Friedrich Workshop on Modelling and Simulation of Coal-fired Power Generation and CCS Process

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Friedrich Workshop on Modelling and Simulation of Coal-fired Power Generation and CCS Process

  1. 1. Efficient simulations of general adsorption cyclesDaniel Friedrich, Maria-Chiara Ferrari, Peter Reid and Stefano Brandani Institute for Materials and Processes University of Edinburgh Mathematical Modelling and Simulation of Power Plants and CO2 Capture d.friedrich@ed.ac.uk
  2. 2. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionMotivationWhy do we need efficient simulation tools? Benefits of simulation Interpretation of experimental results Insight into different physical effects and device behaviour Estimation of device and process parameters Predicting the behaviour of future experiments Design of experiments Optimisation of the process Adsorption processes are very complex 3D problem for pressure, temperature and concentration Different length scales: column, pellets, crystals Different time scales: convection, macro- and micropore diffusion, adsorption, heat transferEfficient simulations Daniel Friedrich
  3. 3. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionExample systemDual Piston Pressure Swing Adsorption (DP-PSA) Low sample requirement Rapid testing of adsorbents Many different configurations Efficient numerical simulation tool required Closed system: needs conservative scheme Dynamic system with many parameters and variables Large Peclet number: shock formation and propagation Long computation to cyclic steady stateEfficient simulations Daniel Friedrich
  4. 4. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionExample systemSimulation of the DP-PSA system Lots of data from this experiment so need a fast and efficient dynamic simulator for the analysis of the experiments and to estimate adsorbent parameters CO2 mole fraction in the column Simulation tool requirements 1 Conservation of mass, energy Mole fraction 0.5 and momentum Fast simulation of one cycle 0 1 Colu 40 Acceleration of convergence mn 0.5 leng 20 th 0 0 Time Robustness and ease of use Test case starting with uniform CO2 /N2 mixture and inducing a CO2 concentration gradient along the column lengthEfficient simulations Daniel Friedrich
  5. 5. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionModelling of adsorption processesAdsorption process model hierarchy Column Pellet Intercrystalline Macropores 0 1 External fluid film Rp z=0 z=Lc rp Idealised spherical crystallitesEfficient simulations Daniel Friedrich
  6. 6. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionModelling of adsorption processesSimple adsorption column model Axial dispersed plug flow Isothermal system LDF mass transfer Langmuir isotherm No frictional pressure drop Ideal gas Gas phase material balance ∂ci 1 − ∂¯i q ∂(ci u) ∂Ji + + + =0 ∂t ∂t ∂z ∂z ∂ci u + |u| D = (ci0+ − ci0− ) ∂z z=0 2 Solid phase material balance ∂¯i q qsi bp Pxi = ki − qi ¯ ∂t 1 + bp PxiEfficient simulations Daniel Friedrich
  7. 7. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionSimulating adsorptionSolution strategy Discretise only the spatial dimension: Method of Lines Gas phase discretised by the Finite Volume Method (FVM) Solid phase discretised by the Orthogonal Collocation on Finite Elements Method (OCFEM) Simulation to Cyclic Steady State Differential Algebraic Equations are solved by state-of-the-art solver SUNDIALS Accelerate the convergence to CSS with extrapolation Benefits Spatial discretisations tailored to the corresponding phase SUNDIALS is robust and simplifies the developmentEfficient simulations Daniel Friedrich
  8. 8. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionSpatial discretisationFlux-limiting Finite Volume Method for convective term Sharp fronts require specialised discretisation schemes Finite Volume Method is inherently conservative: simulations with a low number of grid points are possible Flux-limiting scheme guarantees the correct behaviour of the solution Use higher order methods in smooth regions First-order upwind methods close to the shock Comparison of discretisations Flux−limited 1.2 Upwind 1 Central differences Mole fraction 0.8 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1 Column lengthEfficient simulations Daniel Friedrich
  9. 9. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionSpatial discretisationOrthogonal collocation on finite element method The adsorbed concentration in an adsorbent pellet changes considerably over one cycle but only a small part of the pellet actively takes part in the process. Pellet concentration Uniquely suited to stationary Adsorbed concentration gradients in the solid phase 0.7 Split the domain into small 0.6 elements to handle steep gradients 0.5 1 24 Par ticle 0.5 22 High order of accuracy for a leng th 0 20 T ime small number of grid pointsEfficient simulations Daniel Friedrich
  10. 10. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionTime integrationSUNDIALS Solver for Differential/Algebraic equation systems F (t, y (t), y (t)) = 0 ˙ Based on variable-order, variable-step size Backward Differentiation Formulas Nonlinear systems are solved by Newton iteration Linear systems are solved by direct or iterative solvers Benefits Based on robust and efficient algorithms Modular implementation in C User control over most aspects of the integration A. C. Hindmarsh, P. N. Brown, K. E. Grant, S. L. Lee, R. Serban, D. E. Shumaker, and C. S. Woodward. Sundials: Suite of Nonlinear and Differential/Algebraic Equation Solvers. ACM Transactions on Mathematical Software, 31(3) : 363396, September 2005.Efficient simulations Daniel Friedrich
  11. 11. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionAcceleration to Cyclic Steady StateAcceleration to Cyclic Steady State Cyclic Steady State Many adsorption systems will reach Cyclic Steady State At CSS the system state is not changing between cycles, i.e. y (ktc ) = y ((k + 1)tc ) Sequential approach to CSS can be very slow, i.e. 1000 s of cycles Acceleration schemes 1 Non-sequential cycle calculation: extrapolation algorithms 2 Model and discretisation switch 3 Interpolation of the starting conditionsEfficient simulations Daniel Friedrich
  12. 12. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionAcceleration to Cyclic Steady State extrapolation Extrapolate the next solution from the previous 2m solutions 1 Set x0 = yi algorithm: r 2 Generate xi+1 = F (xi ) −1 =0 r 0 = xr 3 Apply algorithm −1 r r +1 (r +1) (r ) 4 Set yi+1 = (0) s+1 = s−1 + s − s 2m 0 0 0 m depends on the problem eigenvalues 1 1 0 0 2 For the DP-PSA m = 2 or 3 1 0 1 3 2 1 0 Switch to subsequent substitution close 0 2 4 2 1 to CSS 1 3 3 2 0 2 Skelboe, IEEE Transactions on Circuits 3 1 and Systems, 27, 3, 1980 4 0Efficient simulations Daniel Friedrich
  13. 13. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionAcceleration to Cyclic Steady State extrapolation: Convergence to CSS Convergence to CSS Subsequent substitution: linear convergence extrapolation: quadratic convergence In the studied cases 35% faster convergence Comparison of the approach to CSS Approach to CSS in PSA process Subsequent substitution 0.6 ε extrapolation −2 Cyclic difference 10 Mole fraction 0.5 −3 0.4 10 0.3 Subsequent substitution −4 ε extrapolation 10 0.2 0 20 40 60 80 100 0 20 40 60 80 100 Cycle number Cycle numberEfficient simulations Daniel Friedrich
  14. 14. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionModel switch and interpolationModel and discretisation switch Start with the simplest case from the model hierarchy, e.g. isothermal and LDF, and coarse discretisation At CSS switch to the model and discretisation which accurately describe the problem Interpolate the coarse solution to the accurate description Simulate accurate model to CSS Linear interpolation 1 Last grid 0.8 New grid Reduces simulation time by at least an order of Mole fraction 0.6 magnitude 0.4 Simpler than an adaptive 0.2 scheme 0 0 0.2 0.4 0.6 0.8 1 Column lengthEfficient simulations Daniel Friedrich
  15. 15. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionModel switch and interpolationInterpolation of the starting conditions Restart from old solutions Interpolate the initial conditons from previous runs Can reduce the simulation time to CSS by ∼ 50% Especially important for parameter estimation because many runs of the simulation tool have to be performed Comparison of the approach to CSS Subsequent substitution 1 Cold start Extrapolation to CSS Restart Relative simulation time Cyclic difference 0 10 Restart from last solution 0.5 Simulation with −2 variable grid size 10 −4 10 0 20 40 60 80 100 Cycle number Different simulation schemesEfficient simulations Daniel Friedrich
  16. 16. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionSimulation of general adsorption cyclesGeneral adsorption cycles Adsorption systems Multiple adsorption columns Connected by splitters, mixers, valves and tanks Series of cycle steps: pressurisation, feed, purge, . . . Extend DP-PSA simulator to general adsorption cycles Modular system with different units: adsorption columns, valves, splitters, tanks, ... Arbitrary number and connection of the units Simulate different cycle configurations by time events, e.g. switching of valvesEfficient simulations Daniel Friedrich
  17. 17. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionSimulation of general adsorption cyclesCycle simulator interface Simulation of 2-bed, multi-step VSA/PSA cycles Arbitrary number and schedule of cycle stepsEfficient simulations Daniel Friedrich
  18. 18. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionConclusion Model hierarchy describing the adsorption process in different levels of detail Simulation tool for cyclic adsorption processes with tailored discretisation schemes for the fluid and solid phase Several acceleration schemes which accelerate the convergence to CSS by at least an order of magnitude Extended the simulation tool to general adsorption cycles Future work Implement all models from the model hierarchy Parallel implementation on multi-core CPUs and GPUs Integration of PSA/VSA simulator with UnisimEfficient simulations Daniel Friedrich
  19. 19. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionAcknowledgement Financial support EPSRC grant ’Innovative Gas Separations for Carbon Capture’, EP/G062129/1 EPSRC grant ’Fundamentals of Optimised Capture Using Solids’, EP/I010939/1 ARIC: Adsorption Research Industrial Consortium Opportunities in our group 2 Post-doc positions on carbon capture 2 Technician/Research Associate positions to further develop the laboratoriesEfficient simulations Daniel Friedrich
  20. 20. Introduction Modelling adsorption Simulating adsorption Acceleration Cycle simulator ConclusionQuestions? Thank you for your attention! Questions?Efficient simulations Daniel Friedrich

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