pressure drop at 500 rpm is within the error of the experimental data, we will use 500 rpm as a critical point in modeling the pressure drop through the inner chamber. The derived model for laminar flow will be used for rotation speeds less than 500 rpm.
An empirical model that attempted to scale the theoretical pressure drop through the chamber down to fit the experimental data could only allow an accurate fit for rotation rates between 0 and 1000 rpm. The model still deviated for rotation rates higher than 1000 rpm.
A empirical linear model, as shown below, will be used as a process model for rotation speeds greater than 500 rpm since it gave the best fit for rotation rates higher than 500 rpm.
0
2
4
6
8
10
12
14
16
0 500 1000 1500 2000 2500Pre
ssu
re d
rop
th
rou
gh c
ham
be
r an
d f
ilte
r (p
si)
Rotation Speed (RPM)
Pressure drop vs. Rotation Speed
Model, Laminar
Experimental Data
Thus, the resulting model for pressure drop through a rotating system is:
{
Error for Navier-Stokes Model There was no error propogation necessary when calculating the coefficient for pressure drop through the chamber for Navier-Stokes since we assumed the errors for the density of water and radii were negligible. Error for the coefficient was instead estimated as the average of model’s deviation from collected data as shown below:
y = 0.0026400000x + 2.7250000000 R² = 0.9976524478
0
1
2
3
4
5
6
7
8
9
0 500 1000 1500 2000 2500
Pre
ssu
re d
rop
th
rou
gh c
ham
be
r an
d f
ilte
r (p
si)
Rotation Speed (rpm)
Error for Linear Fit w>500 rpm Errors were estimated by taking the standard deviation of the residuals as shown below.
Determining the Design Equation for Pressure Drop through the Algae Cake
When concentrating algae with the spinning filter, algae will begin to accumulate on the surface of the metal filter due to the applied pressure in the chamber, however algae will also begin to detach from the filter as filter rotational speeds are increased. These two forces counteract each other. Assuming that the pressure drops derived for water through the inner chamber and filter will be applicable for an algae solution, a model for the pressure drop across the cake can be back calculated.
As the algae cake builds, the pressure drop through the cake and total pressure drop will both increase until steady state is reached. The total resistance is expressed as follows:
To determine R2 as a function of time, we will calculate the total R through the rotary filter with time using the total pressure drop and measured flux. The total resistance at t = 0 seconds will be subtracted from all resistance values for t>0 seconds, as shown below.
Graphs of R2 vs time (Figure 8), steady-state R2 vs rotation speed (Figure 9), and time to reach steady state vs rotation speed (Figure 10) were generated to give us some insight into the effects of various variables on R2.
Error Propagation
Errors from measuring the flow rate were propagated as shown below:
(User error in flow from reading a set pressure drop)
Thus,
(
) . Errors for R1 was calculated for each trial run and then averaged
to obtain an overall error, giving us
Appenix G: Sample Calculation for Mass of Algae Accumulated on Filter
Using the parameters shown below for the conditions 0 rpm and 5 psi. As mentioned in the report, we failed to take vent concentration or volume measurements, because of this, we have chosen to approximate these values as zero for our calculations, but future groups should be sure to account for them.
Solving for volume of feed solution
+
Solving for mass of algae on filter
Appenix H: Propagation of Error Calculation
