Optimization of microcircuits for chemical mechanisms

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Optimization of microcircuits for chemical mechanisms

Mauro Torsello

Universit`a degli studi di Padova Dipartimento di Scienze Chimiche

9 maggio 2017

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Problem: simulate MFDs prototype systems for chemical reactions in homogeneous phases (micro-reactors) via continuum methods (CM)

General efficient procedure for optimization of micro-reactors complex reaction mechanisms in ‘structured’ channel

Answer: global search algorithms → Genetic Algorithms (GA) Implementation: NS + convection/diffusion model + GA search

Open source library (NS) Convection/diffusion routines Efficient search routines Parallelized implementation

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Simulation and geometry optimization of microreactors

Methods: CFD + genetic algorithms CFD:

1 finite differences

2 spectral elements

3 finite elements

4 finite volumes Why microreactors?

efficient heat dissipation (e.g. strongly exothermic reactions) fast mixing (small channel sections)

low volume of solvents

Very simple industrial scale-up → number-up

Given a generic complex chemical reaction, in liquid phase, we know:

1 All the elementary stage of the entire process (stoichiometric mechanism, is not necessary to know the intimate mechanism)

2 All the diffusion coefficients of the involved species (related to the used solvent) We solve the NS (with the OpenFOAM libraries) and the ADR equations until steady state

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Simulation and geometry optimization of microreactors

Methods: CFD + genetic algorithms CFD:

1 finite differences

2 spectral elements

3 finite elements

4 finite volumes Why microreactors?

efficient heat dissipation (e.g. strongly exothermic reactions) fast mixing (small channel sections)

low volume of solvents

Very simple industrial scale-up → number-up

Given a generic complex chemical reaction, in liquid phase, we know:

1 All the elementary stage of the entire process (stoichiometric mechanism, is not necessary to know the intimate mechanism)

2 All the diffusion coefficients of the involved species (related to the used solvent) We solve the NS (with the OpenFOAM libraries) and the ADR equations until steady state

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Microreactors as miniaturized artificial ’life-forms’

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Fluid motion and chemical transport-reaction decoupled

Solve the Navier-Stokes for the fluid

∂v

∂t + v · ∇v = ν∇²v − ∇π, ∇ · v = 0 Solve the Advection Diffusion Reaction for the chemical species

∂ci

∂t + v · ∇c = D∇²c + R(ci), i = 1, 2, ..., N whith N total number of reagents

transport and reaction phenomena

1 cell centered finite differences (x , y , z; t) → (xi, yj, zk; tn)

2 operator splitting approach: Advection, Diffusion, Reaction treated separately

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Define the bidimensional map of the device Create the related mesh

Apply the boundary conditions (for NS)

v = 0, ∇np = 0,vn= vin, ∇np = 0,∇_nv = 0, p = 0 Solve Navier-Stokes equations

∂v

∂t + v · ∇v = ν∇²v − ∇π, ∇ · v = 0 Apply boundary conditions (for ADR) jn= 0,jn= jin,outflow Solve Advection-Diffusion-Reaction equations

∂ci

∂t + v · ∇c = D∇²c + R(ci), i = 1, 2, ..., N

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v = 0, ∇np = 0,vn= vin, ∇np = 0,∇nv = 0, p = 0 Solve Navier-Stokes equations

∂v

∂ci

∂t + v · ∇c = D∇²c + R(c_i), i = 1, 2, ..., N

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∂v

∂ci

∂t + v · ∇c = D∇²c + R(c_i), i = 1, 2, ..., N

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v = 0, ∇np = 0,vn= vin, ∇np = 0,∇_nv = 0, p = 0 Solve Navier-Stokes equations

∂v

∂ci

∂t + v · ∇c = D∇²c + R(ci), i = 1, 2, ..., N

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∂v

∂ci

∂t + v · ∇c = D∇²c + R(c_i), i = 1, 2, ..., N

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∂v

∂ci

∂t + v · ∇c = D∇²c + R(ci), i = 1, 2, ..., N

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ADR equations

∂c

∂t + ∇ · j = 0

R

, Continuity equation (1)

j_A= cv, j_D= −D∇c, Fluxes

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j = j_A+ j_D, ∂c

∂t + ∇ · (cv) − ∇ · (D∇c) = R, ∇ · v = 0, D = const

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∂c

∂t + v · ∇c = D∇²c + R

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Reaction

∂ci

∂t = R(ci)

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The reaction term (aka source/sink term in the heat equation) does not depend on spatial derivatives (∇) but it couples different ci

Advection-Diffusion-Reaction

∂ci

∂t + v · ∇c_i = D∇²c_i+ R(c_i), i = 1, 2, ..., N

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How to deal with the whole problem? → Operator splitting

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ADR equations

∂c

∂t + ∇ · j =

0

R, Continuity equation (1)

j_A= cv, j_D= −D∇c, Fluxes

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j = j_A+ j_D, ∂c

∂t + ∇ · (cv) − ∇ · (D∇c) = R, ∇ · v = 0, D = const

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∂c

∂t + v · ∇c = D∇²c + R

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Reaction

∂ci

∂t = R(ci)

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∂ci

∂t + v · ∇c_i = D∇²c_i+ R(c_i), i = 1, 2, ..., N

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ADR equations

∂c

∂t + ∇ · j =

0

j_A= cv, j_D= −D∇c, Fluxes (2)

j = j_A+ j_D, ∂c

∂t + ∇ · (cv) − ∇ · (D∇c) = R, ∇ · v = 0, D = const

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∂c

∂t + v · ∇c = D∇²c + R

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Reaction

∂ci

∂t = R(ci)

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∂ci

∂t + v · ∇c_i = D∇²c_i+ R(c_i), i = 1, 2, ..., N

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ADR equations

∂c

∂t + ∇ · j =

0

j = j_A+ j_D,

∂c

∂t + ∇ · (cv) − ∇ · (D∇c) = R, ∇ · v = 0, D = const

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∂c

∂t + v · ∇c = D∇²c + R

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Reaction

∂ci

∂t = R(ci)

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∂ci

∂t + v · ∇c_i = D∇²c_i+ R(c_i), i = 1, 2, ..., N

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ADR equations

∂c

∂t + ∇ · j =

0

j = j_A+ j_D, ∂c

∂t + ∇ · (cv) − ∇ · (D∇c) = R,

∇ · v = 0, D = const

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∂c

∂t + v · ∇c = D∇²c + R

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Reaction

∂ci

∂t = R(ci)

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∂ci

∂t + v · ∇c_i = D∇²c_i+ R(c_i), i = 1, 2, ..., N

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ADR equations

∂c

∂t + ∇ · j =

0

j = j_A+ j_D, ∂c

∂t + ∇ · (cv) − ∇ · (D∇c) = R, ∇ · v = 0, D = const (3)

∂c

∂t + v · ∇c = D∇²c + R

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Reaction

∂ci

∂t = R(ci)

(5)

∂ci

∂t + v · ∇c_i = D∇²c_i+ R(c_i), i = 1, 2, ..., N

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ADR equations

∂c

∂t + ∇ · j =

0

j = j_A+ j_D, ∂c

∂t + ∇ · (cv) − ∇ · (D∇c) = R, ∇ · v = 0, D = const (3)

∂c

∂t + v · ∇c = D∇²c + R (4)

Reaction

∂ci

∂t = R(ci)

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∂ci

∂t + v · ∇c_i = D∇²c_i+ R(c_i), i = 1, 2, ..., N

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ADR equations

∂c

∂t + ∇ · j =

0

j = j_A+ j_D, ∂c

∂t + ∇ · (cv) − ∇ · (D∇c) = R, ∇ · v = 0, D = const (3)

∂c

∂t + v · ∇c = D∇²c + R (4)

Reaction

∂ci

∂t = R(ci) (5)

∂ci

∂t + v · ∇c_i = D∇²c_i+ R(c_i), i = 1, 2, ..., N

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ADR equations

∂c

∂t + ∇ · j =

0

j = j_A+ j_D, ∂c

∂t + ∇ · (cv) − ∇ · (D∇c) = R, ∇ · v = 0, D = const (3)

∂c

∂t + v · ∇c = D∇²c + R (4)

Reaction

∂ci

∂t = R(ci) (5)

∂ci

∂t + v · ∇ci = D∇²ci+ R(ci), i = 1, 2, ..., N (6)

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ADR equations

∂c

∂t + ∇ · j =

0

j = j_A+ j_D, ∂c

∂t + ∇ · (cv) − ∇ · (D∇c) = R, ∇ · v = 0, D = const (3)

∂c

∂t + v · ∇c = D∇²c + R (4)

Reaction

∂ci

∂t = R(ci) (5)

∂ci

∂t + v · ∇ci = D∇²ci+ R(ci), i = 1, 2, ..., N (6)

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Numerical solution of ADR equation

Operator splitting: Strang splitting

Advection operator: symmetrized dimensionally-split scheme [Kuchar´ık]

Diffusion operator: alternate direction implicit [Douglas]

Reaction operator: multistep Backward differentiation formula, variable order variable step

Properties of the numerical algorithm

second order accurate (in both time and space)

the required number of operations is ∝ N, where N is the number of mesh points (non-stiff cases)

the required amount of memory is also ∝ N (non-stiff cases)

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Genetic algorithms Selection Crossover Mutation Elitis´

FITNESS: reaction yield (i.e. product average

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Genetic algorithm and neural network

Learn vertical walk

https://dl.dropboxusercontent.com/u/51621154/MIORSOFT/Projects.html

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Geometry ⇐⇒ bit Matrix (i.e. bidimensional chromosome)

⇐⇒







1 1 0 1 1 1 1 1 1 1 1

0 1 0 1 1 1 1 1 1 1 1

0 1 0 1 1 1 0 1 1 1 1

1 1 0 1 1 0 1 1 1 1 1

1 0 1 1 1 1 1 0 1 1 1

1 1 0 1 1 1 1 1 0 1 1

0 1 0 0 1 0 1 1 1 1 1

1 1 0 0 0 1 1 0 1 0 1

1 0 0 0 1 1 0 1 0 1 1

1 0 0 1 1 0 1 1 0 1 0

1 1 1 1 0 0 1 1 0 1 1







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Geometry ⇐⇒ bit Matrix (i.e. bidimensional chromosome)

⇐⇒







1 1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1

1 1 1 1 1 1 1

1 1 1 1 1 1

1 1 1 1 1 1 1 1







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Genetic algorithms Selection Crossover Mutation Elitism´

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A+B → C Reaction

Generation 0

Maximum fitness: f = ^j^C^outlet

j_A^inlet1

Squares number ∝ search space Structures similar polyominoes

possible number of polyominoes with 56 cells is exactly known

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A+B → C Reaction

Generation 1

j_A^inlet1

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A+B → C Reaction

Generation 2

j_A^inlet1

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A+B → C Reaction

Generation 3

j_A^inlet1

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A+B → C Reaction

Generation 4

j_A^inlet1

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A+B → C Reaction

Generation 1299

j_A^inlet1

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Reaction 1: A+B → C

Fitness: : f =^j

outlet C j_A^inlet1

fitness optimized by the genetic algorithm fitness of the serpentine microdevice

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Reaction 1: A+B → C

a) concentration profile of C in the best GA microdevice b) concentration profile of C in the serpentine microdevice c) velocity magnitude in the best GA microdevice d) velocity magnitude in the serpentine microdevice

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Reaction 2

8 species 3 stages mechanism

A + B−→ C^k (7)

C + D−→ E + F^k (8)

F + G−→ H^k (9)

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Reaction 2

Fitness: : f =^j

outlet2 H j_A^inlet1

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Reaction 2

a) concentration profile of H in the best GA microdevice b) concentration profile of H in the serpentine microdevice c) velocity magnitude in the best GA microdevice d) velocity magnitude in the serpentine microdevice

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Reaction 3

P1 − + − P2−−^k−→ P1 − P2−^F (10)

P1 − + − P3−^k−→ P1 − P3^F (11)

−P2 − + − P2−−→ −P2 − P2−^k^S (12)

−P2 − + − P3−→ −P2 − P3^k^S (13)

P1 − + − P2 − P2−−^k−→ P1 − P2 − P2−^F (14) P1 − + − P2 − P3−^k−→ P1 − P2 − P3^F (15) P1 − P2 − + − P3−→ P1 − P2 − P3^k^S (16) P1 − P2 − + − P2−−→ P1 − P2 − P2−^k^S (17)

−P2 − P2 − + − P2−−→ −P2 − P2 − P2−^k^S (18)

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Reaction 3

Fitness: : f =^j

outlet2 P1−P2−P3

j_P1−^inlet1

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Reaction 3

a) concentration profile of H in the best GA microdevice b) concentration profile of H in the serpentine microdevice c) velocity magnitude in the best GA microdevice d) velocity magnitude in the serpentine microdevice