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Phase Behavior of Petroleum Reservoir Fluids in the Dense Phase or Supercritical Region
Published in Raj Deo Tewari, Abhijit Y. Dandekar, Jaime Moreno Ortiz, Petroleum Fluid Phase Behavior, 2019
Raj Deo Tewari, Abhijit Y. Dandekar, Jaime Moreno Ortiz
Figure 5.4 shows the reduced density–temperature relationship for CO2 in four different phase regions, namely the equilibrium liquid and vapor along the saturation or the vapor pressure curve, the critical and finally the dense phase region. Although not explicitly shown but the pressures (or the reduced pressure, Pr) corresponding to the reduced temperature Tr on the x-axis up to the critical point are the vapor pressures, i.e., Tr = Pr = 1 at the critical point. In other words, if reduced pressure and reduced densities are plotted instead then the data would show similar trend as in Figure 5.4. Obviously, both the densities of the equilibrium phases converge toward a common value at the critical point, i.e., reduced density of 1. Beyond the critical point (fully supercritical region) in order to show the variation in the reduced density as a function of reduced temperature (Tr > 1 as well as Pr > 1), a pseudo extension of the vapor pressure curve is obtained thus diagonally entering the dense phase box such as the one shown in Figure 5.1. CO2 density at the corresponding temperature and pressure values is then predicted and expressed as reduced density of the dense phase (diamonds in Figure 5.4). Again, somewhat similar to the propane data shown in Figure 5.3., the dense phase density values, even at relatively high temperatures, appear to be consistently quite high and liquid-like, as compared to the vapor phase.
Fundamentals of Momentum Transfer
Published in Mohammed M. Farid, Mathematical Modeling of Food Processing, 2010
The behavior of widely different materials can be brought to the same basis by invoking the principle of corresponding states, according to which reduced properties of gases and liquids follow the same relationships with reduced pressure and temperature. Reduced means that the value is normalized by dividing it by its value at the critical point. The reduced temperature and pressure can be interpreted as measurements of the deviation from ideal gas behavior, and hence of the interaction between molecules. Figure 1.4 plots reduced viscosity for many gases and liquids against reduced pressure and temperature.
Odorants for use with flammable refrigerants (1794-TRP)
Published in Science and Technology for the Built Environment, 2020
For a multicomponent mixture, the composition of the vapor phase and the liquid phase changes as the mixture is vaporized. Initially, the vapor phase is richer in the lower boiling point (higher vapor pressure) component of the mixture. As the vaporization continues, the concentration of the lower boiling point component in the vapor phase is reduced, trending toward the feed/liquid composition prior to the start of the vaporization. For the liquid phase, the concentration of the higher boiling point components increases as the more volatile components are vaporized. An increase in temperature or reduction in pressure generally accompanies the progression toward complete vaporization. The temperature or pressure change would represent a loss of efficiency in the refrigerant loop due to either the increase in compressor work or the lower heat transfer coefficient and reduced temperature differential across the heat exchanger (condenser or evaporator).
A novel approach to integration of hot oil and combined heat and power systems through Pinch technology and mathematical programming
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2019
Gholamreza Shahidian Akbar, Hesamoddin Salarian, Abtin Ataei
The concept of limiting hot oil profile is taken from the water Pinch analysis as shown in Figure 5b. They are defined as the minimum inlet and outlet temperatures for the hot oil stream. These allowable temperatures are limited by the minimum temperature difference (). In the new design, this could be the practical minimum temperature difference for a given type of heat exchanger. For a retrofit design, the temperature difference could be selected to comply with the performance limitation of the existing heat exchanger under the revised operating condition of a reduced temperature difference and increased flow rate. In addition, the limiting hot oil profile might be determined by other process constraints, such as corrosion, fouling, and maximum allowable oil temperature. Any hot oil lines at or above this profile is considered a workable design. The limiting profile is used to define a boundary between the feasible and infeasible regions. It should be emphasized that the final design will not necessarily feature the minimum temperature difference incorporated in the limiting data. It simply represents a boundary between the feasible and infeasible conditions. Most heaters in the final network design will feature temperature-driving forces greater than those used for specification of the limiting conditions.
Kinetic crystallisation instability in liquids with short-ranged attractions
Published in Molecular Physics, 2018
System sizes varied from N=1372 to N=10976 as described. We fix the interaction range of the square well potential at of the mean of two interacting particle diameters. We estimate the critical temperature using the results of Largo et al. [54] and interpolate their values to our choice of . This gives a critical temperature and critical volume fraction . We characterise the proximity to criticality with the reduced temperature To calculate the liquid–vapour binodal we set N=4000 and checked some state points with a larger system size of N=10976. For determination of the relaxation time we set N=1372 and equilibrated for at least in the NVT ensemble before sampling for at least a further 10 in the NVE ensemble, except for the deepest quenches (T=0.333, ) where we equilibrate for time units and sample for a further time units. In the case of the crystallization of monodisperse systems, N=10976, except for the deepest quench where N=1372. Our choice of ensemble is here motived by work by Berthier et al. [56,57] and is common practise for simulations of supercooled liquids [58,59].