College of Engineering
University of Wisconsin-Madison

ChE 250

A Technique for Approaching Chemical Engineering Problem Assignments

1. Read the problem statement thoroughly.

2. Attempt to visualize the physical process portrayed in the problem.

3. Draw a simple block diagram or flow sheet depicting your concept of the process. Use separate blocks for each unit of the process that may be involved in material or energy balances, e.g.,
   • Column or tower.

   • Reactor or combustion chamber.

   • Heat exchanger.

   • Pump.

   • Piping.

   • valves, etc.

   The degree of detail will be dictated by the pertinence of the unit to the problem. Carefully indicate all streams entering and/or leaving each unit of the system.

4. List on your diagram physical properties, concentrations, flow rates, etc., which have been given in the problem statement. It is good practice to assign symbols to these quantities and to define them at this point. Indicate the proper units to be used with each numerical quantity. Unless otherwise stated, gas mixture concentrations are given in mole percentages. In liquid mixtures no such generally accepted convention exists. Thus you should be careful to differentiate between weight fractions, molar concentrations, etc.

5. Determine from the problem statement what is desired. What is it that you have been asked to determine, calculate, etc.? Assign symbols to unknown quantities.

6. Define a system. A system is the body of matter or that portion of the universe being subjected to analysis. In chemical engineering problems, a system is usually some portion of a chemical processing plant. In a complicated multiunit process, it is frequently enlightening (or even necessary due to lack of data) to divide the process into several subsystems before an overall balance can be accomplished. Where more than one system is involved, indicate each clearly by an identifying number (e.g., Systems I, II, etc.) Be careful to indicate clearly in these instances which system you are referring to in each particular set of calculations. A safe procedure for defining a system is to draw a closed curve on your process diagram making sure that the curve crosses only those streams entering or leaving the system you have chosen.

7. Pick a basis for your calculations. Much qualitative information can be derived and communicated to other engineers by the simple expedient of picking a system to avoid ambiguity. If quantitative evaluation is required, then in addition to picking a system, a basis must also be selected upon which to base your computations. If no mass or energy transfer, or chemical reaction need be considered, then your system may also form your basis, e.g., gas law calculations on closed systems. However, if material or energy transfer from one portion of your system to another or to the surroundings, chemical reaction, or phase change is involved, a basis distinct from your system will be required for your calculations. A basis can be a unit of time during which the process operates, a quantity of material entering, leaving or remaining in the system, or a quantity of reactants or products in a chemical reaction. If unsteady operation is involved, a differential element of time, mass, or energy will usually form the basis for the solution of chemical engineering problems. A concentration, specific reaction rate, temperature, pressure, or other intensive variable cannot constitute a basis. After selecting a basis. stick to it! If a good basis is selected initially, a subsequent change of basis should not be necessary, irrespective of the degree of complexity of the problem. However, it is often difficulty to see immediately what wall constitute the most convenient basis to use throughout the problem. If a basis must be revised, make sure all calculations are revised to be consistent with the new basis.

   No engineer worth his salt ever becomes so sophisticated that he fails to note his selection of a system and basis in carrying out engineering calculations. This procedure is not something to be learned in your basic courses, only to be forgotten. As time goes on you will learn to be more astute about the selection of systems and bases to simplify calculations, but there is no excuse for bypassing their use.

8. Write the equations for material and/or energy balances. In theory a balance (input = output + accumulation) can be written for each atomic element in the system and the energy. Sufficient data are not always available to complete each of these balances, however. If only a limited number of balances are necessary to solve the problem, pick those balances which are most reliable to make your initial calculations. If a species such as the nitrogen in air goes thorough a system unaltered chemically, this species is usually a convenient balance to use to establish inlet and outlet compositions consistent with your basis.

9. Carefully scrutinize the data in order to determine which data are important to the solution of the problem.

10. If necessary, make engineering estimates of missing data that are essential to the solution of the problem. State the assumptions involved in your estimation procedure.

11. Make and list any simplifying assumptions used in your calculations. If engineers were to wait for the complete development of the experimental data and/or the appropriate theoretical equations necessary to solve their problems, we would still be working on the wheel. To fill the void between theory and practice, the engineer must make extrapolations, interpolations and educated guesses based on his/her training and experience. Now is the time to begin developing this ability. In your problem assignments simplifications are often acceptable due to poor data which do not justify a completely rigorous solution to the problem. More importantly, time limitations may necessitate such simplifications. After all, next to intelligence, time is an engineer's most valuable asset. Hence sacrifices in rigor can frequently be justified on the basis of time saved. You will be called on time and time again as a practicing engineer to rapidly size up a situation and make a decision in the absence of the data or the theory required to obtain a rigorous solution. Learning to supplement mathematical analysis with engineering judgment or "feel" can spell the difference between success and failure in this kind of assignment.

12. Take cognizance of the meaning of significant figures in making your calculations and reporting results. For instance, 1.0/3.0 is not 0.33333, etc., but simply 0.33. Statistically, the variance of the result of a series of multiplications and divisions is the sum of all the individual variances. In practice, this situation usually means that your answer need not contain more significant figures than the poorest individual item of data.

13. Call special attention to the results of intermediate calculations upon which the rest of the solution may depend. This practice gives you and others looking over the problem appropriate points of reference.

14. In engineering problems there are frequently independent methods of solving the problem. If more than enough elemental balances exist to solve the problem, use those left over to check the consistency of the data and to check yourself. To provide a satisfactory check, these balances must be truly independent. Be careful on this point since in complex processes the criteria for independence can be subtle indeed.

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Address questions and comments to thatcher@engr.wisc.edu Last modified on August 31, 1998