Expression batch

Distillation. This is the point at which refining begins and was the first method by which petroleum was refined. Originally, distillation (qv) involved a batch operation in which the stiU was a cast-iron vessel mounted on brickwork over a fire and the volatile materials were passed through a pipe or gooseneck which led from the top of the stiU to a condenser. The latter was a coil of pipe, or a "worm" (hence the expression worm end products), immersed in a tank of miming water. 

Expression Dewaterings of Fibrous Materials. Fibrous materials are frequently dewatered in belt-filter, screw, disk, and roU presses and in batch pot and cage presses. Table 1 Hsts appHcations of screw, roU, and pot presses. Screw and high pressure belt presses are continuous and have replaced batch pot and cage presses in most appHcations. Traditionally, however, batch presses have been used for squee2ing cocoa butter from cocoa beans, which require pressures up to 41 MPa (6000 psi) (39). A description of many types of batch presses is included in Reference 40. 

Learning Curves It is usual to learn from experience. Consequently, the time taken to produce an article, the number of spoiled batches, the cost per unit of production, etc., tend to decrease with the number of units produced. The relationships are expressed for the ideal case by... 

Design Methods for Batch Vacuum Rotary Dryers The rate of heat transfer from the heating medium through the diyer wall to the sohds can be expressed by... 

In the past, expression presses were used in many processes for extracting oil and juice, generally from seeds and fruits such as olives. Batch presses were typically used in these apphcations, and hand unloading of the pressed cake was often required. Batch presses that require hand unloading or extensive cleaning between pressings are rarely used now descriptions of various types are presented in earlier editions of this handbook. This section, therefore, describes mainly continuous presses. 

The well-known difficulty with batch reactors is the uncertainty of the initial reaction conditions. The problem is to bring together reactants, catalyst and operating conditions of temperature and pressure so that at zero time everything is as desired. The initial reaction rate is usually the fastest and most error-laden. To overcome this, the traditional method was to calculate the rate for decreasingly smaller conversions and extrapolate it back to zero conversion. The significance of estimating initial rate was that without any products present, rate could be expressed as the function of reactants and temperature only. This then simplified the mathematical analysis of the rate fianction. 

Three basic fluid contacting patterns describe the majority of gas-liquid mixing operations. These are (1) mixed gas/mixed liquid - a stirred tank with continuous in and out gas and liquid flow (2) mixed gas/batch mixed liquid - a stirred tank with continuous in and out gas flow only (3) concurrent plug flow of gas and liquid - an inline mixer with continuous in and out flow. For these cases the material balance/rate expressions and resulting performance equations can be formalized as ... 

A suspension of aluminum hydroxide in water is to be filtered imder constant pressure in a batch Nutsch filter having a filtering area of 1 m. Each filter cycle is estimated to separate out 0.5 m of suspension. The operating temperature is 25° C. The following expression for the cake resistance was empirically determined from pilot tests ... 

Since the reaction is carried out in a batch system of constant volume, the rate expression for a second order rate law is... 

Given expressions for the crystallization kinetics and solubility of the system, the population balance (equation 2.4) can, in principle, be solved to predict the performance of both batch and of continuous crystallizers, at either steady- or unsteady-state... 

Column efficiency (number of theoretical plates) As in batch chromatography, one needs to determine the efficiency of the column in order to evaluate the dispersion of the fronts due to hydrodynamics dispersion or kinetics limitations. The relationship of N proportional to L can be expressed in terms of the equation for height equivalent to a theoretical plate (HETP) as ... 

For a batch differential distillation where no reflux is used, there is only boilup of a mixture of the desired lighter component, which leaves the kettle, and a desired residual bottoms composition is left in the kettle. This type of distillation follows the Raleigh equation to express the material balance. However, while simple, not having tower packing or trays or reflux does not offer many industrial applications due to the low purities and low yields involved. Repeated charges of the distillate back to the kettle and redistilling w411 improve overhead purity. 

The energy balance for the bioreactor is shown by the following equation. As the fermenter is used batch wise, the heat balance is mathematically expressed as stated in (4.4.1) ... 

Although many industrial reactions are carried out in flow reactors, this procedure is not often used in mechanistic work. Most experiments in the liquid phase that are carried out for that purpose use a constant-volume batch reactor. Thus, we shall not consider the kinetics of reactions in flow reactors, which only complicate the algebraic treatments. Because the reaction volume in solution reactions is very nearly constant, the rate is expressed as the change in the concentration of a reactant or product per unit time. Reaction rates and derived constants are preferably expressed with the second as the unit of time, even when the working unit in the laboratory is an hour or a microsecond. Molarity (mol L-1 or mol dm"3, sometimes abbreviated M) is the preferred unit of concentration. Therefore, the reaction rate, or velocity, symbolized in this book as v, has the units mol L-1 s-1. 

Continuous stirred-tank reactors can behave very differently from batch reactors with regard to the number of particles formed and polymerization rate. These differences are probably most extreme for styrene, a monomer which closely follows Smith-Ewart Case 2 kinetics. Rate and number of particles in a batch reactor follows the relationship expressed by Equation 13. 

In this work, the characteristic "living" polymer phenomenon was utilized by preparing a seed polymer in a batch reactor. The seed polymer and styrene were then fed to a constant flow stirred tank reactor. This procedure allowed use of the lumped parameter rate expression given by Equations (5) through (8) to describe the polymerization reaction, and eliminated complications involved in describing simultaneous initiation and propagation reactions. 

Equations (1.1) to (1.3) are diflerent ways of expressing the overall mass balance for a flow system with variable inventory. In steady-state flow, the derivatives vanish, the total mass in the system is constant, and the overall mass balance simply states that input equals output. In batch systems, the flow terms are zero, the time derivative is zero, and the total mass in the system remains constant. We will return to the general form of Equation (1.3) when unsteady reactors are treated in Chapter 14. Until then, the overall mass balance merely serves as a consistency check on more detailed component balances that apply to individual substances. 

Suppose there are N components involved in a set of M reactions. Then Equation (1.21) can be written for each component using the rate expressions of Equations (2.7) or (2.8). The component balances for a batch reactor are... 

The general conclusion is that density changes are of minor importance in liquid systems and of only moderate importance in gaseous systems at constant pressure. When they are important, the necessary calculations for a batch reactor are easier if compositions are expressed in terms of total moles rather... 

Assuming one wants to be certain that the risk of falsely declaring a good batch B to be different from the previous one A is less than 5%, the symmetrical 95% confidence limits are added to A (see Fig. 1.22) any value B in the shaded area results in the judgment B different from A, Hi accepted, Hq rejected , whereas any result, however suspect, in the unshaded area elicits the comment no difference between A and B detectable, H rejected, Hq retained . Note that the expression A is identical to B is not used by statistical means only deviations can be demonstrated, and similarities must be inferred from their absence. 

In closed systems (batch reactors), the instantaneous overall rate of accumulation of the reactant S is related to the reaction rate by the following expression ... 

The overall cost optimization criterion (5.4-137) to be minimized is composed of two terms. The first, which is called proportional, is related to the yield of both C and E one needs to maximize the yield of C, Yc, while minimising the ratio of yields, Y c. Yc and Kg are nc.f/nB.o and nE./nBA, respectively, n is number of moles, and y is a factor expressing the relative weight of the two terms (y was assumed to be one). The second term, called the non-proportional or fixed cost of operation, is the reciprocal of the ratio of yield of C per batch time, s, and as such it should be minimized, p is the weighing factor (equal to 174 in the process under consideration) in this term. 

The minimal cost of equipment was used as the criterion in the design of the plant, which was to be operated in a non-overlapping mode. For a plant consisting of MB true batch units (MS = 3) and MS semi-continuous units (MS = 5) which are grouped in MST semi-continuous trains (MST = 3), the cycle time is given by Eqn. (7.4-10). Combining this expression with Eqn. (7.4-22) and rearranging yields ... 

Bijn is the batch size for product i in stage / and equipment unit n, and EQj is a set of feasible equipment units to perform task /. P3 is expressed by ... 

---