When you perform design calculations or troubleshoot a process, you may need to know a mixture's phase behavior at certain process condi-tions, or you may need to know what conditions are necessary to recover a certain amount of a component from a mixture. Usually you must rely on a process simulator to get this type of information.
Flash Unit Operation
Figure 32 shows a general schematic of the PRO/II FLASH unit for a vapor-liquid system. PRO/II allows up to three products for this unit and an unlimited number of feeds.
Figure 32:
Three-Phase Equilibrium Flash Unit Operation
Note that Fj denotes the feed streams, V denotes the vapor product, L denotes the liquid product, W denotes either the decanted water or the second liquid product, and zji, yi, x1i, and x2i denote the component mole fractions for the respective streams. Q denotes the duty added or removed from the flash unit operation.
Solution Approach
For simplicity, consider a common special case of the above configura-tion: a flash with a vapor product and a single liquid product. PRO/II uses an iterative approach to solve the mass and energy balances and equilibrium relationships for a given system. For a general two-phase flash, these equations are:
Equilibrium Relationships
In equations (5) - (7), N is the number of components. Note, there are 3N+6 unknowns in this set of equations (F, V, L, zi, xi, yi, Q, T, and P).
However, there are only 2N+3 equations, leaving N+3 variables that must be set. We will discuss how these variables are set in the next sec-tion.
For a bubble point flash, the liquid phase component mole fractions (xi) equal the component feed mole fractions (zi). Additionally, the amount of vapor (V) is equal to zero. Thus, the equilibrium relationship to be solved is:
i = 1,...,N (9)
Similarly, for a dew point flash, the amount of liquid (L) is equal to zero and the vapor phase component mole fractions (yi) equal the component feed mole fractions (zi). Thus, in this case the equilibrium relationship to be solved is:
i = 1,...,N (10)
The PRO/II Reference Manual provides details about the solution algo-rithm. PRO/II allows you to provide estimates of temperature or pressure in order to enhance convergence of the flash algorithm for all types of flashes except isothermal flashes.
Defining the Flash Calculation
From the set of equations given above, you can see that Eq. (6) sets the phase equilibrium behavior for the system. In Eq. (6) the phase equilib-rium ratios or Ki's (also referred to as K-values) are typically functions of temperature, pressure, and composition, making the problem fairly complex. Your selection of a thermodynamic system for the process will greatly affect the solution.
As previously discussed, there are N+3 variables to be specified for each calculation. The feed stream composition and rate comprise N+1 of these variables. This leaves two degrees of freedom to be set in the flash algorithm. You must specify either the flash temperature or pressure.
yi xi
Valve, Mixer, and Splitter Unit Operations
The VALVE, MIXER, and SPLITTER units also perform phase equilibrium calculations. They are each equivalent to an adiabatic flash with zero enthalpy change (duty=0). The temperature is always computed rather than specified, and PRO/II allows an unlimited number of feeds to these units. You can set the pressure or pressure drop; otherwise PRO/II assumes a pressure drop of zero and uses the lowest feed pressure for the product streams. Figures 33-35 depict the schematics for these unit oper-ations.
Figure 33:
Valve Unit Operation
The VALVE unit can have up to three products. Designation and handling of the products for the VALVE unit is as flexible as for the FLASH unit.
MIXER units can only have one product; however, PRO/II always deter-mines the product phase, regardless of which phase (V, L, W, or M) you designate.
The SPLITTER unit combines any number of feed streams and splits the combined feed into products of identical composition and thermal condi-tion. The same phase designation must be used for all products (i.e., liq-uid, vapor, etc.). If you select an incorrect phase designation, PRO/II will reset it to the correct phase, as with the other equilibrium calculation units.
In addition, you must define the stream rates using generalized stream specifications for all but one of the desired products. The SPLITTER unit allows only rate dependent stream specifications. For example, the rate of a component or group of components in a product is a rate dependent specification. The recovery of a fraction of the total feed to the splitter is also a rate dependent specification.
z
Flash Types This section describes the different flash types modeled in PRO/II.
Dew and Bubble Point Flashes
For dew point and bubble point flash calculations, you can designate a pseudo-stream product. This pseudo-stream is in equilibrium with the actual product stream, but does not actually exist. The default rate of the equilibrium pseudo-stream is zero, but you can arbitrarily set its rate using the Define feature within the FLASH unit, or enter a rate directly.
For a bubble point FLASH, the product is a saturated liquid, defined as the liquid product and the pseudo-stream is a saturated vapor, defined by the vapor product.
For a dew point FLASH, the product is a saturated vapor, defined as the vapor product and the pseudo-stream is a saturated liquid, defined by the liquid product.
Defining pseudo-streams can help solve flowsheets in many ways. For instance, suppose that you are given the composition and flowrate for the liquid distillate and reflux of a column; but, you only have the flowrate of the off-gas and not its composition. You can create the off-gas stream by feeding the liquid distillate to a bubble point FLASH and setting up a vapor pseudo-stream with a defined rate that is equal to the known off-gas rate.
Another useful calculation that you can perform with the dew point and bubble point FLASH units is the determination of the "latent heat" of a mixture. To find this quantity, the mixture must be transformed from a saturated liquid to a saturated vapor. The heat required for this phase change is the "latent heat," which is calculated as the difference between the mixture enthalpies at the bubble point and at the dew point at con-stant temperature. Keeping the temperature concon-stant will eliminate sen-sible heat effects in the calculation.
Water and Hydrocarbon Dew Point Flashes
The water dew point of a water-hydrocarbon mixture is the operating condition at which the first drop of free water is formed as the mixture cools (or as the mixture's pressure is raised). Likewise, the hydrocarbon dew point is the operating condition at which the first drop of liquid hydrocarbon is formed.
In PRO/II, the standard dew point calculation finds the first dew point for a mixture. For water-hydrocarbon mixtures with hydrocarbons more vol-atile than water, this is also the water dew point. For water-hydrocarbon mixtures with hydrocarbons less volatile than water, this is also the hydrocarbon dew point. These dew point calculation options are avail-able in PRO/II for water-hydrocarbon systems that are modeled using the
water decant option. For the standard dew point calculation, PRO/II allows only a vapor product (V) and a liquid phase pseudo-stream (L).
However, the hydrocarbon dew point option allows for a free water prod-uct (W), since the water may condense before the hydrocarbon, while the water dew point option allows for a liquid hydrocarbon product (L), since the hydrocarbon may condense before the water. PRO/II does not generate pseudo-streams for these optional dew point calculations.
Entrainment PRO/II can model the entrainment of one product phase in any other product phase. PRO/II performs the entrainment calculations after the
FLASH unit converges. This makes the final product streams different than the flash specifications and not in equilibrium with each other.