Chapter 10. Intro to Material Flow - Comments on Book Exercises

1. Shortest Time constants in Mono Lake Model:

The model that generated the results in Fig. 4.14 is shown in Fig. 4.12 (flow diagram), on page 48 (parameter values) and on page 52 (equlibrium diagram). The equilibrium diagram gives the best place to answer the question about how long a cubic foot of water remains in the lake. Look for the largest outflow in the system. Since the outflows are measured in KAF/yr, ask yourself how long 1 KAF of water would remain in Mono Lake if the lake's volume were under the control of only one flow (the largest outflow). Under the conditions shown in page 52, you would get 12.8 years. This time interval corresponds to an "average time interval" and gives us a feeling for the shortest time constants in the Mono Lake model.

2. Shortest Time Constants if Grant Lake Added to the Model:

You would follow a similar approach to answer the 2nd question on page 120. Look for the largest flow out of Grant Lake and ask youself how long 1 KAF of water would remain in the lake if only the largest flow were active. As you look for the largest outflow, remember that net Grant Lake evaporation is quite small relative to the flow in Rush Creek (i.e., the net evaporation is shown in the lower right part of Fig 5.1 at only 1.3 KAF/yr.)

3. Exercises 3 & 4: if you don't have the "Research" Version of Stella

The diagrams on page 114 were created with the "research" version of Stella. It allows you to assign a converter to name the transit time. In exercise #3, for example, the converter "incubation period" is used to make it clear that the incubation period sets the transit time that controls the flow of "eggs hatching." If you have the "basic" version of Stella, you won't be able to use a separate converter. But you can still complete the exercises by setting the transit time directly within the conveyor's dialogue box.

Two New Exercises

1. Build a Coflow and Check the Units:

Chapter 10 explains the most common approaches to simulate the flow of material through a system. At times, you will find it necessary to keep track of an average attribute of the material that accumulates in the system. A "Coflow" structure is useful in these situations. "Coflow" is short for coincident flows. The Stella documentation (HPS 1992, p. 86) explains how coflows may be used to keep track of an attribute associated with a material flow.

The automobile example shown below will illustrate. It is used to keep track of the average emissions of the cars in use. The primary flow is on the top. It simulates car sales and cars in use. Car retirements is the number of cars in use divided by the average life of cars. Now, suppose the emissions from new cars is expected to vary over time. (The ~ reminds us that the emissions is set with a graph function with time on the horizontal axis.) Also, suppose sales of new cars is also expected to vary over time.

The secondary flows are shown on the bottom. The inflow, additions to fleet emissions, is calculated by multiplying the two time varying inputs:

additions_to_fleet_emissions = car_sales*emissions_from_new_cars

The outflow, reduction in fleet emissions, is calculated in the same format as the outflow in the primary flow. That is:

reduction_in_fleet_emissions = total_emissions_of_cars_in_use/average_life_of_cars

The purpose of the coflow is to find the average emissions for the cars currently in use. Average emissions is the ratio of the two stocks:

average_emissions = total_emissions_of_cars_in_use/cars_in_use

Build the Coflow structure shown above. Turn in a copy of your flow diagram. Then write the units of measure for each variable onto the diagram. You may assume that car sales is measured in million cars per year. Emissions from new cars is measured in pounds per year from an individual car.

2. Simulate the Change in Average Emissions

Run the coflow model with time varying emissions from new cars and with time varying car sales to verify the results for average emissions shown below:

Set the emissions from new cars to decline from 10 to 5 pounds/year per car in the third year of the test. Set the car sales at 1 million cars/yr for most of the simulation. But set the sales to fall to zero for the 3rd, 4th and 5th years of the simulation. Initialize the stock of cars at 10 million and the stock of total emissions at 100 million pounds/year. These values well ensure that the average emissions is 10 pounds per year per car when the simulation begins.

This simulation shows that the average emissions for the cars in use will remain at 10 pounds/year during the first few years after the emissions standard for new cars is cut in half. This makes sense -- the average value will not respond immediately because no new cars are sold during these years. By the 6th year, car sales resume, and the average emissions gradually declines toward the value associated with new cars.