Modeling and control of size distribution for fluidized bed silane - - PowerPoint PPT Presentation

Modeling and control of size distribution for fluidized bed silane decomposition

Christy M. White

• B. Erik Ydstie

Department of Chemical Engineering Carnegie Mellon University Pittsburgh, PA

1400 Installed Capacity (MW) 2002 1992

Photovoltaic Industry

Industry Growth

IEA-PVPS, ‘03 Missing Link

Solar Cell Production

Raw Material SiHCl3 (TCS) Decomposition Crystallization Distillation Wafers IC’s Metallurgical Grade $3-5 per kg Electronic Grade $40-60 per kg Wafers PV Cells Solar Grade Aim: $20 per kg Remelt/Cryst Insufficient

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Silicon Production

H2 SiH4 H2 Si H E A T H E A T Fluid Bed Reactor Continuous Process 650°C Large surface area Dense Phase SiH4 Decomposition Particle Growth Size Distribution SiHCl3 or SiH4 Si H E A T H E A T Siemens Reactor Batch Process 1100°C

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Modeling Particulate Processes

space, time external coordinates

(mass balance)

Crystallization Aerosol Formation Cell Growth Fluidization

Population Balance

internal coordinates size, age, composition continuous phase distributed phase internal flux death and birth terms density distribution external flow terms

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Overall Reaction and Gas Phase

Thermal Decomposition of Silane: Ideal operation: dense zone is a CSTR Gas phase balance equations (SiH4, H2) Reaction rate defined by Lai et al. (1986) Accounting for loss through entrainment → Total reaction: η is fraction of product (powder) lost Behavior along external coordinate axes: position and time

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Solid Phase

Interval i

…

Interval n fi-1 fi fai,j fan qi rxni

Size interval mass balance Assume Derive fi assuming continuous number: can obtain:

Interval j

Behavior along internal coordinate axis: size

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Solution Strategy for Discrete Model

Ordinary differential equations for mass in gas and solid phases Algebraic constitutive equations

+

DAE system solved by MATLAB’s ode15s Adjustable Parameters Example Values Fraction of powder lost Aggregation proportionality constant

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Experimental Data for Validation

Operation of pilot scale reactor

Si powder H2 SiH4 H2 Si H E A T H E A T

Load known initial distribution – sieves used to measure distribution Continuous feed to fluidized bed Withdraw samples regularly ~8-12 samples per run

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Silicon in Reactor

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Particle Size Distribution

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Controlling Continuous Operation

SiH4 H2 feed Si powder H2 Si seed Si product

Objective control: mass of silicon manipulate: external flow rates

System Controller

–

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Inventory Control of Population Balance

Apply inventory control to system: Constant mass in reactor: Constant seed mass:

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Response to Set Point Changes

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System Dynamics

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Silicon Size Distribution

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Summary

• Size interval mass balance predictions of particle

distribution compare well with data

• Simulations of continuous operation and inventory

control indicate that size is controllable

• Further investigate measurability and stability
• Application to other particulate processes or multi-

scale modeling is significant

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Acknowledgements

• NSF Graduate Research Fellowship Program
• Solar Grade Silicon LLC
• Reactech Process Development Inc.
• Ydstie Research Group

Any opinions, findings, conclusions or recommendations expressed in this publication are those

• f the author(s) and do not necessarily reflect the views of the National Science Foundation

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