CN3108: CHEMICAL ENGINEERING PROCESS LAB II
Experiment B1

Adsorption for Protein Isolation

(L) Frederick Chan Yew Meng U065963A
(E) Gan Yue Sern U065873B
(A) Giam Ming Yao Joshua U065944X
(R) Farhana Mehnas D/O Haja N U065763H

Group: M4
Submitted On: 13th October 2008

Contents
Sections Page Summary 1 I Introduction 2 II Theoretical Background 3 III Experimental procedures 6 IV Results and Analysis 8 V Discussion 22 VI Conclusion 28 VII References 28

Summary
This experiment was to determine the adsorption isotherm for bovine serum albumin (BSA) on an anion-exchange adsorption resin with a model that is derived from the experimental data and to draw a breakthrough curve for BSA for different superficial velocities and find out the controlling step occurring within the packed bed.
The Freundlich Isotherm q=αC1v was then found to be a better model to approximate the adsorption isotherm for BSA as compared to Langmuir Isotherm.
From the experimental data, the static capacity determined from Langmuir Isotherm approximation was estimated to be 330.033mg/g and the dynamic capacities flow rates of 5.0, 2.5, 0.5 ml/min were 0.918, 1.431 and 2.066 mg/g respectively, thus agreeing with theoretical knowledge that the static capacities should be larger than dynamic capacities as sufficient time were allowed for equilibrium to reach 24 hours in this experiment. Dynamic capacity also decreased with increasing flow rate as lesser contact time was allowed in each respective run.
In the second part of the experiment, breakthrough curves were obtained after running protein stream through a packed bed. σ2 and (t0σ)2 from the breakthrough curves were plotted against various characteristics which are known to have linear relationship for the controlling step. From the experimental data, the results indicated that the adsorption was diffusion controlled.

I. Introduction
Proteins are biomolecules made up of one or more chains of amino acids linked together by peptide bonds. They are essential for the function and structure of living cells. Besides their biological importance, some proteins, enzymes in particular, are useful as catalysts for certain industrial chemical processes. Proteins are usually contained in microbial cells along with other components such as DNAs and other small and macro-molecules. For protein downstream processing, adsorption could be used as a technique to isolate proteins.
Adsorption is a process that occurs when a gas or liquid solute accumulates on the surface of a solid or a liquid (adsorbent), forming a film of molecules or atoms (the adsorbate). Adsorption is present in many natural physical, biological, and chemical systems, and is widely used in industrial applications such as synthetic resins, and water purification. Adsorption is usually described through isotherms, that is, the amount of adsorbate on the adsorbent as a function of its concentration at constant temperature.
The 2 isotherms that will be used in this experiment to model the data are:
Freundlich Isotherm q=αC1v
Langmuir Isotherm qmgg=qmCK+C
The specific objectives of the experiment are as follows: 1. Establish the adsorption isotherm for a protein-adsorbent system. 2. Appreciate the difference between static and dynamic capacities. 3. Understand the use of breakthrough curves for scaling-up adsorption processes. 4. Understand the different ways to use the breakthrough curves.

II. Theoretical Background
Adsorption
Adsorption is a process whereby a gas or liquid solute binds to the surface of a solid or a liquid known as the adsorbent and forms a film of molecules or atoms known as the adsorbate. The required adsorbates are specifically transferred from the fluid phase to the surface of solid particles which can be in suspension or in a packed column. It is commonly used in protein downstream processing as a protein isolation technique. A typical adsorption process consists of four steps. A feed solution with the targeted proteins is first added to the adsorbent. The proteins then attach onto the adsorbents based on the chemistry of interactions. Following that, the spent feed solution is removed in the third step and finally the adsorbed proteins are desorbed from the adsorbent with a different solvent.
Adsorption isotherms, which relate the equilibrium solute concentration to the adsorption capacity of the adsorbent, are used to describe and analyze the adsorption process. The very first mathematical fit to an isotherm is the Freundlich Isotherm. It is expressed in the following mathematical form: q=αC1v where q = mass of adsorbate / mass of adsorbent
C = equilibrium concentration of adsorbate in solution α and 1v = constants for a given adsorbate and adsorbent at a specific temperature.

However, the most commonly used adsorption isotherm is the Langmuir Isotherm.: qmgg=qmCK+C where q = mass of adsorbatemass of absorbent qm = maximum mass of adsorbatemass of absorbent as C increases
C = Equilibrium concentration of adsorbate in solution
K = 1Langmuir equilibrium constant
Breakthrough Curve
Very often adsorption is conducted in a packed bed. During the process, the feed solution with the proteins flows into the column from the top and exit from the bottom. As the fluid passes through, most of the proteins are adsorbed initially and as a result the solute concentration in the effluent is low. As the adsorption process continues, the effluent concentration slowly rises and then suddenly towards the initial feed concentration. This is when breakthrough has occurred. A plot of the effluent concentration is then known as the breakthrough curve. Analyzing the adsorption process in packed bed is complex due to the unsteady non-linear adsorption isotherm, the in-homogeneities in the packed bed etc.
The Breakthrough Curve is used as a tool to analyze and scale up adsorption processes. This can be done by subjecting the Breakthrough Curve to several mathematical simplifications: * approximating it to a ramp function, which is characterized by a breakthrough time and an exhaustion time * approximating it to an error function (Eqn 1), which is characterized by the breakthrough time and the slope of the breakthrough transfer curve yyF=0.51+erft-t02σt0 ---------- Eqn 1 to: time at half feed concentration
In using the error function approximation, the two parameters give an indication of the controlling mechanism occurring within the packed bed (see Table 1). Controlling step | σ2 is proportional to | (t0σ)2 is proportional to | Equilibrium | 1L | Lv2 | Kinetics of adsorption | vL | Lv | Mass transfer | v0.5L | Lv1.5 | Dispersion | vL | Lv | Diffusion | 1Lv | Lv3 |
Table 1: Typical characteristics of the standard deviation for BTC

Two examples of Breakthrough Curves are shown below:

Figure 1a: A Breakthrough Curve (BTC) for packed bed adsorption

Figure 1b: Another Breakthrough Curve (BTC) for packed bed adsorption

III. Experimental Procedures
Part I: Adsorption Isotherm
Apparatus/Materials:
- 5 g of the adsorption resin Diaion HPA25
- 0.62 mg/ml BSA in 2mM phosphate buffer (pH 7.0)
- A UV-Visible spectrophotometer with wavelength set at 280nm
- A water bath shaker set at 250 rpm and 50oC

Experimental Procedure: 1. 100mg of Diaion HPA25 resin was weighed using a digital balance 2. The weighed sample was added to 20ml of Diaion HPA25 resin which was measured using a measuring cylinder. 3. Steps 1 and 2 was repeated with 6 other weights of Diaion HPA25 to get a total of 7 weighed samples of Diaion HPA25 resin within the range of 100mg to 1000 mg in 20mL of BSA each. 4. The 7 weighed samples were placed into the water bath shaker at 25°C for over 24 hours for them to establish equilibrium. 5. A control for the spectrophotometer was prepared using distilled water 6. The absorbance of each of the 7 samples of Diaion HPA25 resin in BSA was then measured with reference to the control and the concentrations were then calculated based on the calibration curve programmed in the spectrometer.

Part II: Breakthrough Curve
Apparatus:
- HPLC system (properly set up and equilibrated)
- Computer program
Experimental Procedure: 1. BSA was poured into a well and placed into the HPLC system. 2. The method “adsorption buffer” in the computer program was loaded. 3. The pump was switched on and the plot was started by clicking “Plot” on the chromatograph window. Run the program for at least 10mins until the baseline stabilized. 4. The program was stopped and the method “adsorption_breakthrough” was loaded with the desired flow rate was set. 5. The program was started by clicking “Single start” and subsequently clicking “OK” and “Yes”. The program was stopped when a full BTC curve was obtained. 6. The method “adsorption_desorption” was then selected and started by clicking “Plot” on the chromatograph window and allowed to run for about 20 minutes until the baseline is stable. 7. Steps 1 to 8 were repeated with 2 other different flow rates with 2 other flow rates selected in step 4. 8. The data for the 3 different flow rates were processed and printed out in graphical form.

IV. Results and Analysis Part 1: Static Method Run Parameters | Experimental Data | | UV Adsorption (nm) | Solute Concentration, C (mg/ml) | Sample | Mass of Resin added (g) | Volume of
BSA added (ml) | BSA initial concentration (mg/ml) | Run 1 | Run 2 | Average | Run 1 | Run 2 | Average | 1 | 0.100 | 20 | 0.62 | 0.188 | 0.193 | 0.191 | 0.3240 | 0.3322 | 0.3281 | 2 | 0.250 | 20 | 0.62 | 0.138 | 0.158 | 0.148 | 0.2372 | 0.2728 | 0.2550 | 3 | 0.423 | 20 | 0.62 | 0.117 | 0.100 | 0.109 | 0.2025 | 0.1724 | 0.1875 | 4 | 0.550 | 20 | 0.62 | 0.085 | 0.085 | 0.085 | 0.1469 | 0.1461 | 0.1465 | 5 | 0.706 | 20 | 0.62 | 0.085 | 0.084 | 0.085 | 0.1474 | 0.1452 | 0.1463 | 6 | 0.862 | 20 | 0.62 | 0.107 | 0.106 | 0.107 | 0.1844 | 0.1831 | 0.1838 | 7 | 0.993 | 20 | 0.62 | 0.074 | 0.077 | 0.076 | 0.1263 | 0.1330 | 0.1297 | Table 2: Static Method Experimental Data Run Parameters | Calculated Data | | | Sample | Mass of Resin added (g) | Mass of BSA adsorbed per mass of resin, q (mg/g) | Equilibrium Solute Concentration, C (mg/ml) | 1q | 1C | ln C | ln q | 1 | 0.100 | 58.380 | 0.3281 | 58.380 | 3.0479 | -0.4840 | 1.7663 | 2 | 0.250 | 29.200 | 0.2550 | 29.200 | 3.9216 | -0.5935 | 1.4654 | 3 | 0.423 | 20.452 | 0.1875 | 20.452 | 5.3348 | -0.7271 | 1.3107 | 4 | 0.550 | 17.218 | 0.1465 | 17.218 | 6.8259 | -0.8342 | 1.2360 | 5 | 0.706 | 13.419 | 0.1463 | 13.419 | 6.8353 | -0.8348 | 1.1277 | 6 | 0.862 | 10.122 | 0.1838 | 10.122 | 5.4422 | -0.7358 | 1.0053 | 7 | 0.993 | 9.876 | 0.1297 | 9.876 | 7.7131 | -0.8872 | 0.9946 | Table 3: Static Method Calculated Data Sample Calculation For Sample 1, Mass of Resin added = 0.100g Mass of BSA adsorbed = ((0.621 – C) mg/ml) x (20 ml) = 5.838mg Mass of BSA adsorbed per mass of resin, q = 5.838mg/0.100g = 58.38 mg/g Langmuir Isotherm The Langmuir Isotherm is given by the following expression: q=qmCK+C where C = solute concentration (mg/ml) q = Mass of BSA adsorbed per mass of resin (mg/g) K, qm = system constants Rearranging the above equation, we get: 1q=Kqm1C+1qm By plotting against, we should get a straight line with gradient and as y-intercept: Figure 2: Plot of against Freundlich Isotherm The Freundlich Isotherm is given by the following expression: q=αC1v where q = Mass of BSA adsorbed per mass of resin (mg/g) C = solute concentration (mg/ml) α, = system constants Taking log on both sides rearranging: lnq=lnα+1vln⁡(C) By plotting ln(q) against ln(C) , we should get a straight line with gradient , y-intercept ln(α) Figure 3: Plot of ln(q) against ln(C) The plot of adsorption isotherm for BSA on Diaion HPA25 in 2mM phosphate buffer is as follows: Figure 4: Adsorption isotherm for BSA on Diaion HPA25 in 2mM phosphate buffer From the plots of the two isotherm models above (Fig 2 and 3) and comparing their linear fits using R2 values, the adsorption pattern of BSA fits the Freundlich Isotherm model most closely. Freundlich Isotherm Calculations Gradient = = 1.6691 v = 0.5991 y-intercept = ln(α) = 2.5299 α = 12.552 Therefore, the adsorption isotherm for BSA on Diaion HPA25 follows the following relation: q=12.552C1.6691 Part 2: Dynamic Equilibrium BSA flow runs of 0.5ml/min, 2.5ml/min and 5.0ml/min were conducted to obtain BTCs. Run 1 (0.5ml/min) Figure 5: Plot of Intensity against Time for v = 0.5ml/min Run 2 (2.5ml/min) Figure 6: Plot of Intensity against Time for v = 2.5ml/min Run 3 (5.0ml/min) Figure 7: Plot of Intensity against Time for v = 5.0ml/min From the 3 plots of Intensity against Time, the corresponding breakthrough time, Tb, and elution time, Te, for each plot can be obtained and tabulated below. The breakthrough time, Tb, is the time taken to reach 10% of the maximum intensity while the elution time, Te, is defined as the time taken to reach 90% of the maximum intensity. Flow Rate (ml/min) | Tb (min) | Te (min) | 5.0 | 0.597 | 1.162 | 2.5 | 1.280 | 2.731 | 0.5 | 6.933 | 16.331 | Table 4: Tabulation of Tb and Te for various flow rates The given parameters for the apparatus are below: System dead volume = 2.6ml Mass of resin in packed column, MR = 0.26g Calculations The actual breakthrough time is given by the expression: Ta = Tb - Ts where Ta = actual breakthrough time Tb = breakthrough time Also, the dynamic capacity of a system is calculated as follows: Dynamic Capacity= C×Ta×vMR where C = concentration of BSA (mg/ml) Ta = actual breakthrough time (min) v = velocity of flow (ml/min) MR = mass of resin in packed column (g) Sample Calculations For Flow rate = 5.0ml/min, Tb = 0.597min; Te = 1.162; MR = 0.26g; system dead volume = 2.6ml Ts=system dead volumeFlowrate=2.6ml5.0ml/min=0.520 min Ta = Tb – Ts = 0.597min – 0.520min = 0.077min Dynamic Capacity= C×Ta×vMR=0.62mg/ml×0.077min×5.0ml/min0.26g=0.918mg/g Using the above calculations, the dynamic capacity for the other flow rates were calculated and tabulated below: Flow rate, v (ml/min) | Tb (min) | Te (min) | Ts (min) | Ta (min) | Dynamic Capacity (mg/g) | 5.0 | 0.597 | 1.162 | 0.520 | 0.077 | 0.918 | 2.5 | 1.280 | 2.731 | 1.040 | 0.240 | 1.431 | 0.5 | 6.933 | 16.331 | 5.200 | 1.733 | 2.066 | Table 5: Tabulation of derived data Controlling Step in Dynamic Equilibrium The controlling step in dynamic adsorption can be expressed by the following error function approximation equation as follows: yyF=121+erft-t02σt0 The controlling step can be determined by correlating with the characteristics of the standard deviation table in Table 1. Calculation of Standard Deviation From the above equation, setting yyf = 0.1, which is consistent with the 10% maximum intensity represented by t = Tb. t0 is the time at half feed concentration, i.e the time when 50% maximum intensity is reached. Therefore, 0.1=121+erfTb-t02σt0⟹erfTb-t02σt0=0.8 Tb-t02σt0=0.906 Flow rate, v (ml/min) | 5 | 2.5 | 0.5 | Length of column (mm) | 44 | Tb (min) | 0.597 | 1.280 | 6.933 | t0 | 0.747 | 1.579 | 8.981 | | 0.1565 | 0.1477 | 0.1780 | 1L | 0.0227 | 0.0227 | 0.0227 | vL | 0.1136 | 0.0568 | 0.0114 | V0.5L | 0.0508 | 0.0359 | 0.0161 | 1Lv | 0.0045 | 0.0091 | 0.0455 | Lv2 | 1.7600 | 7.0400 | 176.0000 | Lv | 8.8000 | 17.6000 | 88.0000 | Lv1.5 | 3.9355 | 11.1312 | 124.4508 | Lv3 | 0.3520 | 2.8160 | 352.0000 | 2 | 0.0245 | 0.0218 | 0.0317 | (t0)2 | 0.0137 | 0.0543 | 2.5549 | Table 6: Table of calculated data for controlling step Graph for Equilibrium Step Control Figure 8: Plot of σ2 against 1/L Figure 9: Plot of (t0σ)2 against L/v2 Graph for Kinetics of Adsorption Control Figure 10: Plot of σ2 against v/L Figure 11: Plot of (t0σ)2 against L/v Graph of Mass Transfer Control Figure 12: Plot of σ against v0.5/L Figure 13: Plot of (t0σ)2 against L/v1.5 Graph of Dispersion Control Figure 14: Plot of σ2 against v/L Figure 15: Plot of (t0σ)2 against L/v Graph of Dispersion Control Figure 16: Plot of σ2 against 1/Lv Figure 17: Plot of (t0σ)2 against L/v3 Error Analysis 1. The concentration stated in the lab manual and on the label of the BSA solution provided for experimenters was 2.0mg/ml. However, the concentrations that we obtained for the static section of the experiment was drastically low, suggesting that the resin absorbed a significant amount of BSA more than literature values. This prompted to group to investigate the reason behind this significant variation of results from literature value. In our investigation, experimenters took a sample of BSA from the bottle containing the initial BSA solution and used the UV Spectrophotometer to derive its concentration. The measured concentration was 0.62mg/ml, which was far away from the 2.0mg/ml stated in the lab manual. Therefore, after much discussion with the Lab Officer, it was agreed that the initial concentration of 0.62mg/ml be used to represent the calculations more accurately. The concentration of BSA used in the dynamic section was also around 0.62mg/ml. Therefore, after much discussion with the Lab Officer, it was agreed that the initial concentration of 0.62mg/ml be used for both sections so as to represent the calculations more accurately One suggestion to improve current experimental procedure is to take include a blank or control sample in the static component. The initial concentration of BSA in solution should also be measured using the UV spectrophotometer and should not be taken for granted as stated on labels or in the lab manual 2. As a consequence of point (1), the final concentration of the BSA in the static section was rather low due the low initial concentration. Due to this, the range of concentration is very small (0.10-0.35). Coupled with the few experimental points that were taken, the isotherm that was approximated is applicable only to this small range of results. More experiment points over a wider range would have given a closer and more accurate approximation compared to reality. 3. There could be impurities in the BSA solution that might affect experimental results. These impurities might be adsorbed by the resin, preventing more BSA from being adsorbed onto the resin. To reduce this error, the BSA solution should be prepared at the start of every experiment using fresh distilled water and chemicals. 4. It takes a long time for protein adsorption to reach equilibrium. In this experiment, the solution was left to reach equilibrium for 20-24hours. During this time, lateral interactions or protein conformation may affect the solution from reaching equilibrium. The state of equilibrium is not easy to achieve and the concentration calculated after 20-24hours is only a close estimation to equilibrium concentration. 5. It was also observed that some of the resin was stuck on the tracing paper during the transfer from the weighing machine into the tube. Therefore, the noted mass in the experimental results above was an overestimation of the actual amount that was in the tube. Therefore, the adsorption capacity calculated would be smaller than actual due to this error. 6. The resin particles in the static section of the experiment may not be fully exposed to solution. Some resin particles could be stuck to walls of the tube while some particles may be stuck to one another, thus reducing the sites to which are available for adsorption. This would clearly affect the calculated adsorption capacity, causing it to deviate from literature and expected values. 7. The HLPC machine is fully automated and hardly any precautions could be taken other then to reduce contamination of solution by using fresh solutions and covering the solutions with a cap to prevent any impurities from entering the solution. Prolong use of the HLPC would cause the effectiveness of the resin to deteriorate as some protein may be stuck to some sites. To prevent this error, the adsorption capacity of the resin in the column should be monitored closely and replaced once its capacity reaches below a certain threshold value. 8. During the use of the UV spectrophotometer, only 2 culverts were provided. As a result, the culverts have to be washed after each sample. Residual amount of the previous solution would still be present after each wash, affecting the measured reading of the current sample. A solution to this is to use a new culvert for each sample. Since only 2 culverts were provided, experimenters rinsed the culverts with the new sample solution before reloading the culvert with the new sample solution. This was done to minimize contamination from the previous sample.

V. Discussion
1) Fit your data in CI to an appropriate adsorption isotherm
From the experiment conducted, q, the amount of BSA adsorbed per unit resin and C, the concentration of the protein left is determined. With the values obtained, an attempt was made to fit the experimental data into either Langmuir or Freundlich Isotherm. The isotherms can be manipulated as follows before fitting:

Isotherm Used | Equation | Linearized Form | Langmuir Isotherm | q=qmCK+C | 1q=Kqm1C+1qm | Frenudlich Isotherm | q=αC1v | lnq=lnα+1vln⁡(C) |

Langmuir Isotherm Plot:

Figure 18: Plot for 1/q vs 1/C for Langmuir Isotherm approximation

Freundlich Isotherm Plot:

Figure 19: Plot of ln(q) vs ln(C) for Freundlich Isotherm approximation
A plot of 1q vs 1C and ln(q) vs ln(C) were generated for Langmuir and Freundlich isotherms respectively. The sum of least squares, R2 can be used to determine which a better isotherm fit for the experimental data. A value closer to 1 represents a better fit of the experimental data. The summary of the isotherm fits are given below. Freundlich Isotherm | R2 | α | ν | 0.9455 | 12.556 | 0.5991 | Langmuir Isotherm | R2 | qm (Static Capacity) | K | 0.8492 | 330.033 | 5.049 |
Table 7: Summary of the R2 values and parameters of both isotherms.
From the R2 values obtained, it can be determined that Freundlich isotherm fit is a better for the experimental data as the R2 value obtained is greater than that of Langmuir isotherm and is closer to 1.

2) Distinguish between static and dynamic capacities. Based on your results in CI and CII, tabulate the static and dynamic capacities of the anion-exchange resin provided.
Static capacity refers to the absorption of the solute molecules (bovine serum albumin) onto the resin surface (Diaion HPA25) when the fluid medium containing the solute is at rest. Static capacity absorption is also commonly referred to as a semi-batch/batch process as a time frame is required for the system to attain equilibrium. The equilibrium is attained by stirring the mixture continuously over a 24 hr period. The static capacity method is not very viable for industrial use as it has limited potential.
In contrast, dynamic capacity refers to continuous absorption of the solute molecules onto the resin surface when the fluid containing solute is continuously flowing through a packed column with resin. Dynamic capacity at various flow rates can be determined by allowing the solute to flow through the column buffered with absorbent and obtaining the BTC when the inlet and outlet concentrations of the solute are equal. Dynamic capacity is preferred in the industries attributed to its continuous process and been able to use for scaling-up adsorption column.
The selectivity of the resins also plays a part in determining the extent of ion exchange in addition to static and dynamic methods used. A resin with higher selectivity for a particular protein will have greater affinity towards it and hence a greater quantity of the protein will be adsorbed onto the resin. However, various other factors such as size of pores of the resin used, the molecular weight and the structure of the solute is known to affect that static adsorption capacity as these factors in turn affect the equilibrium of the system. As a dynamic adsorption system does not attain equilibrium, these physical factors do not affect the dynamic adsorption capacity as much as the influence of the selectivity of the resin used.
In this experiment, a phosphate buffer was used to induce BSA (bovine serum albumin) adsorption onto the resin surface (Diaion HPA25) to determine both the static and dynamic adsorption capacity. The results are tabulated below: Static Capacity (mg/g) | 330.033 | Flow Rate (ml/min) | Dynamic Capacity (mg/g) | 0.5 | 2.066 | 2.5 | 1.431 | 5 | 0.918 | Table 8: Summary of the static and dynamic capacities
From the above results it can be seen that the static capacity of the resin is significantly higher than the dynamic capacity in all the three flow rates used. This agrees with theoretical understanding as more time is allowed for interaction and hence ion-exchange in the static adsorption whereas in the dynamic adsorption, the solute is in constant flow through the packed column allowing lesser time for contact and hence resulting in a notable decrease in its adsorption capacity of the resin. The dynamic capacity is also seen to be inversely proportional to the flow rate of the solute used. This is so as faster the flow rate, lesser is the time for contact and hence a decrease in the adsorption capacity of the resin.
3) Discuss the use of the ramp approximation for the BTC for scaling-up adsorption columns.
For scaling-up adsorption columns we have to consider two portions of the adsorption column. It consists of the Length of Unused Bed (LUB) and Length Equilibrium Section (LES).

Figure 20: Example of a Break Through Curve (BTC)
From the figure above, The LUB section and the LES section in the BTC can be identified. Therefore, the length of the bed behind the stoichimetric time point (ts) is called the length equilibrium section (LES), which is the required length of the bed if the system had been ideal. The other section, the LUB section, is an additional section of the bed that is required to account for the spreading of the concentration front. Therefore, the length of an adsorber bed needed for a real system is the sum of the LES and LUB.
However a general trend cannot be observed in the BTCs obtained. Hence the LUB method cannot be used (due to integration of the BTC curve). This problem is tackled by undertaking a ramp approximation as shown below:

Figure 21: A ramp approximation for BTC
The ramp function is approximated in such a way that the area below the graph remains relatively constant so as to have minimal effect on the actual experimental data. Hence, now the BTC is expressed in a general constant pattern. This allows us to use to the LUB design method to be used for scaling-up calculations.
In order to determine the stoichiometric time point (ts), it is necessary to integrate the breakthrough curve as follows ts=0te1-ccFdt The ramp approximation is used here to find ts in the following manner: ts=te-12te-tb1=12(te+tb) where te : exhaustion time tb : raw breakthrough time
Then LUB calculation is as the following:
LUB=ts-tbtsLbed
Next, the LES was calculated for the desired breakthrough time, which is one year, with the following equation:
LES=cFtb,desireduρairqFρbed
where cf is the final concentration to be achieved in the outlet, U is the fluid velocity and qF is the output flow rate.
Hence the total length of column needed for the breakthrough time will be the sum of LUB and LES. However, there are some limitations to be taken note of when using the ramp approximation. The break through curve has to be relatively steep to justify the volume that passes through after break through.
4) Based on your data in CII, which is the controlling step during adsorption in the given column?
The controlling step during the adsorption in the given column used in finding the dynamic capacity can be determined via plotting several graphs based on the typical characteristics of the standard deviation for Break Through Curve (BTC). The summary of the plots to be carried is as indicated in Table 1.
The R2 are obtained from the plots presented under the Results and Analysis section of the report Controlling Step | R2 (1) | R2 (2) | Mean | Equilibrium | 0 | 0.9998 | 0.4999 | Kinetics of adsorption | 0.4326 | 0.9924 | 0.7125 | Mass Transfer | 0.5787 | 0.9985 | 0.7886 | Dispersion | 0.4326 | 0.9924 | 0.7125 | Diffusion | 0.8714 | 0.9999 | 0.9357 | where R2 (1) is obtained from graphs proportional to σ2 and R2 (2) is obtained from graphs proportional to (t0σ)2.
Table 11: Summary of R2 values for different controlling step mechanisms.
From the table above, it can be determined that the controlling step for the adsorption of BSA in the column is diffusion controlled. However, this only applies to the narrow range of the flow rate used. For a more accurate representation of the controlling step, more flow rates should be tested to obtain more data points for the plotting of the appropriate graphs. Henceforth this information only severs as a guide for scale-up problems to predict column behavior at other velocities and lengths that were not tested for but fall within the tested range.

VI. Conclusion
The objectives of establishing the adsorption isotherm, appreciating the difference between static and dynamic capacity, understanding the use of BTCs for scaling-up processes and the different ways to use to the BTC were met in the course of the experiment.
The CI results were fitted into Freundlich Isotherm as it gave a larger R2 of 0.9455 indicating a better fit of the model.
From our CI results, the static capacity was determined from the Langmuir Isotherm approximation to be 330.033mg/g. From the CII results, the dynamic capacities were found for three flow rates. It was 0.918, 1.431 and 2.066 mg/g for flow rates 5.0, 2.5, 0.5 ml/min respectively. These results complied with theoretical knowledge that the static capacities should be larger than dynamic capacities as sufficient time were allowed for equilibrium to reach 24 hours in this experiment. Dynamic capacity also decreased with increasing flow rate as lesser contact time was allowed in each respective run.
In the second part of the experiment, σ2 and (t0σ)2 from the breakthrough curves were plotted against various characteristics which are known to have linear relationship for the controlling step. Plots σ2 vs 1/Lv and (t0σ)2 vs L/v3 gave the largest average R2 value of 0.9357 indicating that the adsorption was diffusion controlled.
Using a ramp approximation for scaling-up processes was also investigated in the discussion section of the report.
VII. References
University of California San Diego, UCSD. (n.d.). Design/Scale up. Retrieved 8 October, 2008 from:http://chemelab.ucsd.edu/aeronex/Scale-Up/Scale-Up.html
Cussler, E.L. (1997). Diffusion: Mass Transfer in Fluid Systems, 2nd ed., pp.308-330.
Paul A. Belter, E.L. Cussler, Wei-Shou Hu. Bioseparations: downstream processing for biotechnology, New York: Wiley, c1988.
Roger G. Harrison, et al. Bioseparations science and engineering, New York: Oxford University Press, 2003.

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[ 2 ]. The BSA initial concentration differs from that in the lab manual. Please refer to the error analysis section for reasons why a different value was used in calculations.