Rate-Based Concepts Best Practices for When and How Mass Transfer is - PowerPoint PPT Presentation

Rate-Based Concepts Best Practices for When and How Mass Transfer is Applied in a Column Simulation Peter Poellmann, AQSim Europe OLI Simulation Conference 2014 22 October 2014

Vapor to condenser Reflux from Manway condenser Liquid distributor Structured packing Liquid collector with Liquid feed packing support Manway Liquid distributor Distillation Random packing Support device Column Trays Vapor from reboiler http://www.sulzer.com/en/ Liquid to reboiler Products-and-Services/ Separation-Technology/ Distillation-and-Absorption/Distillation

V 1 Modeling Q 1 Stage 1 F 1 Distillation V 2 U 1 W 2 L 1 Q 2 2 F 2 Countercurrent V 3 cascade of stages – U 2 W 3 generic model U j-1 W j L j-1 Q j Stage j F j F feed U j V j+1 W j+1 V vapor L liquid U N-2 W N-1 Q heat L N-2 U liquid side product Q N-1 N-1 F N-1 W vapor side product V N W N U N-1 L N-1 Q N F N N L N

V 1 Modeling Q 1 Distillation V 2 U 1 L 1 2 Countercurrent V 3 cascade of stages – ordinary distillation L j-1 column Stage j F F feed V j+1 V vapor L liquid L N-2 Q heat N-1 V 1 vapor distillate product V N U 1 liquid distillate product L N-1 L 1 reflux Q N L N bottom product Q 1 condenser duty (-) Q N reboiler duty (+) L N

V 1 Modeling 1 F 1 Distillation V 2 L 1 2 Countercurrent V 3 cascade of stages – absorption column L j-1 Stage j F feed V j+1 V vapor L liquid L N-2 N-1 F N rich/dirty feed gas V N F 1 fresh liquid absorption medium L N-1 V 1 lean/clean off gas F N N L N product/spent absorption medium L N

V n Equilibrium L n-1 Stage W n x i,n-1 y i,n H L,n-1 H V,n T n , p n , x i,n and y i,n are T n-1 T n related by Vapor- P n-1 p n Liquid Equilibrium VLE Stage n F feed F n V vapor Q n L liquid z i,n Q heat H F,n U liquid side product T F,n y i,n+1 x i,n W vapor side product p F,n H V,n+1 H L,n H enthalpy T n+1 T n T temperature p n+1 p n P pressure V n+1 U n x,y,z liquid, vapor or feed compositions i index for component L n n index for stage number => MESH equations

Problems Usually Encoutered in Dealing with Distillation Models • Column solving algorithm usually fails to converge on infeasible specifications of separation or numerics • Solver may diverge even on feasible specifications of the separation job, caused e.g. by numerical trouble, missing estimates, many stages, large flow feeded • Feasibility of separation non-trivial to ensure, e.g. in cases of pinch conditions or distillation boundaries • Divergence behaviour rarely helpful for correction • Among different specifications, some may lead to trouble, while others may run fine • Still today, automated methods for doing distillation design, e.g. finding numbers of stages, locations of feeds or side-stream draw-offs, are not at hand

Bulk vapor Bulk liquid Liquid film Vapor film Mass-Transfer Segment V-L interface V n L n-1 • Bulk and film regions Segment n y i,n x i,n-1 are distinguished in H V,n H L,n-1 each phase • T V,n T L,n-1 Films have contact Q L,,n p V,n P L,n-1 along a V-L interface Q V,n • Each bulk has its own N V,n N L,n N IF,n feed of material and F L,n F V,n heat • Material and heat fluxes x F,i,n y F,i,n q V,n q IF,n q L,n across interface are H L,F,n H V,,F,n defined T L,F,n T V,F,n V n+1 x IF,i,n L n • Exiting streams are not p L,F,n y IF,i,n p V,,F,n y i,n+1 x i,n related by VLE – rather T IF,n H V,n+1 H L,n are conditions at V-L T V,n+1 T L,n interface p V,n+1 p L,n N material flux q heat flux IF vapor-liquid interface => MESHNQ equations

When is Mass-Transfer Applied in a Column simulation ? • When a good VLE model of the physicochemical system is at hand, then the rate-based model is a useful fine-tuning of the column simulation. • Primary motivation for applying mass-transfer in a column simulation is design of the height of the equipment. • Several mass-transfer devices, e.g. random packing elements, structured packing, or trays, can be rated against each other, provided m-t coefficients exist. • Diameter and height lead to volume of packing, thus cost comparisons can be done. • Generally, mass-transfer is applied whenever product purities or emission limits need to be respected.

Examples for Significance of VLE for Distillation • Hydrochloric acid, i.e. Water / HCl – xy Diagram – Separation Factor – Acid concentration column (vacuum distillation) – Desorption / Specific energy consumption • Water / HCl / Chlorine – Solubility of Chlorine in Water – … in hydrochloric acid There is no point trying to apply a rate-based model for distillation, until the VLE is done properly

Hydrochloric Acid / boiling point 1.013 bar 200 150 100 Aspen ElecWiz t_bub (°C) Aspen EHCLFF 50 AspenOLI MSE AspenOLI aq. OLI reference 0 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 -50 -100 x_HCl (kmol/kmol)

HCl Acid / xy Diagram / Pressure 6 bar 1 0,9 0,8 0,7 y_HCl (kg/kg) 0,6 Aspen ElecWiz Aspen EHCLFF 0,5 AspenOLI MSE diag 0,4 0,3 0,2 0,1 0 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5 x_HCl (kg/kg)

HCl Acid / Separation Factor / Pressure 6 bar 1000000 100000 10000 1000 Aspen ElecWiz alpha 100 Aspen EHCLFF AspenOLI MSE 10 1 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5 0,1 0,01 x_HCl (kg/kg)

HCl Acid / Desorption Column HCl Gas Product Motivated by the separation factor, the OLI MSE model should be applied for desorption of HCl gas from hydrochloric acid at elevated pressure. Feed Acid 32% HCl by wt. Acid Flowback ~ 18% HCl

HCl Acid / Desorption / Reboiler Duty 6 bar Desorption of HCl gas from acid 32% wt. 1,2 using 10 equilibrium 1,15 stages at 6 bar(a). 1,1 Qr reboiler duty (kW) 1,05 D product gas flow (kg/h) D_max assumes Qr / D (kWh/kg) 1 desoption down to Aspen ElecWiz 0,95 azeotrope OLI MSE 0,9 0,85 0,8 0,75 0,7 0,9 0,91 0,92 0,93 0,94 0,95 0,96 0,97 0,98 0,99 1 D / D_max

Specification-to-Column-Design Workflow 1. Assume desired separation job as feasible 2. Set up and experiment with equilibrium-staged model, finally put solver loops (design-specs) in, ensuring product purities met all the time (by separate investigation, make sure such loops work robustly) 3. Select numbers of stages and feed locations (integer variables), then specify continuous variables (like, e.g. flow rates, temperatures of feed streams, pressures) Run equilibrium-stage based, analyse, (if necessary, go back to 3.) – until 4. staged column configuration and L, G (i.e. operating point) are fixed 5. Select internals, do hydraulic design, i.e. find diameters of every section 6. Set up for rate-based, e.g. numbers of mass-transfer segments, internals, bed heights, numbers of trays, not to forget numerics of model 7. With solvers (2.) still in, run mass-transfer based model, vary bed heights or tray numbers for minimal energy consumption 8. Establish a cost function for investment of column, decide about energy consumption cost, establish a total cost objective function 9. Vary type of internals, calculate volumes of packed sections, evaluate the total cost objective function (if too large, go back to 7) 10. Design column periphericals, e.g. reboiler, condenser, pumps, valves

Aspects of Applying Mass-Transfer in Column Simulations • Have good VLE model at hand, since m-t model is like fine tuning on eq.-stage based solution • See that eq.-stage based model converges robustly, before attemptimg to go for m-t • Get and accept information on empirical correlations involved for : – Mass-transfer coefficients – Heat-transfer coefficients – Diffusion coefficients – Interfacial area – Pressure drop

Applying Mass-Transfer in Column Simulations – Tricks of the Trade • While a variation of number of stages is hardly ever found in simulators (some can vary down), the m-t model allows for some kind of design by variation of height for fixed number of segments (but see also next point) • Do not over-do with number of segments – rule of thumb is height of segment should not exceed 1/10 of nominal size of packing element – however insert more segments in sections of significant change, look at profiles and go for smoothness • Complex columns with pumparounds may converge better overall, after being cut into pieces made of purely countercurrent or pumped-around sections, even though a flowsheet tear stream is created • If a specific operating point will not converge at all, then try to specify another, easier-to-conerge, maybe even trivial, operating point, and establish a homotopy from the latter to the former (simulators keep results obtained in a run as starting values for the next run) • „No estimates are better than bad estimates“ – they should be inside the range of variation the model will probably take – it can be severly disturbed, if estimates are infeasible, e.g. forgotten from earlier runs