180 Caldecott Ln #119 Oakland CA, 94618 February 4, 2012

Dr. Edward Trujillo Beehive State Engineers Salt Lake City, UT 84112 Dear Dr. Trujillo: On January 10, 2012, you asked a team of J. Dumas, T. Shardey, and myself to determine the time required to double the concentration of a BSA stream using ultrafiltration.

The original memorandum is shown on the last page of this report for your convenience. For the UF10000 membrane the time required to concentrate the BSA was on the order of one hour as shown in Figure 9. The permeate flux and applicable data can be viewed in the appropriate sections. The ∆PM versus permeate flux was non-linear. This observance would be due to Gel formation and the elastic behavior of the membrane.

The permeabilitty for the membrane, buffer and BSA are respectively 0.8547 lbft2s/in2gal; 6.366 lbft2s/in2gal; and 6.863 lbft2s/in2gal.

Use of a diaphragm pulsation dampener and proper use of the pressure regulator would provide a more accurate understanding flux vs. ∆PM graphs. Difficulties with pumping surge due to slugs of air made it difficult to measure pressure accurately or precisely. Overall the error analysis was nearly 20% for the data.

Sincerely,

______________________________

Michael Felzien

PLATE AND FRAME ULTRAFILTRATION UNIT

by

Michael Felzien

Project - Ultrafiltration

Mass Transfer

Assigned: January 10, 2012

Due: February 3, 2012

Submitted: February 3, 2012

Project Team Members for Group C:

Mike Felzien

Jesse Dumas

Tierra Shardey

____________________

Michael Felzien

Chemical Engineering Department

Salt Lake City

University of Utah

2012

ii

SUMMARY

PLATE AND FRAME ULTRAFILTRATION UNIT

Group C:

M. N. Felzien (report author), J. Dumas, T. Shardey.

Report Date: February 3, 2012

The use of plate and frame ultrafiltration for the concentration of proteins is an excellent method where denaturing due to temperature is a concern. When considering the fragile nature of many organic macromolecules the use of ultrafiltration is an attractive method.

The time required to change the concentration from 1.0wt% to 2.0wt% was determined from graph XX.

iii

TABLE OF CONTENTS

I. INTRODUCTION ............................................................................................................................. 5

II. THEORY .......................................................................................................................................... 6

III. APPARATUS AND PROCEDURE ............................................................................................. 10

IV. RESULTS AND DISCUSSION OF RESULTS ........................................................................... 11

NOMENCLATURE ........................................................................................................................... 17

REFERENCES ................................................................................................................................... 18

APPENDICES .................................................................................................................................... 19

A. LABORATORY DATA ............................................................................................................. 19

B. SAMPLE CALCULATIONS ..................................................................................................... 20

C. SPECTROPHOTOMETER CALIBRATION ............................................................................ 21

D. PUMP CURVE CALIBRATION ............................................................................................... 22

E. MAJOR ITEMS OF EQUIPMENT ............................................................................................ 23

F. ERROR ANALYSIS .................................................................................................................. 25

iv

LIST OF FIGURE

Figure 1 – Steady state mass flow and concentration profile. ............................................. 6

Figure 2 – Ultrafiltration (UF) plate and frame copied w/o permission Othmer (2011) ..... 7

Figure 3 - Boundary layer and gel layer copied w/o permission (Othmer). ........................ 7

Figure 4 - Bovine Serum Albumin (BSA) copied w/o permission Wikipedia. ................... 9

Figure 5 - Process & instrumentation diagram for GEA unit. ........................................... 10

Figure 6 – Pure water permeate flux vs. membrane pressure difference. .......................... 13

Figure 7 - Buffer permeate flux vs. membrane pressure difference 0.1Mcitric acid 0.2MNa2HPO4 .................................................................................................................. 14

Figure 8 - BSA permeate flux vs. membrane pressure difference (outliers removed) ..... 15

Figure 9 – Filtration/concentration cycle for BSA ............................................................ 16

Figure 10 - Calibration wt% BSA vs. Absorbance ............................................................ 21

Figure 11 - pump curve. ..................................................................................................... 22

LIST OF TABLES

Table 1 - Raw data from experiment on Jan 19, 2012 Patm=12.24psia. ........................... 19

,

5

I. INTRODUCTION

The current trend within the chemical process industry (CEP) is towards greater benefit for less investment. This trend promulgates the use of novel separation methods such as Ultrafiltration (UF). Ultrafiltration provides an alternative in many cases to traditional separations such as distillation, liquid-liquid extraction and many others. The industrial ultrafiltration market has become a multimillion dollar industry and provides lifesaving and cost effective applications to chemical separations (Othmer 1990). The earliest membranes were homogeneous structures of purified collagen. The first synthetic membranes were made of nitrocellulose. In the late 1950s and 60s the development of highly anisotropic or asymmetric structures (membranes constructed of a very thin, tight surface skin having a porous substructure) aided in ultrafiltration design. This substructure provided the necessary mechanical support for the thin skin without the hydraulic resistance of previous isotropic structures. Flux rates improved substantially with this development.

The primary objective of this project is to provide additional information about the possible use of ultrafiltration for further purification of a proprietary process stream. The protein in question has properties that are similar to BSA, and it is desired to find the time required to concentrate the stream from 1% to 2%.

Since the exact nature of the protein in question was not supplied, a suitable protein of similar makeup was chosen. The use of Bovine Serum Albumin (BSA) was decided to have similar properties for this work. The performance of a UF membrane can be characterized by the determination of the permeate flux, percent reject, and the concentration of solute in the retentate stream (Smith 2005). Ultrafiltration can be used to separate particles from 0.l5 um down to molecules of about 10-3 um. Mass transport in ultrafiltration is dominated by pressure-driven convection, and the flux of all solutes through the membrance is directly proportional to the ultrafiltration rate (see equation 2).

6

II. THEORY

Ultrafiltration is a method of separation that works on a molecular scale due to a pressure gradient between two sides of a semi-permeable membrane. The porous membrane allows molecules of a certain size (or molecular mass) through while retaining larger molecules based upon their atomic weight. The transport of these materials is analytically represented using pore flow models. These equations take into account the major contributing factors. In the diffusive flux to and away from the thin porous membrane.

Figure 1 – Steady state mass flow and concentration profile.

The figure above helps visualize the process occurring for a plate and frame filtration unit. Figure 1A shows the bulk slurry to the left and the membrane shaded. The flow of the solute right slurry is JC while at steady state is balanced by the diffusive flux from the layer. In Figure 1B the bulk concentration CB solute concentration is shown to increase until the gel interface layer is encountered. The gel concentration is constant at this point.

Figure 2 on the next page shows the overall arrangement of plate to frame for a typical filtration cell. The bulk slurries enter on the feed side at an inlet pressure of Pi . The slurry travels over the membrane (which is supported by the frame) and then turns, and meets with additional streams adding to a point (a) near the stop disk. The passage rings (b) allow for the bulk slurry (solute) to flow out of the cell at an outlet pressure of Po. The support plate holds the membrane in place to the frame (similar to a frame for a painting). Lock rings lock each plate and frame together and allows for passage of the bulk flow (retentate).

7

Figure 2 – Ultrafiltration (UF) plate and frame copied w/o permission Othmer (2011)

Figure 3 shows a cross flow plate and frame filtration cell. Generally the flow of the fluid being filter is parallel to the membrane, but perpendicular to the direction of the permeate flux. The turbulence generated by the bulk flow of feed helps remove the solute which is diffusing away from the membrane into the bulk solution. This turbulent motion helps improve mass transfer at the membrane surface, and the buildup of a solute layer (gel layer) on the surface of the membrane is assured relatively high permeate flux from Othmer (2011).

Figure 3 - Boundary layer and gel layer copied w/o permission (Othmer).

Figure 3 also shows the steady state solute concentration profile. The concentration profile develops on the upstream side of the membrane. The permeate flux (the flow of material

8

through the membrane) is related to the concentration CGe of the solute in the gel layer; the concentration CB in the bulk, and the mass transfer coefficient kL with the following equation:

ln GeL

B

CJ k

C

=

(1)

kL depends on the Reynolds number on the slurry side based upon the hydraulic radius of the channel..

When only water is passed through the membrane the Darcy relation best explains the flow. Darcy’s law says that the flow rate is proportional to the pressure gradient.

mK PV

JAt µ

∆= = (2)

Where J is the permeate flux in units of volume per membrane area A, at time t, Km is the hydraulic permeability, µ the viscosity, and P∆ the membrane pressure drop between the

retentate and permeate.

For cross flow ultrafiltration the average trans-membrane pressure drop is:

12M i

P P P∆ = − ∆ (3)

And the flux through the membrane is

R

M

m gel

PJ

R

πυ

∆ − ∆= =

+ (4)

Osmotic pressure is zero for isotonic solutions and applies only for membranes with chemical potential gradients. Equation (4) becomes

1

RM

m gel BSA

PJ

R Rµ

∆=

+ + (5)

Often the viscosity shown above is normalized and does not show in lumped into the resistance values. The highest resistance is that for our protein called Bovine Serum Albumin and is very large compared to the pore sizes and the buffer and water molecules.

9

Bovine Serum Albumin (BSA) is often used as a standard protein marker in the Bradford Protein Assay test. It in conjunction with a dye of Coomassie Brilliant Blue G-250 allows for colorimetric analysis of a protein assay based upon the absorbance shift of the dye. BSA is shown in the Figure below.

Figure 4 - Bovine Serum Albumin (BSA) copied w/o permission Wikipedia.

BSA has a molecular weight of about 66,463 Daltons; Isoelectric Point of 4.7 and a dimension of about 140x40x40Å3 (2.24x10-25m3). With these physical properties BSA is an acceptable protein to model other similar proteins with molecular mass of approximately 66,000 Dalton’s from (Perry 1999).

The BSA molecular conformation and a near zero a-centric factor helps in the steady state diffusion to occur rapidly and to have few molecules pass through the DairyUF 10K.

10

III. APPARATUS AND PROCEDURE

Figure 5 - Process & instrumentation diagram for GEA unit.

11

IV. RESULTS AND DISCUSSION OF RESULTS

Since the mass flux equations are correlated for turbulent flow conditions a simple hydraulic analysis determined the Reynolds number for the geometry of the five plates in parallel was done. The average retentate flow was used for the volumetric flow for the Reynolds calculation. Since the flow was through a square duct and the geometry of the area is complex, the hydraulic radius was calculated. The Reynolds number for flow through a square duct is:

HQ D

Aυ

⋅=

⋅� (6)

For the determination of the hydraulic radius DH, the wetted perimeter and the cross sectional area are needed. The plate and frame of the membrane is considered to be a section of a cylinder. The circumference of the cylinder is the location of the perpendicular flow area, and where the flow would leave the disk. Therefore the area of flow was the thickness of the disk times the circumference of the cylinder, or

( ) ( ) 2316 " 2 " 1.1781inA T C T Dπ π= ⋅ = = ⋅ =i (7)

The wetted perimeter is

( ) ( ) 23162 2 2 2 2 12.94inwettedP T C π= ⋅ + ⋅ = ⋅ + ⋅ = (8)

and

24 4.7123in

0.364in12.941inH

AD

P= = = (9)

The kinematic viscosity for water was found from Perry’s (1999) to be 0.97 cP at 70deg F. This amounted to an intrinsic viscosity of 0.001508 in2/s. Substituting these values into equation (3) gave a value for the Reynolds number of 2002.59. This value is in the transition region and additional turbulence is likely added by further geometrical consideration or by the use of distributors in the plate and frame. However, it should be observed that this should be further investigated and determined to be in the turbulent region.

The next point of concern was the osmotic pressure. It was assumed to be nearly zero for our solution. This would be the case for an isotonic solution. For our buffer solution this would be the case since the molecules could easily diffuse from retentate to permeate side. The buffer was to help stabilize the BSA solution, but also to help treat and pacify the new membranes. BSA is mildly negatively charged and the acetic acid and disodium phosphate can act (to some degree) as a physical absorbed solute on any charged surfaces on the sulonyl membrane pores. This effect would also be a point of further research.

12

The osmotic pressure for our buffer solution would be expected to be zero since the solution would be isotonic. The calculation for this pressure is

i

CRTπ π∆ = =∑ (10)

C is the average concentration of each solute. For our buffer this is

31 2

1 2

0.9595+1.866=0.00441mol/cm

110.72 529.794

n nC

V V

+= =

+ +

Substituting the average concentration for the buffer into equation (7)

3 3(0.00441mol/cm )(82.057atm cm / mol K)(295.65K)(14.6959psi/atm)

1,573psi

CRTπ∆ =

= ⋅ ⋅

=

The calculated osmotic pressure is about 1500 psi for a 0.1 M acetic acid and 0.2 M Na2HPO4 buffer solution. This value seems high and for these experiments. Since the change in osmotic pressure between the retentate side and permeate side was assumed about zero. This value can be accounted for if there is an equal pressure on the reverse side due to the membrane being porous. Small molecules such as citric acid and Na2HPO4.exhibit no net pressure difference due to them being easily transported between the membrane.

With the addition of BSA to our solution there is a hypertonic case and therefore a pressure gradient associated with the difference in chemical potentials. The osmotic pressure for the BSA solution is

7 33

3

.002068mol=1.505x10 mol/cm

13750mL

nC

V

−= =�

7 3 3(1.505x10 mol/cm )(82.057atm cm / mol K)(295.65K)(14.6959psi/atm)

0.0536581161psi

CRTπ−

∆ =

= ⋅ ⋅

=

The value is small when compared to the transmembrane pressure gradient.

The permeate and retentate are isotonic in regards to the buffer solutes. However, in regards to the BSA concentrations the UF membrane is selective to these large molecules and there should be a measureable osmotic pressure.

13

(11)

The transmembrane pressure difference was calculated from the following equation. This equation takes into account pressure drop of solidly in the laminar range. Therefore it can be concluded that there is a kinethrough thedetermining the Reynolds number for a disk was equation The osmotic pressure for the buffer solution was determined using the following equation. It was not clear initially that the osmotic pressures would be negligible.

iC RTπ∆ = (12)

In the above equation iC is the average concentration for the solution and T is the temperature.

The permeate and retentate are isotonic in regards to the buffer solutes. However, in regards to the BSA concentrations the UF membrane is selective to these large molecules and there should be a measureable osmotic pressure.

Figure 6 – Pure water permeate flux vs. membrane pressure difference.

y = -0.0339x2 + 3.082x - 34.859

R² = 0.9968

y = 0.8527x + 21.313

R2=1

15.00

17.00

19.00

21.00

23.00

25.00

27.00

29.00

31.00

33.00

35.00

20 22 24 26 28 30 32 34 36 38 40

Gal

/Ft2 s

∆PM (psi)

Series1

PolyFit

Linear Relaxation

14

Figure 7 shows the pressure drop in psi versus the volumetric flux. The data suggests a non-linear relationship. However, the membrane is elastic and is not ideal. There is elastic deformation as the pressure is increase. When the pressure is decrease to the original pressure value (low pressure) the pressure vs. flux curve will be retained. For this case there was no buffer or BSA in this run. The data was regressed using least square method. Both a linear and quadratic fit are shown. The R2 values are poor, but for our data this case has the best value. The slope of the linear interpolation is used to determine the bulk permittivity coefficient. The reciprocal of this slope is the resistivity of the water solution due to the membrane character. This value was calculated to be 0.8547 lbft2s/in2gal. This value is normalized with the viscosity so other comparisons can be made with solutions of difference viscosities

Figure 7 - Buffer permeate flux vs. membrane pressure difference 0.1Mcitric acid 0.2MNa2HPO4

Figure 7 shows the addition of a buffer which was comprised of 0.1M citric acid and 0.2M disodium phosphate. The addition of the buffer helps maintain pH for the BSA solution, but also helps remove polarization.

y = 0.752x + 2.0969

R² = 0.9672

y = 0.0104x2 + 0.209x + 8.1116

R² = 0.9927

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

40.00

10 15 20 25 30 35 40 45 50

Flux (gal/ft2*s)

Linear (Flux (gal/ft2*s))

Poly. (Flux (gal/ft2*s))

15

The permittivity of the membrane and the buffer was found to be 0.752 which gives a resistance of 6.366 lbft2s/in2gal for the buffer concentration layer. When this normalized with the solution viscosity the difference is within 20% of the given value.

The addition of low ionic strength buffers helps maximize the electrostatic repulsion between the negatively charged BSA and the negatively charged membrane. This electrostatic exclusion causes a dramatic increase in the separation, with relatively little change in the membranes physical permittivity (permeability).

Figure 8 - BSA permeate flux vs. membrane pressure difference (outliers removed)

Figure 8 shows the BSA solution. The value is 1.4747 lbft2s/in2gal for the Rbulk value. The resistance due to BSA is And when calculated is 6.863 lbft2s/in2gal and the bulk resistance is 1.47470. lbft2s/in2gal.

16

Figure 9 – Filtration/concentration cycle for BSA

y = 0.0004x2 + 0.0038x + 1.3887R² = 0.9881

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0 10 20 30 40 50 60

wt.

% B

SA

Time, min

wt. % BSA

Poly. (wt. % BSA)

17

NOMENCLATURE

Nomenclature Symbol Description Units

A membrane area m2

C concentration kg/m3

Cb concentration of all retaned species kg/m3

C Ge concentration of gel kg/m3

C B concentration of bulk solution kg/m3

average transmembrane pressure drop psifiltrate pressure psi

P pressure psi

k L mass transfer coefficient -

J permeate flux on membrane filtration rate -

K m membrane hydraulic permeability coefficient -

fluid viscosity cPmembrane pressure drop -inlet pressure psioutlet pressure psimembrane resistance cm2

/s

gel resistance -effective diffusivity in liquid film cm2/sosmotic pressure psi

µ

MP∆

MP∆

iP

oP

MR

GR

eD

fP

π

18

REFERENCES

1. Warren L. McCabe, Julian C. Smith and Peter Harriot. Unit Operations of Chemical Engineering. McGraw-Hill. New York (2005)

2. Kirk and Othmer. Encyclopedia of Chemical Technology. John Wiley & Sons, Inc. New York (2011)

3. Perry, Robert H., Editor. Perry’s Chemical Engineering Handbook. 7th Edition. McGraw-Hill, New York. (1999)

4. Wright AK, Thompson MR (February 1975). Hydrodynamic structure of bovine serum albumin determined by transient electric birefringence. Biophys. J. 15 (2 Pt 1): 137–41. doi:10.1016/S0006-3495(75)85797-3. PMC 1334600. PMID 1167468.

5. Michael L. Shuler, Fikret Kargi. Bioprocess Engineering Basic Concepts. 2nd Edition. Prentice Hall PTR, New Jersey (2002).

19

APPENDICES

A. LABORATORY DATA

Table 1 - Raw data from experiment on Jan 19, 2012 Patm=12.24psia.

retentate permeate (gpm) (psia) (psia) (gpm)1.025 0.051 20.5 1.0 14.3 0.7 0.00745 0.000

- - 29.6 1.5 19.5 1.0 0.02403 -

- - 20.9 1.0 18.0 0.9 0.01618 -

1.574 0.079 18.0 0.9 18.0 0.9 0.01894 0.001

2.097 0.105 31.8 1.6 20.9 1.0 0.02782 0.001

2.348 0.117 34.0 1.7 21.7 1.1 0.03253 0.002

2.878 0.144 41.0 2.0 22.4 1.1 0.05248 0.003

3.396 0.170 43.9 2.2 23.8 1.2 0.04881 0.002

iP

oPδ± δ± δ± δ±

20

B. SAMPLE CALCULATIONS

For a plate and frame UF unit the Reynolds number must be in the turbulent range on the retentate side.

Re =Calculation of the membrane pressure drop is as follows

Calculation of permittivity and resistive coefficient using slope of Table 3 Kw = 0.8527gal/ft2.

m2 2

lbg1 2.048

m s ft s=

1MPa 145.0377psi=

The permittivity of the membrane is the calculated as follows

w wK Kµ=

7 2

7 2

(1.40686x10 psi s)(0.8527gal/ft )

1.19963 10 gal/ftWK

x

−

−

= ⋅

=

wKJ P

µ= ∆

The preceding equation is a form of Darcie’s equation and is an ideal case. The actual physical behavior of the membrane pressure changes non-linearly due to compaction and yielding of the plastic like membrane (Polypropylene-backed Polyethersulfone).

21

C. SPECTROPHOTOMETER CALIBRATION

Figure 10 - Calibration wt% BSA vs. Absorbance

22

D. PUMP CURVE CALIBRATION

Figure 11 - pump curve.

y = 1.2492x2 - 9.0519x + 21.906

R² = 0.9794

0

5

10

15

20

25

0 1 2 3 4

Ax

is T

itle

Axis Title

Series1

Poly. (Series1)

23

E. MAJOR ITEMS OF EQUIPMENT

1. GEA Model M membrane Filtration Pilot Plant.

Standard Features • 15 liter balance tank with electronic level transmitter • One lab-size spiral wound membrane housing, 1.8" x 12" • One lab-size ceramic membrane housing, 0.75" x 10" • Feed pump with 1 HP variable speed drive • Tubular heat exchanger • Inlet and outlet pressure gauges • Temperature indicator • Manual flow control valves • Flow indicators: one permeate, one concentrate • Assembled on a tubular stainless steel base with casters

Operating Conditions • Pressure up to 6 bar (87 psig) • Temperature up to 93° C (200° F) • Flow up to 1,000 l/h (4.4 gpm)

Utility Requirements • Floor Space 30" x 48" x 65" • Shipping Wt. 350 lbs. • Voltage/ph 220V, 1 ph • Total HP 1 • Feed Tank Cap. 19.4 L • Min. Vol. w/Spiral Module Approx. 1.25 L • Min. Vol. w/Other Modules Approx. 0.75 L • Permeate Outlet 3/8" ID FLEX (3/4" TC) • Concentrate Outlet 3/4" ID FLEX (3/4" TC) • Max. Flow 1000 L/H • Max. Pressure 6 bar • Tank Drain 3/4" TC • Tank Bypass 3/4" TC • Heating/Cooling Inlet 1/8" FNPT • Heating/Cooling Outlet 1/8" FNPT • Caster Mounted Yes

2. Plate and Frame stack assembly.

24

Plate and Frame stack assembly (Continued from previous).

E

25

F. ERROR ANALYSIS

For brevities the error analysis was shown to be at max 20%. The errors shown in the graphs are from laboratories measurement. Error was propagated until the final maximal error of 20% was calculated.

26

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