Volume scaleup factor

Consider the scaleup of a stirred tank reactor. It is common practice to scale using geometric similarity so that the larger reactor will have the same shape as the small reactor. Suppose the volume scaleup factor is given by Eq. (1). 

If the pilot reactor is turbulent and closely approximates piston flow, the larger unit will as well. In isothermal piston flow, reactor performance is determined by the feed composition, feed temperature, and the mean residence time in the reactor. Even when piston flow is a poor approximation, these parameters are rarely, if ever, varied in the scaleup of a tubular reactor. The scaleup factor for throughput is S. To keep t constant, the inventory of mass in the system must also scale as S. When the fluid is incompressible, the volume scales with S. The general case allows the number of tubes, the tube radius, and the tube length to be changed upon scaleup ... 

The scaleup factor for inventory is the same as that for volume when the density is constant ... 

One engineering design area, i.e., impacted by nonideal reactor behavior and the accompanying fluid residence time distribution(s) is scaleup. Suppose that a reactor study is conducted at the pilot scale level and that the conversion (or the equivalent) associated with volume flow rate Qs are judged to be acceptable. The classical scaleup problem is to then design a larger process with flow rate qs which results in the same conversion. The scaleup factor SF is. 

When scaling in parallel, the number of tubes scales directly with the inventory scaleup factor, S. Factors for other forms of scaleup for incompressible fluids are given in Table 10.2. This table includes three geometric scaleup factors. They are for volume, S, radius Sr, and length, Sl. They are related by Eq. (4) so that only two are arbitrarily adjustable. 

Example 1.7 predicted that power per unit volume would have to increase by a factor of 100 in order to maintain the same mixing time for a 1000-fold scaleup in volume. This can properly be called absurd. A more reasonable scaleup rule is to maintain constant power per unit volume so that a 1000-fold increase in reactor volume requires a 1000-fold increase in power. Use the logic of Example 1.7 to determine the increase in mixing time for a 1000-fold scaleup at constant power per unit volume. 

The power input to the fluid by the pump, Q AP, increases dramatically upon scaleup, as The power per unit volume of fluid increases by a factor of... 

Example 4.7 A fully turbulent, baffled vessel is to be scaled up by a factor of 512 in volume while maintaining constant power per unit volume. Determine the effects of the scaleup on the impeller speed, the mixing time, and the internal circulation rate. 

Thermal effects can be the key concern in reactor scaleup. The generation of heat is proportional to the volume of the reactor. Note the factor of V in Equation (5.32). For a scaleup that maintains geometric similarity, the surface area increases only as Sooner or later, temperature can no longer be controlled,... 

Example 5.11 The results of Table 5.1 suggest that scaling a tubular reactor with constant heat transfer per unit volume is possible, even with the further restriction that the temperature driving force be the same in the large and small units. Find the various scaling factors for this form of scaleup for turbulent liquids and apply them to the pilot reactor in Example 5.10. 

The factor of 4 increase in (mj) allows Pg/Vi)2 to decrease to 0.3(Eg/F/),. This suggests that the installed horsepower for the full-scale plant would be about a third of that calculated for a conservative scaleup with constant power per volume. This wiU have a major impact on cost and is too large to ignore. The engineer can do any of the following ... 

These results are consistent with a scaleup from the pilot-scale operation. Although power per volume is reduced and impeller to tank diameter ratio is increased, torque per volume is about half and tip speed is the same. With any realistic scaleup, some factors unavoidably must change, while the important ones are held constant. In a different situation and process, a different variable, such as power per volume, might be held constant. Other variables, such as blend time, could be calculated, at each step in the scaleup. 

Scaleup of laboratory data is a critical step and requires considerable experience. Since scaleup is subject to many factors that are not quantifiable, it is based primarily on experience and is a function of the specific dryer. When the heating surface is known, it is easy to calculate the working volume and the dryer s geometrical volume (Fig. 7). 

This book deals with the scaleup of chemical reactors. The product from the scaled-up reactor should be the same as the product from the pilot reactor. The extent of reaction should be the same in the two reactors and thus the mean residence time t should held constant upon scaleup. According to Equation 1.40, inventory and throughput are increased by the same factor when t is held constant. Unless explicitly stated otherwise, it is understood that inventory, volume, and throughput all increase proportionately ... 

For constant power per unit volume with a factor of 10 scaleup in linear dimensions, the agitator speed in the large reactor must be = 0.6 times that in the small reactor. If the... 

For turbulentflow in tubes, a series scaleup by a factor of 2 at constant t increases both u and L by a factor of 2, but the pressure drop increases by a factor of 2 - = 6.73. A factor of 100 scaleup increases the pressure drop by a factor of 316,000 The external area of the reactor, 2nRL, increases as S, apace with the heat generated by the reaction. The Reynolds number also increases as S, and the inside heat transfer coefficient increases by (see Chapter 5). There should be no problem with heat transfer if the pressure drop is acceptable. The input of power by the pump, 2 AP, increases dramatically upon series scaleup, as. The power per unit volume of fluid increases... 

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