Capital cost minimum

FIG. 22-55 Typical capital-cost schematic for membrane equipment showing trade-off for membrane area and mechanical equipment. Lines shown are from families for parallel hues showing hmiting costs for membrane and for ancillary equipment. Abscissa Relative membrane area installed in a typical membrane process. Minimum capital cost is at 1.0. Ordinate Relative cost. Line with positive slope is total membrane cost. Line with negative slope is total ancillary equipment cost. Curve is total capital cost. Minimum cost is at 1.0. 

Another variable that needs to be set for distillation is refiux ratio. For a stand-alone distillation column, there is a capital-energy tradeoff, as illustrated in Fig. 3.7. As the refiux ratio is increased from its minimum, the capital cost decreases initially as the number of plates reduces from infinity, but the utility costs increase as more reboiling and condensation are required (see Fig. 3.7). If the capital... 

In general, the final network design should be achieved in the minimum number of units to keep down the capital cost (although this is not the only consideration to keep down the capital cost). To minimize the number of imits in Eq. (7.1), L should be zero and C should be a maximum. Assuming L to be zero in the final design is a reasonable assumption. However, what should be assumed about C Consider the network in Fig. 7.16, which has two components. For there to be two components, the heat duties for streams A and B must exactly balance the duties for streams E and F. Also, the heat duties for streams C and D must exactly balance the duties for streams G and H. Such balemces are likely to be unusual and not easy to predict. The safest assumption for C thus appears to be that there will be one component only, i.e., C = 1. This leads to an important special case when the network has a single component and is loop-free. In this case, ... 

FIgur 7.4 If film transfer coefficients difier significantly, then nonvertical h t transfer is necessary to achieve the minimum area. (Reprinted from Linnhoff and Ahmad, Cost Optimum Heat Exchanger Networks I. Minimum Energy and Capital Using Simple Models for Capital Cost," Computers Chem. Engg., 7 729, 1990 with permission from Elsevier Science, Ltd.)... 

Thus, if film transfer coefficients vary significantly, then Eq. (7.6) does not predict the true minimum network area. The true minimum area must be predicted using linear programming. However, Eq. (7.6) is still a useful basis to calculate the network area for the purposes of capital cost estimation for the following reasons ... 

Increasing the chosen value of process energy consumption also increases all temperature differences available for heat recovery and hence decreases the necessary heat exchanger surface area (see Fig. 6.6). The network area can be distributed over the targeted number of units or shells to obtain a capital cost using Eq. (7.21). This capital cost can be annualized as detailed in App. A. The annualized capital cost can be traded off against the annual utility cost as shown in Fig. 6.6. The total cost shows a minimum at the optimal energy consumption. 

Distillation capital costs. The classic optimization in distillation is to tradeoff capital cost of the column against energy cost for the distillation, as shown in Fig. 3.7. This wpuld be carried out with distillation columns operating on utilities and not integrated with the rest of the process. Typically, the optimal ratio of actual to minimum reflux ratio lies in the range 1.05 to 1.1. Practical considerations often prevent a ratio of less than 1.1 being used, as discussed in Chap. 3. 

The tick-off heuristic. Once the matches around the pinch have been chosen to satisfy the criteria for minimum energy, the design should be continued in such a manner as to keep capital costs to a minimum. One important criterion in the capital cost is the number of units (there are others, of course, which shall be addressed later). Keeping the number of units to a minimum can be achieved using the tick-off heuristic. To tick off a stream, individual units are made as... 

If the feed, solvent, and extract compositions are specified, and the ratio of solvent to feed is gradually reduced, the number of ideal stages required increases. In economic terms, the effect of reducing the solvent-to-feed ratio is to reduce the operating cost, but the capital cost is increased because of the increased number of stages required. At the minimum solvent-to-feed ratio, the number of ideal stages approaches infinity and the specified separation is impossible at any lower solvent-to-feed ratio. In practice the economically optimum solvent-to-feed ratio is usually 1.5 to 2 times the minimum value. 

The main advantage of HGMS is high efficiency of separation even at relatively high dow rates and minimum pressure drops across the filter. The capital cost is very high, and only large installations are attractive economically because capacity increases with the square of the diameter of the canister while the weight of copper conductor increases linearly with diameter. 

A low temperature of approach for the network reduces utihties but raises heat-transfer area requirements. Research has shown that for most of the pubhshed problems, utility costs are normally more important than annualized capital costs. For this reason, AI is chosen eady in the network design as part of the first tier of the solution. The temperature of approach, AI, for the network is not necessarily the same as the minimum temperature of approach, AT that should be used for individual exchangers. This difference is significant for industrial problems in which multiple shells may be necessary to exchange the heat requited for a given match (5). The economic choice for AT depends on whether the process environment is heater- or refrigeration-dependent and on the shape of the composite curves, ie, whether approximately parallel or severely pinched. In cmde-oil units, the range of AI is usually 10—20°C. By definition, AT A AT. The best relative value of these temperature differences depends on the particular problem under study. 

Alternating current is converted to direct current (dc) for the smelting cells by siUcon rectifiers. High conversion efficiency (over 99%) and minimum capital costs are achieved when the rectified voltage is 600—900 V dc. Because aluminum smelting cells operate at 4.5—5.0 V, 130 or more cells are coimected in series, forming what the industry calls a potline, which may operate at 50—360 kA. 

Reboiler. The case shown in Figure 8 is common for reboilers and condensers on distillation towers. Typically, this AThas a greater impact on excess energy use in distillation than does reflux beyond the minimum. The capital cost of the reboiler and condenser is often equivalent to the cost of the column they serve. 

The estimated (DCFRR) and the estimated (NPV) are both functions of the estimated cumulative revenue from annual sales X As, the estimated cumulative total annual cost or expense X Ate, and the estimated fixed capital cost Cfc of the plant. The revenue from annual sales for each year is in turn the product of the sales price and sales volume. Initially it is desirable to select those values from the distribution cui ves of X As, X Ate, and Cfc which enable the maximum and minimum (DCFRR) and (NPV) to be calculated. 

Types and Accuracy of Estimates Capital-cost estimates may be required for a variety of reasons, among others to enable feasibility studies to be carried out, to enable a manufacturing company to select from alternative investments, to assist in selection from alternative designs, to provide information for planning the appropriation of capital, and to enable a contractor to bid on a new project. It is therefore essential to achieve the greatest accuracy of estimation with a minimum expenditure of time and money. 

Conversely, however, the cost of downtime can be very high and this creates a minimum risk philosophy which runs contrary to the capital cost factor. The balance between these two forces has to be clearly stated to allow the materials engineer to operate effectively. 

Determine the minimum operating cost for the process of Example 6.2 when the reactor consists of two equal-volume CSTRs in series. The capital cost per reactor is the same as for a single reactor. 

The cost of a closed atmospheric cylindrical storage vessels can be considered to be proportional to the mass of steel required. Derive a simple expression for the dimensions of such a storage tank to give minimum capital cost. Assume the top and bottom are both flat. 

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