Ask Russ Rhinehart - How does one develop First-Principles Dynamic Models numerically?

Russ' Response:

Here are eight steps in developing a dynamic model. Details and examples can be accessed under the Modeling/Simulation menu on my web site, www.r3eda.com.

1. Inventory - Decide the inventory that accumulates. Tank level changes in time. But, level does not go into or flow out of a tank. Liquid material is the inventory that flows in, or out, or accumulates. Level is a response to the liquid inventory. Temperature is a response to heat inventory.
2. Control Volume - Decide the space in which the inventory accumulates. This is called the control volume, CV.
3. Keep It Simple - Assume conveniences. Only consider first-principles mechanisms. First, get the impressive dynamic model working. The complexities could be added later, if they are important.
4. IOGA - IOGA is the acronym for Inflow, Outflow, Generation, and Accumulation. Inflow is the quantity of inventory that goes into the CV from outside. Outflow is the quantity that leaves the CV. Generation is the quantity that is generated within the CV. Accumulation is the quantity that accumulates within the CV. The equation concept is Inflow – Outflow + Generation = Accumulation.
5. Constitutive Relations - Determine the equations that relate the response variables to the inventory. For instance, if the response is temperature, and the inventory is thermal energy, the elementary constitutive relation is Q=MCp∆T.
6. Rearrange - Present the rate of accumulation as a function of the influences – the model!
7. Initial State - Specify the initial values of influences and states. At the start time of a simulation the tank may be half full or the contents at a temperature of 67 *F.
8. Solve Numerically - Don’t use calculus! Solve the model using simple numerical methods as an executable line of computer code.

In subsequent Pods, I’ll introduce how to simulate environmental vagaries, how to calibrate and validate models, and how to use the models to evaluate the various economic indicators of transient events.  I hope to visit with you later. Meanwhile, visit my web site www.r3eda.com to access information about modeling, control, optimization, and statistical analysis.