Abstract: Methods are provided to use water-free quench liquids to obtain pyrolytic liquid products with reduced formaldehyde content. Products include liquids with improved hydroxyacetaldehyde content.

Abstract: The invention relates to a method for producing a urea solution with a target urea concentration using water flows recovered from the urea production process. At least part of the water flows recovered from the urea production process are only partially purified to produce the urea solution. The invention further relates to a process condensate treatment plant to implement the method for producing a urea solution with a target urea concentration, and a urea production plant comprising such process condensate treatment plant.

Abstract: The disclosure pertains to a urea production plant and process using a high-pressure CO2 stripper, downstream medium-pressure treatment unit and a medium-pressure dissociator receiving urea synthesis solution from the reactor, wherein gas from the treatment unit and dissociator are condensed in a first condenser and off-gas from the synthesis section is condensed separately in a second condenser. A revamping method is also described.

Abstract: The present disclosure relates to a method of decomposing a phenolic by-product, including: a step of feeding and thermally cracking a phenolic by-product stream to and in a decomposition apparatus, recovering an active ingredient from a top discharge stream, and discharging a high-boiling substance through a bottom discharge stream; a step of pressurizing each of a side discharge stream of the decomposition apparatus and a bottom discharge stream of the decomposition apparatus; a step of mixing the pressurized side discharge stream of the decomposition apparatus and the pressurized bottom discharge stream of the decomposition apparatus with each other to form a mixed stream; and a step of passing a part of the mixed stream through a reboiler, circulating the part of the mixed stream to the decomposition apparatus, and discharging a residual mixed stream.

Abstract: A system and method for removing nitrogen from natural gas using two fractionating columns, that may be stacked, and a plurality of separators and heat exchangers, with horsepower requirements that are 50-80% of requirements for prior art systems. The fractionating columns operate at different pressures. A feed stream is separated with a vapor portion feeding the first column to produce a first column bottoms stream that is split into multiple portions at different pressures and first column overhead stream that is split or separated into two portions at least one of which is subcooled prior to feeding the top of the second column. Optional heat exchange between first column and second column streams provides first column reflux and reboil heat for a second column ascending vapor stream. Three sales gas streams are produced, each at a different pressure.

Abstract: The present disclosure is in the field of ‘pharmacognosy’ and ‘chemistry of natural products’. The present disclosure generally relates to a process of isolation and purification of Biochemical Constituents from algae. The present disclosure particularly relates to a process of isolation and purification of Biochemical Constituents from a biomass of cyanobacteria. The present disclosure provides a process for isolating and extracting phycocyanins, chlorophylls, proteins and polysaccharides from the spirulina biomass.

Abstract: The present invention relates to a process for purifying ethylenediamine, in which a) a mixture comprising water (H2O), ethylenediamine (EDA) and N-methylethylenediamine (NMEDA) is introduced into a rectification column (NMEDA removal column), where the mixture introduced comprises at least the amount of water as required for the formation of a high-boiling azeotrope of EDA and water at the appropriate bottom temperature; and the EDA-comprising bottom product from the NMEDA removal column is introduced into a second rectification column (EDA dewatering column), wherein the pressure at the top of the EDA dewatering column is adjusted such that the boiling temperature of the mixture obtained at the top is 10° C.

Abstract: An integrated process for producing cumene and purifying isopropanol is described, in which a crude isopropanol stream containing in excess of 0.1 wt % water is separated into a dry isopropanol fraction containing no more than 0.1 wt % water and a wet isopropanol fraction containing the remainder of the water in said crude isopropanol stream. The dry isopropanol fraction is recovered and the wet isopropanol fraction is contacted with benzene in an alkylation zone under alkylation conditions such that at least part of the isopropanol reacts with the benzene to produce an effluent stream comprising cumene.

Abstract: The invention relates to a process for purifying aniline produced by gas-phase hydrogenation of nitrobenzene, by fractional condensation of the crude reaction product obtained in gaseous form so that at least two liquid process products, a partial condensate (PK) and a total condensate (TK), are obtained.

Abstract: The invention relates to a column, with a jacket, extending along a longitudinal axis, which jacket bounds a first jacket space and a second jacket space arranged over it along the longitudinal axis, a chimney tray, extending crosswise to the longitudinal axis, that separates the two jacket spaces from one another. The at least a first chimney extends from the tray along the longitudinal axis, and projects into the second jacket space. The chimney has a peripheral wall defining an opening, via which the two jacket spaces are connected to one another for gas feed, and a chimney top. On the peripheral wall, a flat impact element is arranged tilted toward the longitudinal axis in such a way that a liquid phase flowing downward from the chimney top along the longitudinal axis strikes the flat impact element diminishing the momentum input of the liquid phase that stands on the chimney tray.

Abstract: A process to separate a multi-component hydrocarbon stream which includes ethylene and other components with at least some of the components being present in a number of phases, is provided. The process includes in a first flash stage, flashing the multi-component hydrocarbon stream, from an elevated pressure and temperature to a pressure in the range of 10-18 bar(a), producing a first ethylene-containing vapor stream at a pressure in the range of 10-18 bar(a) and a multi-phase stream which includes some ethylene. In a second flash stage, the multi-phase stream is flashed to a pressure of less than 6 bar(a), producing a second vapor stream at a pressure of less than 6 bar(a) and a bottoms stream. The first ethylene-containing vapor stream is removed from the first flash stage, the second vapor stream is removed from the second flash stage and the bottoms stream is removed from the second flash stage.

Abstract: A system for molecular targeting and separating includes a microwave energy source; a vapor source; a column configured and positioned to receive microwave energy from the microwave energy source and vapor from the vapor source; and a condenser, the condenser in communication with the column, the condenser configured to condense the vapor after the vapor receives the microwave energy.

Abstract: A rotary evaporator comprising a motor, a rotary joint movably inserted to a motor rotor of the motor by a sleeve in an axial direction, a collection flask attached to the rotary joint at one end of the joint, with a condenser attached to the other end of the joint. The condenser is adapted to receive a cooling coil from an immersion cooler. The cooling coil is attached to the base unit of the immersion cooler via an insulated hose. The rotary evaporator is adapted to provide various ways to remove heat from the flask in the water bath, whether by mechanically lowering the water bath, dropping fluid from the bath into an underlying reservoir, or raising and lowering the rotary evaporator out of the bath. Where the rotary evaporator is raised and lowered, the immersion cooler can remain in place if the hose connecting the base unit to the cooling coil is sufficiently long, or the condenser includes a flexible portion that accommodates the upward and downward movement.

Abstract: Systems and methods for extracting recoverable materials from source materials are provided. Source materials are introduced into a furnace. A condition is created within the furnace in which a gaseous pressure within the furnace is less than an atmospheric pressure outside of the furnace by removing air from within the furnace with a vacuum pump. Hydrocarbons contained within the source material are separated from the source material without using a significant amount of water by heating the source material to a temperature sufficient to cause the hydrocarbons to liquefy or vaporize. The liquefied hydrocarbons or vaporized hydrocarbons are then captured.

Abstract: A water recovery process for a steam assisted gravity drainage system for a heavy oil recovery facility, the process comprising a flash drum and a flash drum heat exchanger/condenser, wherein the water recovery process receives hot water produced by a facility at a temperature above the water atmospheric boiling point and cools it to a temperature below the water atmospheric boiling point before transferring it to the remaining section of the water recovery process.

Abstract: A rotary evaporator (1) having a cooler (6), wherein temperature sensors (15, 17) are disposed in the inlet (14) and outlet (16) of the coolant into or out of the cooler (6), and a volume flow rate of the coolant through the cooler (6) is determined. The initiation or termination of condensation in the cooler (6) is derived from an increase or decrease in the difference of the temperatures (X) at the temperature sensors (15, 17). The volume of the condensed distillate (10) is determined from the difference in temperatures (X), and a distillation volume control is performed. By regulating the heating power of the heater (11) and/or the pressure in the system, the loading of the cooler (6) is controlled as a function of the difference in temperatures (X).

Abstract: Disclosed are methods for purifying a process water, which can comprise providing a process water comprising a first concentration of a first dissolved gas and a first concentration of a first dissolved ion, filtering the process water to create a filtered process water comprising a second concentration of the first dissolved gas, and evaporating the filtered process water to create a water vapor comprising a second concentration of the first dissolved ion that is less than the first concentration of the first dissolved ion.

Abstract: An embodiment of a distillation system is disclosed having an influent column with an influent column first end and an influent column second end and having therein, a gas deflector. The influent column may contain at least an influent liquid and vapor from the influent liquid. The influent column first end may be in fluid communication with an influent liquid source. A distillation system is disclosed as having at least one effluent column having an effluent column first end and an effluent column second end and further comprising a condensation chamber adjacent the effluent second end. The effluent column may be positioned within the influent column and may contain at least an effluent liquid and vapor. A primary vacuum source may be in fluid communication with an influent column and positioned at an influent second end. A blower may be provided and connected to the condensation chamber.

Abstract: A method of recycling mixtures of hydrochloric and hydrofluoric acid. In particular, a method of recycling hydrofluoric acid and boron fluoride mixtures. A process for upgrading mixtures of fluoroboron compounds contaminated with chlorides as an aqueous solution of boron fluoride hydrates, including a step of vacuum distillation. Also, a method of producing gaseous boron trifluoride.

Abstract: The present invention describes a process to reduce or eliminate at least one pollutant in a starting material, said starting material is at least one of an oil, a fat, its derivatives and mixtures thereof, of animal, krill, algae or microbial origin or biofuel, being totally or partially esterified or transesterified, or of vegetable origin, being raw, esterified or transesterified, to which optionally it is added a fluid, said fluid is at least one of an ester, a partial glyceride, a monoglyceride, a diglyceride and mixtures thereof, subjecting the starting material to at least one stage of extraction or chromatography or distillation. The process of the invention provides a product suitable to be used in food, pharmacy, cosmetic and as a dietary supplement.

Abstract: High purity cyclohexasilane and a method for increasing the purification efficiency thereto are provided. The method for producing cyclohexasilane of the present invention is characterized in that, in distilling crude cyclohexasilane to obtain purified cyclohexasilane, the absolute pressure during distillation is set to 2 kPa or less, and the heating temperature of crude cyclohexasilane is set to 25 to 100° C. The cyclohexasilane of the present invention contains pure cyclohexasilane at a rate of 98% by mass or more and 100% by mass or less.

Abstract: A process is proposed for the treatment of a recycling stream (1) from a plant for the production of polyarylene ether sulfones via polycondensation of aromatic bishalogen compounds and of aromatic bisphenols or their salts in the presence of at least one alkali metal carbonate or ammonium carbonate or alkali metal hydrogencarbonate or ammonium hydrogencarbonate in an N-alkyl-2-pyrrolidone as solvent, comprising from 60 to 90% by weight of water, from 10 to 40% by weight of N-alkyl-2-pyrrolidone and, as contaminant detrimental to specification, up to 5000 ppm by weight of the alkylsuccinimide corresponding to the N-alkyl-2-pyrrolidone and, alongside this, up to 1000 ppm by weight of other substances with higher boiling point than N-alkyl-2-pyrrolidone, in particular inorganic salts, based in each case on the total weight of the recycling stream (1), where the entirety of the components gives 100% by weight, giving a pure N-alkyl-2-pyrrolidone stream (2) which can be returned to the plant for the productio

Abstract: The present invention comprises a process for recovery of sulfolane used in a solvent-extraction or extractive-distillation process. A recovery column for the sulfolane solvent comprises a liquid-jet ejector for maintaining the needed vacuum conditions, preferably using water as the liquid.

Abstract: A method for treating process distillate heavies produced during uranium fluoride purification is described. The heavies contain primarily uranium hexafluoride, UF6, and molybdenum oxytetrafluoride, MoOF4. The uranium hexafluoride is removed via distillation at reduced pressure leaving essentially MoOF4 containing <0.1% of residual uranium hexafluoride. This mixture is hydrolyzed in water, then treated with a solution of sodium hydroxide until a pH of at least 7.5 is reached. The precipitated sodium diuranate and sodium fluoride are removed by filtration. The filtrate is reacted with calcium chloride to precipitate the molybdenum values as calcium molybdate containing trace quantities of calcium fluoride.

Abstract: A system and method for preparation of meat flavorants, and flavorants, having increased flavor and aromatic intensity and which more closely resemble the natural flavor and aroma of cooked meat. Preheated edible, food grade oils and fats are exposed to temperatures between 290° C. and 475° C. under vacuum, in the presence of oxygen. The developing flavor vapors are immediately and completely removed from the heated oils and fats. The mixture of air-purge/flavor-vapor is immediately carried away from the heat transfer surface of the edible oil or fat. An evaporator, preferably a spinning disc, spinning band or thin film evaporator, without a condenser is used as process equipment. The air-purged flavor-vapors are diffused and absorbed in an absorption device into suitable food-grade liquids.

Abstract: The present invention relates to a method for purification of bilge and sludge water on a ship, especially at sea, using excess heat from the ship's engine(s) to a level of oil contamination of less than 15 ppm. The invention also relates to a plant for carrying out the method, and a vessel including such plant, as well as the use of the method and plant.

Abstract: A system and method for separating a fluid mixture is provided which employ vacuum distillation apparatus, and optionally, gas-handling apparatus operable to introduce a gas into the liquid mixture prior to being dispersed within the vacuum distillation apparatus. The liquid mixture is dispersed within the vacuum distillation apparatus as micro-sized droplets. When used, the gas that has been introduced into the liquid mixture is rapidly liberated from the micro-sized droplets thereby causing the droplets to break into still smaller droplets thereby maximizing the vaporization of the more volatile components in the liquid mixture.

Abstract: In one embodiment, the invention is to a process for purifying acetic anhydride. The process includes the steps of feeding a liquid crude acetic anhydride stream directly to a distillation column and separating the liquid crude acetic anhydride stream to produce a light ends stream, a sidedraw and a residue stream. The sidedraw comprises substantially pure acetic anhydride product. The distillation column is operated at a pressure less than 101 kPa. The substantially pure acetic anhydride product comprises greater than 98 wt. % acetic anhydride, has a permanganate time of greater than 10 minutes, and has an APHA color of less than 10.

Abstract: A method for distilling a starting material that includes a liquid Fd to be distilled, uses a gas-tight container system that is resistant to excess and/or negative pressure. The container system includes a condenser for condensing the liquid Fd, which has turned to vapor and whose temperature can be adjusted, to give the condensation product, and a vapor chamber connecting the evaporator and the condenser. The pressure and temperature in the vapor chamber are monitored and controlled so that distillation is always carried out in a range close to the saturation vapor pressure of the liquid Fd to be distilled. If the pressure is too high, it is reduced so that especially foreign gas is removed. An installation includes a container for distillation according to method.

Abstract: Provided is a method for recovering high-concentration and high-purity amine from amine-containing waste water generated from nuclear power plants and thermal power plants. The method includes: capturing amine and concentrating waste water using a cation exchange resin; separating amine from the concentrated amine-containing waste water; and carrying out further separation of amine via distillation. The method may be applied to treat amine, which causes an increase in biochemical oxygen demand (BOD) and total nitrogen concentration, drastically at the time of its generation from waste water of nuclear power plants and thermal power plants. In this manner, the method may prevent an increase in load of existing waste water treating plants and avoid a need for modifying the equipment in the existing plants.

Abstract: Embodiments of the invention are directed toward a novel pressurized vapor cycle for distilling liquids. In an embodiment of the invention, a liquid purification system is revealed, including the elements of an input for receiving untreated liquid, a vaporizer coupled to the input for transforming the liquid to vapor, a head chamber for collecting the vapor, a vapor pump with an internal drive shaft and an eccentric rotor with a rotatable housing for compressing vapor, a condenser in communication with the vapor pump for transforming the compressed vapor into a distilled product, and an electric motor with motor rotor and magnets hermetically sealed within the fluid pressure boundary of the distillation system.

Abstract: The present invention provides a process for handling ?9-THC, which comprises preparing a solution of ?9-THC in a solvent which exists as a gas at room temperature and atmospheric pressure. The invention also provides solutions of ?9-THC in the solvent and solid preparations of ?9-THC.

Abstract: Methods and systems for controlling the pressure of distillation columns, for example those operating under vacuum pressure and conventionally equipped with a steam ejector system, are described. Representative distillation columns are used in the separation of thermally unstable components, such as the physical solvent sulfolane, having relatively low volatility. Such columns are employed in aromatic hydrocarbon extraction processes for the recovery of purified C6-C8 aromatic hydrocarbons from a hydrocarbon feed stream (e.g., obtained from the catalytic reforming of naphtha).

Abstract: Organic waste disposal technologies are disclosed herein. A multistage processing of sewage sludge into synthetic fuel and chemical products is carried out by means of a direct thermo-chemical liquefaction process. The process enables the minimization of coke formation by utilizing steam stripping in the processing of sewage sludge.

Abstract: A pump includes: a branch pipe extending from a pump body for branching a part of raw water introduced from outside through a raw water inlet; a first tank having an exhaust pipe of an engine accommodated therein, the raw water supplied via the branch pipe being evaporated by heat of the exhaust pipe; a second tank provided over the first tank and having the branch pipe accommodated therein, vapor produced by evaporation of the raw water in the first tank being condensed into water droplets in the second tank; and a communication pipe interconnecting the first and second tanks in communication with each other.

Abstract: A divided exchange column includes a shell column having a first longitudinal axis, a cylindrical wall spaced apart from and surrounding the first longitudinal axis and defining a first interior space, a first divided wall column having a second longitudinal axis substantially parallel to the first longitudinal axis, and a second divided wall column having a third longitudinal axis substantially parallel to the first and the second longitudinal axes, where the first divided wall column and the second divided wall column are positioned in the first interior space of the shell column.

Abstract: Processes for removing color bodies from crude succinic acid comprising distillation of crude succinic acid and collecting the distillate in a water-containing receiver. The color bodies substantially remain in the distillation bottoms and the purified succinic acid in the water-containing receiver is substantially free of color bodies.

Abstract: Methods for reducing sulfides from fluid streams are provided. The methods comprise adding secondary amine-formaldehyde adduct (SAFA) scavengers to fluid streams. The SAFA scavengers added comprise less than about 40 wt % N-methyl secondary amines of the total weight of SAFA scavengers. Methods for distilling N-methyl secondary amines from secondary amine-formaldehyde adduct (SAFA) scavengers are also provided. Purified SAFA scavengers are also disclosed.

Abstract: A desalination process including heating brine in a preheating chamber and transferring the brine to a rotary kiln to be sprayed against the wall structure of the rotary kiln to boil to steam and a residue of salt/impurities, the exiting steam being pressurized in a compressor and passed to an externally powered heater to be heated and then fed to a hollow wall structure of the rotating kiln in which the steam condenses to pure water to be transferred to the preheating chamber to preheat the incoming brine, the rotating kiln being arranged to rotate past a scraper to remove salt/impurities from the wall structure for collection at the base of the kiln.

Abstract: Provided herein are compounds of the formula: in which n is an integer equal to or greater than 1; R2 is selected from hydrogen and optionally substituted alkyl that is saturated or unsaturated, and branched or unbranched; and R1, R3, and R4, independently for each occurrence, are selected from optionally substituted alkyl that is saturated or unsaturated, and branched or unbranched, wherein compositions comprising the compounds are characterized by particular combinations of values for estolide number, kinematic viscosity, and pour point. Also provided are compositions containing the compounds and methods of making both the compounds and compositions thereof.

Abstract: Provided is a substrate treating apparatus. The substrate treating apparatus according to embodiments of the present invention may include a cleaning chamber cleaning foreign objects on a substrate, and a recycling unit recycling by recovering a mixed solution including a first chemical and a second chemical used in cleaning of the substrate, wherein the recycling unit includes a separation unit separating the mixed solution recovered from the cleaning chamber, a recovery line connecting the separation unit and the cleaning chamber and allowing the mixed solution to flow into the separation unit, a decompression line having one end connected to the separation unit and exhausting the mixed solution evaporated from the separation unit, and a decompression unit installed in the decompression line and reducing pressure in the separation unit.

Abstract: The invention relates to a method for controlling, manually or automatically, the composition or quality of one or more products removed from the head, the sump or a lateral removal point of the distillation column having a built-in heat-exchanger. The method is characterized in that, by changing the pressure in the column, in the region of the product removal, the new boiling temperature of the product is determined from the vapor pressure curve of the product at said pressure and the temperature of the distillation removal is adjusted to said new boiling temperature by means of the modified coolant flowing through the heat-exchanger, preferably in the counter direction.

Abstract: A water purification system having an oil and vapor separation subsystem for removing many heavy duty and toxic contaminants from the water. The subsystem removes volatile vapors from the feed water, heats the feed water, and by imparting a swirling vortex action to the heated water, the oils are separated from the water. The water separated from the oil is pumped by a high pressure pump through a helical coil that is heated to a high temperature by the burner. The high temperature, hot water is then fed to an expansion nozzle in an expansion chamber to flash the hot water into steam. The steam is passed through a condenser which converts the steam to purified water.

Abstract: An evaporator is provided for evaporation of liquid from a solution or liquid mixtures, together with methods of operation of the evaporator. The evaporator comprises a chamber (1); a liquid reservoir (3) for holding a heat transfer liquid exposed to the interior of the chamber; a support (6) for supporting a container (8) in the chamber, such that the liquid sample in the container is exposed to a fluid path (15) for connection to a condenser (16), the fluid path being separated from the chamber interior, and at least a portion of the container is closely thermally coupled to the chamber interior; and means (4) for heating the heat transfer liquid in the reservoir to create heat transfer liquid vapor, which in use condenses and releases latent heat of vaporization to the liquid sample in the container. As the temperature of the sample is dependent on the saturated vapor temperature of the liquid in the reservoir, the temperature of the samples is reliably limited, thereby avoiding overheating.

Abstract: A vacuum dehydrator for processing an oil containing entrained contaminants such as water, air, and particulates comprises a tower enclosing upper and lower chambers. A random packing is contained in the upper chamber. The oil is preheated to a temperature above the boiling point of water and is introduced into the upper chamber for downward flow through the random packing into the lower chamber. Entrained air and water is retained as water vapor in the upper chamber, and particulates are retained in the random packing. Heated ambient air is introduced into the lower chamber for upward flow through the random packing into the upper chamber, and the upper chamber is cooled to condense the water vapor. Oil and condensed water are pumped respectively from the lower and upper chambers.

Abstract: An apparatus and method for the regeneration of captured gas rich capture medium such as an absorption solution and the recovery of absorbed gas therefrom, an apparatus and method for the removal and recovery of a target gas from a gas stream, and the use of the same for post combustion carbon capture on a thermal power plant are described. The apparatus and method make use of a regenerative heating process. The apparatus and method are distinctly characterized by the use of a heat pump to utilize low grade heat, for example from elsewhere in the process, as a source of thermal energy for the heating process.

Abstract: Processes for the recovery of ethanol, useful as a fuel, from various cellulosic feedstock materials fermented to produce ethanol-containing beer are disclosed. The present invention provides a method and a system for ethanol recovery from highly viscous fermented citrus waste biomass. The systems overcome various challenges, including effectively stripping the ethanol from biomass beer in an energy efficient and economical manner that may allow for the further dehydration of the ethanol/water mix in a traditional rectifier distillation column. In certain embodiments, a series of flash stages and beer stripping columns are capable of operating with highly viscous slurries and/or feedstocks containing high levels of solids.

Abstract: The present invention discloses a process and apparatus for utilization of waste heat of flue gas liberated from different heat sources to provide high quality water from sea/brackish.

Abstract: The present invention relates to a process and a system for producing alcohol by distillation with energy optimization using split-feed technology. The process of the present invention comprises the steps of: a) splitting a stream of wine to feed two depuration columns , the depuration column generating a stream of phlegma and the depuration column generating a stream of phlegma and a stream of vinasse; b) feeding the stream of phlegma into at least one rectification column generating a top flow and a stream of hydrated alcohol; c) effecting the heat exchange between the top flow from at least one rectification column and the stream of vinasse from the depuration column in at least one heat exchanger; and d) feeding the stream of phlegma into a rectification column generating a stream of hydrated alcohol. The present invention further relates to hydrated alcohol produced by the process described above and to a process for producing anhydrous alcohol.

Abstract: The present invention relates to a mixture of ethylenediamine (EDA) and N-methyl-ethylenediamine (Me-EDA) with a low content of Me-EDA, which comprises at least 99.5% by weight of ethylenediamine, and wherein the concentration of N-methylethylenediamine is in the range from 0.005 to 0.15% by weight. The present invention further relates to a process for distillative workup of a mixture comprising EDA, Me-EDA and water, by introducing the mixture into a distillation column which is operated at a column top pressure of 10 mbar to 4 bar, wherein the weight ratio of water to ethylenediamine in the mixture used is a*X:Y where X is the proportion by weight of water and Y is the proportion by weight of ethylenediamine at the azeotropic point of a binary mixture of water and ethylenediamine at the column top pressure in question, and a is a real number with a value of 0.9 or more.