Capacity exponents

The ratio method is also particularly useful for quick estimates over a range of capacities after a calculated estimate for one size has been made (10). The calculated estimate can be separated into groups C, C2,. .., according to individual equipment exponents n, n2,. Then an overall plant capacity exponent n can be calculated from... 

Example 4 Seven-Tenths Rule A company is considering the manufacture of150,000 tons annually of ethylene oxide by the direct oxidation of ethylene. According to Remer and Chai (1990), the cost capacity exponent for such a plant is 0.67. A subsidiary of the company built a 100,000-ton aimual capacity plant for 70 million fixed capital investment in 1996. Using the seven-tenths rule, estimate the cost of the proposed new facility in the third quarter 2004. 

From Table 5, the equipment vs. capacity exponent is given as 0.54 ... 

Plot the 1985 purchased cost of the shell-and-tube heat exchanger outlined in the previous problem as a function of the surface area from 100 to 2000 ft2. Note that the purchased-cost-capacity exponent is not constant over the range of surface area requested. 

Estimate by the turnover-ratio method the fixed-capital investment required for a proposed sulfuric acid plant (battery limit) which has a capacity of 140,000 tons of 100 percent sulfuric acid per year (contact-catalytic process) using the data from Table 19 for 1990 with sulfuric acid cost at 72 per ton. The plant may be considered as operating full time. Repeat using the cost-capacity-exponent method with data from Table 19. 

Table 2.4 Process-Productivity Factor and Capacity Exponents for Equation 2.1 ...

If we know the cost of a piece-of-equipment at one capacity and the capacity exponent, n, then we can calculate its cost at another capacity. We can find cost data in References [10], [13], [15], [16], and [36]. More recent cost data are contained in References [4], [30], [31], and [37]. Table 2.9 contains costs and capacity exponents of some common equipment. The correlation range given in Table 2.9 gives the size limits for each piece-of-equipment. You should not extrapolate Equation 2.6 too far beyond the limits specified. For example, from Table 2.9, the cost of a... 

EquipmenI Size Capacity Units FOB Cos k January 1990 Correlation Range Capacity Exponent, n Direci-Cost Factor, fjx-... 

Obtain purchased-equipment costs for carbon steel at the tabulated size and capacity exponent from Table 2.9. 

Capacity, planf 155-156, 349-361 Capacity exponents for equipmenf 170 for plants, 183-184, 186-187 Capital ... 

Equipment cost capacity exponents for, 165 estimation by scaling, 169-171 (See also specific name and Cost of equipment)... 

Based on a known cost C of an investment of capacity Qi and so-called capacity exponent CEX, the cost C2 of a new capacity Q2 can be calculated using Eq. (1). Since the cost function is nonlinear, a piecewise linear approximation, e.g. the one proposed by Croxton et al. [4], of the cost function has to be applied leading to an overall linear model. The time horizon is divided into 1 year time periods. 

Each operation unit capacity is assumed to be designable within an upper and lower boundary to accommodate for any considered production rate. The product demand forecasts are given for a ten year horizon. The costs are represented by power functions which vary in terms of capacity exponents and hence different investment decisions for the process units are expected. The capacity exponents (c.f Table 1) for the cost functions are taken from Peters and Timmerhaus [5]. For the piecewise linear approximation of the cost function, two time intervals are considered as default. Due to maximum capacity restrictions, the overall capacity of the reactor and the product absorption unit is achieved by an installation of at least three parallel reactors and two... 

Even though the three-dimensional XY-model accurately predicts the experimentally observed hexatic scattering, the model is unsatisfying for two reasons. First, heat capacity data taken on the 80SI system suggest that the heat capacity exponent, a, is approximately 0.5.22 Second, the original motivation for the stacked hexatic model of well-ordered smectic liquid crystal phases was the intuitive idea that the weakly coupled smectic layers should display some of the novel physics predicted to occur in two dimensions. It is unsatisfying not to have any remnants of that two-dimensional physics survive in the three-dimensional model. 

The exponents in the above power laws are called critical exponents. Table4.1 compiles a selected number of them together with their definition, thermodynamic conditions, and van der Waals values. Here pi - pg is the density difference across the coexistence curve. This quantity is called order parameter. Notice that by construction the order parameter vanishes above Tc. In addition, 8T = T — Tc and 8P = P — Pel- Notice also that we have not yet talked about the heat capacity exponent a. The prime indicates the same critical exponent below Tc. The van der Waals theory yields the same values for the two exponents listed here, i.e. a = a ... 

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