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## Ordinary Differential Equation Models

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**1. **Ordinary Differential Equation Models Classification of ODE models
Liquid storage tanks
Chemical reactors
Cellular metabolic networks

**2. **Mathematical Modeling Motivation
Yields improved understanding of physicochemistry
Provides rigorous framework for data analysis
Allows prediction without additional experimentation
Core competency of any chemical engineer
UMass ChE curriculum
ChE 120 – mass and energy balance modeling
ChE 226, 325 – thermodynamic modeling
ChE 230 – fluid transport modeling
ChE 320 – chemical reaction modeling
ChE 333 – heat and mass transfer modeling
ChE 338 – separation unit modeling
ChE 444 – plant-wide modeling
ChE 446 – control system modeling

**3. **Classification of ODE Models Order
Linearity
Explicit versus implicit

**4. **Classification of ODE Models cont. Dimension
Current focus: systems of first-order, explicit ODEs

**5. **Liquid Storage Tank Standing assumptions
Constant liquid density r
Constant cross-sectional area A
Other possible assumptions
Steady-state operation
Outlet flow rate w0 known function of liquid level h

**6. **Mass Balance Models Mass balance on tank
Steady-state operation:
Valve characteristics
Linear ODE model
Nonlinear ODE model

**7. **Stirred Tank Chemical Reactor Assumptions
Pure reactant A in feed stream
Perfect mixing
Constant liquid volume
Constant physical properties (r, k)
Isothermal operation

**8. **Plug-Flow Chemical Reactor Assumptions
Pure reactant A in feed stream
Perfect plug-flow
Steady-state operation
Isothermal operation
Constant physical properties (r, k)

**9. **Plug-Flow Chemical Reactor cont. Overall mass balance

**10. **Cellular Metabolic Networks

**11. **Yeast Glycolysis

**12. **Model Formulation Intracellular concentrations
Intermediates: S1, S2, S3, S4
Reducing capacity (NADH): N2
Energy capacity (ATP): A3
Reaction scheme

**13. **Stoichiometric Model Assumptions
Intracellular and extracellular steady state
Measure glucose influx J0 and acetaldehyde/pyruvate efflux J
Steady-state mass balances

**14. **Kinetic Model Reaction scheme
Reaction kinetics for v2-v6
Reaction kinetics for v1

**15. **Kinetic Model cont. Intracellular mass balances
Conserved quantities
ODE model