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What DPB Does DPB Is a Mathematica package Data Read from a spread sheet file “Re-grid” size points Interconvert number and weight data Extraction and fitting Extract nucleation, growth, aggregation, selection or sink rate constants Fit models to rate constants Simulation

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The Population Balance Equation


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slide1
What DPB Does

DPB

Is a Mathematica package

Data

Read from a spread sheet file

“Re-grid” size points

Interconvert number and weight data

Extraction and fitting

Extract nucleation, growth, aggregation, selection or sink rate constants

Fit models to rate constants

Simulation

Uses a discretised population balance

Solves dynamic problems

Solves steady-state problems

Plotting

Rate constants

Moments

Particle size distributions

Find out how

AIChEJ, 34, no. 11, 1821, 1988

J. Coll. Interf. Sci., 203, no 1, 155, 1996

BreakageSizeDependence

AggregationSizeDependence

NucleationSizeDependence

GrowthSizeDependence

SinkSizeDependence

SelectionSizeDependence

AggregationDrivingForce

NucleationDrivingForce

GrowthDrivingForce

SinkDrivingForce

SelectionDrivingForce

NucleationRateConstant

AggregationRateConstant

GrowthRateConstant

SinkRateConstant

SelectionRateConstant

Crystallisation Example.

Batch experiments with calcium oxalate yield PSDs at regular time intervals. Aggregation and apparent nucleation rates are extracted and correlated. The PBE is solved to predict moments and the PSD.

An Interactive Population Balance Tool: DPBM.J. Hounslow, Particle Products Group, Department of Chemical and Process EngineeringThe University of Sheffield, U.K.

The Population Balance Equation

A statement of continuity relating particle-size distributions (PSDs) to underlying rate processes, such as the rates of growth and aggregation. PSDs are described by number probability density functions n(l,t), where l is particle size and t is time.

In words: Accumulation = Nucleation + Growth + Aggregation + Breakage + Sink

In symbols:

In DPB:

AIChE Miami 1998