# Help with k\_kin in SMA isotherm **URL:** \ **Category:** Chromatography Modeling\ **Created:** [March 28, 2024, 5:59am UTC](https://forum.cadet-web.de/t/help-with-k-kin-in-sma-isotherm/908 "2024-03-28T05:59:58Z")\ **Posts on this page:** 11\ **Page:** 1
**Author:** ![danPh](https://forum.cadet-web.de/letter_avatar_proxy/v4/letter/d/b77776/32.png) [@danPh](https://forum.cadet-web.de/u/danPh)\ **Post date:** [March 28, 2024, 5:59am UTC](https://forum.cadet-web.de/t/help-with-k-kin-in-sma-isotherm/908/1 "2024-03-28T05:59:58Z")
Hi, I’m new to CADET-Process and chromatography modelling in general. I’m attempting to replicate the results of GoSilico modelling software by Cytiva for a CEX Column Chromatography using CADETProcess. The isotherm parameters in GoSilico are: > Equilibrium (SMA) = 7e-7 > Charge (SMA) = 10.11 > **Kinetic (SMA) = 1.8e-8** > Shielding = 0 It seems like they are [using this SMA derivation](https://www.sciencedirect.com/science/article/pii/S1383586614005681) with k\_kinetic being the inverse of k\_d ![image](https://forum.cadet-web.de/uploads/default/original/2X/f/f43e196f188468e495ec12f0b1b1a53b260e9d44.png) My current CADET-Process snippet for the binding model is like below. I’m setting rapid equliibrium is\_kinetic=False, but not sure how to incorporate the k\_kinetic parameter in there. Any help would be appreciated! Warm regards, Daniel ```auto component_system = ComponentSystem(['Salt', 'Protein']) binding_model = StericMassAction(component_system) binding_model.is_kinetic = False binding_model.adsorption_rate = [0, 7E-07] binding_model.desorption_rate = [0, 1] binding_model.capacity =1400 binding_model.characteristic_charge = [0, 10.11] binding_model.steric_factor = [0, 0] #shielding binding_model.reference_liquid_phase_conc = 1 binding_model.reference_solid_phase_conc = 1 # k_Kinetic (SMA) = 1.8e-8 ``` ---
**Author:** ![lieres](https://forum.cadet-web.de/user_avatar/forum.cadet-web.de/lieres/32/1238_2.png) [@lieres](https://forum.cadet-web.de/u/lieres)\ **Post date:** [March 28, 2024, 9:12am UTC](https://forum.cadet-web.de/t/help-with-k-kin-in-sma-isotherm/908/2 "2024-03-28T09:12:12Z")
Hi Dan, Welcome to the forum. It seems like you already have the answer. It can sometimes be beneficial to apply parameter transformations before executing specific optimization tasks. Using k\_{kin} and k\_{eq} instead of k\_a and k\_d is a classic of such transformations. In the end it only matters that the original parameters are uniquely determined by the transformd ones. However, I would prefer to use k\_{kin} = k\_d as then larger values indicate faster processes. ---
**Author:** ![danPh](https://forum.cadet-web.de/letter_avatar_proxy/v4/letter/d/b77776/32.png) [@danPh](https://forum.cadet-web.de/u/danPh)\ **Post date:** [March 28, 2024, 9:47am UTC](https://forum.cadet-web.de/t/help-with-k-kin-in-sma-isotherm/908/3 "2024-03-28T09:47:53Z")
Thanks for your response! I think my question was unclear. What I’m trying to ask is, where do I put the `k_Kinetic = 1.8e-8` into my current `binding model`? Currently, it’s commented out, and the binding model is set to use k\_{eq} only with `is_kinetic = False`. When I tried to set k\_{d} = \frac{1}{k\_{kin}} and k\_a = \frac{k\_{eq}}{k\_{kin}} for `is_kinetic = True`, I cannot complete the simulation. The full code (non-working due to is\_kinetic=True) is like below: ```auto c_salt_low = 10 c_salt_high = 335.735 c_protein = 0.00667 flow_rate = 2.312e-8 load_time = 0 wash_time = 713.22 elution_time = 2448.12 cycle_time = 12293.77 k_Kinetic = 1.8e-8 k_eq = 7e-7 ########### This doesn't work :( ########### component_system = ComponentSystem(['Salt', 'Protein']) binding_model = StericMassAction(component_system) binding_model.is_kinetic = True binding_model.adsorption_rate = [0, k_eq/k_Kinetic] binding_model.desorption_rate = [0, 1/k_Kinetic] binding_model.capacity =1400 binding_model.characteristic_charge = [0, 10.11] binding_model.steric_factor = [0, 0] binding_model.reference_liquid_phase_conc = 1 binding_model.reference_solid_phase_conc = 1 ################################################ # ########### This works, but no k_Kinetic ########### # component_system = ComponentSystem(['Salt', 'Protein']) # binding_model = StericMassAction(component_system) # binding_model.is_kinetic = False # binding_model.adsorption_rate = [0, k_eq] # binding_model.desorption_rate = [0, 1] # binding_model.capacity =1400 # binding_model.characteristic_charge = [0, 10.11] # binding_model.steric_factor = [0, 0] # binding_model.reference_liquid_phase_conc = 1 # binding_model.reference_solid_phase_conc = 1 # ################################################ # Column column = LumpedRateModelWithPores(component_system, 'column') column.binding_model = binding_model column.length = 0.2 column.diameter = 0.0113 column.bed_porosity = 0.89 column.particle_radius = 43e-5 column.particle_porosity = 0.83 column.axial_dispersion = 4e-07 column.film_diffusion = [5e-06, 5e-06] column.c = [c_salt_low, 0] column.q = [binding_model.capacity, 0] # Unit Operations inlet = Inlet(component_system, name='inlet') inlet.flow_rate = flow_rate outlet = Outlet(component_system, name='outlet') # Flow Sheet flow_sheet = FlowSheet(component_system) flow_sheet.add_unit(inlet) flow_sheet.add_unit(column) flow_sheet.add_unit(outlet, product_outlet=True) flow_sheet.add_connection(inlet, column) flow_sheet.add_connection(column, outlet) # Process process = Process(flow_sheet, 'lwe') process.cycle_time = cycle_time c_load = np.array([c_salt_low, c_protein]) c_wash = np.array([c_salt_low, 0]) concentration_difference = np.array([c_salt_high, 0.0]) - np.array([c_salt_low, 0.0]) gradient_duration = process.cycle_time - elution_time gradient_slope_ = concentration_difference/gradient_duration process.add_event('load', 'flow_sheet.inlet.c', c_load) process.add_event('wash', 'flow_sheet.inlet.c', c_wash, wash_time) process.add_event('grad_start', 'flow_sheet.inlet.c', [[c_salt_low, gradient_slope_[0]], [0, gradient_slope_[1]]], elution_time) # Simulation process_simulator = Cadet() process_simulator. __dict__ ['timeout']=10.0 simulation_results = process_simulator.simulate(process) #time out 10 sec outputs = simulation_results.solution.column.outlet from CADETProcess.plotting import SecondaryAxis sec = SecondaryAxis() sec.components = ["Salt"] sec.y_label = '$c_{salt}$' _ = simulation_results.solution.column.outlet.plot(secondary_axis=sec) ``` ---
**Author:** ![ronald.jaepel](https://forum.cadet-web.de/user_avatar/forum.cadet-web.de/ronald.jaepel/32/986_2.png) [@ronald.jaepel](https://forum.cadet-web.de/u/ronald.jaepel)\ **Post date:** [March 28, 2024, 3:39pm UTC](https://forum.cadet-web.de/t/help-with-k-kin-in-sma-isotherm/908/4 "2024-03-28T15:39:30Z")
Hey Dan, I can reproduce the error and will look into it. It’s afaik unexpected behavior and your code looks correct. ---
**Author:** ![danPh](https://forum.cadet-web.de/letter_avatar_proxy/v4/letter/d/b77776/32.png) [@danPh](https://forum.cadet-web.de/u/danPh)\ **Post date:** [March 29, 2024, 6:57am UTC](https://forum.cadet-web.de/t/help-with-k-kin-in-sma-isotherm/908/5 "2024-03-29T06:57:36Z")
Thanks Ron - I look forward to hearing from you. On a side note, I did try removing the timeout 10 seconds, but the code still doesn’t work, so I put it back. ---
**Author:** ![Flynn](https://forum.cadet-web.de/user_avatar/forum.cadet-web.de/flynn/32/1045_2.png) [@Flynn](https://forum.cadet-web.de/u/Flynn)\ **Post date:** [March 29, 2024, 9:37am UTC](https://forum.cadet-web.de/t/help-with-k-kin-in-sma-isotherm/908/6 "2024-03-29T09:37:32Z")
Just wondering, would setting some of the zeros to a negligibly small number solve this problem? ---
**Author:** ![danPh](https://forum.cadet-web.de/letter_avatar_proxy/v4/letter/d/b77776/32.png) [@danPh](https://forum.cadet-web.de/u/danPh)\ **Post date:** [March 29, 2024, 1:20pm UTC](https://forum.cadet-web.de/t/help-with-k-kin-in-sma-isotherm/908/7 "2024-03-29T13:20:56Z")
I tried multiple non-zero values (setting every 0 to 1e-5, 1e-4, 1e-3), but it didn’t work for any of them ☹ I think the `k_d = 1/k_Kinetic = 55555555.55` is way to big compared to `k_a = k_eq/k_Kinetic = 38.88`; but not sure how to address it… Any suggestion on changing `reference_liquid_phase_conc` and `reference_solid_phase_conc` ? ---
**Author:** ![Flynn](https://forum.cadet-web.de/user_avatar/forum.cadet-web.de/flynn/32/1045_2.png) [@Flynn](https://forum.cadet-web.de/u/Flynn)\ **Post date:** [March 29, 2024, 5:01pm UTC](https://forum.cadet-web.de/t/help-with-k-kin-in-sma-isotherm/908/8 "2024-03-29T17:01:53Z")
I can reproduce this in CADET-Core so it’s not a CADET-Process problem. I did some investigations and I think this is a numerical issue. The solver repeatedly failed to converge when switching to the wash phase, meaning the parameter values you provided are giving the solver a hard time. Regarding the reference solution, please find the document [here](https://cadet.github.io/master/modelling/binding/index.html#reference-concentrations). The reference solution is designed to minimize problems like this. However, I also tried a couple of reference solutions for you but the error still persists. Therefore, I would suggest 1. double check the parameter values, do all these parameters make sense, are they close to those reported in the literature? For instance, 10.11 seems to be big and 7e-7 seems to be small. I can produce the same results switching between `is_kinetic=True` and `is_kinetic=False` when 10.11 is changed to 5. 2. continue trying other reference values. 3. switch to a different unit system for all parameters and test other reference solutions. Hope it helps, Flynn. ---
**Author:** ![ronald.jaepel](https://forum.cadet-web.de/user_avatar/forum.cadet-web.de/ronald.jaepel/32/986_2.png) [@ronald.jaepel](https://forum.cadet-web.de/u/ronald.jaepel)\ **Post date:** [March 29, 2024, 8:54pm UTC](https://forum.cadet-web.de/t/help-with-k-kin-in-sma-isotherm/908/9 "2024-03-29T20:54:47Z")
Hey Flynn, thanks for your input! I agree, it’s a numerical issue. As you said, the simulation fails at the first section switch, during the re-initialization. Apparently, NaN’s get computed, but I don’t yet know why. Here’s the debug log: ```auto [Debug: integrate::1253] Solve from 713.22 to 713.22 => IDA_SUCCESS [Debug: integrate::1279] === #Steps: 202 === #Residual evals: 203 === #Error test fails: 0 === #Newton iters: 203 === #Conv test fails: 0 === Last step size: 3.87311 === Next step size: 7.74621 [Debug: integrate::1253] Solve from 713.22 to 714 => IDA_TSTOP_RETURN [Debug: integrate::1279] === #Steps: 202 === #Residual evals: 203 === #Error test fails: 0 === #Newton iters: 203 === #Conv test fails: 0 === Last step size: 3.87311 === Next step size: 7.74621 [Debug: integrate::1091] ###### SECTION 1 from 713.22 to 2448.12 [Debug: notifyDiscontinuousSectionTransition::138] Switching from valve configuration 0 to 1 (sec = 1 wrapSec = 1) [Debug: notifyDiscontinuousSectionTransition::151] Unit op 0 (INLET) port -1 comp -1 => 1 (LUMPED_RATE_MODEL_WITH_PORES) port -1 comp -1 [Debug: notifyDiscontinuousSectionTransition::151] Unit op 1 (LUMPED_RATE_MODEL_WITH_PORES) port -1 comp -1 => 2 (OUTLET) port -1 comp -1 [Debug: integrate::1104] ---====--- CONSISTENCY ---====--- [Debug: updateDynamicModelFlowRates::226] Flow out unit 0 port 0: 2.312e-08 [Debug: updateDynamicModelFlowRates::215] Flow in unit 1 port 0: 2.312e-08 [Debug: updateDynamicModelFlowRates::226] Flow out unit 1 port 0: 2.312e-08 [Debug: updateDynamicModelFlowRates::215] Flow in unit 2 port 0: 2.312e-08 [Debug: residualNorm::479] Residual: 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[Debug: integrate::1106] ==========> Consistency error prev: 7.93019e+07 [Debug: updateDynamicModelFlowRates::226] Flow out unit 0 port 0: 2.312e-08 [Debug: updateDynamicModelFlowRates::215] Flow in unit 1 port 0: 2.312e-08 [Debug: updateDynamicModelFlowRates::226] Flow out unit 1 port 0: 2.312e-08 [Debug: updateDynamicModelFlowRates::215] Flow in unit 2 port 0: 2.312e-08 [Debug: consistentInitialConditionAlgorithm::513] Residual post state: 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[Debug: updateDynamicModelFlowRates::226] Flow out unit 0 port 0: 2.312e-08 [Debug: updateDynamicModelFlowRates::215] Flow in unit 1 port 0: 2.312e-08 [Debug: updateDynamicModelFlowRates::226] Flow out unit 1 port 0: 2.312e-08 [Debug: updateDynamicModelFlowRates::215] Flow in unit 2 port 0: 2.312e-08 [Debug: residualNorm::479] Residual: 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[Debug: integrate::1117] ==========> Consistency error post Full: 1.27983e-08 [Debug: integrate::1132] y = 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[Debug: integrate::1133] yDot = 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[Debug: integrate::1134] Contains NaN: y = 0 yDot = 0 [Trace: residualDaeWrapper::217] ==> Residual at t = 713.22 sec = 1 [Debug: updateDynamicModelFlowRates::226] Flow out unit 0 port 0: 2.312e-08 [Debug: updateDynamicModelFlowRates::215] Flow in unit 1 port 0: 2.312e-08 [Debug: updateDynamicModelFlowRates::226] Flow out unit 1 port 0: 2.312e-08 [Debug: updateDynamicModelFlowRates::215] Flow in unit 2 port 0: 2.312e-08 [Trace: linearSolveWrapper::313] ==> Solve at t = 713.22 alpha = 1e+06 tol = 0.33 ``` My current theory is, that the kinetic constant is too small (i.e. too fast), and that CADET overshoots, but I don’t really know. I’ll put this onto the agenda for our next team meeting. But regarding your current issue @danPh : 1. For the reproduction of your GoSilico results: that’s all rapid equilibrium anyways with a kKin that fast. With that combination of parameters for charge, capactiy etc. the kKin parameter only starts getting noticeable above 1e25, so some 30 orders of magnitude above your GoSilico values. So you can run your simulations with is\_kinetic=False or set kKin to anything higher than 1e-6 (e.g. 1) and you should get the same results you would get if CADET didn’t crash with kKin=1e-8. 2. I think 10.11 for the characteristic charge is reasonable. 3. For your own simulations/ parameter estimations etc moving forward, I would recommend using reference concentrations as much as you can as they stabilize the numerics of the SMA isotherm. The values we recommend are the stationary phase capacity and the maximum salt concentration for bound and solved reference concentrations respectively. But note that the ka and kd CADET takes are the transformed ka and kd, so changing the reference concentrations is going to change the simulation results. If you want to have an exchange about reference concentrations feel free to join us at the CADET Office hour and we can talk about it 🙂 ---
**Author:** ![Flynn](https://forum.cadet-web.de/user_avatar/forum.cadet-web.de/flynn/32/1045_2.png) [@Flynn](https://forum.cadet-web.de/u/Flynn)\ **Post date:** [March 30, 2024, 9:17am UTC](https://forum.cadet-web.de/t/help-with-k-kin-in-sma-isotherm/908/10 "2024-03-30T09:17:43Z")
Thanks for confirming that the characteristic charge is reasonable. I think I have some ideas on what’s going on now. The problem is k\_{kin}. In ChromX: k\_{kin,i} \frac{\partial q\_i}{\partial t} = k\_{eq,i} \bar{q}\_{salt}c\_{p,i} - c\_{salt}^{\nu\_i} q\_i k\_{kin} = 1.8e-8, the left hand side is practically 0. @danPh How did you get this number? Have you tried 1.8e-7, 1.8e-6 or 1.8e-9 in ChromX? Does it give you the same result? My guess is that such a small number in ChromX is used to denote equilibrium as the time derivative part is practically 0. Anyway, for such a small k\_{kin} you should look for `is_kinetic=False` . Regarding the CADET simulation using `is_kinetic=True`, it fails because the rate constants are too big, possibly making the problem stiffer when switching phases. Therefore, this problem can be addressed by loosening some constraints in IDA to help the solver to further adapt its order and step sizes at ‘difficult times’. For instance, changing either `max_errtest_fail` to 10 or `init_step_size` to 1e-15 in the `/solver/time_integrator` group can solve this problem. I can produce the following result using `is_kinetic=True` even without using reference concentrations: ![image](https://forum.cadet-web.de/uploads/default/original/2X/7/799b6b977a8fe94f5326e25f927f9ed4d21e005f.png) I still recommend using reference concentrations and setting `is_kinetic=False` in this case. ---
**Author:** ![danPh](https://forum.cadet-web.de/letter_avatar_proxy/v4/letter/d/b77776/32.png) [@danPh](https://forum.cadet-web.de/u/danPh)\ **Post date:** [April 2, 2024, 10:36am UTC](https://forum.cadet-web.de/t/help-with-k-kin-in-sma-isotherm/908/11 "2024-04-02T10:36:59Z")
Hi Flynn & Ron, Thank you for your support. I’m also discussing with my colleagues about the small value of k\_{kin} from GoSilico - I suspected that as Flynn said, it’s just an indicator of rapid equilibrium. I decided to perform inverse fitting of both `k_eq` and `charge` with CADET, and the newly fitted values are different from the GoSilico’s values, but the quality of the fit as well as the generalizability is very good. I think the underlying binding model implemented by GoSilico might have some differences with CADET’s one. Again, much appreciated!