Patent Publication Number: US-8543242-B2

Title: Method and apparatus for managing volatile organic content in polyolefin

Description:
RELATED APPLICATIONS 
     This application is a divisional application of U.S. patent application Ser. No. 13/093,588 filed on Apr. 25, 2011, which is a divisional of U.S. patent application Ser. No. 11/895,712 filed on Aug. 27, 2007, now U.S. Pat. No. 7,957,947 issued on Jun. 7, 2011, which claims the benefit under 35 U.S.C. §119(e) of U.S. Provisional Patent Application No. 60/840,163 filed on Aug. 25, 2006, each of which are incorporated by reference herein. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates generally to polyolefin production and to reducing volatile organic content (VOC) associated with the polyolefin. Techniques include the construction and implementation of a purge column model to calculate or estimate the VOC content in the polyolefin stream exiting the purge column. The techniques facilitate the design and operation of the polyolefin manufacturing process. 
     2. Description of the Related Art 
     This section is intended to introduce the reader to aspects of art that may be related to aspects of the present invention, which are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present invention. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art. 
     As chemical and petrochemical technologies have advanced, the products of these technologies have become increasingly prevalent in society. In particular, as techniques for bonding simple molecular building blocks into longer chains (or polymers) have advanced, the polymer products, typically in the form of various plastics, have been increasingly incorporated into various everyday items. For example, polyolefin polymers, such as polyethylene, polypropylene, and their copolymers, are used for retail and pharmaceutical packaging, food and beverage packaging (such as juice and soda bottles), household containers (such as pails and boxes), household items (such as appliances, furniture, carpeting, and toys), automobile components, pipes, conduits, and various industrial products. 
     Specific types of polyolefins, such as high-density polyethylene (HDPE), have particular applications in the manufacture of blow-molded and injection-molded goods, such as food and beverage containers, film, and plastic pipe. Other types of polyolefins, such as low-density polyethylene (LDPE), linear low-density polyethylene (LLDPE), isotactic polypropylene (iPP), and syndiotactic polypropylene (sPP) are also suited for similar applications. The mechanical requirements of the application, such as tensile strength and density, and/or the chemical requirements, such thermal stability, molecular weight, and chemical reactivity, typically determine what type of polyolefin is suitable. 
     One benefit of polyolefin construction, as may be deduced from the list of uses above, is that it is generally non-reactive with goods or products with which it is in contact. This allows polyolefin products to be used in residential, commercial, and industrial contexts, including food and beverage storage and transportation, consumer electronics, agriculture, shipping, and vehicular construction. The wide variety of residential, commercial, and industrial uses for polyolefins has translated into a substantial demand for raw polyolefin, which can be extruded, injected, blown or otherwise formed into a final consumable product or component. 
     To satisfy this demand, various processes exist by which olefins may be polymerized to form polyolefins. These processes may be performed at or near petrochemical facilities, which provide ready access to the short-chain olefin molecules (monomers and comonomers), such as ethylene, propylene, butene, pentene, hexene, octene, decene, and other building blocks of the much longer polyolefin polymers. These monomers and comonomers may be polymerized in a liquid-phase polymerization reactor and/or gas-phase polymerization reactor to form a product comprising polymer (polyolefin) solid particulates, typically called fluff or granules. The fluff may possess one or more melt, physical, rheological, and/or mechanical properties of interest, such as density, melt index (MI), melt flow rate (MFR), copolymer content, comonomer content, modulus, and crystallinity. The reaction conditions within the reactor, such as temperature, pressure, chemical concentrations, polymer production rate, and so forth, may be selected to achieve the desired fluff properties. 
     In addition to the one or more olefin monomers, a catalyst for facilitating the polymerization of the monomers may be added to the reactor. For example, the catalyst may be a particle added via a reactor feed stream and, once added, suspended in the fluid medium within the reactor. An example of such a catalyst is a chromium oxide containing hexavalent chromium on a silica support. 
     Further, a diluent may be introduced into the polyolefin reactor. The diluent may be an inert solvent and/or inert hydrocarbon, such as isobutane, propane, n-pentane, i-pentane, neopentane, and n-hexane, which is liquid at reaction conditions. However, some polymerization processes may not employ a separate diluent, such as in the case of selected examples of polypropylene production where the propylene monomer itself acts as the diluent. In general, the diluent may facilitate circulation of the polymer slurry in the reactor, heat removal from the polymer slurry in the reactor, and so on. 
     The slurry discharge of the reactor typically includes the polymer fluff as well as non-polymer components, such as unreacted olefin monomer (and comonomer), diluent, and so forth. In the case of polyethylene production, the non-polymer components typically comprise primarily diluent, such as isobutane, having a small amount of unreacted ethylene (e.g., 5 wt. %). This discharge stream is generally processed, such as by a diluent/monomer recovery system (e.g. flash vessel or separator vessel, purge column, etc.) to separate the non-polymer components from the polymer fluff. 
     The recovered diluent, unreacted monomer, and other non-polymer components from the recovery system may be treated, such as by treatment beds and/or a fractionation system, and ultimately returned as purified or treated feed to the reactor. Some of the components may be flared or returned to the supplier, such as to an olefin manufacturing plant or petroleum refinery. As for the recovered polymer (solids), the polymer may be treated to deactivate residual catalyst, remove entrained or dissolved hydrocarbons, dry the polymer, and pelletize the polymer in an extruder, and so forth, before the polymer is sent to customer. 
     The competitive business of polyolefin production drives manufacturers in the continuous improvement of their processes in order to lower production costs, to address environmental concerns, and so on. In an industry where billions of pounds of polyolefin product are produced per year, small incremental improvements can result in significant economic benefit, environmental progress, and so forth. 
     A particular issue in polyolefin production is the undesirable carryover of volatile organics (e.g., diluent, monomer, and other hydrocarbons) with and in the polymer fluff particles exiting the “wet end” of the polyolefin manufacturing process (e.g., exiting a purge column in the monomer/diluent recovery system). This stream of fluff particles exiting the wet end is generally transferred to the “dry end” (e.g., through a pneumatic conveying system) where the fluff may be stored in silos, extruded into pellets, and then loaded as pellets into containers or railcars, and the like. The hydrocarbon in the stream of polymer fluff exiting the wet end (e.g., exiting a purge column) may be entrained with the polymer fluff, dissolved in the polymer fluff, absorbed and/or adsorbed on the polymer fluff, contained within pores of the polymer fluff, and so on. The hydrocarbon may be undesirably released to the atmosphere at various points in the dry end process (e.g., in the extrusion and product loadout systems), resulting in the loss of hydrocarbon, exceeding of environmental permitting allowances, and so on. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Advantages of the invention may become apparent upon reading the following detailed description and upon reference to the drawings in which: 
         FIG. 1  is a block flow diagram depicting an exemplary polyolefin manufacturing system for producing polyolefins in accordance with one embodiment of the present techniques; 
         FIG. 2  is a process flow diagram of an exemplary feed system of the polyolefin manufacturing system of  FIG. 1  in accordance with one embodiment of the present techniques; 
         FIG. 3  is a process flow diagram of an exemplary catalyst preparation system of the feed system of  FIG. 2  in accordance with one embodiment of the present techniques; 
         FIG. 4  is a process flow diagram of an exemplary catalyst activation system in accordance with one embodiment of the present techniques; 
         FIG. 5  is a process flow diagram of an exemplary reactor system and a diluent/monomer recovery system of the polyolefin manufacturing system of  FIG. 1  in accordance with one embodiment of the present techniques; 
         FIG. 6  is a diagrammatical representation of the exemplary polymerization reactor of  FIG. 5  showing the flow of cooling medium through the reactor jackets in accordance with one embodiment of the present techniques; 
         FIG. 7  is a diagrammatical representation of an exemplary continuous takeoff discharge of the polymerization reactor of  FIG. 5  in accordance with one embodiment of the present techniques; 
         FIG. 8  is a cross section along line  8 - 8  of  FIG. 7  showing a ram valve arrangement in the continuous take off discharge assembly in accordance with one embodiment of the present techniques; 
         FIG. 9  is a diagrammatical representation of a tangential location for the continuous take off assembly in accordance with one embodiment of the present techniques; 
         FIG. 10  is a process flow diagram of the extrusion/loadout system of  FIG. 1  in accordance with one embodiment of the present techniques; 
         FIG. 11  is an exemplary plot of VOC (part per million or ppm) in the polymer fluff stream exiting a purge column versus the polymer fluff temperature (° F.) in the purge column in accordance with one embodiment of the present techniques; 
         FIG. 12  is an exemplary plot of VOC (ppm) in the polymer fluff stream exiting a purge column versus the purge time (or residence time) in minutes in the purge column in accordance with one embodiment of the present techniques; 
         FIG. 13  is an exemplary plot of VOC (ppm) in the polymer fluff stream exiting a purge column versus the ratio of entering purge gas to polymer fluff (pound of gas per pound of polyethylene) in accordance with one embodiment of the present techniques; 
         FIG. 14  is an exemplary plot of VOC (ppm) in the polymer fluff stream exiting a purge column versus the average particle size in microns (μm) of the polymer fluff in the purge column in accordance with one embodiment of the present techniques; 
         FIG. 15  is an exemplary plot of VOC (ppm) in the polymer fluff stream exiting a purge column versus the pressure (pounds per square inch or psig) of the purge gas (primarily nitrogen) entering the purge column in accordance with one embodiment of the present techniques; 
         FIG. 16  is an exemplary plot of purge gas temperature (° F.) versus the purge time (minutes) in a purge column in accordance with one embodiment of the present techniques; 
         FIG. 17  is a model process schematic of an the diluent/monomer recovery system depicted in  FIG. 5  in accordance with one embodiment of the present techniques; 
         FIG. 18  is a material balance schematic for a an exemplary purge column in accordance with one embodiment of the present techniques; and 
         FIG. 19  is a schematic of an exemplary interface for a purge column model in accordance with one embodiment of the present techniques. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     One or more specific embodiments of the present invention will be described below. In an effort to provide a concise description of these embodiments, not all features of an actual implementation are described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers&#39; specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure. 
     The present techniques provide for a model of a purge column in a polyolefin manufacturing process. Embodiments of the purge column model may be employed to design the purge column, as well as improve the design of upstream and downstream systems as a function of purge column performance. The purge column model may also be employed to manage and improve the operation of the purge column including providing insight on operating conditions of reducing the VOC of the polymer stream exiting the purge column 
     It should be noted though the discussion at times may focus on the production of polyethylene and its copolymers, the disclosed techniques afford benefits in the design and operation of purge columns or purge separators in the production of other polyolefins, such as polypropylene, polybutylene, and so on. Finally, it should be apparent that the various techniques may be implemented in a multiplicity of combinations. 
     I. Introduction 
     As discussed, polyolefin processes generally employ hydrocarbon (diluent, monomer, etc.) in the production of the polyolefin polymer. For example, a diluent (e.g., inert hydrocarbon solvent such as isobutane) may be used as carrier for the polymer in the reactor (loop reactor, gas phase reactor) to facilitate circulation (or bed fluidization) and heat removal in the reactor. The inert solvent and other hydrocarbons (e.g., monomer such as ethylene) are entrained or dissolved in the polymer, and are typically purged from the polymer in a purge separator or purge column with an inert gas (e.g., nitrogen). This purging system reduces carryover of hydrocarbons (VOC&#39;s) in the raw or virgin polymer (i.e., fluff, flake, etc.) that was generated in the reactor (prior to being extruded into pellets, for example). For environmental and economic reasons, the purged hydrocarbons, purge gas (e.g., nitrogen) are recovered and reused. 
     In an exemplary polyethylene production system utilizing one or more loop reactors, a diluent isobutane is used as the carrier in the reactor. The isobutane is purged from the polymer in a purge column with nitrogen to tolerable hydrocarbon or VOC (volatile organic compound) limits. As discussed below, the nitrogen-rich gas having hydrocarbon discharging from the purge column is sent to an isobutane-nitrogen recovery unit (INRU) for the recovery and reuse of the hydrocarbons and nitrogen. Embodiments of the present techniques facilitate the design and operation of the purge column, and in particular, in the design and operation to reduce the VOC content of the polyolefin stream exiting the purge column. Such polymer may then be sent to an extrusion and/or product loadout area, for example. It has been generally determined or confirmed via the present techniques that factors affecting the VOC of the polymer stream exiting the purge column include, for example, fluff temperature, purge time, nitrogen flow and purity, fluff particle size, purge pressure, and resin density (or amorphous fraction), and so on. It should be emphasized that the present techniques may also be applicable to other polyolefin systems including those that employ other types of liquid-phase polymerization reactors and also gas-phase reactors. 
     The present invention provides for one or more models and other techniques for designing, rating, operating, and the like, a polyolefin purge column (or separator) and for evaluating the impact of process parameters on purge column performance, for example. Embodiments of the model(s) may be based on mass transfer theory and generally predict the hydrocarbon VOC for polymer stream leaving the purge column. In one example, the model is written in a Visual Basic Application program with an Excel worksheet as interface for model input and output. It should be noted that embodiments of the model have been validated with plant data from existing polyolefin processes (polyethylene and their copolymers). The validated model may be used to establish an approximate order of significance of the process variables that influence degassing of polymer fluff in the purge column. 
     In certain examples for a given resin density, the variables for reducing VOC in the polymer stream leaving the purge column, in decreasing order of effectiveness, may be as follows: purge column temperature, residence time or bed level of polymer in purge column; flow rate and hydrocarbon purity of purge nitrogen; particle size of polymer fluff; and operating pressure of purge column. Plant engineers and operators can rely on this exemplary list in selecting effective variables for reducing VOC in the polymer stream leaving the purge column and nitrogen waste in the purge column, as well. 
     Lastly, it should be noted that the present techniques including the purge column models also provide insight and improvement of processes upstream and downstream of the purge column. For example, the operation of the upstream catalyst system and/or reactor system may be adjusted in an effort to generate a desirable particle size distribution, as indicated by purge column model. In another example, the design and/or operation of the flash line coupled to the discharge of the loop reactor may be adjusted. In this particular example, the present techniques provides for placement of vents on the steam lines to the flash line to facilitate removal of non-condensable components 
     II. Polyolefin Production Process—an Overview 
     In the production of polyolefin, the polymerization reactor(s), which polymerize monomer into polyolefin, and the extruder(s), which convert the polyolefin into polyolefin pellets, are typically continuous operations. However, a variety of both continuous and batch systems may be employed throughout the polyolefin process. An exemplary nominal capacity for a typical polyolefin plant is about 600-800 million pounds of polyolefin produced per year. Exemplary hourly design rates are approximately 85,000 to 90,000 pounds of polymerized polyolefin per hour, and 90,000 to 95,000 pounds of extruded polyolefin per hour. However, it should be emphasized that the foregoing numerical values are only given as examples. Moreover, it should also be emphasized that the following discussion of the exemplary manufacturing process  10  is not meant to limit the applicability of the present purge column model and associated techniques. 
     A. Feedstocks 
     Turning now to the drawings, and referring initially to  FIG. 1 , a block diagram depicts an exemplary manufacturing process  10  for producing polyolefins, such as polyethylene homopolymer, polypropylene homopolymer, and/or their copolymers. Various suppliers  12  may provide reactor feedstocks  14  to the manufacturing system  10  via pipelines, trucks, cylinders, drums, and so forth. The suppliers  12  may comprise off-site and/or on-site facilities, including olefin plants, refineries, catalyst plants, and the like. Examples of possible feedstocks  14  include olefin monomers and comonomers (such as ethylene, propylene, butene, hexene, octene, and decene), diluents (such as propane, isobutane, n-hexane, and n-heptane), chain transfer agents (such as hydrogen), catalysts (such as Ziegler catalysts, Ziegler-Natta catalysts, chromium catalysts, and metallocene catalysts), co-catalysts (such as triethylaluminum alkyl, triethylboron, and methyl aluminoxane), and other additives. In the case of ethylene monomer, exemplary ethylene feedstock may be supplied via pipeline at approximately 800-1450 pounds per square inch gauge (psig) at 45-65° F. Exemplary hydrogen feedstock may also be supplied via pipeline, but at approximately 900-1000 psig at 90-110° F. Of course, a variety of supply conditions may exist for ethylene, hydrogen, and other feedstocks  14 . 
     B. Feed System 
     The suppliers  12  typically provide feedstocks  14  to a reactor feed system  16 , where the feedstocks  14  may be stored, such as in monomer storage and feed tanks, diluent vessels, catalyst tanks, co-catalyst cylinders and tanks, and so forth. In the system  16 , the feedstocks  14  may be treated or processed prior to their introduction as feed  18  into the polymerization reactors. For example, feedstocks  14 , such as monomer, comonomer, and diluent, may be sent through treatment beds (e.g., molecular sieve beds, aluminum packing, etc.) to remove catalyst poisons. Such catalyst poisons may include, for example, water, oxygen, carbon monoxide, carbon dioxide, and organic compounds containing sulfur, oxygen, or halogens. The olefin monomer and comonomers may be liquid, gaseous, or a supercritical fluid, depending on the type of reactor being fed. Also, it should be noted that typically only a relatively small amount of fresh make-up diluent as feedstock  14  is utilized, with a majority of the diluent fed to the polymerization reactor recovered from the reactor effluent. The feed system  16  may prepare or condition other feedstocks  14 , such as catalysts, for addition to the polymerization reactors. For example, a catalyst may be activated and then mixed with diluent (e.g., isobutane or hexane) or mineral oil in catalyst preparation tanks. 
     Further, the feed system  16  typically provides for metering and controlling the addition rate of the feedstocks  14  into the polymerization reactor to maintain the desired reactor stability and/or to achieve the desired polyolefin properties or production rate. Furthermore, in operation, the feed system  16  may also store, treat, and meter recovered reactor effluent for recycle to the reactor. Indeed, operations in the feed system  16  generally receive both feedstock  14  and recovered reactor effluent streams. In total, the feedstocks  14  and recovered reactor effluent are processed in the feed system  16  and fed as feed streams  18  (e.g., streams of monomer, comonomer, diluent, catalysts, co-catalysts, hydrogen, additives, or combinations thereof) to the reactor system  20 . It should be noted that the feed system  16  is a source of the volatile organic compounds in the polymer fluff exiting the purge column. Moreover, the design and/or operation of the feed system may be adjusted in response to various results provided by the present purge column models. 
     C. Reactor System 
     The reactor system  20  may comprise one or more reactor vessels, such as liquid-phase or gas-phase reactors. The reactor system  20  may also comprise a combination of liquid and gas-phase reactors. If multiple reactors comprise the reactor system  20 , the reactors may be arranged in series, in parallel, or in any other suitable combination or configuration. In the polymerization reactor vessels, one or more olefin monomers are polymerized to form a product comprising polymer particulates, typically called fluff or granules. The fluff may possess one or more melt, physical, rheological, and/or mechanical properties of interest, such as density, melt index (MI), melt flow rate (MFR), copolymer or comonomer content, modulus, and crystallinity. The reaction conditions, such as temperature, pressure, flow rate, mechanical agitation, product takeoff, component concentrations, polymer production rate, and so forth, may be selected to achieve the desired fluff properties. 
     In addition to the one or more olefin monomers, a catalyst that facilitates polymerization of the monomer is typically added to the reactor. The catalyst may be a particle suspended in the fluid medium within the reactor. In general, Ziegler catalysts, Ziegler-Natta catalysts, metallocenes, and other well-known polyolefin catalysts, as well as co-catalysts, may be used. An example of such a catalyst is a chromium oxide catalyst containing hexavalent chromium on a silica support. 
     Further, diluent may be fed into the reactor, typically a liquid-phase reactor. The diluent may be an inert hydrocarbon that is liquid at reaction conditions, such as isobutane, propane, n-pentane, i-pentane, neopentane, n-hexane, cyclohexane, cyclopentane, methylcyclopentane, ethylcyclohexane, and the like. The purpose of the diluent is generally to suspend the catalyst particles and polymer within the reactor. Some polymerization processes may not employ a separate diluent, such as in the case of selected polypropylene production where the propylene monomer itself may act as the diluent. 
     A motive device may be present within the reactor in the reactor system  20 . For example, within a liquid-phase reactor, such as a loop slurry reactor, an impeller may create a turbulent mixing zone within the fluid medium. The impeller may be driven by a motor to propel the fluid medium as well as any catalyst, polyolefin fluff, or other solid particulates suspended within the fluid medium, through the closed loop of the reactor. Similarly, within a gas-phase reactor, such as a fluidized bed reactor or plug flow reactor, one or more paddles or stirrers may be used to mix the solid particles within the reactor. Moreover, the design and/or operation of the reactor system may be adjusted in response to various results provided by the present purge column models. 
     D. Diluent/Monomer Recovery, Treatment, and Recycle 
     The discharge  22  of the reactors within system  20  may include the polymer fluff as well as non-polymer components, such as diluent, unreacted monomer/comonomer, and residual catalyst. The discharge  22  may be subsequently processed, such as by a diluent/monomer recovery system  24 , to separate non-polymer components  26  (e.g., diluent and unreacted monomer) from the polymer fluff  28 . The untreated recovered non-polymer components  26  may be further processed, such as by a fractionation system  30 , to remove undesirable heavy and light components. Fractionated product streams  32  may then be returned to the reactor system  20  via the feed system  16 . On the other hand, the non-polymer components  26  may recycle more directly to the feed system  16  (as indicated by reference numeral  34 ), bypassing the fractionation system  30 . Indeed, in certain embodiments, up to 80-95% of the diluent discharged from the reactor bypasses the fractionation system in route to the polymerization reactor. 
     As for the fluff  28 , it may be further processed within the recovery system  24  and in the extrusion/loadout system  36 , to prepare it for shipment, typically as pellets  38 , to customers  40 . Although not illustrated, polymer granules intermediate in the recovery system  24  and typically containing active residual catalyst may be returned to the reactor system  20  for further polymerization, such as in a different type of reactor or under different reaction conditions. The polymerization and diluent recovery portions of the polyolefin manufacturing process  10  may be called the “wet” end  42  or “reaction” side of the process  10 , and the extrusion/loadout  36  portion of the polyolefin process  10  may be called the “dry” end  44  or “finishing” side of the polyolefin process  10 . 
     E. Extrusion/Loadout System 
     In the extrusion/loadout systems  36 , the fluff  28  is typically extruded to produce polymer pellets  38  with the desired mechanical, physical, and melt characteristics. Extruder feed may comprise additives, such as UV inhibitors and peroxides, which are added to the fluff products  28  to impart desired characteristics to the extruded polymer pellets  32 . An extruder/pelletizer receives the extruder feed, comprising one or more fluff products  28  and whatever additives have been added. The extruder/pelletizer heats and melts the extruder feed which then may be extruded (e.g., via a twin screw extruder) through a pelletizer die under pressure to form polyolefin pellets. Such pellets are typically cooled in a water system disposed at or near the discharge of the pelletizer. An exemplary energy-saving technique includes the use of a pellet water pump (e.g., having a 15-50 horsepower motor) to transport the extruder pellets in the pellet water to the loadout area. This is contrast to traditional approach of employing a conventional conveying loop, which typically uses a pellet blower operating at about 250-500 horsepower. 
     In general, the polyolefin pellets may then be transported to a product load-out area where the pellets may be stored, blended with other pellets, and/or loaded into railcars, trucks, bags, and so forth, for distribution to customers  40 . In the case of polyethylene, pellets  38  shipped to customers  40  may include low density polyethylene (LDPE), linear low density polyethylene (LLDPE), medium density polyethylene (MDPE), high density polyethylene (HDPE), and enhanced polyethylene. The various types and grades of polyethylene pellets  38  may be marketed, for example, under the brand names Marlex® polyethylene or MarFlex™ polyethylene of Chevron-Phillips Chemical Company, LP, of The Woodlands, Tex., USA. 
     F. Customers, Applications, and End-Uses 
     Polyolefin (e.g., polyethylene) pellets  38  may be used in the manufacturing of a variety of products, components, household items and other items, including adhesives (e.g., hot-melt adhesive applications), electrical wire and cable, agricultural films, shrink film, stretch film, food packaging films, flexible food packaging, milk containers, frozen-food packaging, trash and can liners, grocery bags, heavy-duty sacks, plastic bottles, safety equipment, coatings, toys and an array of containers and plastic products. Further, it should be emphasized that polyolefins other than polyethylene, such as polypropylene, may form such components and products via the processes discussed below. 
     Ultimately, the products and components formed from polyolefin (e.g., polyethylene) pellets  38  may be further processed and assembled for distribution and sale to the consumer. For example, a polyethylene milk bottle may be filled with milk for distribution to the consumer, or the fuel tank may be assembled into an automobile for distribution and sale to the consumer. 
     To form end-products or components from the pellets  38 , the pellets are generally subjected to further processing, such as blow molding, injection molding, rotational molding, blown film, cast film, extrusion (e.g., sheet extrusion, pipe and corrugated extrusion, coating/lamination extrusion, etc.), and so on. Blow molding is a process used for producing hollow plastic parts. The process typically employs blow molding equipment, such as reciprocating screw machines, accumulator head machines, and so on. The blow molding process may be tailored to meet the customer&#39;s needs, and to manufacture products ranging from the plastic milk bottles to the automotive fuel tanks mentioned above. Similarly, in injection molding, products and components may be molded for a wide range of applications, including containers, food and chemical packaging, toys, automotive, crates, caps and closures, to name a few. 
     Extrusion processes may also be used. Polyethylene pipe, for example, may be extruded from polyethylene pellet resins and used in an assortment of applications due to its chemical resistance, relative ease of installation, durability and cost advantages, and the like. Indeed, plastic polyethylene piping has achieved significant use for water mains, gas distribution, storm and sanitary sewers, interior plumbing, electrical conduits, power and communications ducts, chilled water piping, well casing, to name a few applications. In particular, high-density polyethylene (HDPE), which generally constitutes the largest volume of the polyolefin group of plastics used for pipe, is tough, abrasion-resistant and flexible (even at subfreezing temperatures). Furthermore, HDPE pipe may be used in small diameter tubing and in pipe up to more than 8 feet in diameter. In general, polyethylene pellets (resins) may be supplied for the pressure piping markets, such as in natural gas distribution, and for the non-pressure piping markets, such as for conduit and corrugated piping. 
     Rotational molding is a high-temperature, low-pressure process used to form hollow parts through the application of heat to biaxially-rotated molds. Polyethylene pellet resins generally applicable in this process are those resins that flow together in the absence of pressure when melted to form a bubble-free part. Pellets  38 , such as certain Marlex® HDPE and MDPE resins, offer such flow characteristics, as well as a wide processing window. Furthermore, these polyethylene resins suitable for rotational molding may exhibit desirable low-temperature impact strength, good load-bearing properties, and good ultraviolet (UV) stability. Accordingly, applications for rotationally-molded Marlex® resins include agricultural tanks, industrial chemical tanks, potable water storage tanks, industrial waste containers, recreational equipment, marine products, plus many more. 
     Sheet extrusion is a technique for making flat plastic sheets from a variety of pellet  38  resins. The relatively thin gauge sheets are generally thermoformed into packaging applications such as drink cups, deli containers, produce trays, baby wipe containers, and margarine tubs. Other markets for sheet extrusion of polyolefin include those that utilize relatively thicker sheets for industrial and recreational applications, such as truck bed liners, pallets, automotive dunnage, playground equipment, and boats. A third use for extruded sheet, for example, is in geomembranes, where flat-sheet polyethylene material is welded into large containment systems for mining applications and municipal waste disposal. 
     The blown film process is a relatively diverse conversion system used for polyethylene. The American Society for Testing and Materials (ASTM) defines films as less than 0.254 millimeter (10 mils) in thickness. However, the blown film process can produce materials as thick as 0.5 millimeter (20 mils), and higher. Furthermore, blow molding in conjunction with monolayer and/or multilayer coextrusion technologies lay the groundwork for several applications. Advantageous properties of the blow molding products may include clarity, strength, tearability, optical properties, and toughness, to name a few. Applications may include food and retail packaging, industrial packaging, and non-packaging applications, such as agricultural films, hygiene film, and so forth. 
     The cast film process may differ from the blown film process through the fast quench and virtual unidirectional orientation capabilities. These characteristics allow a cast film line, for example, to operate at higher production rates while producing beneficial optics. Applications in food and retail packaging take advantage of these strengths. Finally, polyolefin pellets may also be supplied for the extrusion coating and lamination industry. 
     III. Polymerization Reactor Feed System 
     Referring to  FIG. 2 , a process flow diagram of an exemplary reactor feed system  16  (of  FIG. 1 ) is depicted. In this embodiment, monomer  50  (e.g., ethylene) is fed through monomer treaters  52  to the liquid phase reactor (e.g., loop slurry reactor) in the reactor system  20 . Furthermore, a mass flow meter  53 , instead of an orifice plate meter, may be used to measure the flow rate of ethylene to the reactor. Indeed, the flow rate of ethylene monomer  50  to the reactor generally is typically measured (and controlled) to facilitate desired operating conditions (e.g., slurry density, comonomer/monomer ratio, production rate, etc.) in the reactor and to provide the desired properties of the polyethylene formed in the reactor. The exemplary mass flow meter  53  used to measure the ethylene monomer flow may be an orifice-plate type differential pressure meter, Coriolis mass meter, and so forth. 
     Recycle diluent  54  (e.g., isobutane) with a relatively small amount of entrained monomer may be returned from the diluent/monomer recovery system  24  (e.g., corresponding to stream  34  of  FIG. 1 ) and sent to the polymerization reactor. In the example of “direct” recycle to the reactor, the recycled diluent  54  may be cooled and passed through a heavies knockout pot  56 , where heavy components are removed out of a bottom discharge and sent via a centrifugal pump  58 , for example, as feed  60  to the fractionation system  30 . The overhead  62  of the knockout pot  56  may be further cooled in a heat exchanger  66  and collected in a recycle diluent surge tank  68  for feed to the reactor. Downstream, a centrifugal pump  70  may deliver the diluent  72  through recycle diluent treaters  74  to the loop slurry reactor. It should be noted that a relatively small amount of fresh diluent (not illustrated) may be added in the fractionation system  30 , for example, to make-up for diluent losses in the manufacturing process  10 . Furthermore, comonomer  76  (e.g., 1-hexene) may be added to the suction of pump  70  or at other points in the recycle diluent circuit for addition to the reactor. The monomer treaters  52  and recycle diluent treaters  58  may include molecular sieve or aluminum packing, for example, configured to remove catalyst poisons from the monomer, recycle diluent, comonomer feeds, and other feeds. 
     Other feed components may be added to the loop slurry reactor. For example, hydrogen  60  may be added to control the molecular weight of the polyolefin formed in the reactor. Furthermore, other additives, such as antistatic materials, may be injected into the reactor, as indicated by reference numeral  78 . The various component streams may combine into a single feed stream  80  for feed to the loop slurry reactor. Further, as discussed below, diluent  82  that is substantially olefin-free may be recycled from the fractionation system  30  through treaters  84  for use in the preparation of the catalyst fed to the reactor. Indeed, diluent  82  may act as a carrier of the catalyst stream  88  discharged from the catalyst preparation system  86  in route to the loop slurry reactor. Lastly, treaters have been traditionally employed to process the various feeds, such as to remove catalyst poisons from the comonomer, fresh isobutane, and hydrogen. 
     Referring to  FIG. 3 , a process flow diagram of the catalyst preparation area  86  is depicted. A catalyst mix tank  140  receives catalyst  142 , for example, from a portable container. Olefin-free monomer  82  mixes with the catalyst in the catalyst mix tank  140 . An agitator  144  having a motor and drive  146  and blade  148  may facilitate mixing of the diluent  82  and the catalyst  142  in the mix tank  140 . The process catalyst  150  discharges from the mix tank  140  and may enter, for example, a catalyst run tank  152  for metering to the loop slurry reactor. The run tank  152  may also have an agitator  154  having a motor/drive  156  and agitator blade  158  to maintain the catalyst mixed with the diluent. The catalyst may be metered, for example, by a positive displacement pump  160  to the loop slurry reactor as feed stream  88 . Additionally, additives, such as co-catalysts (e.g., triethylaluminum)  162 , may be added to the catalyst  88  fed to the reactor. Finally, it should be noted that prior to mixing and metering the catalyst, the catalyst may be activated. For example, in the case of a chromium oxide catalyst, a catalyst activator may convert the chromium Cr3+ to Cr6+ for injection into the polymerization reactor. While in the reactor and in contact with the ethylene monomer, for example, the chromium Cr6+ may reduce to Cr2+. Moreover, the design and/or operation of the catalyst system may be adjusted in response to various results provided by the present purge column models. 
     Referring to  FIG. 4 , a process flow diagram of a catalyst activator system  170  is depicted. The activated catalyst product of system  170  is fed to the catalyst mix tank  140  (catalyst  142 ) of  FIG. 3 . In  FIG. 4 , the catalyst activator includes an internal vessel  172  containing the catalyst, and an external furnace  174 . Catalyst from the supplier may be held in a holding vessel  176  and fed via to the internal vessel via an on/off valve  178 , for example. Fuel  180  may be added via a sparger or pilot  182 , for example, into the furnace  180 , and the fuel  180  may be combined with air  184  injected into the furnace via an air filter  186  and air blower  188 . Combustion may take place inside the furnace in the region  190 , for example. The region  192  surrounding the internal vessel  172  may experience operating temperatures in an exemplary range of 800 to 1700° F. The heated fluid from this region  192  may discharge to the atmosphere  194 , as depicted by arrow  196 . 
     In addition to high heat, oxygen may be supplied to activate the catalyst. Air  198  may be injected into the bottom of the internal vessel  172  to provide the presence of oxygen inside the vessel, with heat provided by the surrounding furnace  174 . The air entering the vessel  172  may exit at the top via an internal air filter  200 , for example, and then discharge to the atmosphere, as indicated by reference numeral  202 . The activated catalyst may discharge from vessel  172  into a catalyst tote bin  206 , or other container. Furthermore, nitrogen  208  may facilitate discharge of the activated catalyst into the tote bin  206 , and also provide an inert atmosphere in the tote bin  206 . In general, catalyst activation processes include passing dry air through a catalyst bed at a constant rate, while applying heat, until the catalyst reaches the desired temperature, at which point the catalyst is held at the activation temperature for the proper length of time. Moreover, the design and/or operation of the catalyst activation system may be adjusted in response to various results provided by the present purge column models. 
     IV. Polymerization Reactor System 
     Referring to  FIG. 5 , a process flow diagram of an exemplary polymerization reactor system  20  (of  FIG. 1 ) and diluent/monomer recovery system  24  (also of  FIG. 1 ) are depicted. As discussed above, the reactor system  20  may comprise one or more polymerization reactors, which may in turn be of the same or different types. Furthermore, in multiple reactor systems, the reactors may be arranged serially or in parallel. Whatever the reactor types comprising the reactor system  20 , a polyolefin particulate product, generically referred to as “fluff” herein, is produced. To facilitate explanation, the following examples are limited in scope to specific reactor types believed to be familiar to those skilled in the art and to single reactors or simple combinations. To one of ordinary skill in the art using this disclosure, however, the present techniques are simply and easily applicable to more complex reactor arrangements, such as those involving additional reactors, different reactor types, and/or alternative ordering of the reactors or reactor types. Such arrangements are considered to be well within the scope of the present invention. 
     One reactor type comprises reactors within which polymerization occurs within a liquid phase. Examples of such liquid phase reactors include autoclaves, boiling liquid-pool reactors, loop slurry reactors (vertical or horizontal), and so forth. For simplicity, a loop slurry reactor  42  that produces polyolefin, such as polyethylene, polypropylene, and their copolymers, will be discussed in the context of the present techniques though it is to be understood that the present techniques are similarly applicable to other types of liquid phase reactors. 
     The loop slurry reactor  210  is generally composed of segments of pipe connected by smooth bends or elbows. An exemplary reactor  210  configuration includes eight jacketed vertical pipe legs, approximately 24 inches in diameter and approximately 200 feet in length, connected by pipe elbows at the top and bottom of the legs. As discussed below, reactor jackets  212  are normally provided to remove heat from the exothermic polymerization via circulation of a cooling medium, such as treated water, through the reactor jackets  212 . 
     The reactor  210  may be used to carry out polyolefin polymerization under slurry conditions in which insoluble particles of polyolefin are formed in a fluid medium and are suspended as slurry until removed. A motive device, such as pump  214 , circulates the fluid slurry in the reactor  210 . An example of a pump  214  is an in-line axial flow pump with the pump impeller disposed within the interior of the reactor  210  to create a turbulent mixing zone within the fluid medium. The impeller may also assist in propelling the fluid medium through the closed loop of the reactor at sufficient speed to keep solid particulates, such as the catalyst or polyolefin product, suspended within the fluid medium. The impeller may be driven by a motor  216  or other motive force. 
     The fluid medium within the reactor  210  may include olefin monomers and comonomers, diluent, co-catalysts (e.g., alkyls, triethylboron, methyl aluminoxane, etc.), molecular weight control agents (e.g., hydrogen), and any other desired co-reactants or additives. Such olefin monomers and comonomers are generally 1-olefins having up to 10 carbon atoms per molecule and typically no branching nearer the double bond than the 4-position. Examples of monomers and comonomers include ethylene, propylene, butene, 1-pentene, 1-hexene, 1-octene, and 1-decene. Again, typical diluents are hydrocarbons which are inert and liquid under reaction conditions, and include, for example, isobutane, propane, n-pentane, i-pentane, neopentane, n-hexane, cyclohexane, cyclopentane, methylcyclopentane, ethylcyclohexane, and the like. These components are added to the reactor interior via inlets or conduits at specified locations, such as depicted at feed stream  80 , which generally corresponds to one of the feed streams  18  of  FIG. 1 . Likewise, a catalyst, such as those previously discussed, may be added to the reactor  210  via a conduit at a suitable location, such as depicted at feed stream  88 , which may include a diluent carrier and which also generally corresponds to one of the feed streams  18  of  FIG. 1 . In total, the added components generally compose a fluid medium within the reactor  210  within which the catalyst is a suspended particle. 
     The reaction conditions, such as temperature, pressure, and reactant concentrations, are regulated to facilitate the desired properties and production rate of the polyolefin in the reactor, to control stability of the reactor, and the like. Temperature is typically maintained below that level at which the polymer product would go into solution. As indicated, due to the exothermic nature of the polymerization reaction, a cooling fluid may be circulated through jackets  212  around portions of the loop slurry reactor  210  to remove excess heat, thereby maintaining the temperature within the desired range, generally between 150° F. to 250° F. (65° C. to 121° C.). Likewise, pressure may be regulated within a desired pressure range, generally 100 to 800 psig, with a range of 450-700 psig being typical. 
     As the polymerization reaction proceeds within the reactor  210 , the monomer (e.g., ethylene) and comonomers (e.g., 1-hexene) polymerize to form polyolefin (e.g., polyethylene) polymers that are substantially insoluble in the fluid medium at the reaction temperature, thereby forming a slurry of solid particulates within the medium. These solid polyolefin particulates may be removed from the reactor  210  via a settling leg or other means, such as a continuous take-off, as depicted discharge stream  22 . In downstream processing, the polyethylene discharged from the reactor may be extracted from the slurry and purified. 
       FIG. 6  depicts an exemplary polymerization reactor  210  of  FIG. 5  and shows a counter-current flow scheme of cooling medium through the reactor jackets  212 A-H. Again, the loop reactor  210  is generally composed of segments of pipe connected by smooth bends or elbows. A motive device, such as pump  214 , circulates the fluid slurry in the reactor  210 . An example of a pump  214  is an in-line axial flow pump with the pump impeller disposed within the interior of the reactor  210 . A coolant system  250  removes heat from the loop reactor  210  via reactor jackets  212 A-H. The coolant system  250  provides a coolant supply  252  (e.g., treated water) and processes a coolant return  254 . 
     As the polymerization reaction proceeds within the reactor  210 , the reaction conditions may be controlled to facilitate the desired degree of polymerization and the desired reaction speed while keeping the temperature below that at which the polymer product would go into solution. As mentioned, due to the exothermic nature of the polymerization reaction, cooling jackets  212 A-H may be provided around portions of the closed loop system through which a cooling fluid is circulated as needed to remove excess heat (heat of reaction), thereby maintaining the temperature within the desired range, generally between 150° F. to 250° F. (65° C. to 121° C.). 
     In general, reactor temperature varies linearly with changes in the reactor system operating conditions. An accepted assumption in the art is that heat generated in the reactor by the exothermic polymerization is linear with the polyolefin production rate (i.e., pounds per hour of polyolefin polymerized). Thus, reactor temperature, which is an indication of the energy or heat in the reactor, varies linearly with production rate. As appreciated by those of ordinary skill in the art, typical reactor temperature control may involve a proportional-integral-derivative (PID) algorithm. 
     V. Diluent/Monomer Recovery System 
     A. Flash Chamber 
     Returning to  FIG. 5 , the discharge  22  from the reactor  210  may flow through an in-line flash heater  222  and into a flash chamber  224 . The in-line flash heater  222  may be a surrounding conduit that uses steam or steam condensate, for example, as a heating medium to provide indirect heating to the discharge  22 . Thus, the loop slurry reactor  210  effluent (discharge  22 ) is heated prior to its introduction into the flash chamber  224 . Also, before the discharge  22  enters the flash chamber  224 , water or other catalysts poisons may be injected into the discharge  22  to deactivate any residual catalysts in the discharge  22  stream. Because these injected components are catalysts poisons by definition, they are typically completely removed, or at least substantially removed, from any recovered material (e.g., monomer or diluent) recycled to the reactor  210 . 
     In the flash chamber  224 , most of the non-solid components of the reactor discharge  22  are withdrawn overhead as vapor in the flash gas  226 . Note, it is this recycled flash gas  226  that may bypass the fractionation system in route to the reactor  210  (i.e., via the feed system  16 ). In polyethylene production, this vapor is typically primarily diluent, such as isobutane or other diluents previously mentioned. It may also contain most of the unreacted monomer (e.g., ethylene) and other light components, as well as unreacted comonomer (e.g., 1-hexene, butene, 1-pentene, 1-octene, and 1-decene) and other heavy components (e.g., hexane and oligomers). In general light components or “lights” may be defined at those light components with lower boiling points than the diluent employed. In contrast heavy components or “heavies” may be defined as those components having higher boiling points than the diluent. An exemplary approximate composition of the flash gas  226  is 94 wt. % isobutane, 5 wt. % ethylene, and 1 wt. % other components. A level or volume of fluff may be maintained in the flash chamber  224  to give additional residence time of the fluff in the chamber  224  to facilitate separation of liquid and vapor entrained in the porous fluff particles. 
     The flash gas  226  may be processed in equipment such as cyclones, bag filters, etc., where entrained fluff solids are removed and returned to the flash chamber  224  or to downstream equipment, such as the purge column discussed below. The flash gas  226  may also travel through a deoxygenation bed, for example. Furthermore, the flash gas  226  may be cooled or condensed in a heat exchanger (e.g., shell-and-tube construction) prior to its recycle to the feed system  16  or fractionation system  30 . 
     As for the solids (polymer) in the flash chamber  224 , they are withdrawn with a small amount of entrained diluent (and monomer) and sent to a purge column  228  via solids discharge  230 . As will be appreciated by those of ordinary skill in the art, the solids discharge  230  conduit may include valve configurations that allow polymer to flow downward through the conduit while reducing the potential for vapor to flow between the purge column  228  and the flash chamber  56 . For example, one or more rotary or cycling valves may be disposed on the solids discharge  230  conduit. Furthermore, a relatively small fluff chamber may also be disposed on the conduit to handle the discharge of the fluff solids from the flash chamber  224  to the purge column  228 . Such a discharge to the purge column  228  may include appropriate valve configurations, a surge chamber, or simply a conduit, and so on. Moreover, other arrangements in the flash/purge system are applicable. For example, the fluff solids from the flash chamber  224  may discharge to a lower pressure flash chamber (with the lower pressure flash gas compressed for recycle to fractionation system  30  and reactor) prior to introduction of the fluff solids to the purge column  228 . 
     Finally, as discussed, the system  10  may provide for direct recycle of 80 to 95 wt. % of the diluent and unreacted monomer recovered from the in the monomer/recovery system  24  to the feed and reactor systems  16  and  20 . For example, flash gas  226  ( FIG. 7 ) which discharges from the flash chamber  224  overhead, and which generally corresponds to the recycle stream  34  of  FIG. 1 , may be sent as the recycle diluent  54  stream ( FIG. 2 ) directly to the reactor  210  via the surge tank  68 . Such direct recycle significantly reduces the load on the fractionation system  30 , including the load on the fractionation columns and reboilers in the system  30  (as compared with no direct recycle). Thus, the fractionation columns and associated reboilers (e.g., steam reboilers) may be significantly reduced in size (e.g., reduced by 80-95% of the conventional size) for the same capacity polyolefin plant. Steam usage is significantly reduced and substantial energy by employing the smaller columns. Lastly, it should be noted that the design and/or operation of the fractionation system  30  may be adjusted in response to the output of the present purge column models. 
     B. Purge Column 
     The primary solids feed to the purge column  228  is typically the solids discharge  230  (polyolefin fluff) that exits the flash chamber  224 . A purpose of the purge column  228  is to remove residual hydrocarbon from the entering solids streams and to provide substantially-clean polymer fluff  232  with relatively small amounts of entrained volatile organic content (VOC). The fluff  232  may be transported or conveyed to the extrusion/loadout system  36  for conversion to pellets  38 , and for distribution and sale as polyolefin pellet resin to customers  40 . In general, the treated polymer particles discharged from purge column  228  as polymer fluff  232  may be processed in a conventional finishing operation, such as a screw extruder, in the extrusion/load out system  36  ( FIG. 1 ). 
     In the exemplary purge column system illustrated, nitrogen is circulated through purge column  228  to remove residual hydrocarbons via overhead discharge  234 . This discharge  234  may be sent through a separation unit  236 , such as a membrane recovery unit, pressure swing adsorption unit, refrigeration unit, and so forth, to recover nitrogen via nitrogen stream  238 , and to discharge a separated hydrocarbon stream  240  as feed to the fractionation system  30 . In the art, the separation unit  236  may be known as an Isobutane Nitrogen Recovery Unit (INRU) or Diluent Nitrogen Recovery System (DNRU). Moreover, fresh nitrogen  242  may be added to the nitrogen circuit to account for nitrogen losses in the purge column  228  system. Finally, it should be noted that the hydrocarbon stream  240  may beneficially provide feed to the fractionation system  30  (see  FIG. 13 ). For example, the hydrocarbon stream  240  discharging from the separation unit  236  makes available hydrocarbon feed that may be processed to give the olefin-free diluent used in catalyst preparation. 
     An exemplary purge column  228  may be cylindrical vessel having a relatively tall vertical section, a cover or head at the top, sloped sides or conical shape at the bottom with an opening for polymer fluff discharge. The polymer fluff to be degassed of volatile hydrocarbons may enter the vessel at the top, while the purge gas, typically nitrogen, may be introduced to the vessel in the slopped bottom sides. Flow may be countercurrent between the purge gas and polymer fluff in the vessel. Again, in certain embodiments, the hydrocarbon rich purge gas leaves the vessel through an opening at the top, while the degassed fluff leaves at the bottom of the vessel. 
     Degassing effectiveness in the vessel may be predicated on the maintenance of uniform plug flow of the polymer fluff and purge gas in the vessel, thereby ensuring good contact between the two. The diameter of the vessel typical range from 5 to 6 feet, but its length (L/D ratio) is chosen to achieve a residence time (e.g., 30 to 180 minutes) sufficient for degassing the polymer fluff. Example L/D ratios may range from 4 to 8, or outside this range. Lastly, it should be noted that internals may be employed in the purge column, such as a distributor plate for introducing purge gas (nitrogen), an inverted cone for facilitating plug glow of the polymer (e.g., reduce bridging or channeling of the polymer fluff), and so on. 
     C. Alternate Configurations of the Diluent/Monomer Recovery System 
     As will be appreciated by those of ordinary skill in the art, a variety of configurations may be employed in the diluent/monomer recovery system  24 . For example, the solids discharge  230  from the flash chamber  224  may be sent to another reactor (e.g., a gas phase reactor) instead of to the purge column  228  or to a low-pressure flash chamber. The polymer may then later enter the purge column  228  (i.e., from the gas phase reactor or low-pressure flash chamber). If discharged to another reactor from the flash chamber  224 , catalyst poison may not be injected upstream in the discharge  22 , and, thus, residual active catalysts remain for further polymerization. In another configuration, the purge column  228  may be combined with a downstream extruder feed tank. The separation unit  236  associated with the purge column  228  may then accommodate the new purge column/extruder feed tank combination, for example. 
     VI. Continuous Take Off of the Reactor Effluent Discharge 
       FIGS. 7-9  illustrate a continuous take-off mechanism of the reactor discharge  22 . Referring to  FIG. 7 , a continuous takeoff mechanism  280  disposed on a pipe elbow of the loop slurry reactor  210 , is depicted. The continuous takeoff mechanism  280  includes a take-off cylinder  282 , a slurry withdrawal line  284 , an emergency shut-off valve  285 , proportional motor valve  286  to regulate flow, and a flush line  287 . The reactor  210  may be operated “liquid” full, and because the reactor liquid contents are slightly compressible, pressure control of the liquid through the system may be accomplished with a valve. Further, where diluent input is held substantially constant, and the proportional motor valve  58  may be used to control the rate of continuous withdrawal and to maintain the total reactor pressure within designated set points. 
     Referring to  FIG. 8 , which is taken along section line  8 - 8  of  FIG. 7 , a smooth-curved pipe elbow having the continuous take-off mechanism  280 , is depicted. Thus the illustrated pipe elbow may be considered am appendage-carrying elbow. As shown, the mechanism includes take-off cylinder  282 , which is attached, in this instance, at a right angle to a tangent to the outer surface of the elbow. Further, coupling to the cylinder  282  is the slurry withdrawal line  284 . Disposed within the take off cylinder  282  is a ram valve  288 , which may serve at least two purposes. First, it may provide a clean-out mechanism for the take-off cylinder if it should ever become fouled with polymer, for example. Second, it may serve as a shut-off valve for the entire continuous take-off assembly. 
       FIG. 9  shows an attachment orientation for the take-off cylinder  282 , which is affixed tangentially to the curvature of the elbow and at a point just prior to the slurry flow turning upward. The opening may be elliptical to the inside surface, for example, and further enlargement may be implemented to improve solids take-off. Finally, it should be noted that a variety of orientations of the attachment of the take-off cylinder  282  may be implemented. 
     A continuous take-off of product slurry of an olefin polymerization reaction carried out a loop reactor in the presence of an inert diluent allows operation of the reactor at a much higher solids concentration than with the conventional settling leg(s) used to discharge the polymer. For example, production of predominantly ethylene polymers (polyethylene) in isobutane diluent has generally been limited to a maximum solids concentration in the reactor of 37-40 weight percent (wt. %) with the settling leg configuration. However, the continuous take-off (CTO) has been found to allow significant increases in solids concentration. As a result, solids concentration of greater than 50 wt. % in the reactor may be implemented with the continuous takeoff. It should be emphasized that in a commercial operation, as little as a one percentage point increase in solids concentration is of major significance. Such an increase, for example, allows higher production rates of polyethylene. 
     VII. Extrusion/Loadout System 
     Referring to  FIG. 10 , a process flow diagram of the extrusion/loadout system  36  of  FIG. 1  is depicted. Polyolefin fluff  232  from the purge column  228  ( FIG. 5 ) may be pneumatically transferred, for example, using a dilute phase blower, through a valve  340  in the extruder/loadout system  36 , and either into conduit  342  to the fluff silo  344 , or into conduit  346  to the extruder feed tank  348 . The fluff silo  344  may be used to provide surge capacity during shutdown of the extruder (or of other operations) in the extrusion/loadout system  36 . On the other hand, the fluff silo  344  may also accumulate fluff to allow for full-rate operation of the extruder while the upstream polymerization reactor  210  “catches up” during start up of the reactor  210 . The polyolefin fluff in silo  344  may be pneumatically transferred to the extruder feed tank through rotary valve  350  with the aid of a blower system  351 . 
     Typically, however, the primary flow of polyolefin fluff  232  (which may generally correspond to fluff  28  of  FIG. 1 ) is to the extruder feed tank  348  via conduit  346 . Downstream, rotary valve fluff  352  may feed polyolefin fluff  354  to the extruder  356 , where the extruder heats, melts, and pressurizes the polyolefin fluff  354 . As will be appreciated by those of ordinary skill in the art, the fluff  354  from the extruder feed tank  348  may be metered to the extruder  356  with a variety of meters, such as smart flowmeter-type, master-feeder type, and so forth. Furthermore, additives may be injected into the fluff  354  stream at an addition rate that may be based on a specified ratio to the mass flow rate of the fluff  354 . This ratio or “slave” feed of additives to fluff  354  may be specified at a value to generate a desired recipe, for example, for each polyolefin grade or product, and to give the desired properties of the downstream polyolefin pellets. Furthermore, the additive addition may be accomplished with a liquid additive system, loss-in-weight-feeders, and the like. In certain embodiments, one or more of lost-in-weight feeders may be used to meter a pre-mixed additive package fed from a bulk container, for example, to the extruder  356  via the fluff  354  stream, an extruder  354  feed hopper, directly to the extruder  354 , and so on. 
     In general, the extruder  356  may melt, homogenize, and pump the polyolefin polymer and additives through a pelletizer  358 , which may include a screen pack and heated die head, for example, which pelletizes the mixture of fluff and additives. Further, pelletizer knife blades (i.e., under water) may cut the polyolefin melt extruded through the die into pellets. The pellets are typically quenched by water  360  and may travel in a pellet-water slurry  362  from the pelletizer  358  to a pellet dewatering dryer  364 . The dryer  364  may separate the free water and then dry the remaining surface water from the pellets by centrifugal force. The dried pellets  366  may discharge onto a scalping screen  368 , for example, which removes oversized and undersized pellets from on-specification pellets  370 . 
     Water  360  may be supplied to the pelletizer  358  from a water tank  372  via a centrifugal pump  374  and cooler  376  (e.g., shell and tube heat exchanger). Water  378  removed from the pellet dryer  364  may return to the water tank  372 . The polyolefin pellets  370  exiting the scalping screen  368  may fall by gravity through a rotary valve  380  into a dense-phase pneumatic conveying line  382 , for example, and transported to pellet silos  384 . The pellet silos may include storage tanks, blenders, off-specification storage tanks, and so on. In the illustrated embodiment, the blower package  385  provides nitrogen and/or air  388  to convey the pellets  370  via conveying line  382  to the pellet silos  386 . Polyolefin pellets  390  may be loaded into rail cars  392 , hopper cars, trucks, tote bins, bags, and so on. Pellets  390  may be loaded into hopper cars, for example, using a gravity type, air assisted, multiple-spout, loading system. Such a system may allow the hopper car to be automatically loaded at a rate higher than the polymerization and extrusion production rate. Thus, extra “time” generated by the higher loadout rates may be exploited to provide time to move the hopper cars or rail cars after filling, and to spot the next empty car. Lastly, it should be noted that VOC in the polyolefin fluff stream  232  from the purge column  228  ( FIG. 5 ) may collect at various points in the extrusion/loadout system  36 . Moreover, the VOC may escape or be vented to the atmosphere from various points in the extrusion/loadout system  36 . 
     VIII. Purge Column Model 
     A. Exemplary Results 
       FIGS. 11-16  show example results of sensitivity studies with an exemplary model to evaluate the impact of purge parameters (e.g., fluff temperature, residence time, nitrogen flow, particle size, and pressure) on the VOC of polyolefin polymer (i.e., fluff) stream leaving the purge column. The exemplary model is based on mass-transfer theory discussed in detail the following sections below. As expected, the VOC of the polymer stream decreased for higher fluff temperature, longer residence time, higher purge gas flow (e.g., inert gas, nitrogen, air, etc.), smaller polymer particle size, and lower purge pressure. It is believed that these parameter trends generally enhance the diffusion of absorbed or adsorbed hydrocarbon components from the polymer. Highlights of the exemplary results are discussed below. 
       FIG. 11  is an exemplary plot  400  of model results of VOC  402  in ppm (part per million—volatile organics in the polyolefin fluff stream leaving the purge column) versus the temperature  404  of the polyolefin (fluff) in degrees Fahrenheit. The curve  406  illustrates an example inverse relationship between the VOC  402  and the fluff temperature  404 . In this example, increasing polyolefin fluff temperature in the purge column from 160° F. to 176° F. (10% change) resulted in about 80% reduction in VOC, from 128 ppm to 25 ppm, as depicted in the exemplary plot  400  of  FIG. 11 . 
       FIG. 12  is an exemplary plot  410  of model results of VOC  412  in ppm in the polyolefin (fluff) stream discharging from the purge column (e.g., purge column  228 ) versus the purge time  414  in minutes. In this embodiment, the purge time  414  is the residence time of the polyolefin fluff in the purge column. The curve  416  illustrates an example inverse relationship between VOC  412  and purge time  414 . In this example, increasing purge time  414  from 60 minutes to 75 minutes (25% increase) resulted in about 73% reduction in VOC  412 , from 34 ppm to 9 ppm. However, with this desired increase in purge time  414 , production rate of polyolefin fluff discharging from the upstream polymerization reactor (e.g., loop reactor  210 ) was decreased by 20% in the model to account for inventory control in the purge column. 
       FIG. 13  is an exemplary plot  420  of model results of VOC  422  in the polyolefin leaving the purge column versus the ratio  424  of the flow rate of purge gas (in this example, nitrogen) to the purge column to the flow rate of polyolefin polymer leaving the purge column. As with the aforementioned variables, the curve  426  illustrates an example inverse relationship of VOC  422  versus the ratio  424  of flow rates. In this embodiment of the model, increasing purge gas from 694 pounds per hour (lb/hr) to 810 lb/hr (17% increase) resulted in about a 40% reduction in VOC from 50 ppm to 30 ppm. In this calculation, the residence time and fluff temperature in the purge column were maintained constant. 
       FIG. 14  is an exemplary plot  430  of model results of VOC  432  in the polyolefin (fluff) stream discharged from the purge column versus average particle size  434  in  10   −6  meters (microns or μm) the polyolefin polymer (fluff). A proportional relationship exists between VOC  432  and polymer particle size  434 , as illustrated by exemplary curve  436 . In one sensitivity example of the model, with reducing fluff particle size from 800 microns to 600 microns (25% decrease), the VOC  432  was reduced by about 43% from 47 ppm to 26 ppm. 
       FIG. 15  is an exemplary plot  440  of model results of VOC  442  in the polyolefin (fluff) stream discharged from the purge column versus the pressure  444  of the purge gas (e.g., inert gas) entering the purge column. The curve  446  illustrates an example proportional relationship between VOC  442  and purge pressure  444 . In the exemplary model, reducing purge pressure  444  from 5 pounds per square inch (psig) to 3 psig, a 40% reduction, resulted in about a 36% reduction in VOC from 44 ppm to 28 ppm. 
       FIG. 16  is a plot  450  of exemplary model results of purge temperature  452  (i.e., temperature of the polyolefin in the purge column) versus the purge time  454  (i.e. residence time of the polyolefin in the purge column). The curve  456  represents the trade-off between purge temperature  454  (fluff temperature) and purge time  454  (residence time), while maintaining the constant VOC in the polyolefin stream and the inventory in the purge column. In these example results of the purge column model, an approximate 10% drop in purge (fluff) temperature from 170° F. to 153° F. generally corresponds to a need for about a 50% increase in purge time (residence time) in the purge column from 59 minutes to 88 minutes to maintain VOC (no increase) in the polyolefin stream discharging from the purge column. 
     Table 1 summarizes an exemplary order of the effects of the parameters on VOC reduction for an example resin in this case study. The example resin is grade TR-418F obtained from Chevron Phillips Chemical Company LP of The Woodlands, Tex. The resin TR-418F generally has a fluff bulk density of 0.90 to 0.97 pound per cubic feet. Ultimate applications of such a resin may include film, pipe, blow-molding, and the like. Analysis with the resin is only given as an example, and not meant to limit the present techniques to a particular resin or particular grade of resin. Moreover, the present techniques and purge column model may accommodate a variety of unimodal or bimodal polyolefin polymers or resins, resins produced with a single reactor or multiple reactors in series, and so on. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Exemplary Impact/Order of purge parameter on VOC 
               
               
                 reduction for polymer 
               
            
           
           
               
               
               
               
            
               
                   
                   
                   
                 /ΔVOC/VOC/ 
               
               
                 Parameter (Par) 
                 ΔPar/Par 
                 ΔVOC/VOC 
                 ΔPar/Par| 
               
               
                   
               
            
           
           
               
               
               
               
            
               
                 Temperature (F.) 
                 1.4% 
                 −21.2% 
                 15.0 
               
               
                 Residence Time (min) 
                 7.3% 
                 −30.2% 
                 4.2 
               
               
                 Purge Gas Flow (lb/hr) 
                 3.2% 
                 −8.7% 
                 2.8 
               
               
                 Particle Size (μm) 
                 5.2% 
                 13.3% 
                 2.5 
               
               
                 Purge Pressure (psig) 
                 −15.9% 
                 −15.4% 
                 1.0 
               
               
                   
               
            
           
         
       
     
     In this example of TR-418F polyolefin resin, the approximate order of significance in reducing VOC in the polyolefin polymer stream exiting the purge column is fluff temperature, residence time, purge gas (e.g., nitrogen) flow, fluff particle size, and purge pressure. In this embodiment, high fluff temperature had the most impact on VOC reduction for the polymer. Therefore, in this instance, the highest possible purge column fluff temperature achieves the highest possible recovery of hydrocarbons in the INRU and reduces potential VOC emissions in the plant. The highest possible purge column temperature may be generally achieved by running at the highest possible flash gas temperature before encountering temperature-related operational problems (e.g., limited by the softening point or melting point of the polyolefin). It should be noted that the flash gas temperature is generally controlled via the upstream flash line heaters. In this example, heating the purge gas has relatively little impact on degassing as the heat capacity of the purge gas (e.g., nitrogen) is typically low and the mass flow of the purge gas compared to the mass flow of the polymer is miniscule. 
     The reduced VOC observed for smaller fluff particle size suggests it may be beneficial to employ catalyst or reactor technology for producing polymer with smaller particle size. Apart from potential better circulation in the upstream polymerization reactor for such smaller particle resins, the small particles may lead to better degassing in the purge column for the resin, especially the low-density type. The selected minimum or low end of the polymer particle size may be determined by needs of circulation in the reactor, settling efficiency of the polyolefin fluff transfer systems. 
     In summary, the exemplary purge column models of the present techniques may present a significant contribution to the array of tools for supporting polyolefin production. The model can be used for plant support and for evaluating purge column designs and operation. The model is general and applies to the degassing of non-molten polyethylene resins, generally irrespective of their technology of production (liquid phase polymerization gas-phase polymerization, loop reactor, autoclave reactors, fluidized bed reactors, stirred reactors, etc.). 
     B. Exemplary Process Schematic of Model 
       FIG. 17  is an exemplary process schematic of one embodiment of the purge column model.  FIG. 17  shows an exemplary diluent/monomer recovery system  24  including the flash line heater  22 , flash vessel  224 , and purge column  228 . Hydrocarbon or diluent-rich polyolefin polymer slurry is withdrawn from the upstream polymerization reactor  210  (e.g., via a continuous take-off from the reactor  210 ). The slurry is heated in the flash line heater  222  with steam to boil-up the hydrocarbon liquid (e.g., diluent and unreacted monomer and comonomer) associated with the polymer into vapor. Steam  458  enters a jacket (i.e., annulus of outer conduit over inner conduit) of the flash line heater  222  and exits as steam condensate  459 . More than one continuous take-offs (and more than one associated flash line heater  222 ) may be employed for a given reactor  210 . 
     The polymer-vapor mixture is flashed in the flash tank  224  to separate out the hydrocarbon vapor (flash gas  226 ) from the polymer fluff (discharged as polyolefin stream  230 ). As discussed, in this embodiment, stream  230  which includes polymer fluff and any entrained hydrocarbon are sent to the purge column  228  for purging with recycled purge gas (nitrogen)  238  (and fresh purge gas (nitrogen)  242 ) to reduce the hydrocarbon content (or volatile organic content) of the polyolefin polymer to desirable or allowable limits. It should be noted that the flash gas  226  may be processed by a bag filter  464  (or cyclone) and the flash gas  226 A then sent to a heavies column in the fractionation system  30 , for example. Any solid particles recovered via the bag filter  464  may be sent to the purge column, for example. Likewise, the overhead hydrocarbon-rich purge gas  234  exiting the top of the purge column  228  may be processed in a bag filter  466 , where solids  470  (e.g., polymer solids) are removed and returned to the purge column  228 . 
     The process configuration for the present models may incorporate a discharge of polyolefin polymer form the flash vessel  224  to travel through a rotary valve  460 , as well as through other equipment, such as fluff surge chambers, etc. Also, the nitrogen entering the purge column may be heated in a heat exchanger  472  employing steam  474 , for example. Further, the polyolefin fluff exiting the bottom portion of the purge column may travel through one or more rotary valves  462  and  232  in the extrusion part of the plant. 
     As indicated, several factors may influence the effectiveness of the purge column  228  in degassing the polymer, namely, purge temperature, purge time, purge gas (nitrogen) purity and flow rate, particle size, purge pressure, polymer density, and so on. The present techniques provide for one or more models for designing and rating purge columns  228  to select the various mix of parameters for the effective purging of polymer resins. Again, while portions of the present discussion may focus on construction and use of a model for purge columns  228  in the loop slurry polyethylene plant, the model is readily applicable and adaptable to address the purging of polymer in general, such as in the loop polypropylene plants, gas-phase plants, and so forth. 
     C. Model Description 
     It is assumed in embodiments of the purge column model that the purge time is the residence time (T res ) of polymer in the purge column. Thus, if the production rate of the plant is W PE , the inventory of polymer in the column (W inv ) is,
 
 W   inv   =W   PE   *T   res   (1).
 
     Then, given the bulk density of polymer (ρ b ) in the column and the diameter of the column (D bed ), the height of inventory in the column (H bed ) becomes,
 
 H   bed   =W   inv /(0.25 πD   bed   2 ρ b )  (2).
 
     For an operating plant, the inventory of the purge column is generally expressed as a fraction (f bed ) of the operating window between the minimum inventory level (H LL ) and the maximum inventory level (H HL ) of the column. In which case the inventory level for the column becomes,
 
 H   bed   =H   LL   +f   bed *( H   HL   −H   LL )  (3).
 
     Therefore, the residence time and the material inventory for the purge column can be estimated for an operating plant from equations 1-2. Having determined the residence time and inventory for the purge column, the next step in the model may be to estimate the height of a separation stage (HETP) and the number of stages (N) for the column,
 
 N=H   bed   /HETP   (4).
 
     In one example, the method of Oanda and et al. (Kister, 1992) is used in the model to estimate HETP for the column and its number of separation stages.  FIG. 18  depicts the stage-wise material flow  480  having stages  484  for a component i (e.g., a particular hydrocarbon such as isobutane) in the purge column. As shown, stage  1  ( 486 ) is the bottom of the column, stage N ( 482 ) is the top of the column, the polymer being purged is fed at the top (at  492 ) of the column, and the purge gas (e.g., nitrogen) is fed at the bottom (at  488 ) of the column. The hydrocarbon purge gas leaves the top (at  490 ) of the column and the polymer leaves the bottom (at  494 ) of the column. The material balance for a component (i) for a stage (k) in the column is therefore,
 
 F   ik+1   +G   ik−1   =F   ik   +G   ik   ;k= 1 , . . . ,N   (5).
 
     The terms F ik+1  and F ik  are, respectively, the component mass flows in the polymer entering and leaving the stage. Similarly, G ik−1  and G ik  are the component mass flows for the gas entering and leaving the stage. The mass balance in equation 5 can be expressed in terms of component degassing rate for a stage (E ik ) as follows,
 
 E   ik   =F   ik+1   −F   ik   =W   PE ( X   ik+1   −X   ik ); k= 1 , . . . ,N;i= 1  . . . NC   (6a)
 
 E   ik   =G   ik   −G   ik−1   =G   k   Y   ik   −G   k−1   Y   ik−1   ;k= 1 , . . . ,N;i= 1  . . . NC   (6b).
 
     Equation 6a gives the material balance for the polymer-phase in the column, while equation 6b gives the material balance for the gas-phase in the column. The X ik+1  and X ik  (equation 6a) are the mass fractions of component in the polymer entering and leaving the stage, while Y ik−1  and Y ik  (equation 6b) are the corresponding mass fractions for the purge gas for the stage. Equation 6a assumes that the amount of hydrocarbon dissolved in the polymer is small compared to the quantity of the polymer. 
     In these embodiments, the above material balance equations assume that the hydrocarbon contents of the polymer (F iN+1  and X iN+1 ) for degassing in the purge column are known. In the loop process, F iN+1  and X iN+1  can be estimated from the upstream flash gas (e.g., flash gas  226 ) composition of either the upstream flash vessel (e.g., flash vessel  224 , high pressure flash, intermediate pressure flash vessel, low pressure flash vessel, etc.), assuming equilibrium between the flash gas and the polymer. Of course, both flow and composition are usually known for the purge gas (i.e. G i0  and Y i0 ). Thus, in this example, the material feeds to the column are defined. The model estimates the material streams (flow and composition) leaving the column: F i1  and X i1  for the polymer and G iN  and Y iN  for the gas. 
     In this example, assuming spherical particles for the polymer and using correlations by Qi et. al. (1996), one can estimate the mass fraction of components for the polymer for a stage in the column as follows, 
                     X   ik     =         (       X     ik   +   1       -     X   isk       )     ⁢     Φ   ik       +     X   isk               (   7   )                 Φ   ik     =       ∑     n   =   1     ∞     ⁢       6       n   2     ⁢     π   2         ⁢     exp   (     -         n   2     ⁢     π   2     ⁢     D   i     ⁢     t   k         R   p   2         )                 (     8   ⁢   a     )                 t   k     =       T   res     /   N             (     8   ⁢   b     )               
where:
 
     X isk =Surface mass fraction of component for polymer particle 
     D i =Diffusion coefficient for component for polymer (sqcm/s) 
     t k =Residence time for polymer for stage k (s) 
     R p =Mean radius for polymer particle (cm). 
     If the component in the gas leaving a stage is assumed to be in equilibrium with the component on the surface of the polymer leaving the stage, the surface concentration for component in the polymer can be estimated from Hutchinson and Ray correlation (1987), for example, as follows,
 
 X   isk =α v   *KVLE   i   *P   atm   *y   ik   *MW   i /(1000*ρ PE )  (9)
 
Log( KVLE   i )=−2.38+1.08( T   ci   /T ) 2   (10a)
 
α v =(ρ cr −ρ PE )/(ρ cr −ρ am )  (10b)
 
where:
 
     α v =Fraction amorphous phase for polymer 
     KVLE i =Equilibrium constant for component for polyethylene 
     P atm =Purge column pressure (atm) 
     y ik =Mole fraction for component for purge gas leaving stage k 
     MW i =Molecular weight of component 
     ρ PE =Polymer density (g/cc) 
     T ci =Critical temperature for a component 
     T=Temperature of purge column 
     ρ am =Amorphous density of polymer (˜0.852 g/cc) 
     ρ cr =Crystalline density of polymer (˜1.01 g/cc). 
     Hutchinson and Ray&#39;s correlations (equations 9-10) may accommodate a wide range of polyethylene resins, from the amorphous (e.g. LLDPE) to the less amorphous (e.g. HDPE). These exemplary correlations, therefore, are suitable for estimating hydrocarbon and non-hydrocarbon solubility in all polyethylene resins, from the loop slurry process or other processes. 
     D. Model Solution 
     In certain embodiments, the model may be solved by closing the overall material balance for the column, expressed as,
 
 DF   i   =F   iN+1   +G   i0   −F   i1   −G   iN   (11).
 
     The term DF i  is the difference in material flow to and from the column for a component. In the examples, the model solution means driving this difference (DF i ) to zero or to a negligible value (e.g., 10 −6 ) for all components in the column. This solution method for the column is generally iterative with material flows to and from the column counter-current, with the feed streams (polymer and purge gas) known, and the product streams (degassed polymer and hydrocarbon-rich vapor) typically unknown a priori. Thus, in this example, an initial value of one of the product streams from the column, vapor (G iN ) or polymer (F i1 ), is estimated (e.g., an initial guess based on operating experience) to begin the column solution. The estimated stream is varied iteratively until generally all material balances for the column are closed. As an example, the vapor stream leaving the top of the column may be assumed and the steps in the algorithm in Table 2 followed to solve the material balance for the column. 
     
       
         
           
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Exemplary Algorithm for Solving Purge Column Model 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                 1. 
                 Assume vapor flow from the column (i.e. G iN , y iN ). 
               
               
                 2. 
                 Estimate from y iN  and equation 9 the surface concentration (X isN ) 
               
               
                   
                 of component for polymer particles leaving stage N. 
               
               
                 3. 
                 Estimate from X isN  and equation 7 the bulk concentration of 
               
               
                   
                 component (X iN ) for the polymer leaving stage N, the amount still 
               
               
                   
                 adsorbed in the polymer (F iN  = W PE X iN ), and the amount degassed 
               
               
                   
                 for stage N (i.e. E iN  = W PE (X iN+1  − X iN ). Note that the feed 
               
               
                   
                 composition of polymer (X iN+1 ) to the column is known. 
               
               
                 4. 
                 Estimate from the material balance in equation 6(a, b) the vapor 
               
               
                   
                 feed to stage N from stage N−1 (i.e. G iN−1  = G iN  − E iN ) and its mole 
               
               
                   
                 fraction (y iN−1 ). 
               
               
                 5. 
                 Repeats steps 2-4 for stages k = N−1, N−2, . . . , 2,1. 
               
               
                 6. 
                 Evaluate DF i  (equation 11) to check for material balance closure 
               
               
                   
                 for the column. 
               
            
           
           
               
               
               
            
               
                   
                 a. 
                 If |DF i | = 0 (or 10 −6 ), model solved and stop iteration. 
               
               
                   
                 b. 
                 If |DF i | &gt; 0 (or 10 −6 ), continue iteration by adjusting the 
               
               
                   
                   
                 vapor flow from the column (G iN  and y iN ) and repeating 
               
               
                   
                   
                 steps 2 - 6 until step 6a is satisfied. 
               
               
                   
                   
               
            
           
         
       
     
     E. Model Construction and Interface 
     As an example, the model may be implemented in Visual Basic Applications with an Excel worksheet as an interface (see, e.g.,  FIG. 19 ) for model input and output. Instructions for running the model may be provided to the user or for automatically operating the model.  FIG. 19  depicts an exemplary interface  500  for the purge column models. The interface  500  is a spreadsheet having parts or boxes  502 ,  504 ,  506 ,  508 ,  510 ,  512 ,  514 ,  516 ,  518 , and  520  for inputting data (e.g., into spreadsheet cells within the boxes). These parts or boxes may also provide model output in spreadsheet cells. Input cells may be highlighted in a different color than output cells, for example. The inputs and outputs may be the individual hydrocarbon component concentrations and the total VOC. VOC results may be provided in box  522 . Purge gas results may be input or output in box  424  in this exemplary interface As shown in the model interface of  FIG. 19 , apart from the primary purge gas feed  516  to the bottom of the column  228 ; the model can also simulate the impact on purging the use of secondary purge gas  518  on a stage in the column  228 . 
     In this exemplary interface, which may be displayed on a monitor of a personal computer, for example, boxes  502  through  510  provide for model inputs. Model results may also be displayed in these boxes and calculated automatically by the model. Lastly, buttons  526 ,  528 , and  530  (e.g., with underlying Visual Basic commands) may be selected or clicked to operate the model based on different types of inputs and constraints. In this example, button  526  may be selected to estimate ppm composition of the individual hydrocarbon components in the fluff feed to the purge column (displayed in box  510 ) based on data supplied by the user in boxes  506  and  508 . 
     In this exemplary interface, to run the model, the user may supply bed level data in box  504 , and then select or click on (i.e., with a mouse pointer) button  528  to run the command “Purge Fluff for Given Bed Level” to estimate the residence time of the purge column and the fluff VOC after purging for that length of time. On the other hand, the user may supply the purge time in box  504  and then select the button  530  to run the command “Purge Fluff for Given Purge Time” to estimate the fluff VOC after purging for that length time. 
     The predicted fluff VOC may differ from plant data, if known. In this case, known plant data may be placed in box  512  in this interface, and the button  532  selected to run the command “Fit Purge Model to Plant Data” to adjust diffusion parameters in the model to fit model predictions to the plant data. Given desired VOC for polymer, model can estimate the purge gas flow to achieve this goal. To do this, VOC target data may be entered in the interface in box  524 , and the button  534  selected to run the command “Estimate Purge Gas Given VOC” to estimate the purge gas rate composition to satisfy the VOC target for the polymer fluff exiting the purge column  228 . 
     F. Model Validation 
     Plant data were collected from polyethylene operating facilities for validating the model. Paired sample data was collected, a sample of the feed from the flash tank to the purge column, and a sample of the polymer fluff leaving the purge column. Sampling procedures for testing VOC in the manufacturing facility may involved connecting a sample cylinder to a sample port at the top or bottom of the purge column and opening and closing valves on the port and cylinder to collect the sample. The date and time of each sample collection may be recorded for the retrieval of process data for the column from the plant data historian at later dates. The samples may be then analyzed in the laboratory in the plant facility to measure the hydrocarbon content of each polymer fluff sample, within 10 minutes of collection, for example. Organic or hydrocarbon entrainment may be estimated for each sample. An exemplary entrainment calculation includes estimating the void volume between polymer particles in the feed to the purge column and the mass of flash gas from the flash tank that will be contained in this volume, as follows,
 
Ent i   =y   i   *P*MW   i   *W   PE (1/ρ b −1/ρ PE )/ RT   (12)
 
where:
 
     Ent i =Entrainment for a component (lb/hr) 
     MW i =Molecular weight of a component 
     P=Flash tank pressure (atm) 
     R=Gas constant (0.7304 atm·cuft/lb-mole·R) 
     T=Flash tank temperature (F) 
     W PE =Reactor production rate (lb/hr) 
     y i =Flash gas component mole fraction 
     ρ b =Fluff bulk density (lb/cuft) 
     ρ PE =Polymer solid density (lb/cuft). 
     Entrainment corrections may or may not include hydrocarbons from process leaks, which are difficult to measure or even estimate. A strategy for accounting for process leaks may be to add a fraction of gas from the flash tank to the entrainment gas, depending on the pressure difference between the flash tank and the purge column, and so on. In certain examples, it is believed that such leaks could account for about 4% of material flows around the purge column in plants. 
     A summary of equation variables is listed below. 
     Notations 
     D bed  Purge column diameter (ft) 
     D i  Coefficient of diffusion for a component (m 2 /s) 
     DF i  Material balance error for a component (lb/hr) 
     E ik  (Degassing rate of component for polymer (lb/hr) 
     Ent i  Entrainment for a component (lb/hr) 
     f bed  Bed level fraction in purge column (%) 
     F ik  Flow rate for a stage for adsorbed component for polymer (lb/h) 
     G k  Flow rate for a stage for purge gas (lb/h) 
     G ik  Flow rate for a stage for a component for purge gas (lb/h) 
     HETP Height of a stage in purge column (in) 
     H bed  Inventory level of polymer in purge column (ft) 
     H LL  Minimum inventory level for purge column (ft) 
     H HL  Maximum inventory level for purge column (ft) 
     MW i  Molecular weight of a component 
     KVLE i  Equilibrium constant for a component for polymer 
     N Number of stages for purge column 
     NC Number of material components in the purge column 
     P Flash tank pressure (atm) 
     P atm  Purge column pressure (atm) 
     PPM Mass fraction of component in polymer 
     R Ideal gas constant (0.7304 atm·cuft/lbmol·R) 
     R p  Radius of polymer particle (m) 
     T ci  Temperature of emulsion phase in the bed (F) 
     T Purge column or flash tank temperature (F) 
     t k  Purge column residence of polymer for a stage (s) 
     T res  Purge column polymer residence time (h) 
     W inv  Purge column inventory (lb) 
     W PE  Polymer withdrawal rate for reactor (lb/h) 
     X ik  Average mass fraction of component for polymer 
     X isk  Mass fraction of component at polymer particle surface 
     y ik  Mole fraction of component for purge gas for a stage 
     Greek Letters 
     α v  Fraction of amorphous phase for polymer 
     ρ am  Density of amorphous polymer (g/cc) 
     ρ cr  Density of crystalline polymer (g/cc) 
     ρ b  Bulk density of polymer (lb/cuft) 
     ρ PE  Density of polymer (g/cc) 
     Φ ik  Parameter for a stage in equation 8a 
     Indices 
     i A component in the purge column or flash tank 
     k A stage in the purge column.