METHOD FOR MONITORING A FILTRATION PROCESS

Abstract

In at least one embodiment, the method for monitoring a filtration process in which a first solution is processed by a filter system (100) comprises: receiving first measurement data which are indicative for at least one input process variable (V1_M, V2_M), wherein the at least one input process variable (V1_M, V2_M) is a process variable of the filtration process measurable during the filtration process with help of a measurement unit (11, 31), determining output data by executing a filtration process model (4) and using the first measurement data, whereinexecuting the filtration process model (4) comprises solving at least one physical equation describing the interaction between solutes of the first solution, at least one parameter of the filtration process model (4) is dependent on the at least one input process variable (V1_M, V2_M) derived from the first measurement data, the output data is indicative for at least one modeled process variable (V3_P, V4_P) of the filtration process.

Claims

1. Method for monitoring a filtration process in which a first solution is processed by a filter system, the method comprising receiving first measurement data which are indicative for at least one input process variable, wherein the at least one input process variable is a process variable of the filtration process measurable during the filtration process with help of a measurement unit, determining output data by executing a filtration process model and using the first measurement data, wherein executing the filtration process model comprises solving at least one physical equation describing the interaction between solutes of the first solution, at least one parameter of the filtration process model is dependent on the at least one input process variable derived from the first measurement data, the output data is indicative for at least one modeled process variable of the filtration process.

2. Method according to claim 1, further comprising analyzing the output data in order to adjust the filtration process when necessary and/or wherein determining the output data is done during the filtration process and/or in real time.

3. Method according to claim 1, wherein the at least one physical equation is based on the Poisson-Boltzmann equation.

4. Method according to claim 1, wherein the filtration process model is based on a cell model approach, in the cell model approach, the first solution is reduced to a single Wigner-Seitz cell containing one molecule of a product of the first solution in its center, the radius R.sub.WS of the Wigner-Seitz cell is defined by the concentration of the product c.sub.M in the first solution and is $R_{ws}={\left(\frac{3}{4N_A{c}_M}\right)}^{\frac{1}{3}}$ with N.sub.A being the Avogadro constant.

5. Method according to claim 1, wherein at least one further parameter of the filtration process model is dependent on the composition of the first solution and/or of a second solution mixed to the first solution during the filtration process, and/or the charge and/or surface charge density of a solute in the first solution.

6. Method according to claim 1, wherein the at least one modeled process variable extractable from the output data is the concentration of a solute of the first solution and/or of a permeate of the filtration process, and/or the at least one modeled process variable is a measurable process variable, and the at least one modeled process variable is the pH value of the first solution and/or of a permeate of the filtration process.

7. Method according to claim 1, further comprising receiving second measurement data which are indicative for at least one reference process variable, wherein the at least one reference process variable is a process variable of the filtration process measurable during the filtration process with help of a measurement unit and representing the same process variable as at least one modeled process variable, comparing the at least one reference process variable with the at least one modeled process variable, adjusting at least one parameter of the filtration process model based on the comparison in order to adapt the at least one modeled process variable to the at least one reference process variable.

8. Method according to claim 1, further comprising generating a control signal based on the output data, wherein the control signal is configured for controlling at least one controllable process parameter of the filtration process and/or to call for controlling of the at least one controllable process parameter.

9. Method according to claim 1, wherein at least one solute of the first solution is a biological molecule comprising at least one of: a protein, a peptide, a nucleic acid, a virus.

10. Method according to claim 1, wherein the at least one input process variable is at least one of: pH value of the first solution, pH value of a second solution mixed to the first solution during the filtration process, electrical conductivity of the first solution and/or the second solution, absorption and/or absorbance of the first solution and/or second solution, temperature of the first solution and/or second solution, flowrate of the first solution and/or of the second solution during mixing to the first solution, information whether the second solution is currently mixed to the first solution or not.

11. Device comprising a processor configured to perform the method of claim 1.

12. Computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the method according to claim 1.

13. Computer-readable data carrier comprising instructions which, when executed by a computer, cause the computer to carry out the method according to claim 1.

14. Filter system for a filtration process comprising: a device according to claim 11, at least one measurement unit for measuring a process variable of the filtration process, a first solution reservoir for storing the first solution, a filter module with an inlet fluidically coupled to the first solution reservoir and an outlet for removing a permeate of the filtration process.

15. Filter system according to claim 14, further comprising a second solution reservoir for storing a second solution, wherein the second solution reservoir is fluidically coupled to the first solution reservoir, at least one measurement unit is arranged to measure a process variable of the first solution, and at least one measurement unit is arranged to measure a process variable of the permeate of the filtration process.

Description

[0078] Hereinafter, the method for monitoring a filtration process, the device and the filter system described herein will be explained in more detail with reference to drawings on the basis of exemplary embodiments. Same reference signs indicate same elements in the individual figures. However, the size ratios involved are not necessarily to scale, individual elements may rather be illustrated with exaggerated size for better understanding.

[0079] FIG. 1 shows an exemplary embodiment of the filter system,

[0080] FIG. 2 shows results of an exemplary embodiment of the method for monitoring a filtration process,

[0081] FIGS. 3 to 5 show flowcharts of exemplary embodiments of the method for monitoring a filtration process.

[0082] FIG. 1 shows an exemplary embodiment of a filter system 100 for a filtration process. The filter system 100 comprises a first solution reservoir 1 for storing a first solution, a filter module 2 and a second solution reservoir 3. The first solution reservoir 1 is fluidically connected to an inlet of the filter module 2 via a first connection 17. Several measurement units 11, 12, 13, 14 are assigned to the first connection 17. Measurement unit 11 may be a pH sensor for measuring the pH value of the first solution flowing through the first connection 17. Measurement unit 12 may be a conductivity sensor for measuring the electrical conductivity of the first solution flowing through the first connection 17. Measurement unit 13 may be an absorption/absorbance sensor for measuring the absorption/absorbance of radiation, e.g. of UV radiation or visible light or IR radiation, by the first solution flowing through the first connection 17. Measurement unit 14 may be a pressure sensor for measuring the pressure of the first solution in the first connection 17. A pump 16 is assigned to the first connection 17 and may control the flowrate of the first solution pumped from the first solution reservoir 1 to the filter module 2. Additionally, there may be a measurement unit in form of flowmeter for measuring the flowrate of the first solution flowing through the first connection 17.

[0083] The filter module 2 may comprise a semipermeable membrane. The semipermeable membrane may be configured to let a solvent of the first solution and some solutes, e.g. excipients, in the first solution pass but to retain a dissolved product in the first solution. The filter module 2 comprises an outlet for removing the permeate passing through the semipermeable membrane. Measurement units 21, 22, 23, 24 are assigned to this outlet or to a connection from this outlet, respectively. Measurement unit 21 may be a pH sensor for measuring the pH value of the permeate, measurement unit 22 may be configured to measure the pressure of the permeate, measurement unit 23 may be a conductivity sensor for measuring the electrical conductivity of the permeate and measurement unit 24 may be a flowmeter for measuring the flow rate of the permeate. A pump 26 is assigned to the outlet of the filter module 2 in order to remove the permeate.

[0084] The filter module 2 comprises a further outlet through which the retentate leaves the filter module. The further outlet is fluidically connected to the first solution reservoir 1 via a second connection 18 through which the retentate is guided into the first solution reservoir 1. A measurement unit 15 in form of a pressure sensor and/or a flowmeter are assigned to the second connection 18. Furthermore, a valve 19 is assigned to the second connection 18.

[0085] A second solution reservoir 3 for storing a second solution is fluidically connected to the first solution reservoir 1 via a third connection 37. The second solution may be guided through the third connection 37 into the first solution reservoir 1. A measurement unit 31, e.g. in form of a pH sensor or conductivity sensor or absorption sensor or pressure sensor or flowmeter may be assigned to the third connection 37. It is also possible to use two or more of the mentioned sensors for measuring properties of the second solution. Furthermore, a pump 36 is assigned to the third connection 37 in order to pump the second solution from the second solution reservoir 3 into the first solution reservoir 1.

[0086] As can be seen in FIG. 1, measurement signals or measurement data, respectively, measured with the different measurement units are received by a device 10. The device 10 may comprise at least one processor for performing the method for monitoring a filtration process as described herein.

[0087] The filter system 100 shown in FIG. 1 may be a filter system for performing an ultrafiltration and diafiltration (UFDF) process. At the beginning of the filtration process, an initial first solution is stored in the first solution reservoir 1 and a second solution is stored in the second solution reservoir 3. The initial first solution may comprise a dissolved product. The product may be biological molecule, like a protein, a peptide, a nucleic acid or a virus. Besides the product, the initial first solution may comprise further solutes, like amino acids, carbohydrates and/or salt ion. The second solution may comprise a solute in form of a buffer component.

[0088] In a first ultrafiltration step, no second solution is pumped into the first solution reservoir 1. The initial first solution is pumped from the first solution reservoir 1 to the filter module 2. The semipermeable membrane of the filter module 2 may allow some of the solutes but the product to pass. A permeate comprising the passed solutes can be pumped away with help of the pump 26. The remainder of the first solution (retentate) which has not passed through the semipermeable membrane comprises the product and is guided back to the first solution reservoir 1. The retentate gradually replaces the initial first solution so that that the composition of the first solution changes. During this ultrafiltration step, the concentration of the product in the first solution is increased.

[0089] After that, a diafiltration step may be performed in which the second solution containing the buffer component is pumped into the first solution reservoir 1 with help of the pump 36 and is mixed to the first solution. At the same time, the first solution is pumped from the first solution reservoir 1 through the filter module 2. For example, the flowrate of the second solution pumped into the first solution reservoir 1 is the same as the flowrate of the permeate pumped away from the filter module 2 with help of the pump 26. Thus, the volume of the first solution containing the product remains constant. Moreover, when the flowrates are equal, also the concentration of the product in the first solution remains constant. However, the composition of the first solution containing the products changes due to removal of the permeate containing solutes and the adding of the second solution containing the buffer component.

[0090] After the diafiltration process, a second ultrafiltration step may be performed, in which again no second solution is pumped into the first solution reservoir 1 but only permeate is removed. In this step, the product may be concentrated in the first solution to its final concentration.

[0091] The device 10 may be configured to perform the method for monitoring the filtration process. An exemplary embodiment of the method is as follows: In one step, first measurement data are received by the device 10. The first measurement data are indicative for at least one input process variable, e.g. for the pH value of the second solution and the pH value of the first solution at the beginning of the filtration process, i.e. the pH value of the initial first solution. In a further step of the method, output data are determined by executing a filtration process model 4 using the first measurement data. The execution of the filtration process model 4 comprises solving a physical equation describing the interaction between the solutes of the first solution, wherein at least one parameter of the process filtration model, e.g. of the physical equation, is dependent on the at least one input process variable extractable from the first measurement data. The output data are indicative for at least one modeled process variable of the filtration process, e.g. for the concentration of the product in the first solution and/or the pH value of the permeate as a function of time.

[0092] An exemplary embodiment of the filtration process model 4 may be as follows:

1. Mass Balance

[0093] The filtration process model 4 may predict the concentration of solutes in the retentate/first solution by solving global mass balance equations for the filter system 100. The mass balance equations are solved based on measurements in the second solution and in the first solution. The mass balance equations consider interactions between the product and other solutes, e.g. excipients.

[0094] Solution streams going in and out of the filter module 2 are considered to contain small solutes like buffer substances, carbohydrates, and amino acids with a concentration c.sub.i. The product, e.g. a protein, on the other hand, cannot pass through the semipermeable membrane and, therefore, is fully retained in the retentate. The product concentration c.sub.M in the retentate is therefore defined by the mass balance

[00003]$\begin{array}{cc}\frac{{\mathrm{dc}}_M\left(t\right)}{\mathrm{dt}}=-\frac{c_M\left(t\right)}{V_{\mathrm{Ret}}\left(t\right)}\left(Q_{\mathrm{DF}}\left(t\right)-Q_{\mathrm{Perm}}\left(t\right)\right),& \left(1\right)\end{array}$

where t represents the process time, V.sub.Ret is the total retentate volume within the system, Q.sub.DF is the flowrate of the second solution added to the first solution, and Q.sub.Perm is the flowrate of the permeate. The index Ret is herein used for the retentate/first solution, the index DF is used for the second solution and the index Perm is used for the permeate. The flowrates Q.sub.DF and Q.sub.Perm can be measured, for instance, using flowmeters. The temporal change of V.sub.Ret is defined by the balance

[00004]$\begin{array}{cc}\frac{{\mathrm{dV}}_{\mathrm{Ret}}\left(t\right)}{\mathrm{dt}}=Q_{\mathrm{DF}}\left(t\right)-Q_{\mathrm{Perm}}\left(t\right).& \left(2\right)\end{array}$

[0095] During ultrafiltration, no second solution is added to the first solution (Q.sub.DF=0) and the product is concentrated. During diafiltration, the volumetric flowrate of the second solution is assumed to be equal the volumetric flowrate of the permeate (Q.sub.DF=Q.sub.Perm) and V.sub.Ret is constant.

[0096] Small solutes, particularly excipients, like buffer components and amino acids in the first solution are not retained by the filter module 2 and can leave the filter system 100 via the outlet of the filter module 2 as described by

[00005]$\begin{array}{cc}\frac{{\mathrm{dc}}_{\mathrm{Ret},i}\left(t\right)}{\mathrm{dt}}=\frac{Q_{\mathrm{DF}}\left(t\right)}{V_{\mathrm{Ret}}\left(t\right)}\left(c_{\mathrm{DF},i}\left(p{H}_{\mathrm{DF}}\right)-c_{\mathrm{Ret},i}\left(t\right)\right)-\frac{Q_{\mathrm{Perm}}\left(t\right)}{V_{\mathrm{Ret}}\left(t\right)}\left(c_{\mathrm{Perm},i}\left(t,c_M,c_{\mathrm{Ret}},p{H}_{\mathrm{Ret}}\right)-c_{\mathrm{Ret},i}\left(t\right)\right).& \left(3\right)\end{array}$

[0097] Solving the ordinary differential equations above, the product concentration c.sub.M(t), the first solution volume V.sub.Ret(t), and the excipient concentrations c.sub.Ret,i(t) can be described as a function of the process time. The concentration of the excipients inside the permeate

[00006]$\begin{array}{cc}{c}_{\mathrm{Perm},i}=f\left(t,c_M,c_{\mathrm{Ret}},p{H}_{\mathrm{Ret}}\right)& \left(4\right)\end{array}$

is thereby a function of the current concentrations in the retentate c.sub.Ret, the product concentration c.sub.M, and the pH value in the retentate pH.sub.ret. The concentration of an excipient inside the second solution

[00007]$\begin{array}{cc}{c}_{\mathrm{DF},i}=f\left(p{H}_{\mathrm{DF}}\right)& \left(5\right)\end{array}$

may be a function of the measured pH value in the second solution (pH.sub.DF).

2. Composition of Solutions

[0098] The filtration process model 4 may use the pH value of the second solution, equilibrium equations, and the conditions of electroneutrality in the second solution reservoir 3 to determine the composition of the second solution mixed to the first solution via pump 36. Likewise, the composition of the first solution can be determined. Therefore, the following formulas are applicable for the first solution as well.

[0099] The second solution (as well as the first solution and the permeate) may contain various solutes, particularly excipients, such as buffer components, amino acids and salts. Depending on the pH value, some of these excipients can be present in different protonation states and thus ionized forms. Therefore, the exact ion composition of the second solution depends on the pH value. Considering, for instance, a second solution that contains a buffer component i with known total concentration c.sub.i. The buffer component possesses n dissociation sites. In this case, the buffer component i itself can be present in n+1 ionization states. Thus, the total concentration of buffer component i is equal to

[00008]$\begin{array}{cc}{c}_i={.Math.}_{j=1}^{n+1}{c}_{i,j}\left(pH\right),& \left(6\right)\end{array}$

where c.sub.i,j is a function of the pH value. The first ionization state j=1 denotes the fully protonated state indicated by H.sub.nA.sup.m, where m represents the charge of the fully protonated state. Considering the general dissociation reaction of the buffer substance

[00009]$\begin{array}{cc}{H}_{n-j+1}{A}^{m-j+1}{H}_{n-j}{A}^{m-j}+H^{+}& \left(7\right)\end{array}$

and its equilibrium constant

[00010]$\begin{array}{cc}{K}_j^{*}=\frac{\left[H_{n-j}{A}^{m-j}\right]}{\left[H_{n-j+1}{A}^{m-j+1}\right]}10^{-pH},& \left(8\right)\end{array}$

the concentrations of the ionization states are defined by the measured pH value according to

[00011]$\begin{array}{cc}{c}_{i,1}\left(pH\right)={c_i\left(10^{-pH}\right)}^n{\left({\left(10^{-pH}\right)}^n+{.Math.}_{k=1}^n{\left(10^{-pH}\right)}^{n-k}{.Math.}_{l=1}^k{K}_l^{*}\right)}^{-1}& \left(9\right)\end{array}$$\mathrm{and}$$$\begin{gathered} \begin{array}{cc}{c}_{i,j}\left(pH\right)={c_i\left(10^{-pH}\right)}^{n-j+1}{.Math.}_{k=1}^{j-1}{K_k^{*}\left({\left(10^{-pH}\right)}^n \\ +{.Math.}_{k=1}^n{\left(10^{-pH}\right)}^{n-k}{.Math.}_{l=1}^k{K}_l^{*}\right)}^{-1},j=2.Math.n+1.& \left(10\right)\end{array} \end{gathered}$$

[0100] In the second solution, the charge of all ionized forms is balanced by counter-ions. The concentration of these counter-ions entering the mass balance equation above is not known but can be derived from the condition of electroneutrality in the second solution reservoir 3. If the charge of the j-th ionization state is denoted by z.sub.i,j, the concentration of counter-ions c.sub.c results from the electroneutrality condition

[00012]$c_C\left({pH}_{DF}\right)=\left|\underset{i}{.Math.}\underset{j}{.Math.}{z}_{i,j}{c}_{i,j}\left({pH}_{DF}\right)\right|.$

3. Product-Excipient Interaction

[0101] The filtration process model 4 may use the Poisson-Boltzmann equation to describe interactions between the product and smaller solutes (excipients) in the first solution.

[0102] If we assume that the retentate/first solution and the permeate are in thermodynamic equilibrium (Donnan equilibrium), the relationship c.sub.Perm,i=f (t, c.sub.M, c.sub.Ret, PH.sub.Ret) in the mass balance above is given by the Boltzmann relation

[00013]$\begin{array}{cc}{c}_{P\mathrm{erm},i}=\underset{j}{.Math.}\frac{c_{Ret,i,j}}{1-}\exp \left(z_{i,j}\frac{e\stackrel{}{}\left(c_{M,}{c}_{\mathrm{Ret},}{pH}_{ret}\right)}{k_{b}T}\right),& \left(11\right)\end{array}$

where is the average electrostatic potential in the first solution, k.sub.b represents the Boltzmann constant, T is the absolute temperature, N.sub.A is the Avogadro number, and

[00014]$\begin{array}{cc}=\frac{4}{3}{a}_M^3{c}_M{N}_A& \left(12\right)\end{array}$

describes the volume fraction of the first solution occupied by the product with known radius a.sub.M. The product z.sub.i,je in the exponent is a measure for the interaction between an excipient and the product. If the term is positive, the excipient is repelled by the product. If the term is negative, the excipient is attracted by the product and retained within the retentate. The average electrostatic potential can be interpreted as the Donnan potential describing the unequal solute concentration distribution across the membrane due to interactions between the product and other solutes. It must suffice the electroneutrality condition on the permeate side

[00015]$\begin{array}{cc}0=\underset{i}{.Math.}\underset{j}{.Math.}{z}_{i,j}{c}_{Perm,i,j}=\underset{i}{.Math.}\underset{j}{.Math.}{z}_{i,j}\frac{c_{Ret,i,j}}{1-}\exp \left(z_{i,j}\frac{e\stackrel{}{}\left(c_{M,}{c}_{\mathrm{Ret},}{pH}_{ret}\right)}{k_{b}T}\right)& \left(13\right)\end{array}$

and the Poisson-Boltzmann equation on the retentate side

[00016]$\begin{array}{cc}\frac{{}^2\left(r\right)}{r^2}+\frac{2}{r}\frac{\left(r\right)}{r}=-\frac{e}{{}_0}\underset{i}{.Math.}{z}_i\frac{c_{Ret,i}}{1-}\exp \left(\frac{z_{i}e}{k_{b}T}\left(\left(r\right)-\stackrel{}{}\right)\right).& \left(14\right)\end{array}$

[0103] The Poisson-Boltzmann equation may be solved using the cell model. Within the cell model, the first solution is reduced to a single Wigner-Seitz (WS) cell containing one product molecule at its center. The WS cell may be spherical in shape. In this case, the radius of the WS cell R.sub.WS is defined by the product concentration according to

[00017]$\begin{array}{cc}{R}_{ws}={\left(\frac{3}{4N_A{c}_M}\right)}^{\frac{1}{3}}.& \left(15\right)\end{array}$

[0104] Using the cell model, the Poisson-Boltzmann equation can be solved numerically using the boundary condition

[00018]$\begin{array}{cc}\frac{}{r}{|}_{r=a_M}=-\frac{e{z}_M\left({pH}_{ret}\right)}{4a_M^2{}_0}& \left(16\right)\end{array}$

at the surface of the product molecule, and the condition

[00019]$\begin{array}{cc}\frac{}{r}{|}_{r=Rws}=0& \left(17\right)\end{array}$

at R.sub.WS, where z.sub.D represents the net charge of the product molecule. Solving the Poisson-Boltzmann equation leads to (c.sub.M, c.sub.Ret, PH.sub.ret) and thus c.sub.Perm,i=f (t, c.sub.M, c.sub.Ret, PH.sub.Ret) for the mass balance equation.

Product Charge

[0105] The filtration process model 4 calculates the charge of the product z.sub.M(pH.sub.ret) used in the Poisson-Boltzmann equation above based on the known primary sequence when the product is a protein.

[0106] The net charge of the protein z.sub.M can be derived theoretically from the known primary sequence of the protein. Proteins are biopolymers which are based on amino acids as building blocks. The order in which the amino acids are arranged in the polypeptide chain defines the protein's primary sequence. The net charge depends on the number of ionizable amino acids in the primary sequence and their pKa values. Considering an ionizable amino acid side chain j with charge .sub.j of the protonated form HA.sup.i, the dissociation reaction

[00020]${HA}^{{}_j}{A}^{{}_j-1}+H^{+}$

is defined by the equilibrium constant of the amino acid

[00021]$K_j=10^{-\mathrm{pKj}}=\frac{\left[A^{{}_j-1}\right]}{\left[{HA}^{{}_j}\right]}10^{-pH},$

whereby square brackets depict molar concentrations. The ionizable amino acids may, e.g., include arginine, histidine, lysine, aspartic acid, and glutamic acid. In this case, z.sub.M is defined by

[00022]$\begin{array}{cc}{z}_M\left({pH}_{ret}\right)=\underset{j}{.Math.}{N}_j\frac{{}_j+\left({}_j-1\right)10^{{pH}_0-{\mathrm{pK}}_j}}{1+10^{{pH}_0-p{K}_j}},& \left(18\right)\end{array}$

where N.sub.j denotes the number of the j-th ionizable side chain in the primary sequence and pH.sub.0 is the pH-value at the surface of the protein defined by

[00023]$\begin{array}{cc}{pH}_0={pH}_{ret}+\frac{1}{\ln \left(10\right)}\frac{e}{k_{b}T}\left(\left(a_M\right)-\stackrel{}{}\right).& \left(19\right)\end{array}$

[0107] FIG. 2 shows modeled process variables extracted from the output data obtained by using this filtration process model 4. The filtration process model 4 was applied to describe the ultrafiltration and diafiltration (UFDF) process of the protein glucose oxidase as the product of the first solution. The charge of the product glucose oxidase was calculated using the following table:

TABLE-US-00001 Amino acid Quantity pK value Lysine 30 10.4 Arginine 44 12.0 Histidine 38 6.3 Glutamic acid 60 4.4 Aspartic acid 72 4.0 tyrosine 54 9.6 N termini 2 7.5 C termini 2 3.8

[0108] At the beginning of the UFDF process, the protein was dissolved in 50 mM sodium acetate buffer with 50 mM sodium chloride (pH 6.5). The initial protein concentration in the initial first solution was 5 g/L. During a first ultrafiltration step (UF1), the protein was concentrated to an intermediate concentration of 50 g/L. Afterwards, the protein was diafiltrated over 10 diavolumes (DV) using 20 mM succinate as the second solution (pH 7.0). In a second ultrafiltration step (UF2), the first solution was concentrated to a final protein concentration of 180 g/L.

[0109] The ordinary differential equations (ODEs) Eq. (1)-Eq. (3) were solved in MATLAB (The Mathworks, Natick, Massachusetts, USA) using the ODE solver ode15s. At every time step, pH.sub.ret and were determined iteratively so that is in compliance with both the electroneutrality condition in the permeate [Eq. (13)] and the Poisson-Boltzmann equation in the first solution [Eq. (14)]. First, pH.sub.ret was guessed and used to determine the concentrations of microions c.sub.Ret,i,j is the retentate/first solution according to the buffer equilibrium Eq. (9)-Eq. (10). Knowing c.sub.Ret,i,j, was determined to suffice the electroneutrality condition on the permeate side [Eq. (13)]. Afterwards, the Poisson-Boltzmann equation within the WS cell was solved using Eq. (18) for z.sub.M of glucose oxidase. Using for example a regula falsi approach, the unknown pH.sub.ret can be varied until sufficed both the electroneutrality condition [Eq. (13)] and the Poisson-Boltzmann equation within the WS cell. Alternatively, the pH in the first solution pH.sub.ret can be derived from measurement data that are indicative for pH.sub.ret.

[0110] The filtration process model 4 of this exemplary embodiment determines output data which are indicative for the modeled process variable which are: the pH values of the permeate and the retentate and concentrations of different solutes.

[0111] The upper picture of FIG. 2 shows the pH values of the permeate (dashed line) and the retentate (solid line) as a function of the product concentration in the retentate or first solution. As the product concentration increases with time during the filtration process, the x-axis also represents a time axis. The different steps of the filtration process UF1, DF, and UF2 are also indicated.

[0112] In the second picture of FIG. 2, the concentration of an excipient, namely of acetate, in the permeate (dashed line) and the retentate (solid line) as a function of the product concentration in the retentate is shown.

[0113] In the third picture of FIG. 2, the concentration of an excipient, namely of succinate, in the permeate (dashed line) and the retentate (solid line) as a function of the product concentration in the retentate is shown.

[0114] In the fourth picture of FIG. 2, the concentration of an excipient, namely of chloride, in the permeate (dashed line) and the retentate (solid line) as a function of the product concentration in the first retentate is shown.

[0115] FIG. 3 shows a flowchart of an exemplary embodiment of the method for monitoring a filtration process. The filtration process is, e.g., done with the filter system 100 of FIG. 1. First measurement data which are indicative for two input process variables V1_M, V2_M measured with help of two measurement units 11, 31 are received and used as an input for the filtration process model 4. The input process variables may be, e.g., the pH value of the second solution V2_M and the pH value of the first solution V1_M at the beginning of the filtration process. However, also additional or other input process variables, like the electrical conductivity and/or the absorption of the first solution and the second solution may be used. The filtration process model 4 is, e.g., the model as described before. Parameters of this filtration process model 4 dependent on the input process variables V1_M, V2_M.

[0116] With help of the filtration process model 4, output data are generated which are indicative for modeled process variables V3_P, V4_P. The modeled process variable V3_P may be, e.g., the concentration of the product and/or excipients in the first solution as a function of time. The modeled process variable V4_P may be, e.g., the pH value of the retentate and/or of the permeate (see also first picture of FIG. 2). Additionally or alternatively, the modeled process variable V4_P could be the absorption and/or the electrical conductivity of the permeate and/or retentate. The modeled process variables may, e.g., be displayed on a screen. A user may then study the modeled process parameters V3_P, V4_P.

[0117] FIG. 4 shows a flowchart of a further exemplary embodiment of the method for monitoring a filtration process. The method is similar to the one described in connection with FIG. 3. However, in FIG. 4, second measurement data are additionally received which are indicative for a reference process variable V4_R measured with the measurement unit 21. The reference process variable V4_R may be, e.g., the pH value of the permeate at a certain time during the filtration process. In a further step of the method, the modeled process variable V4_P at that certain time may now be compared with the reference process variable V4_P. Based on this comparison, the filtration process model 4 may be adapted. For example, a parameter of the filtration process model, e.g. the assumption about the composition of the first solution at the beginning of the filtration process and/or of the second solution is adapted based on this comparison. In this way, the modeled process variable V4_P can be adapted to the reference process variable V4_R. In this way, the filtration process model 4 can be optimized during the filtration process in order to better describe the actual measured reference process variable(s).

[0118] FIG. 5 shows yet another exemplary embodiment of the method for monitoring a filtration process. This exemplary embodiment is similar to the one of FIG. 4. However, in case of FIG. 5, a control signal is generated based on the output data of the model 4, particularly based on the modeled process variable V3_P. For example, the modeled process variable V3_P represents the concentration of the product or another solute in the first solution and/or in the permeate as a function of time. The modeled process variable V3_P may be compared to a desired concentration of the product or the solute during or at the end of the filtration process. This comparison may be done automatically, e.g. by the device 10. If the deviation between the modeled process variable V3_P and the desired value exceeds a certain threshold, a control signal may be generated in order to adjust the filtration process or in order to call for an adjustment of the filtration process. The generation of the control signal may also be done by the device 10. For example, the control signal may be used to control a controllable process parameter and/or an actuator of the filter system 100. By way of example, the controllable process parameter may be the time of the different filtration steps UF1, DF, UF2 and/or the flowrate with which the permeate is removed from the filter module 2 and/or the flowrate with which the second solution is mixed to the first solution during the diafiltration step DF. This may be done by controlling at least one of the pumps 26 and 36 and/or the valve 19. Also, the controlling of the pump(s) may be done automatically.

[0119] The invention described herein is not limited by the description in conjunction with the exemplary embodiments. Rather, the invention comprises any new feature as well as any combination of features, particularly including any combination of features in the patent claims, even if said feature or said combination per se is not explicitly stated in the patent claims or exemplary embodiments.

REFERENCE NUMBER LIST

[0120] 1 first solution reservoir [0121] 2 filter module [0122] 3 second solution reservoir [0123] 4 filtration process model [0124] 10 device [0125] 11, . . . , 15 measurement unit [0126] 16 pump [0127] 18 second connection [0128] 21, . . . , 24 measurement unit [0129] 26 pump [0130] 31 measurement unit [0131] 36 pump [0132] 37 third connection [0133] 100 filter system [0134] V1_M, V2_M input process variable [0135] V3_P, V4_P modeled process variable [0136] V4_R reference process variable [0137] UF1 first ultrafiltration step [0138] UF2 second ultrafiltration step [0139] DF diafiltration step