Engineering Aspects of FlowNMR Spectroscopy Setups for Online Analysis of Solution-Phase Processes

In this article we review some fundamental engineering concepts and evaluate components and materials required to assemble and operate safe and effective FlowNMR setups that reliably generate meaningful results.


Name Description
Back-mixing / dispersion The mixing of liquid flowing through a pipe along the axis of travel by shear forces [laminar flow], eddies [turbulent flow], baffles, convection and/or molecular diffusion.
Back pressure regulator A device that sustains a fixed pressure upstream of itself at its inlet, opening only when a set threshold has been reached (either by releasing a spring-loaded valve or rupture of a bursting disk).
Bodenstein number Ratio of how much substance is introduced from convection versus diffusion. Used to quantify the amount of back-mixing in liquids flowing through a cylindrical pipe.
Cavitation Process of unwanted gas or vapour bubble formation in liquids inside a positive displacement pump due to the suction pressure created by the pump exceeding gas solubility or vapour pressure of the liquid.
Check valves A valve that only allows the movement of a fluid in one direction.
Closed-loop setup Piping set up that does not allow sample to be exposed to the environment. Pump head Maximum height with which a pump can move fluid against gravity.
Push-fit connection A type of lose tubing connection that can be affected without tools.
Residence time distribution (RTD) Probability distribution of the time a fluid spends in a flow system.
Reynold's number Ratio of inertial forces to viscous forces within a fluid moving through a confinement. Used to determine whether a flow is laminar (Re <3000) or turbulent (Re >3000).

Slippage
An uncontrolled movement of fluid through a pumping mechanism, flow valve or back-pressure regulator.
Stroke velocity Speed at which a round of the pump's mechanism is completed.
Suction pressure Pressure drop felt at the section of tubing between the sample reservoir and the pump inlet.
Swept volume Volume of fluid moved by one stroke of the pump.

Tailing
Broadening of a normal distribution RTD curve to longer residence times due to dead volumes within the system.

Pump testing under pressure
A Cori-flow Mini M13 (Bronkhorst) flow meter was inserted into the flow path and the FlowNMR apparatus was flushed and filled with toluene (4 mL/min) for 20 minutes to remove residual solvent.
Toluene (15 mL) and a Teflon-coated stirrer bar were charged to the pressure reactor, which was then S9 sealed, checked for leaks and connected to the FlowNMR apparatus in a recirculating setup. Pressure and flow rate data acquisition was started, and the relevant pump (either the peristaltic, doublepiston, annular gear, rotating-tetra piston or diaphragm pump) was set to 4 mL/min, heat exchanger 1, 2, the probe and the hotplate were set to 50 °C and allowed to equilibrate. The reactor was increasingly pressurised to 5, 10 and 20 bar at 20 minute intervals. The reactor was then vented, repressurised to 10 bar and left for another 20 minutes to check pressure performance after being pressurised and depressurised.

RTD experiments for FlowNMR apparatus
The UV flow cell (PEEK SMA-Z, Ocean Optics) was inserted at the end of the flow path (see Figure S1)

Pulsation and NMR spectroscopy
The dependent on application C = not recommended -= no data available S12

Injection Capillary
The connections to the fused silica capillary were made for ease of tip replacement and flow tube repair -details of the fittings and parts for this modification can be seen below in Figure S3 and S4.
The silica capillary is connected to the body of the flow tube via a push-fit connection with a polymer sleeve (1/16" FEP) that is secured in a 1/16" compression fitting. This other end of the sleeve is then connected to the transfer line via UNF 6-40 flat unions and fittings, which can be used for both 1/16" and 1/32" tubing sizes.

Equation S2
This calculation gives a value of roughly 1/147.26 as seen below:

Equation S3
Therefore, the final equation with desired units is as follows: S14 A summary of all these terms and their units can be found below in Table S2:

Velocity Imaging
A solution of chromium(III) 2,4-pentanedionate (2.0 mg, 0.57 mM) in chloroform (9.5 mL CDCl 3 and 0.5 mL CHCl 3 , total 10.0 mL) was circulated through the flow system using a peristaltic pump (Vapourtec SF-10). Velocity imaging experiments were carried out at seven flowrates from 0.0 to 4.0 mL min -1 using the sequence in Figure S5 described by Morris. 10 A diffusion delay, Δ, of 0.08 s was used, with 29 diffusion delay imbalance times, ΔΔ. These ranged from −0.07 and +0.07 s and included a greater density of data points at the centre of the distribution (small ΔΔ). Eight scans were used for each value of ΔΔ, and p30 was set to 1000 μs. Figure S5: From Swan et al. 10 When the diffusion delay imbalance ΔΔ = 0, the pulse sequence is equivalent to a convection compensated DOSY experiment.
The maximum velocity at each flowrate was determined by curve fitting ( Figure S6). For each flowrate, peak integrals at different diffusion delay imbalance values, ΔΔ, were exported and fit to Equation S5 using a nonlinear least squares fit in MS Excel. A G is the gradient pulse shape factor, S 0 is the maximum signal amplitude, and γ is the gyromagnetic ratio. The result of the curve fit gives v max , the values of which are shown in Figure S6 as a function of volumetric flow rate. Heat transfer in the system was modelled on conduction through a pipe wall combined with volumetric flow rate in a heating system (see Figure S8). [11][12][13][14] Equation S5 calculates heat conduction through a pipe wall where Q̇ is heat flow (W), k is the overall heat transfer coefficient of the system (W/m 2 .K), A is the surface area of heat flow (outer tubing surface, m 2 ) and ΔT is the temperature difference between the solvent temperature (T solv ) and external temperature(T ext ) (K).

Equation S6
Equation S7 is used for determining the surface area of a cylinder (outer tubing surface) where r is the radius of the pipe and L is the length of the tubing.

Equation S10
Equation S11 defines the volumetric flowrate for a heated system 15 where V̇ is the volumetric flowrate (m 3 /s), Q̇ is the heat flow (kW), C p is the heat capacity of the solvent (kJ/kg.K), ρ is the density of the solvent (kg/m 3 ), T in and T out are the inlet and outlet temperature of the tubing respectively (K).

̇= ( -)
Equation S11 Resistance term for solvent inside tubing Resistance term for tubing material Resistance term for surrounding liquid or gas S20 Equation S11 is then rearranged to make the outlet temperature the subject in Equation S12.
= -̇̇E quation S12 By substituting kAΔT for Q̇ we achieve a single calculation for the outlet temperature including all variables, in Equation S13 . A summary of all of these terms and their units can be found beneath in Table S4.
= -∆̇E quation S13 Now we have achieved the outlet temperature for a length of tubing we must define the length of tubing we want to study. In order to achieve a temperature profile that asymptotically approaches the target temperature we must perform the calculation over short lengths, with the T in of an increment being equal to the T out of the previous increment. This is then iterated to the desired length to create a temperature profile. Varying the size of the length increment had little effect on the magnitude of heat loss observed in the temperature profile ( Figure S9). Length values for plots throughout the study use 1.0 cm increments. It is noted that the heat transfer coefficient for air (α air ) can vary greatly due to many factors and its flow is not always easily characterizable. From Table S5 we can estimate that the alpha will be between 10 and 100 W/m 2 .K. The effect of this value on the overall temperature gradient can be seen in Figure   S10. To determine the most appropriate α air for the system studied an experiment was carried out under the same conditions at different tubing length to achieve a temperature gradient over length. This curve was then compared to calculation and the optimal heat transfer coefficient was selected.

S24
In all the heat transfer models in this study the following assumptions are made:  The flow within the transfer line is classified as laminar.
 The outside temperature is uniform (room temperature or uniformly heated transfer fluid).
 Insulative foam used for passive insulation has the same heat transfer properties as Armaflex TM insulation. 16  The heat transfer coefficient of air (α air ) is 35 as estimated by experiment (SX.X) A summary of all tubing and solvents studied and their physical properties used in the model can be found below in table S6.

Thermal Model Validation
A stirred 1 L reservoir of water was heated to 40 °C by a hotplate, 1.42 m of polyetheretherketone tubing (PEEK, OD 1/16", ID 0.76 mm) connected to a Vapourtec SF-10 peristaltic pump was inserted into the reservoir, secured with a rubber septum. Thermocouples were positioned in the heating block, reservoir, and tubing exit. The water was flowed directly onto the thermocouple and was S25 allowed to come to thermal equilibrium for 20 minutes. Single point readings were taken and the tubing was progressively cut to shorten the total path length (Table S7, Figure S12). 10 cm was added to the overall length to account for the tubing within the peristaltic pump. For simplicity this was assumed to have similar heat transfer properties to the PEEK tubing ( Figure S13 -Thermal Image).   Crosshairs indicate the surface temperature of the heat exchanger tubing and Armaflex insulation.

Residence Time Distribution
Residence time distribution can be utilised to characterise the behaviour of reactors and flow systems. [22][23][24][25] Step injection experiments were performed in this study to obtain the RTD profiles. A tracer (fluorescein) was injected into the reactor at t = 0 to determine the RTD experimentally by measuring the tracer's concentration, C, in the effluent stream as a function of time. The concentration at the outlet was measured by UV-vis spectroscopy at a constant flow rate (1-6 mL/min), until the concentration of tracer in the flow path to the reaction vessel was saturated in the effluent. The absorbance data was normalised to the concentration obtaining the non-dimensional curve F(t) going from 0 to 1.
The cumulative distribution F(t) can be determined directly from a step input. The variable C(t) is the concentration at time t. Creating this normalised distribution function allows flow performances of different magnitudes inside the system to be compared directly.

Pump inlet
Pump outlet To reaction

From flow tube
To flow tube From reaction

S28
The step and pulse responses were then related by:

Equation S16
Where E(t) is the RTD function of the setup.    Where ti is I th observation of time, where I represents the sample points, Ci is the residence time at the I th observation of the tracer output, where I is the sample points.
The mean value of the variable is equal to the first moment of the RTD function, E(t). The area under the curve of a plot of tE(t) as a function of t will yield τ.
Where τ is large, this shows a slow decay of the output transient, C(t), and E(t) for a pulse input. Where τ is small, this shows a rapid decay of the transient, C(t), and E(t) for a pulse input.

Propagation of uncertainty:
A propagation of uncertainty analysis was carried out to ascertain the effect of the individual variables' deviation on the uncertainty of our results from our residence time distribution (RTD) experiments.
The approach of combining individual experimental uncertainties on the input parameters to obtain the deviation on the output is not applicable in this case, because there is no single equation linking the input parameters to the output (intermediate fitting step). Our approach was therefore to estimate the experimental deviation of the variables demonstrating the highest magnitude of deviation (namely the flow rate and absorbance) to propagate their effects on the final parameters calculated. They were set to their maximal deviations (nominal value of 5% and 3.5% respectively) at a representative value, after which the fitting process was applied, and the output parameters were then compared to what they came out to be with the nominal value of the input. This difference on the output was then used as an estimate of its uncertainty to calculate the deviation associated with the mean residence time (τ). This method resembles a Monte-Carlo simulation of uncertainty propagation, 26 i.e. varying the input together, within the limits of their distribution and watching how much the output varies.
The RTD data obtained was then fitted to the CSTR cascade model where the method used to fit the data was to minimise the sum of absolute values of differences between the observed data and the CSTR cascade by changing the parameters. We found a curve of best fit by using a series of solutions from the Broyden-Fletcher-Goldfarb-Shanno algorithm (BFGS) 27 and a form of a random walk to explore the surfaces, using the textbook equations as an initial starting point. A new starting point S37 very close to the best solution was then picked and the BFGS was run again to obtain the new solution.
This was repeated until the best solution wasn't modified for a fixed number of steps. This heuristic allowed for the exploration of the surface by retaining the best solution while testing many alternative sensible starting points, thus giving confidence about the quality of the obtained solution when the algorithm converged to one best solution. This stochastic method (BFGS) was run from several starting points then recorded and analysed the obtained solutions. This was repeated five times to generate an average for the output parameters (vessel and tailing numbers etc).

Fitting the RTD to a cascade of ideal CSTRs:
The hydrodynamics dictate whether the RTD of a real reactor deviates from that of an ideal reactor. A variance greater than 0 suggests dispersion in the apparatus which could be due to turbulence, diffusion, or a non-uniform velocity profile. An ideal CSTR is characterised by the instantaneous and complete mixing of the flow at the inlet of the apparatus, as well as the same homogenous composition during all times in the apparatus.
The RTD is an exponential which can be written as:

Equation S19
In this type of reactor, the mean is T and variance is 1, and the fluid placed into the system is never completely gone. Obtaining mixing instantaneously is not feasible due to the delay between any fluid passing from the inlet to the outlet. The RTD of a real reactor therefore deviates from the desired exponential decay. E will be subject to a finite delay before reaching its maximum or minimum value, which will be indicative of the rate of mass transfer in the reactor.
The CSTR cascade equation used to model RTD corresponds to: Generalizing this method to a series of n CSTRs gives the RTD for n CSTRs in series, E(t).
We analysed the residence time distribution to determine the number of ideal vessels, n, in series that give around the same residence time distribution as the nonideal flow system investigated. As n gets larger, the characteristics of the flow setup approach those of an ideal plug flow reactor.

S38
Mathematical equation to calculate the variance of the residence time: Mathematical equation used to calculate an approximation of N (tanks in series) to allow for a starting point for fitting the RTD data with the CSTR model: The following plots show the best fit of RTD together with the best CSTR model we were able to find using the method described above. The following graphs show the fitting of the CSTR model to the data: S39 HPLC pump (a) Figure S30. RTD profiles of the FlowNMR apparatus fitted to CSTR model for the double-piston HPLC pump as derived from FlowUV-vis spectroscopy at 334 nm using 12 mM fluorescein in acetone as the marker in a step change displacement experiment, at 1-6 mL/min at 25˚C.
Table S12. Sample tailing from surface area differences.

RTD to flow tip
The following plots show the best fit of RTD together with the best CSTR model we were able to find using the methods described in 10.1.