Introduction to Modeling of Engineering Systems

UNIVERSITY OF NEW HAVEN

TAGLIATELA COLLEGE OF ENGINEERING

EASC2211 Introduction to Modeling of Engineering Systems Fall 2015

TO: EASC2211 Students - Section 02 and 06

FROM: Dr. Cheryl Li, EASC Instructor

RE: Project 1 – Consulting on the Operation of a Solids Separation Process

Date: October 15, 2015

You are working as a consulting engineer and have been hired by a small manufacturing plant. The plant

engineer asks your advice on a solids-separation process, requiring that you develop a model to predict

the behavior over time for a transient process. The process has an operating cycle that requires periodic

removal of accumulated solids. Your model will be used to advise the client about the timing of the solids

removal. The results of your work should be presented in a technical memo, with calculations attached,

written for the plant engineer. The memo should include data tables and plots (in the memo) to explain

and justify your recommendations. The delivery date for your work is Nov. 2 (Section 02) or Nov. 3

(Section 06). Preliminary results will be required a week earlier to assure that progress is being made.

Solids Separation Process

A separation process is used to remove solids from a mixture using a settling tank. The feed stream flows

slowly through the settling tank allowing most of the solids to settle and remain in the tank. The liquid

stream leaving this tank, called the overflow, has a small residual amount of solids, which varies with the

fraction of solids currently in the settling tank. The liquid leaving the settling tank accumulates in a

storage tank. The process operates continuously until the concentration (measured as mass fraction) of

solids in the storage tank reaches a predetermined level. At that point the process is stopped so that the

settling tank can be cleaned out and a new storage tank is connected.

Some preliminary laboratory work provides the following information:

 The fraction of solids (y kg solids/kg) in the overflow stream varies with the solids concentration in the settling tank (x kg solids/kg) according to this equation: y=0.040 x

 A maximum solids fraction of 0.30 kg solids/kg is allowed in the settling tank. Once it reaches the maximum concentration the process must be stopped for solids removal.

 A maximum solids concentration of 0.60% (0.0060 kg solids/kg) is allowed in the product collection tank. Note that this concentration is the value for the accumulated product in the

storage tank, not the concentration in the overflow stream as it leaves the settling tank.

 The specific gravity of the solution can be estimated by the relationship 1.2/(1.2-x), where x is the fraction of solids. This relationship applies to all mixtures in streams or vessels.

The stream to be processed has 8.00 mass % solids and flows at a rate of 6.0 kg/min. Assume that the

total mass in the settling tank remains constant, but the concentration, density and volume change with

time. Initially the settling tank contains 120. liters of pure water, with no solids. The product collection

tank is empty at the start of the process.

Simulation Model

Complete the required work in four phases:

1. Develop the simulation model by writing mass balances (total mass and solids) for both the settling tank and the storage tank.

2. Set up an Excel sheet to integrate the transient balances to track the accumulation of solids in the settling tank and the accumulation of solids and water in the storage tank.

UNIVERSITY OF NEW HAVEN

TAGLIATELA COLLEGE OF ENGINEERING

EASC2211 Introduction to Modeling of Engineering Systems Fall 2015

3. Generate relevant data and establish a recommended operation time for the process 4. Complete a technical memo that contains required information and data displays

Your model will be based on the transient mass balances for the settling tank and the collection tank. Set

up total mass and solids balances in rate form for the tanks. Since the total mass in the settling tank is

constant, the accumulation rate of total mass is zero, but the solids balance will have a non-zero

accumulation rate. Numerical integration will be needed for tracking the solids concentration in each tank.

As part of your work you must determine the appropriate time step to produce results that are accurate

to three significant figures. Accuracy of numerical integration can be controlled by comparing the

results at a specific time (e.g., mass fraction solids in settling tank at 20 minutes) for two runs made with

different step sizes. Pick a time step size and then re-run the integration with the time step cut in half.

Repeat until you see no difference in the third significant figure. You will need to explain your time step

choice in your memo using an appropriate table to justify the accuracy of your model to the client.

Once you have developed your model provide a recommended time for running the process before

stopping to remove the solids from the settling tank. The information given above from the laboratory

work provides your design constraints. The operators will observe the volume in the settling tank as a

simple way to monitor the process, so you will need to indicate the final volume at which they should

stop the process. Since the operation requires some flexibility it will be important to provide plots of

solids concentration in the settling and collection vessels as a function of time, as well as plots of volumes

vs time. This will enable the plant engineer to make adjustments to your recommended operating time

when necessary.

Report Requirements

Report your results to Mr. Ian T. Graytor, Senior Plant Engineer, in a technical memo, no longer than 3

pages. Appropriate data tables and plots should appear in the memo along with your explanation of your

work and your recommendations. Briefly discuss the basis for your model (basic mass balance equations

used) and the mathematical techniques employed. A portion of your spreadsheet should be attached as an

appendix to the technical memo. Do not include the full table of numerical integration results (it will

likely be hundreds of lines), but do include a diagram of the process with variables, equations and enough

of the results to allow the client to understand and possibly reproduce your work.

Students may work in pairs to develop the models, but each student must write and submit his or her own

memo. A copy of your spreadsheet showing preliminary results (just a page or 2) should be submitted by

Oct. 28 (S02) or Oct. 29 (S06) to assure that progress is being made. Identify both team members in the

heading of the spreadsheet. The technical memo with appendix is due Nov. 2(S02) or Nov. 3(S06). Note

that this is a PITCH project in which technical communications is a major focus. The project grade will

depend on the quality of communications in the memo and spreadsheet as well as the technical merit of

the work. Refer to PITCH documents on memos and data displays.