Process units, tearing

For the methanol synthesis process illustrated in Fig. 4-1, Example 1, assume that there are algorithms for calculating the outputs of each process unit from the inputs. Determine how many stream variables must be specified and decide what these should be so that a unique solution exists for the mass and energy balances. Identity all recycle loops, tear streams for these loops, and a calculation sequence. 

For a process flow sheet obtained in Problem 3, assume that algorithms are available to calculate the outputs from each process unit from known inputs. Determine the number of stream variables that must be specified, decide what they should be, identify all recycle loops, select tear streams for these loops, and establish a calculation sequence. 

Chemical industries need various types of items for their safe, pollution-free operation. The process units and machineries need reliable spare parts for the smooth running. The wear and tear of various equipments is comparatively more in chemical industries than other industries due to corrosive nature of many chemicals and presence of fumes, dust, and gases. 

A process can also be represented by its adjacency matrix, which can be formed without first drawing the graph, by just assigning each unit a number and placing a nonzero entry in column j and row i if there is a stream directed from unit j to unit /. Once the adjacency matrix is formed, it can be partitioned into blocks of units that must be solved simultaneously exactly as described in Section IV. It is the tearing of these blocks that is of interest here. In both of the methods of tearing discussed here the objective is to tear a block so that the minimum number of variables will have to be assumed in solving the process equations involved in the block. 

Lee (L2) proposed a different algorithm for tearing, which also obtains the tears for the minimum number of variables associated with the torn streams. The procedure is completely different from that of Sargent s in that the loops of material flow are determined first and tears made so that all the loops are broken. The algorithm requires a previous knowledge of the loops of material flow and which units and streams are included in each loop. The loops can be found by forming the adjacency matrix for the process, and determining the loops in the matrix by Steward s method as described in Section IV. 

Given a description of a multiple-unit process, determine the number of degrees of freedom, identify a set of feasible design variables, and if there are cycles in the flowchart, identify reasonable tear stream variables and outline the solution procedure. Draw a sequential modular block diagram for the process, inserting necessary convergence blocks. 

The first unit called is always the one following the tear stream.) The call of SEP would result in the recalculation of h from the separation process balances (stream S4R). CONVC would compare this value with the one initially assumed. If the two values agree to within a specified tolerance, the calculation would be terminated otherwise, the new value would be used to begin another journey around the cycle. The nature of the iterative procedure performed by CONVC is discussed in greater detail in Appendix A.2. 

For single-unit processes, it is usually desirable to pick design variables that minimize the number of state equations that must be solved simultaneously. For multiple-unit processes, it is desirable to pick design variables to minimize the number of cycles on the flowchart. When doing calculations for cycles on flowcharts, it is desirable to tear as many cycles as possible with the minimum number of tear stream variables. These rules of thumb may not always lead to the most efficient calculations and they may contradict one another, however, so that finding the best combination of design and tear stream variables may require considerable trial-and-error for complex processes. 

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