Differential Piston System

For the opening and closing movements of the mould tool a minimal volume of oil is required. The oil volume required fi om the pump results fi om the differential siuface and stroke of the piston (approx. 7% of the clamping cylinder volume). The rest of the oil flows through the borings in the main piston as a result of the piston stroke. The pressure cycle is shown in Figmes 3.16-3.18. 

When opening with increased opening force (high pressme opening) the control piston closes the main piston. The main piston and opening piston now open the mould with 50 bar pressme. 

When the injection imit is in the vertical position and braking is selected, the borings in the main piston are closed shortly before the end of the opening motion. This ensmes an exact positioning of the movable platens in their lower-most end position. Sinkage of the movable platem on an idle machine is also avoided. 

---

In biphase systems velocity of the steam is often 10 times the velocity of the liquid. If condensate waves rise and fill a pipe, a seal is formed with the pressure of the steam behind it (Fig. 2). Since the steam cannot flow through the condensate seal, pressure drops on the downstream side. The condensate seal now becomes a piston accelerated downstream by this pressure differential. As it is driven downstream it picks up more liquid, which adds to the existing mass of the slug, and the velocity increases. 

Perfectly mixed stirred tank reactors have no spatial variations in composition or physical properties within the reactor or in the exit from it. Everything inside the system is uniform except at the very entrance. Molecules experience a step change in environment immediately upon entering. A perfectly mixed CSTR has only two environments one at the inlet and one inside the reactor and at the outlet. These environments are specifled by a set of compositions and operating conditions that have only two values either bi ,..., Ti or Uout, bout, , Pout, Tout- When the reactor is at a steady state, the inlet and outlet properties are related by algebraic equations. The piston flow reactors and real flow reactors show a more gradual change from inlet to outlet, and the inlet and outlet properties are related by differential equations. 

Unlike stirred tanks, piston flow reactors are distributed systems with one-dimensional gradients in composition and physical properties. Steady-state performance is governed by ordinary differential equations, and dynamic performance is governed by partial differential equations, albeit simple, first-order PDEs. Figure 14.6 illustrates a component balance for a differential volume element. 

The force exerted by the substance within the cylinder on the lower force of the piston under these conditions is the product of the pressure exerted by the substance on the surface of the piston and the area of the piston. Moreover, the product of the area and the differential displacement of the piston is equal to the differential change of volume. The integral J F dh is then equal to P dV. This relation is the only change that is made in Equation (2.15) or a similar equation for quasistatic processes. The frictional effects or the collisions result in a temperature increase either of the surroundings, or of both the system and surroundings as the case may be, or the effects may be interpreted in terms of heat, as discussed above. 

A cutaway drawing of the rotating-cylinder reactor is shown in Fig. 35. The mechanical aspects of the reactor system were designed to provide temperature control, fluid containment, and process measurements. The apparatus consists of a stainless steel (SS) holder and glass cylinder in which rides an SS piston, sealed by two Viton O-rings. Piston movements is monitored by a linear variable differential transformer (type 250 HCD, Schaevetz Engineering) attached to the piston and fixed relative to the cylinder. 

In practice the measurement is usually carried out in an open system as represent id by part C In fig. 1.7b. The total heat evolved (in A+B+C) follows from the First Law, bq = - bU + pdV where we let the differentials apply to an infinitesimal downward movement of the frictionless piston. When the displacement of the piston results in transport of dn moles from the gas phase to the adsorbate. 

For the determination of the differential values of r and / the PVT cell containing mercury and a known volume of reservoir fluid is immersed in the constant temperature bath at reservoir temperature and the pressure is reduced 200 psi below the saturation pressure by withdrawing mercury from the cell through the mercury pump. The cell and its contents are thoroughly agitated until equilibrium is established and the volume of the gas-oil system is recorded. The gas is bled off through the metering device and at the same time the piston of the mercury pump is slowly advanced to keep the pressure in the cell constant. When the gas has been bled off, the volume of the residual oil in the cell is measured and recorded. The volume of the... 

In the latter case, the work done by the expanding gas and the piston will be W = / F d x. The work of the gas would be Vf = p dV if the process were reversible, that is, if the force F divided by the piston area were differentially less at all times than the pressure of the gas, and if the piston were frictionless but in a real process some of the work done by the gas is dissipated by viscous effects, and the piston will not be frictionless, so that the work as measured by J F dx will be less than / p dV. For these two integrals to be equal, none of the available energy of the system could be degraded to heat or internal energy. To achieve such a situation we have to ensure that the movement of the piston is frictionless and that the motion of the piston proceeds under only a differential imbalance of forces so that no shock or turbulence is present. Naturally, such a process would take a long time to complete. 

MA.). The exclusion limit of this column system is 1.7 x 10° determined with polystyrene standards (Waters Assoc., Milford, MA). The HPLC system consists of a piston pump (mini-pump, Milton Roy Co., Hollywood, Fla.), the columns, a Rheodyne injector 7125 an R—U Differential Refractometer, and a Speedomax H recorder (Leeds and Northrop, Phila., PA), with THF as the eluant. 

Since the well-known familiar forms of general principles have been deduced and always written for a system, consider first a system coinciding with the control volume at the final state while including in the initial state the piston-cylinder assembly as well as the control volume. Let E, E2 and E, E"v denote the initial and final values of the total energy of the system and the control volume, respectively. The first law of thermodynamics for the system undergoing a differential process is2... 

Piston flow reactors and most other flow reactors have spatial variations in concentration such as fl = a z). Such systems are called distributed. Their behavior is governed by an ODE when there is only one spatial variable and by a partial differential equation (PDE) when there are two or three spatial variables or when the system has a spatial variation and also varies with time. We turn now to a special type of flow reactor where the entire reactor volume is well mixed and has the same concentration, temperature, pressure, and so forth. There are no spatial variations in... 

From the results of part (a) we find that for the gas all e.xpansion proces.ses are reversible (i.e.. there are no dissipative mechanisms within the gas). However, from part fb), we. see that when the piston, cylinder, and gas are taken to be the system, the expansion process is irreversible unless the expansion occurs in differential steps. The conclusion, then, is that the irreversibility, or the dissipation of mechanical energy to thermal energy, occurs between the piston and the cylinder. This is, of course, obvious from the fact that the only source of dissipation in this problem is the friction between the piston and the cylinder wall. ... 

The sequence in the treatment of a core with a polymer gel system is similar to that just described and typically involves three steps. First, the initial permeability of the core sample is measured with brine. Then the core is treated with a polymer/crosslinker solution at a constant rate using a dual piston HPLC pump and a transfer cell (see Figure 5) while monitoring pressure with a differential pressure transducer. The core effluent is fractionated for analysis. This includes the determination of polymer and crosslinker concentration, the measurement of sample gelation tendencies, and the investigation of rock/polymer interactions. Finally, after a waiting period to allow gelation, the final permeability of the core is measured with brine to evaluate the effectiveness of the treatment. 

The presence of the membrane makes this system different from the multiphase, multicomponent system of Sec. 9.2.7, used there to derive conditions for transfer equilibrium. By a modification of that procedure, we ean derive the conditions of equilibrium for the present system. We take phase P as the reference phase because it includes both solvent and solute. In order to prevent expansion work in the isolated system, both pistons shown in the figure must be fixed in stationary positions. This keeps the volume of each phase constant dF = dF = 0. Equation 9.2.41 on page 236, expressing the total differential of the entropy in an isolated multiphase, multicomponent system, becomes... 

---