Constant pressure/variable volume method

Characterization of Mixed-Gas Permeation Properties. The mixed-gas permeation properties of isotropic PMP films were determined for several /i-butane/methane mixtures. The permeation experiments were performed using the constant pressure/variable volume method (8) at a feed pressure of 150 psig and atmospheric permeate pressure (0 psig). The feed temperature was varied between 0 C and 50°C. The following -butane/methane feed mixtures were used 1, 2, 4, 6, and 8 mol% w-C4H10 in CH4, respectively. The stage-cut, that is, the permeate flow rate to feed flow rate was less than 1%. Thus, the residue composition was essentially equal to the feed composition. The feed, residue, and permeate compositions were determined with a gas chromatograph equipped with a thermal conductivity detector. 

The permeate flux, J, measured by the constant pressure/variable volume method is given by (8) ... 

The effects of physical aging on the pure-gas permeation properties of PMP were determined with nitrogen by both the constant pressure/variable volume method (15 psia permeate pressure) and the constant volume/variable pressure method (0 psia permeate pressure). The experiments were carried out at 25°C the feed pressure was 50 psig. 

Gas permeation experiments were carried out for carbon dioxide, oxygen and nitrogen. The method used to measure the gas permeability was the constant pressure or variable volume method. For the measurements a home-made system was used [32]. It comprised a two-compartment flat sheet permeability cell. The feed stream circulates in the bottom compartment tangentially to the composite films and permeates through them to be collected in the top compartment where a flowmeter is connected. Due to the asymmetry of the composites the permeation experiments were carried out both for the top and bottom surfaces of the composite films facing the feed stream. 

To include the volume as a dynamic variable, the equations of motion are determined in the analysis of a system in which the positions and momenta of all particles are scaled by a factor proportional to the cube root of the volume of the system. Andersen [23] originally proposed a method for constant-pressure MD that involves coupling the system to an external variable, V, the volume of the simulation box. This coupling mimics the action of a piston on a real system. The piston has a mass [which has units of (mass)(length) ]. From the Fagrangian for this extended system, the equations of motion for the particles and the volume of the cube are... 

Thus, in a reversible process that is both isothermal and isobaric, dG equals the work other than pressure-volume work that occurs in the process." Equation (3.96) is important in chemistry, since chemical processes such as chemical reactions or phase changes, occur at constant temperature and constant pressure. Equation (3.96) enables one to calculate work, other than pressure-volume work, for these processes. Conversely, it provides a method for incorporating the variables used to calculate these forms of work into the thermodynamic equations. 

The state of a multivariant system is defined by assigning values to either the temperature, volume, and mole numbers of the components or the temperature, pressure, and mole numbers. Thus, we define heat capacities at constant volume or heat capacities at constant pressure for such closed systems. The equations and method of calculation are exactly the same as those outlined for univariant systems when the heat capacity at constant volume is desired. For the heat capacity at constant pressure, Equation (9.14) or (9.15) and the set of equations, one for each component, illustrated by Equation (9.18) are still applicable. The method of calculation is the same, with the exception that the volume of the system is a dependent variable... 

Since temperature, pressure, and composition are the appropriate independent variables for the Gibbs free energy we must now write out the entropy and volume in the form 5 = S(T, P, n, ) and V = V(T, P, , ), take their differential forms, and substitute these in Eq. (1.20.19a). Following the method used in setting up Eq. (1.13.4c), we next introduce the heat capacity at constant pressure, the appropriate Maxwell relation, as well as a and We also introduce the partial molal entropy S, and volume V,- to obtain... 

Aromatic Compounds in NaX. Molecular transport of aromatic compounds in zeolite NaX has been studied by both nmr and uptake measurements. On the basis of Equation 4,and if surface barriers are absent, both methods should lead to comparable results. Though uptake measurements by the variable - pressure, constant - volume method by Biilow and coworkers (16,17) apparently are in satisfactory agreement with the nmr data (18), extensive uptake measurements including chromatographic methods are continuously found to yield diffusivities of about two orders of magnitude below these values (19,20). In principle, this discrepancy might be explained by the existence of surface barriers, which remain invisible for nmr studies of intracrystalline diffusion, but which may control the uptake rate. 

Constant pressure MD can be implemented either by extended system methods that couple the dynamical system to an external variable V which is the volume of the simulation box (Andersen, 1980) or by constraint methods that use a Lagrange multiplier determined from Gauss principle (Evans and Morriss,... 

Using the variable change method (see section 2.1.5) we see that between the heat capacities at constant volume and pressure, we obtain the following relation ... 

Static methods. In which the system of interest is enclosed in a magnetically stirred variable volume cell [64, 76] which in some cases contains a window. The temperature and pressure within the cell are accurately metered. The cell volume may be changed either using a mercury piston or a mechanical piston and samples of the fluid phases present may be obtained, if required, under conditions of constant temperature and pressure by suitably reducing the cell volume. In the windowed cell version [76] sampling is unnecessary for binary systems since the cell may be charged with known amounts of the two components and conditions adjusted to obtain trace presence only of one of the phases. In this way the dew- and bubble-point curves for binary systems may be established and similarly the solubilities of solids in compressed fluids may be determined. 

Dew and Boiling-point Method. In essence this technique consists in introducing a mixture of known composition into an evacuated equilibrium container of variable volume (Refs. 6, 7, 9, 16,17, 18, 20, 28). The system is maintained at a constant temperature, and by varying the volume the pressure is observed at which condensation... 

In molecular dynamics (MD) simulation atoms are moved in space along their lines of force (which are determined from the first derivative of the potential energy function) using finite difference methods [27, 28]. At each time step the evolution of the energy and forces allow the accelerations on each atom to be determined, in turn allowing the atom changes in velocities and positions to be evaluated and hence allows the system clock to move forward, typically in time steps of the order of a few fs. Bulk system properties such as temperature and pressure are easily determined from the atom positions and velocities. As a result simulations can be readily performed at constant temperature and volume (NVT ensemble) or constant temperature and pressure (NpT ensemble). The constant temperature and pressure constraints can be imposed using thermostats and barostat [29-31] in which additional variables are coupled to the system which act to modify the equations of motion. 

The bulk modulus and the compressibility can be calculated by running molecular dynamics simulations to give equilibrium volumes at variable pressure. A simple method for the approximate calculation of the bulk modulus and of the elastic stiffness constants in the three main directions of a solid, using static simulation, will now be described, to illustrate how a macroscopic property like an elastic stiffness constant... 

Stainless steel capillaries (1 m length and 0.1 to 0.2 mm i.d.) transport the gas from the variable volumes to the ion source. The changeover valve alternately connects the reference and sample bellows to either the ion source or vacuum and the isotope compositions of the two gases are measured in turn. This method ensures a constant flow of gas through the capillaries at all times. To maintain viscous flow conditions, a pressure of 20 mbar in the inlet system is required. This constitutes a lower limit of gas suitable for analysis with the dual inlet system. The smallest practical volume of an inlet system is -250 pL. This represents 200 nmol of gas at 20 mbar. In some cases, there is not enough sample material available to produce sufficient quantities of gas and alternative analytical methods must be employed, e.g. isotope ratio monitoring. 

The disk was mounted on the membrane-coupling holder, which can withstand up to a pressure of 150psi. The system ensures that there is no pressure drop or leak at any point. The transport properties of membranes were measured using the variable pressure constant volume method. Fig.l shows the experimental setup of gas permeation apparatus. The membrane holder or the diffusion cell has two compartments, the feed side and the permeate side. The permeate side was kept under vacuum for 24 hrs to remove residual gas molecules and to obtain accurate measurements. 

Helical-lobe compressors are best suited for base-load applications where they can provide a constant volume and pressure of discharge gas. The only recommended method of volume control is the use of variable-speed motors. With variable-speed drives, capacity variations can be obtained with a proportionate reduction in speed. A 50 per cent speed reduction is the maximum permissible control range. 

The equilibrium state is generated by minimizing the Gibbs free energy of the system at a given temperature and pressure. In [57], the method is described as the modified equilibrium constant approach. The reaction products are obtained from a data base that contains information on the enthalpy of formation, the heat capacity, the specific enthalpy, the specific entropy, and the specific volume of substances. The desired gaseous equation of state can be chosen. The conditions of the decomposition reaction are chosen by defining the value of a pair of variables (e.g., p and T, V and T). The requirements for input are ... 

Robert Boyle (1627-1691), an English scientist, noticed that gases can be compressed. He used J-shaped tubes to show that gas pressure and gas volume at a constant temperature and amount are inversely related. His experiments were performed with one variable, and his conclusions were drawn from experimental observations. He argued that theories should be the result of experimental observations, and therefore he considered is the founder of the modem scientific method. 

In order to evaluate each of the derivatives, such quantities as (V" — V-), (S l — Sj), and (dfi t/x t)T P need to be evaluated. The difference in the partial molar volumes of a component between the two phases presents no problem the dependence of the molar volume of a phase on the mole fraction must be known from experiment or from an equation of state for a gas phase. In order to determine the difference in the partial molar entropies, not only must the dependence of the molar entropy of a phase on the mole fraction be known, but also the difference in the molar entropy of the component in the two standard states must be known or calculable. If the two standard states are the same, there is no problem. If the two standard states are the pure component in the two phases at the temperature and pressure at which the derivative is to be evaluated, the difference can be calculated by methods similar to that discussed in Sections 10.10 and 10.12. In the case of vapor-liquid equilibria in which the reference state of a solute is taken as the infinitely dilute solution, the difference between the molar entropy of the solute in its two standard states may be determined from the temperature dependence of the Henry s law constant. Finally, the expression used for fii in evaluating (dx Jdx l)TtP must be appropriate for the particular phase of interest. This phase is dictated by the particular choice of the mole fraction variables. 

Permeametry Method This method is based on the fact that the flow rate of a fluid through a bed of particles depends on the pore space, the pressure drop across the bed, the fluid viscosity, dimensional factors such as the area of the bed, and specific surface area (S. The determination of permeability can be made either under continuous steady-state flow (constant flow rate) or under variable-flow (constant-volume) conditions. 

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