Recycle tearing

Again, we propose for each unit correct specifications, but we would like to know if these are feasible for the whole flowsheet. The recycle tear stream is cut in two parts, 8 and 9. The calculation sequence is Mixer, Reactor, Flash, and Splitter. We denote with Fh and Fm the partial flow rates of hydrogen and methane in the stream 9. After one pass through the calculation sequence, the partial flow rates of the components in the stream 8 will change. The convergence is obtained when the difference in the component flow rates of the streams 8 and 9 becomes smaller than an error. Consider nd... 

To execute a sequential solution for a set of modules, you have to tear certain streams. Tearing in connection with modular flowsheeting involves decoupling the interconnections between the modules so that sequential information flow can take place. Tearing is required because of the loops of information created by recycle... 

In contrast to the copolymerization of cyclic carbonates, the molecular weights are lower in the epoxide copolymerization 6,41 43). We assume that this is due to the presence of proton donors in the reaction mixture. They occur as impurities in epoxides 19,20) or anhydrides, moisture in all components of the copolymerization system, or their presence is a consequence of the high rate of hydrolysis of cyclic anhydrides 21). Proton donors added to the monomer feed remarkably decrease the molecular weight42 even in the copolymerization of ethylene glycol carbonate at 200 °C. Under these conditions, when recyclization of phthalic acid takes place 64) and the released C02 can tear off moisture to the gas phase, the molecular weight Mv decreases without proton donors from 45200 to 7100 in the presence of 5% phthalic acid or ethylene glycol or to 9300 in the presence of 15% water42,54. ... 

At this point all the units in the flowsheet are installed and converged. The last issue is to converge the recycle stream. The initial guessed values are adjusted to be close to the calculated values of flow and composition leaving the split S1. When these two streams are fairly close, the source of the recycle stream is defined as the split SI and the recycle stream is defined as a Tear stream. The flowsheet did not converge when the default convergence method... 

In Fig. 2, the recycle stream has been selected as the tear stream. A guess for xn must first be made, then the equations for units 1, 2, and 3 are solved. The output of unit 3, y3i, is then compared with the original guess for xn. The problem is solved when y3i has converged to X12 within the desired tolerance. The nonlinear algebraic equations to be solved can be written as xn = g(xn) or f(.Xn) = 12 - g(xn) = 0 and solved using the techniques discussed in Section III. Notice that the streams between units 1 and 2 or 2 and 3 could also have been chosen as the tear stream in Fig. 2. 

Pho, T. K. Lapidus, L., "Topics in Computer Aided Design. Part I - An Optimum Tearing Algorithm for Recycle Streams", AIChE J(1973) 19, No. 6 ... 

One stream in each recycle loop must be chosen as the tear stream for that loop. It is the one to be assumed, checked for convergence, and iterated. There is not an unambiguous guideline for this choice, nor is it usually critical which stream is chosen. If there is one for which it is easier to make a reasonable initial estimate, probably it should be selected. The actual recycle stream is often selected as the tear stream. 

A decision must be made whether the two recycle loops, units 10 and 11, are to be converged simultaneously or separately. Simultaneous convergence, as illustrated by Fig. 4-8o, is approached by checking and reestimating both tear streams once in each iteration. Separate convergence proceeds by converging the... 

Many flow-sheeting programs perform the partitioning, solution ordering, and tearing functions discussed above and present the user with one or more choices of solution sequence and tear variables. FLOWTRAN, however, does not do this. The user must identify the recycle loops, the calculation sequence, and the tear streams. The preceding example illustrated their identification and selection. 

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. 

The solution is to tear the cycle. We can tear it in any of three places between the mixing point and the reactor, between the reactor and the separation process, or between the separation process and the mixing point. The first choice involves the trial-and-error determination of two variables, the second one involves three variables, and the third involves only one (hi). The fewer variables you have to determine by trial and error, the more likely you are to succeed. Let us therefore choose the recycle stream as the tear stream. 

Networks of recycle loops are commonly encountered in large processes, and a suitable choice of a tear stream may minimize the number of iterations required to solve the balance equations of such systems. For example, consider the block diagram shown below. There are two cycles in this process 52-S3-S4 and S3-S5-S7. To solve the system equations you could, for example, tear both S4 and S7, which would require the inclusion of two convergence blocks and hence the simultaneous solution of two iterative loops however, you can instead tear one stream common to both cycles (S3), probably decreasing the computation time required to achieve the solution. 

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