1. Process and System Characterization Describe and characterize transport and transformation phenomena based reactor dynamics ( 반응공학 ) – natural and engineered systems Key point – distribution of constituents in a system 1. Masses enter and leave the system across its boundaries. 2. Masses are mixed within the system boundaries. Reactor Approach

2. Process Complexity Levels of characterization of systems and processes = f (system complexity, reaction complexity) Process complexity = f (scale, components)  Mega system – scale induced  Micro system – component induced  Macro system – in between

3. Process Modeling Mathematical models –characterizing and describing a system and its processes (components, composition, related transport and transformation) Procedures 1. Characterization of system boundaries 2. Selection, definition, and description of system components 3. Description of major transport and transformation processes by mathematical expressions 4. Development of simplifying assumptions 5. Formulation of mathematical equations comprising the overall system model 6. Development of algorithms for solution of the model equations 7. Calibration of the model with data specific to the system 8. Verification of the model with independent data 9. Application of the model for analysis, prediction, or design Principles for modeling – thermodynamics and continuity ( 열역학과 연속성 )  Conservation of energy, mass and momentum in the system boundaries  Balances in energy, mass and momentum in the system boundaries

4. Material Balance Basic framework for mathematical modeling - based on energetics, kinetics, and reactor dynamics Starting point – defining boundaries for control volume Control volume (CV, V c ) – the smallest system for which material balance is applied

5. Material Balance General form Net rate of mass transport through the control volume Net rate of mass transformation within the control volume (V c ) Net rate of mass change within the control volume (V c ) Net rate of mass input across the CV boundaries Net rate of mass output across the CV boundaries Net rate of reaction within the CV (V c ) Net rate of accumulation within the CV (V c )

6. Material Balance Steady/unsteady state ( 정상 / 비정상 상태 ) temporally stable/unstable conditions in a system (CV) existence of net changes in components of a system as a function of time, involving transformation as well as transport different from “equilibrium ( 평형 상태 )” Note - Steady state satisfies even in the ongoing internal reactions.

7. Material Balance Differentiation of a CV “Point form”, Homogenous in the differentiated CV

8. Material Balance Ex) Find mathematical models describing water balance and constituent balance for a system illustrated below.

9. Modeling Procedures 1) Problem specification Clarification of the customers’ objectives Two information sources 1. Management objectives, control options, and constraints 2. Collection of data (or pre-existing data) – physics, chemistry, biology of the target system  Acknowledging problem objectives, quality variables, and basic structure of the target systems (temporal, spatial, and kinetic mechanisms of the systems)

10. Modeling Procedures 2) Model Selection Use of existing models Development of a new model  Theoretical development – critical issue → model complexity,  “as simple as possible, but not too simple”  Numerical specification and validation – numerical solution and test for its mathematical expressions (mass balance, simple solutions, range of conditions, graphical evaluation, benchmarking)

11. Modeling Procedures 3) Primary application For identifying data deficiencies and theoretical gaps For identifying which model parameters are most important (e.g., sensitivity analysis) 4) Calibration Varying the model parameters to obtain an optimal agreement between the model calculations and data set in a systematic way Governing functions and physical parameters (boundary conditions and loads, initial conditions, and physics) Calibration parameters (kinetics) Adjustment of model parameters Fix the system parameters measured with sufficient precision Adjust the estimated parameters until a best fit

12. Modeling Procedures 5) Confirmation - verification Applying the newly developed model for new several data sets – governing functions and physical parameters can be changed to reflect new conditions, but no change in kinetic parameters) No match? → additional mechanism characterization, model refinement, fine tune Use pilot-scale physical model for the verification of a design model – prototype studies 6) Management Application Predict the environmental improvement by changing model parameters and governing functions

13. Modeling Procedures 7) Post-Audit Lessons from the implementation of models in remedial actions (before and after)