Peak broadening in small columns is dominated by spreading in the extra column volume and not by hydrodynamic dispersion or mass transfer resistances. Computational fluid dynamics (CFD) permits to study the influence ofthese effects separately.
Journal of Chromatography A, 1599 (2019) 55–65 Contents lists available at ScienceDirect Journal of Chromatography A journal homepage: www.elsevier.com/locate/chroma Dissecting peak broadening in chromatography columns under non-binding conditions Dmytro Iurashev a , Susanne Schweiger a , Alois Jungbauer a,b , Jürgen Zanghellini a,b,c,∗ a b c Austrian Centre of Industrial Biotechnology, 1190 Vienna, Austria University of Natural Resources and Life Sciences, 1190 Vienna, Austria Austrian Biotech University of Applied Sciences, 3430 Tulln, Austria a r t i c l e i n f o Article history: Received January 2019 Received in revised form 27 March 2019 Accepted 28 March 2019 Available online 30 March 2019 MSC: 00-01 99-00 Keywords: Computational fluid dynamics Scalability Peak broadening effects Extra column volume Hydrodynamic dispersion Film mass transfer Pore diffusion Mass transfer mechanism a b s t r a c t Peak broadening in small columns is dominated by spreading in the extra column volume and not by hydrodynamic dispersion or mass transfer resistances Computational fluid dynamics (CFD) permits to study the influence of these effects separately Here, peak broadening of three single component solutes – silica nanoparticles, acetone, and lysozyme – was experimentally determined for two different columns (100 mm × mm inner diameter and 10 mm × mm inner diameter) under non-binding conditions A mass transfer model between mobile and stationary phases as well as a hydrodynamic dispersion model ® were implemented in the CFD environment STAR-CCM+ The mass transfer model combines a model of external mass transfer with a model of pore diffusion The model was validated with experiments performed on the larger column We find that extra column volume plays an important role in peak broadening of the silica nanoparticles pulse in that column; it is less important for acetone and is weakly pronounced for lysozyme Hydrodynamic dispersion plays the dominant role at low and medium flow rates for acetone because we are in a regime of 1–10 ReSc Mass transfer is important for high flow rates of acetone and for all flow rates of lysozyme Then, peak broadening was predicted in the smaller column with the packed bed parameters taken from larger column The scalability of the prepacked columns is demonstrated for acetone and silica nanoparticles by excellent agreement with the experimental data In contrast to the larger column, peak broadening in the smaller column is dominated by extra column volume for all solutes Peak broadening of lysozyme is controlled only at high flow rates by mass transfer and overrides extra column volume and hydrodynamic dispersion CFD simulations with implemented mass transfer models successfully model peak broadening in chromatography columns taking all broadening effects into consideration and therefore are a valuable tool for scale up and scale down Our simulations underscore the importance of extra column volume © 2019 The Author(s) Published by Elsevier B.V This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) Introduction Peak broadening under non-binding conditions is caused by extra column dispersion, hydrodynamic dispersion in the column and mass transfer resistances [1] The (relative) contribution of these mechanisms varies at different scales For instance, in process development, virus clearance studies and exploration of the design space are done at very small scale [2,3] Here we observed completely different dispersion mechanism compared to pilot and full scale operation [4,5] Thus, knowledge about the performance ∗ Corresponding author E-mail address: juergen.zanghellini@boku.ac.at (J Zanghellini) URL: http://www.biotec.boku.ac.at/19055.html (J Zanghellini) at each scale is of utmost importance in preparative and industrial chromatography of proteins, because during scale up and scale down we may over or underestimate the separation power of a column with severe consequences Despite the tremendous importance of chromatographic separation in downstream processing, a reliable quantitative understanding of the dispersion mechanisms involved is currently lacking [6] General (theoretical) descriptions of dispersion mechanisms have often been made by neglecting extra column dispersion [7,8] This assumption is valid when the column is sufficiently large and extra column dispersion can be neglected [9–12] In protein chromatography, however, it is not practicable to use such columns as the costs of material consumption for these experiments are prohibitively large Moreover, the effect of extra column dispersion is difficult to assess experimentally [9,13,14] https://doi.org/10.1016/j.chroma.2019.03.065 0021-9673/© 2019 The Author(s) Published by Elsevier B.V This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/) 56 D Iurashev et al / J Chromatogr A 1599 (2019) 55–65 Fig ÄKTA pure 25 M2 chromatography workstation; schematic drawing Extra column volume is shown with continuous lines Chromatography column is detailed in Fig Attempts have been made to extrapolate from total peak dispersion of columns with different sizes to the extra column dispersion This approach is time consuming, because several experiments must be conducted with columns of different length but same column inlet an outlet While the extra column dispersion remains identical in this experimental design the dispersion in the column increases [12] To overcome theses problems, we utilize computational fluid dynamics (CFD) to analyze the flow properties of chromatography columns In fact, CFD simulations have the potential to provide deeper insight into the different dispersion processes [15,16] and predict the (relative) contribution of each effect [17,18] It was shown that CFD modelling with resolved extra-particle channels in chromatography columns can quantify components of hydrodynamic dispersion in packed beds on different length and time scales [19] Moreover, such micro-scale simulations in combination with mass-transfer models are able to mimic adsorption [20] as well as adsorption and diffusion in the beads [21] To reduce the computational burden, we performed simplified macro-scale simulations that not resolve extra-particle channels Rather packed beds are modelled as medium with uniform porosity Here we demonstrate that a properly calibrated CFD simulation is not only able to properly dissect the impact of various dispersion mechanisms, but is also able to accurately extrapolate the qualities of a chromatography column Specifically, we experimentally characterized a large chromatography column with three different solutes, reconstructed and calibrated the experimental setup in silico, and (quantitatively correctly) predicted the contributions of individual peak broadening mechanisms in an identically constructed smaller column Materials and methods 2.1 Chromatographic workstation All experiments were made on an ÄKTA pure 25 M2 chromatography system (GE Healthcare), schematically shown in Fig and Table Extra particle porosity , particle parameter dp , pore size sp , inner diameter Di , length L, and volume Vc of the used columns Column ID 8–100 5–10 [–] 0.318 0.318 dp [m] sp [nm] Di [mm] L [mm] Vc [mL] 75 75 100 100 100 10 5.027 0.1964 detailed in supplementary Table S1 The total volume of all of the parts of the workstation from the middle of the injection loop to the middle of the UV detector (without the columns) is the extra column volume = 0.208 mL The used parts of the workstation (injection loop, valves, tubing and detectors) are simulated by CFD simulations in their respective dimensions 2.2 Chemicals Tris, sodium chloride and disodium hydrogen phosphate dehydrate were purchased from Merck Millipore Acetone was obtained from VWR Silica nanoparticles (1000 nm diameter, surface plain) were purchased from Kisker Biotech Lysozyme from chicken egg white was obtained from Sigma Aldrich 2.3 Columns Two pre-packed MiniChrom columns (Repligen) were used for the experiments and reconstructed in silico, see Fig The filters of both columns were made out of polypropylene/ polyethylene fibers and had a thickness of 0.42 mm Assuming a 50:50 mixture of the two polymers, the density and the weight of the membrane were used to calculate a porosity of the filters of 0.51 The columns were packed with Toyopearl Gigacap S-650M (Tosoh) This strong cation exchange medium has a particle diameter of dp = 75 m and a pore size of 100 nm The main parameters of the two evaluated columns, referred to as “8–100” and “5–10”, are summarized in Table Other dimensions are listed in Supplementary Table S2 D Iurashev et al / J Chromatogr A 1599 (2019) 55–65 57 Fig MiniChrom chromatography column of the setup shown in Fig 2.4 Pulse response experiments Silica nanoparticles were used to characterize the flow behaviour outside of the beads since their diameter was too large to penetrate the pores 10 L of mixture was injected into the column; HQ-H2 O was used as mobile phase The extra particle porosity was calculated based on the peak maximum of the peak profile measured at the UV detector at a wavelength of 280 nm and was equal for all the further discussed solutions Acetone was used as a small non-interacting tracer Due to its small molecular size, it is able to diffuse into the interior of the beads Acetone was injected at a concentration of 1% (v/v) at a volume of 10 L to the column The mobile phase was 50 mM Tris, 0.9% (w/v) sodium chloride, pH 8.0 (pH adjusted with HCl) The total porosity t of the packed bed was calculated from the first peak moment corrected by the extra column volume (determined by pulses through the workstation alone [22,9]) of the runs through the 8–100 column at a superficial velocity of 150 cm/h from triplicate measurements Lysozyme was injected at non-binding conditions to the column in order to evaluate hindered diffusion of large molecules inside the pores 10 L lysozyme at a concentration of mg/mL was injected in running buffer (25 mM Na2 PO4 , M NaCl, pH 6.5) to the column The total porosity t of the 8–100 column was calculated in the same way as for acetone; it is smaller than for acetone since not the whole pore space is accessible to lysozyme The effective diffusivity of lysozyme inside the pores was determined by direct numerical integration of the peaks at velocities from 60 to 150 cm/h and calculated as described in Section Parameters of the solutes used are summarized in Table 2.5 Simulations The program used for CFD simulations is STAR-CCM+® (Siemens PLM Software, Plano, TX, USA) Eq (10) was already present in the software The source term on the right hand side of Eq (9) as well as Eqs (11)–(16) are incorporated into the software The coefficient of hydrodynamic dispersion is computed by Eq (S.4.2) The flow of the solutes is modelled as passive scalar transport, i.e., flow properties not depend on the solute concentration Indeed, concentrations of the solutes are so low that their influence on the thermophysical parameters are negligible [23] We assume that porosity is uniform and particles are of the same size (i) Radial variations of porosity were neglected since the col- umn to particle diameter ratios are much larger than 30 [24,25] (67 and 107 for the smaller and larger column, respectively) (ii) For narrow particle size distributions results are not affected by these distributions [26] These authors [26] define “narrow” if the ratio of dp90 /dp10 for a packing is around 1.5, which is the case in our setups dp90 and dp10 denote particle diameter values above and below which 10% of the total particle weight are found Two types of axisymmetric model setups were used to show the influence of the extra column effects 2.5.1 Without extra column volume This setup covers only the chromatography column (parts No 8–16 in Supplementary Table S2) with short tubes (radius 0.125 mm, length 10 mm) added before and after the column A numerical quadrilateral mesh consisting of 26,493 and 11,395 cells was generated in this setup for the 8–100 and 5–10 column, respec® ® tively Computational time of each run on cores of Intel Xeon Processor E5-2643 v4 was and 3.5 h for the larger and the smaller column, respectively Value of the passive scalar at the inlet boundary is When the volume of the Injection Loop (see Fig and Table S1) has entered the setup, this boundary condition changes to value The reported peaks are postponed by extra column volume value normalized by column volume, since the extra column volume is absent in this setup 2.5.2 With extra column volume This setup contains not only the column but all parts listed in Supplementary Tables S1 and S2 The numerical mesh contained 164,513 and 149,269 cells for the 8–100 and 5–10 column, respectively (see Supplementary Fig S1) Computational time of each run ® ® on cores of Intel Xeon Processor E5-2643 v4 was 29 and 26 h for the larger and the smaller column respectively In order to verify that the resolution of the used mesh was sufficient, several runs with a finer mesh with 378,300 cells (about 2.53 times more than the rough mesh) were performed in the smaller column, which resulted in a difference of less than 0.7% in terms of normalized root mean square deviation (NRMSD), see Eq (3) The initial condition of the simulations imitates the one of the experiment – the value of the passive scalar is equal to in the Injection Loop, and to elsewhere We modelled the pulse response experiments (see Section 2.4) of the three solutes acetone, lysozyme, and silica nanoparticles The solutes vary by their ability to diffuse into the beads Thus different transport equations are used 58 D Iurashev et al / J Chromatogr A 1599 (2019) 55–65 Table Parameters of the pulse response experiments on the 8–100 column Values are determined for the 8–100 column and assumed to be identical to the values of the 5–10 column Calculations of De values are presented in Appendix C Solute t Silica nanoparticle Acetone Lysozyme [–] 0.318 0.831 0.658 u [cm/h] D0 [cm2 /s] 250 30–500 60–500 4.29E−9 1.16e−5 1.1e−6 Silica nanoparticles not enter into the beads, thus Eq (10) is used to simulate their transport through the chromatography column Since both acetone and lysozyme can diffuse into the beads, transport Eq (9) is employed Additionally, when acetone and lysozyme diffusion into the beads pores is assumed to be infinitely fast, the simplified transport Eq (17) is used Two columns described in Section 2.3 are used to model silica nanoparticles, acetone and protein pulse propagation Both numerical setup types – with and without extra column volume – are used to model transport of the solutes The diffusion–dispersion coefficient is calculated by Eq (18) only for the packed bed region; elsewhere it is equal to the diffusion coefficient and dispersion is modelled explicitly In this work, the concentrations are normalized by their maximum values; the volume passed through the setup and moments of the distributions are normalized by the respective column volume De [cm2 /s] Sc [–] v’ [–] CL [–] 4.3e−6 1.07e−7 2.33E+6 7.68e+2 9.545e+3 1.64E+9 16.9–282 357–2978 0.5 1.35–2.23 3.47–3.6 Theory 3.1 Column porosity Three different porosities can be distinguished in a chromatography column: (i) The extra particle porosity, , which is the ratio of the fluid volume outside of the particles to the column volume; (ii) the intra particle porosity, p , which describes the intrinsic porosity of the beads and is given by the ratio of the fluid inside the beads to the bead volume, and (iii) the total porosity, t , which is the ratio of the total fluid volume in the column (including the fluid held inside the beads) to the column volume These three porosities are related by [1]: t = + (1 − ) p (4) 3.2 Determination of effective diffusivity 2.6 Moments computation When in-pores diffusion does not dominate in mass transfer as for acetone, De can be computed by [1] The time dependence of the solute concentration at the UV detector (or at the outlet for the simulations without extra column volume) is approximated by an exponentially modified Gaussian distribution [1]: cd (t) = 2 ∼ exp ∼ + ∼ ∼2 ∼ / − 2t ∼ erfc + ∼2 ∼ / −t √ ∼ (1) The parameters ˜ , ˜ , and ˜ were estimated by least square fitting of the experimental and simulated data to Eq (1) The mean , variance , skewness and reduced height equivalent to a theoretical plate (HETP) h were calculated as [1]: = ˜ + ˜, ∼3 =2 ∼3 = ˜ + ˜ 2, ∼2 , h= ∼2 L (2a) (2b) dp Agreement between simulations and experiments is measured by the NRMSD, T (5) p, where D0 is the molecular diffusion of the solute in the solvent, p is the tortuosity factor of the in-beads pores, and p is the diffusional hindrance coefficient Alternatively, the effective diffusivity can be determined from non-interacting pulse injections at different velocities The resulting pulses are evaluated in terms of HETP and a Van Deemter plot is generated In case of mass transfer limited diffusion as for proteins, the slope of the Van Deemter plot is positive and linear and equivalent to the constant C of the Van Deemter equation Using Eq (6) the effective diffusivity De can be calculated from the C, the extra particle porosity , the retention factor k and the particle diameter dp [1]: De = k 1+k 1− dp2 30C (6) The velocity field in the workstation and in the columns is determined by solving the momentum equation for a stationary laminar flow of an incompressible fluid [27]: u∇ u + ∇ p − ∇ u = 0, (7) ∞ ( −∞ p 3.3 Transport equations 2.7 Quality assessment NRMSD = p D0 De = cd (t − ˜ ) exp cd (t − ˜ ) sim | − | ) dt, maxt cd maxt cd (3) where the superscripts “exp” and “sim” indicate experimental and simulated data sets, respectively, and T denotes the duration of experiments Note that both distributions are shifted by ˜ The integration in Eq (3) was performed numerically by first fitting the experimental as well as the simulated chromatograms to Eq (1) and then summing up the differences between both fits at equidistant sampling points averaged over some sufficiently large time period where is the density of the liquid, u is the velocity vector, p is the pressure, and is the kinematic viscosity of the fluid Since the passive scalar is used for solute transport modelling (see Section 2.5), pressure and velocity fields are stationary and Eq (7) does not include unsteady terms Pressure gradient in a porous media is calculated by the Carman–Kozeny equation [1]: ∇p = − 150 (1 − )2 dp2 u (8) D Iurashev et al / J Chromatogr A 1599 (2019) 55–65 3.4 Mass transfer model There are three distinct conditions of the solute transport through the chromatography column packed with porous beads where Sh = kf dp /D0 denotes the Sherwood number computed from the volume-to-surface mass transfer coefficient k f = kf dp /6, and v represents the reduced velocity, v = The solute is larger than the size of the bead’s pores Thus the solute cannot penetrate into the beads and the column can be treated as a column packed with non-porous beads The solute is slightly smaller than the size of the bead’s pores Thus the solute penetrates into the beads with finite speed and the column can only be treated with a descriptive model of the mass transfer The solute is much smaller than size of the bead’s pores that the mass transfer of the solute between the mobile and solid phase can be model as infinite fast In general, the transport of a solute through a chromatography column with porous beads can be described by ∂( c) + ∇ ( uc) − D∇ ( c) = −(1 − ) ∂t ∂( cp ) , p ∂t (9) where the right-hand side that takes the solute diffusion into the beads into account [28] Here c and cp denote the concentration of the solute in the packed column and bead, respectively, u is the vector of the superficial velocity in the packed column, and D is the diffusion–dispersion coefficient 3.4.1 No in-beads diffusion (no mass transfer) If a solute is unable to penetrate the beads, i.e (9) simplifies to p = 0, then Eq ∂( c) + ∇ ( uc) − D∇ ( c) = ∂t (10) Such a situation is referred to as the no mass transfer model 3.4.2 Mass transfer limited (MTL) diffusion If a solute is able to penetrate the beads with finite velocity, then the so called linear driving force model [29] ∂( cp ) = ktot (c − cp ), ∂t (11) is commonly used to describe in-beads diffusion, where ktot denotes the total mass transfer coefficient With this assumption, Eq (9) transforms into ∂( c) + ∇ ( uc) − D∇ ( c) = −(1 − ) p ktot (c − cp ), ∂t (12) referred to as the MTL model In this work all solutes are non-binding, and mass transfer can be seen as external film mass transfer and subsequent in-beads pore diffusion Saturation concentration of the solute in the stationary phase is assumed to be equal to the concentration in the mobile phase corrected for the intra-particle porosity Thus, the total mass transfer coefficient can be computed as [1] ktot = ( p kf + (13) where kf is the film mass transfer coefficient, and kp is the pore diffusion mass transfer coefficient kf can be found with help of the Kataoka relationship [30]: Sh = 1.85 0.33 v udp D0 (15) Finally, the pore diffusion mass transfer coefficient can be fairly well approximated by [31]: kp = 60De p dp (16) 3.4.3 Instantaneous in-beads diffusion, local equilibrium assumption (LEA) If a solute diffuses quickly (ktot → ∞) into the beads, then the solute concentration in the mobile phase and inside the particles become identical (cp → c) and Eq (9) simplifies to t ∂( c) + ∇ ( uc) − D∇ ( c) = ∂t (17) This case is referred to as LEA Note that Eq (17) depends on both, the total porosity t and the extra particle porosity , while the no mass transfer model in Eq (10) depends only on the latter 3.5 Diffusion and dispersion The diffusion–dispersion coefficient D can be represented as function of the velocity in the column D = CL udp , (18) where CL is a non-dimensional parameter [32] CL values for the solutes used in this work are shown in Fig For acetone and lysozyme they are computed by Eq (S.4.2) proposed by Delgado [24] For silica nanoparticles this value is equal to 0.5 as recommended by Tsotsas and Schlünder [33] for large v numbers 3.6 Separation of peak broadening effects It is possible to assume that the reduced HETP of silica nanoparticle peaks can be represented as the sum of two components corresponding to the broadening reason – extra column volume and hydrodynamic dispersion: hTotal,SNP = hECV + hD , (19) where hTotal,SNP is the total reduced HETP, hECV is the peak broadening due to extra column volume, and hD is the broadening due to the hydrodynamic dispersion in the packed bed Taking into account that simulations “with extra column volume” account for extra column effects and dispersion, and simulations “without extra column volume” only for dispersion, the components of Eq (19) are computed as follows: hTotal,SNP = hwECV , hECV = hwECV − hnoECV , hD = (20) hnoECV , where hwECV −1 ) , kp 1− 59 , (14) is the reduced HETP computed from simulations with extra column volume, and hnoECV – from simulations without extra column volume In a similar way, the reduced HETP of acetone and lysozyme peaks can be represented as the sum of three components: hTotal,Ace/Lys = hECV + hMT + hD , (21) where hMT is the broadening because of mass transfer into the beads 60 D Iurashev et al / J Chromatogr A 1599 (2019) 55–65 Fig Dependence of CL parameter on v for the solutes used in this work (SNP denotes silica nanoparticle) The employed range of CL values are shown in bold Table Structured summary of the set of simulations S1 to S16 Columns indicate solutes [blue, silica nanoparticle (SNP); cyan, acetone (Ace); green, lysosomes (Lys)], rows indicate column sizes (dark fill color, column 8–100; light fill color column 5–10) Table Moments and reduced HETP of the data from experiment and simulations of the 8–100 column Silica nanoparticle pulse; errors are relative to the experimental values Experiment h Taking into account that simulations of acetone and lysozyme transport with ECV and MTL account for extra column effects, mass transfer and dispersion, simulations without ECV and with MTL – for mass transfer and dispersion, and simulations with ECV and LEA – for extra column effects and dispersion, the components of Eq (21) are computed as follows: hTotal,Ace/Lys = hwECV +MTL , hECV = hwECV +MTL − hnoECV +MTL , hMT = hwECV +MTL − hwECV +LEA , hD = hTotal − hECV − hMT , Simulation Without extra column volume With extra column volume Value [–] Value [–] Error [%] Value [–] Error [%] 0.3648 1.14E−3 1.0202 11.42 0.3767 3.26E−4 0.3682 3.0632 3.3 −71.4 −63.9 −73.2 0.3817 9.80E−4 1.1030 8.9706 4.6 −14.0 8.1 −21.4 4.1 Model validation: analysis of the 8–100 column First, the model of the hydrodynamic dispersion in the packed bed and the mass transfer model are validated using experiments performed on the 8–100 column (22) where hwECV+MTL is the reduced HETP computed from simulations with ECV and MTL, hnoECV +MTL – from simulations without ECV and with MTL, and hwECV+LEA – from simulations with ECV and LEA Results and discussion In the following we first calibrated our approach on the larger column and then validated it on the smaller column This strategy was adopted as extra column volume effects are typically more prominent in smaller columns [9] and a scale-down therefore presents a more selective test than a scale-up All parameters used and simulations performed in this work are summarized in Tables and , respectively In general, we noticed that all computed solute distributions showed noticeable radial inhomogeneity The concentration of solutes across the columns are illustrated in Supplementary Fig S2 These inhomogeneities underline the relevance of an accurate description of the real, three dimensional geometry of the columns also including the extra column volume 4.1.1 For silica nanoparticles extra column volume is the dominant broadening mechanism We simulated the flow of silica nanoparticles through the larger, 8–100 column with and without extra column volume (simulation S2 and S1 in Table 3, respectively) Excellent (overall) agreement between experiment and simulation was found, when the extra column volume was taken into account (NRMSD = 2.4% versus NRMSD = 12.9% without extra column volume, see Supplementary Fig S3) Moreover, compared to the simulation without extra column volume, the run with extra column volume strongly reduced the estimation error in the pulse parameters , , and h, while it modestly increased in , see Table This is explained by the very low diffusion of the silica nanoparticle in the water and the resulting strong effect of the longitudinal dispersion of the silica nanoparticle in the extra column volume components Low diffusion of the silica nanoparticles in water (see Table 2) results in the strong hydrodynamic dispersion of the silica nanoparticles in the extra column volume components Thus, simulation S1 that does not account for the extra column volume, strongly disagrees with the experiment According to the decomposition analysis presented in Section 3.6, extra column volume accounts for 65.9% of the signal broadening, meanwhile hydrodynamic dispersion in the column is responsible only for 34.1% of the broadening D Iurashev et al / J Chromatogr A 1599 (2019) 55–65 61 Table Moments and reduced HETP of the data from experiment and simulations of the 5–10 column Silica nanoparticle pulse; errors are relative to the experimental values Experiment Simulation Without extra column volume h Fig Reduced HETP as function of reduce velocity for the 8–100 column subject to acetone and lysozyme pulses 4.1.2 For acetone extra column volume is irrelevant for peak broadening In contrast to silica nanoparticles, acetone (and lyzosome) are small enough to penetrate the beads Thus, in the following simulations in-beads diffusion was considered according to the MTL-model in Eq (9) Again, all parameters used are listed in Table We simulated the flow of acetone through the larger, 8–100 column with and without extra column volume (simulation S4 and S3 in Table 3, respectively) at various flow rates covering one order of magnitude (in terms of the reduced velocity v ) No difference was found between simulations as well as between simulations and experiments, see Supplementary Fig S4 Both sets of simulations predicted flow profiles that agreed with the experimental data over the whole range of studied flow rates with average error of 2.0% of the NRMSD A similar agreement was found for the reduced HETP, see Fig 4, and moments of distributions, see Supplementary Fig S9 To investigate whether or not in-bead diffusion is essentially an instantaneous process, we repeated the simulations described above, but use of the LEA, see Eq (17), rather than the MTL model to describe mass transfer The extra column volume was considered, too, and this new set of simulations is referred to as S5, see Table However, with increasing flow velocity usage of the LEA worsened the agreement with experiments Average NRMSD for this simulation set is 4.9% Thus, we conclude that acetone slowly diffuses into the beads while propagating through the column at high speed Upon decomposing the reduced HETP values, we found dispersion to be the single most dominating mechanism of peak broadening at low and medium flow rates, see Fig However, the impact of mass transfer grows stronger with increasing flow rates and reaches comparable contributions at the highest flow rate investigated (v = 282) as expected from van Deemter equation [34] 4.1.3 For lysozyme mass transfer is dominating peak broadening We simulated the flow of lysozyme through the larger, 8–100 column as summarized in Table Like acetone, lysozyme are able With extra column volume Value [–] Value [–] Error [%] Value [–] Error [%] 2.1631 0.9731 1.9573 27.730 1.7409 0.0081 1.2690 4.518 −19.5 −99.2 −35.2 −83.7 1.7887 0.5369 1.8418 22.375 −17.3 −44.8 −5.9 −19.3 to diffuse into beads With our parameters, see Table 2, lysozyme probe the space at larger reduced velocities that were not accessible with acetone Thus, a larger reduced velocity range is covered for each column Again simulations and experiments agreed well (average NRMSD = 6.1% for the sets of simulations S6 and S7, see Supplementary Fig S5) Consistently with our findings for acetone, we found the effects of extra column volume to be irrelevant, in-bead diffusion growing stronger with v and dominating peak broadening, see Fig and Fig At very high reduced velocities, v 3000, peak broadening is essentially determined by in-bead mass transfer only Consequently, simulation set S8 that does not account for mass transfer, has worse agreement with experiments and average NRMSD = 19.2% 4.2 Model testing: predicting performance of the 5–10 column In the two preceding sections we developed and validated a hydrodynamic model of a large chromatography column (8–100) Here, we predict the performance parameters of pulse response experiments of an identically constructed, smaller column (5–10) As the columns were constructed in the same way, we assumed that porosity values, dispersion coefficients and mass transfer coefficients are identical in both columns We predicted the flow of silica nanoparticles, acetone and lysozyme through the small 5–10 column We ran simulations with and without extra column volume and modeled in-bead diffusion employing LEA and the MTL model An overview of all sets of simulations is listed in Table Subsequently we experimentally verified our predictions for silica nanoparticles and acetone We found that the predicted pulse shapes at the UV detector agreed reasonably well with the verification experiments (see Fig and S10) when effects of the extra column volume were included (average NRMSD = 4.3% and 5.0% for silica nanoparticles, and acetone, respectively; also see Table as well as Fig and supplementary Fig S6 for the corresponding chromatograms) However, in contrast to our simulations, the experiments with silica nanoparticles showed a second peak at around column volume, see Fig Its origin is not yet clear and scope of further investigation A decomposition of the (predicted) reduced HETP values revealed that for all solutes the effects of the extra column volume dominate peak broadening [see Fig for data on acetone and lysozyme (for the corresponding chromatograms see Supplementary Figs S6 and S7, respectively), data on silica nanoparticles not shown] In the case of silica nanoparticles and acetone, extra column volume is responsible for more than three quarters of the signal broadening Even for lysozyme at very high flow rates (v ≈ 3000) the effects of the extra column volume account for about half of the predicted broadening 62 D Iurashev et al / J Chromatogr A 1599 (2019) 55–65 Fig Separated influence of each reason of the peak broadening for various reduced velocities; 8–100 column, acetone and lysozyme pulses Fig Silica nanoparticle concentration at the UV detector, 5–10 column, u = 250 cm/h The dominance of effects due to the extra column volume is reasonable and expectable as the extra column volume is about the same as the volume of the 5–10 column while it makes only 5% of the volume of the larger 8–100 column For acetone the effects of the extra column volume and hydrodynamic dispersion account for at least 90% of observed peak broadening, while dispersion due to in-bead diffusion is essentially irrelevant Indeed, our simulations show good overall agreement with experiments irrespective of the used mass transfer model (NRMSD = 5.0% and 3.9% for the simulation S12 and S13, respectively; see Table for a description of the simulations), confirming the negligible contribution of in-bead diffusion However, as for the larger column, the impact of in-bead diffusion increases with the flow rate, becoming roughly equal to the contribution of the extra column volume at very high flow rates, see the case for lysozyme at v ≈ 3000 in Fig Conclusions Here we used 2D computational fluid dynamics (CFD) coupled with mechanistic mass transfer models to investigate and separate effects of peak broadening in chromatography columns 2D CFD simulations naturally capture the anisotropic propagation of the solute in extra column volume and in packed bed and not require to employ dispersed plug flow reactors (DPFRs) and continuous stirred tank reactors (CSTRs) as it is the case of 1D models [35,36] Several benchmark cases of non-binding solute transport in two differently sized chromatography columns were reported The solutes (silica nanoparticles, acetone, and lysozyme) differed (i) by their ability to diffuse into the pores of the beads and (ii) by their diffusion-dispersion behaviour as characterized by the coefficient CL The different properties of the solutes allowed us to probe a wide range of reduced velocities (from 10 to 10,000) D Iurashev et al / J Chromatogr A 1599 (2019) 55–65 Fig Dependency of reduced HETP on velocity; 5–10 column, acetone and lysozyme pulses The good agreement between experiments and simulations supports not only the validity of the CFD approach but also illustrates the good scalability of the studied columns, which – in turn – indicates a good quality of the bed packing Our simulations confirm the dynamic variability of dispersion mechanism of across scales (see Fig 9) Even in the large column, 63 where the extra column volume makes less than 5% of the total column volume, the extra column volume is the dominating peak broadening mechanism, when the column is operated with silica nanoparticles That impact decreases to less than 10% when the column is used together with the other solutes For the larger column, hydrodynamic dispersion in the packed bed is the dominant mechanism of peak broadening at low and medium flow rates of acetone At higher v values, i.e at high flow rates of acetone and all the studied flow rates of lysozyme, in-beads diffusion is the dominant mechanism of peak broadening For both solutes extra column volume accounts for no more than 10% of the peak broadening In contrast, extra column volume plays the dominant role for all the studied flow rates of acetone and low and medium flow rates of lysozyme for the smaller column Only at high flow rates of lysozyme, extra column volume and mass transfer are almost equally important This implies that low-diffusive solutes at high flow rates characterise the column rather than extra column volume In order to adapt our approach to an uncharacterised column one (i) needs to identify the parameters and (ii) differentiate the contributions by means of CFD We need to conduct at least one experiments with a non-penetrating solute to determine the extraparticle porosity and at least two more at different flow rates for each additional penetrating solute to determine intra-particle porosity p and effective diffusivity De These parameters can be used for the analysis of the same column or extrapolated to another column with the same packing resin Two CFD simulations have to be run at the flow rate of interest to estimate the contribution of extra column volume If the solute is able to diffuse into the beads, one additional simulation should be run to differentiate between MTL and hydrodynamic dispersion effects Fig Separated influence of each reason of the peak broadening for various reduced velocities; 5–10 column, acetone and lysozyme pulses 64 D Iurashev et al / J Chromatogr A 1599 (2019) 55–65 Fig Dependency of reduced HETP due to extra column volume on superficial velocity and diffusivity of the solute for both columns Area of the markers correspond to the relative contribution of extra column volume to reduced HETP Acknowledgements This work has been supported by the Federal Ministry of Science, Research and Economy (BMWFW), the Federal Ministry of Traffic, Innovation and Technology (BMVIT), the Styrian Business Promotion Agency SFG, the Standortagentur Tirol, the Government of Lower Austria and ZIT – Technology Agency of the City of Vienna through the COMET-Funding Program managed by the Austrian Research Promotion Agency FFG The authors would like to thank Astrid Dürauer and Rupert Tscheließnig for the helpful discussions Appendix A Supplementary data Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.chroma.2019.03 065 References [1] G Carta, A Jungbauer, Protein Chromatography: Process Development and Scale-up, John Wiley & Sons, 2010 [2] R.L Fahrner, H.L Knudsen, C.D Basey, W Galan, D Feuerhelm, M Vanderlaan, G.S Blank, Industrial Purification of Pharmaceutical Antibodies: Development, Operation, and Validation of Chromatography Processes, Biotechnol Genet Eng Rev 18 (1) (2001) 301–327, http://dx.doi.org/10 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peak broadening, see Fig and Fig At very high reduced velocities, v 3000, peak broadening is essentially determined by in- bead... was injected at non-binding conditions to the column in order to evaluate hindered diffusion of large molecules inside the pores 10 L lysozyme at a concentration of mg/mL was injected in running... rates of lysozyme, in- beads diffusion is the dominant mechanism of peak broadening For both solutes extra column volume accounts for no more than 10% of the peak broadening In contrast, extra