1. An Interactive Population Balance Tool: DPB M. J
An Interactive Population Balance Tool: DPB M.J. Hounslow, Particle Products Group, Department of Chemical and Process Engineering The 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:
SelectionRateConstant
SelectionDrivingForce
SelectionSizeDependence
BreakageSizeDependence
AggregationRateConstant
AggregationDrivingForce
AggregationSizeDependence
NucleationRateConstant
NucleationDrivingForce
NucleationSizeDependence
GrowthRateConstant
GrowthDrivingForce
GrowthSizeDependence
SinkRateConstant
SinkDrivingForce
SinkSizeDependence
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
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.
AIChE Miami 1998