Method for online estimation of reactor split for multimodal polyolefins

ES 2 347 802 T3

DESCRIPTION

TECHNICAL FIELD OF THE INVENTION

The invention relates to the field of reactor control in the process of preparing olefin-based polymers containing one or more monomers. More specifically, the invention relates to on-line prediction and monitoring of reactor fractionation (i.e., the weight fraction of a particular resin component) in multi-modal resins produced by multiple catalysts in polymerization reactors (e.g. , a single-phase gas phase reactor). The control of fractionation is essential to control the properties of the resin, and essential to maintain the properties of the product. The method of the present invention relies on mathematical relationships obtained from material and kinetic equilibrium models, rather than physical measurements of fractionation.

BACKGROUND OF THE INVENTION

The characteristics of the product of bimodal resin systems, which is a resin product that is produced by more than one catalyst system, depends on the distribution of the molecular species. When more than one catalyst and one or more monomers are used to produce a polymeric product (for example, the product that is a mixture of different homopolymers / and co- or terpolymers), precise control of the multiple polymerization reactions in the reactor to achieve repeatability when producing the products. The need to control a reactor is traditionally satisfied by periodically analyzing the reaction product. In the production of bimodal resin systems, for example, very often this is done by analyzing the polymeric product at some point in time after the material has been produced. But this practice suffers from the disadvantage that said measurement is a cumulative fractionation of the reactor, that is, a time average of the product produced as it is sampled from a reactor. Furthermore, although the analytical procedure to obtain the actual fractionation data can be performed using different analytical techniques, for example CPG or CEM (gel permeation or size exclusion or molecular weight measurements), it is highly dependent on resin sampling, preparation of the sample, generating the data, and reducing the data into an estimate of the fraction of each polymer in the product (for example, the CEM data must be deconvolved, and estimating individual molecular weight distributions). Because the time required to determine the fractionation of the reactor using this procedure can be several hours (between the actual polymerization and the analysis of

ES 2 347 802 T3 fractionation), the data may be of little or no use even if the sampling, measurement and interpretation of the data are accurate and precise. Furthermore, measurement by CEM (size exclusion chromatography) is quite expensive and susceptible to errors and as such somewhat unsuitable for process control, especially continuous process control. Accordingly, there is a need for improvements in the control of a continuous mixed catalyst polymerization process. The present invention provides some solutions to this problem.

BRIEF SUMMARY OF THE INVENTION

The present invention relates to a system and a process that allows predicting and controlling the production and composition (and, in this way, the physical properties) of a mixture of olefin-based polymers, in a polymerization reactor system, using the least two different catalyst systems to produce at least two polymeric systems that can contain the same single monomer or two or more different monomers. It has been unexpectedly found that the instantaneous production rates of different polymeric species within the reactor and their corresponding mass fractions produced by each different catalyst are linearly proportional to the incorporation of the monomers, reactants or other active species of the produced product.

In one aspect of the invention, polymers prepared from multiple catalysts (eg, a bimodal catalyst system, such as a Zeigler-Natta catalyst and a metallocene catalyst) exhibit different mass fractions, which typically and additionally have different average molecular weights, one polymer having a relatively higher weight fraction in one composition and the other a relatively lower weight fraction; the instantaneously produced mass fraction of each polymer is linearly related to the monomer or monomer or reactant incorporation ratio divided by the instantaneous production rate of the reactor.

In another aspect of the invention, the polymers produced have different comonomer weight fraction distributions; the polymers may or may not have the same or different average molecular weights, but the comonomer distribution may be reflected in changes in reactor fractionation.

In one aspect of the invention, a method is provided for calculating the instantaneous fractionation of the reactor of a polymerization reaction, the process comprising the steps of: producing, under different reaction conditions, at least two polymeric compositions, each composition comprising at least two different polymers, each polymer having at least one monomer or reactant incorporation

ES 2 347 802 T3 different; determining for each polymer composition: the incorporation of at least one monomer or reactant, a corresponding reactor production rate and reactor fractionation; and determining a linear equation defined by the reactor fractionations and the corresponding monomer or reactant incorporation ratios, divided by the production rate of the corresponding reactor.

In another aspect of the invention, a method is provided for controlling reactor fractionation in a multimodal polymerization reaction, comprising the steps of: applying a predetermined linear relationship to control a polymerization reaction in a reactor, polymerizing at least one monomer in the presence of at least two catalysts in the reactor; obtain periodic data of incorporation and production speed of the reactor; and periodically adjusting at least one reaction variable to maintain a desired reactor split in accordance with the predetermined linear relationship. This procedure can be applied during an ongoing polymerization reaction or in a different reactor, where linear parameters are applied with a procedure controller for the reaction. The process can be further characterized by controlling at least one reactor process variable or monomer addition or other reactant addition to maintain a desired reactor split. The procedure allows the control of the fractionation balance between multiple polymeric components in a polymerization where the polymers have different molecular parameters.

In another aspect of the invention there is provided a process for producing a polymer composition by controlling reactor fractionation in a multimodal polymerization, comprising the steps of: determining a desired reactor fractionation for a multimodal polymer composition based on a physical property of the composition polymeric; polymerizing at least one monomer in the presence of at least two catalysts under conditions that produce the desired reactor fractionation; and periodically adjusting at least one reaction variable according to a predetermined linear relationship to maintain the desired reactor fractionation.

In yet another aspect of the invention, instantaneous splits are used to calculate an average cumulative time split.

The foregoing has broadly outlined the technical features and advantages of the present invention so that the detailed description of the invention that follows may be better understood. Additional features and advantages of the invention will be described later herein, which is the subject of the invention claims. It should be appreciated that the specific conception and realization

The described ES 2 347 802 T3 can easily be used as a basis for modifying or designing other structures, to accomplish the same purposes as the present invention. It should also be noted that said equivalent constructions do not depart from the invention as set forth in the appended claims. The new features that are believed to be characteristics of the invention, both in its organization and in its operating procedure, together with other objects and advantages, will be better understood from the following detailed description, when considered in connection with the figures. attached. It should be expressly understood, however, that each of the figures is provided for the purpose of illustration and description only and is not intended to be a definition of the limits of the present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present invention, reference is now made to the following descriptions, taken in conjunction with the accompanying drawing, in which:

Figure 1 is a schematic of a typical fluidized bed reactor useful for the practical implementation of the processes of the present invention.

Figure 2 is a graph of ethylene incorporation versus time, according to Example 1.

Figure 3 is a graph of reactor fractionation versus hydrogen incorporation divided by reactor production rate.

Figure 4 is a graph of the fractionation of the reactor from the incorporation of ethylene, according to Example 1.

Figure 5 is a graph of the fractionation of the reactor from the incorporation of hexene, according to Example 1.

Figure 6 is a graph of the estimated reactor fractionation from hydrogen incorporation in a commercial reactor and a comparison to the cumulative reactor fractionation calculated based on a moving average of the instantaneous fractionations.

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates to a system and process that allows the production of olefin-based polymers in a reactor system that uses at least two different catalytic systems to produce at least two basic polymers that are combined in a single product (for example, bimodal polyolefins) where one product has a relatively higher incorporation by weight of a specific reactant and the other a relatively less incorporation by weight of a specific reactant. A main objective of

ES 2 347 802 T3 the invention is to estimate and then control reactor fractionation based on measured values ​​obtained from the reactor and / or polymerization using the discovery that there is a linear relationship between the instantaneous fractionation of the reactor and the rate of incorporation of a particular monomer or reactant.

The following definitions are used in this disclosure:

The term "one or one" as used herein in the specification may mean one or more. As used herein in the claim (s), when used in conjunction with the term comprising, the terms "one" or "one" may mean one or more than one. As used herein "other" can mean at least one second or more.

Analytical measurement refers to any experimental technique that provides reproducible data or information regarding the preparation, or analysis of, any reactant, product, or process to produce a reactant or product of the present invention.

Average molecular weights or molecular weight refers to any type of molecular weight average as applied in polymer science to describe a distributed amount of molecular weight, where the polymer can be described by a mathematical distribution function such as, but not limited to , such as Z-average molecular weights, weight average, number average, viscosity average, or light scattering average, as are well known in the art. Typically these averages are expressed in terms of grams per mole or some other similar units as is known in the art. In the case of non-polymeric molecules, the usual and accepted definition of molecular weight as known in the art applies.

Bimodal polymerization refers to any polymeric product or composition that can be shown to exhibit at least two different distributions of some physical property, such as monomer incorporation weight fraction for a copolymer or weight or mass / mass fraction distributions for two or more polymers. The term is considered to include polymerizations in which three or more distributions may be present and may therefore be referred to as a multimodal polymerization (eg, a trimodal polymerization).

A chemical analysis refers to any technique that provides compositional information for a multimodal, bi- or polymeric composition, based on chemical reactions between a reagent and a polymeric composition, so that the analysis will differentiate between the different portions of the reactor fractionation.

Chromatography, in the context of polymer analysis, refers to any analytical technique that separates molecules from the polymer and can be used to show a

ES 2 347 802 T3 relative contribution to the mass fraction of a polymer sample, for example a bimodal polymerization. Included in this definition are so-called CEM: size exclusion chromatography or CPG: gel permeation chromatography, which are well known in the art of polymer analysis.

Copolymer refers to any composition or reaction product that results in the production of a molecule or molecules comprising at least two monomers; a terpolymer would be included in this definition.

Incorporation or rate of incorporation refers to the amount of any monomer or reactant or other additive incorporated into a polymeric product or composition per unit of time and is a function of rate. Incorporation can also be defined as the amount of a monomer or reactant that has been incorporated into the molecular structure of a polymer. Incorporation can also be defined as the flow rate of a monomer or other reactant in a reactor minus the flow rate of that reactant that escapes from the reactor and is not incorporated into a polymerization product or resin. For example, in the case of a gas phase polymerization reactor, uptake is the flow rate of a reactant into the reactor minus the amount of reactant that escapes through the reactor purge, minus the amount of dissolved escaping reactant ( although unreacted) in the polymeric product or in the void spaces between the polymeric particles leaving the reactor minus the flow or in the monomer or reactant per unit time in the reactor (ie dm / dt). Amounts of monomers or reactants can be measured with devices such as mass flow meters or chromatographs, or other measuring devices, provided they are capable of producing information that can be used to determine, alone or with appropriate calibration or standards, amounts. reactants or monomers. Other useful devices for determining incorporation include thermometers, thermocouples, thermostats, and the like, such devices being able to provide information for calculating incorporation on a thermodynamic, kinetic, or material equilibrium basis: All of these useful known scientific devices and procedures can be used in conjunction with programmable reaction controllers (eg, programmable digital computers) in a systematic and cooperative manner, providing so-called real-time information regarding the incorporation or incorporation rates of useful material components. in the methods of the present invention.

Flash fractionation refers to the ratio of the fraction (by mass or weight) of a component of a bimodal or multimodal polymerization to the sum of all the components present at a particular time in a polymerization. For example, when a relatively higher molecular weight polymer and a relatively higher molecular weight polymer are present

ES 2 347 802 T3 relatively smaller, the instantaneous fractionation can be expressed as (for example, for the component with the highest molecular weight): S = PjA ™ / (pR^p.m + PR^P.M ) Eq. 1 in which S is the instantaneous fractionation, PR^P.M is the production rate of the high molecular weight component, and PR^P.M is the rate of production of the low molecular weight component.

Linear relationship or linear correlation refers to any mathematical approximation or function that can be used to define a line that has a constant slope and a cut on a coordinate axis.

Production rate is the temporary rate of production of a polymeric product and can be measured as pounds per hour (pounds / h) or tons per hour (t / h). The production rate is also the sum of all the incorporations of all the reactants and monomers that react to form a polymer composition at a particular time. Values ​​for production rate can be obtained from reactor heat balance and reaction mass balance data or other reactor data, in a manner similar to that used to determine incorporation.

Polymer composition refers to the product of a polymerization reaction.

Predetermined linear relationship or equation refers to a linear relationship or equation related to the relationship between a monomer or reactant incorporation rate and a corresponding reactor production rate and corresponding reactor fractionation for a bi- or multimodal polymerization reaction. . The definition also encompasses a linear relationship between any measurable physical quantity that is proportional to the fractionation of the reactor and which, when it changes, changes the fractionation of the reactor as well.

Primary resin refers to one of the polymeric products of a polymerization reaction produced by a catalyst in a binary or multi-catalytic system. It can refer to the largest fraction of a reactor fractionation.

Process variable refers to any polymer, reactor, or reaction variable that can be used to control the production of a polymeric product. The term may be considered to include pressure, temperature, gas composition, monomer or monomer addition (s) or concentrations, reactant addition (s) or concentrations, catalyst or catalyst addition (s), and the like.

Product characteristics refers to the physico-chemical properties of a bimodal polymer composition comprising polymers synthesized by at least two different catalysts including, but not limited to, molecular weight, melting point, flow point, melting index, melting point. freezing, modulus (Young's, elastic, loss,

ES 2 347 802 T3 and the like), viscosity, yield point, refractive index, transparency, or other optical property, heat distortion temperature, radiation resistance, fracture energy, and the like. Product characteristics can also be determined using computer calculations or predictions.

Resin refers to the product of a polymerization reaction and can be used synonymously with the term polymer or polymeric product or polymerization product or polymeric composition.

Reactant refers to any reagent, or other material added to a polymerization reaction that is incorporated into a polymerization product in a directly, indirectly, or estimated measurable fraction. For example, hydrogen or aluminum alkyls and the like.

Reactor process variable, reactor variable, reaction variable, process variable, or other similar term refers to any material or reactor process control that can be varied to control the output of a reactor and includes, but is not limited to, temperature. , pressure, gas composition, catalyst, catalyst supply rate, flow rates, reactor outlet rates, material inlet rates, concentrations of material and the like.

Reactor production rate refers to the exit rate of a polymer composition resulting from a polymerization reaction and is often expressed as kilograms per tons per hour or minute, and can be determined by a material and / or heat balance using thermodynamic procedures and / or kinetic when it can be measured directly.

Reactor fractionation or fractionation refers to the fraction (weight or mass or other fraction) of a resin product produced by a particular catalyst in a total polymer sample.

Relative production rate refers to the rate of production of a primary resin relative to the rate of production of a secondary resin, and is a measure of reactor fractionation.

Secondary resin refers to a polymeric product of a polymerization reaction produced by a second catalyst in a binary catalyst system.

Total resin production rate refers to the polymer or resin product output from the reactor and is often expressed as kilograms or tons per minute or hour.

In one aspect of the invention a method is provided for calculating the instantaneous fractionation of the reactor of a polymerization reaction, the process comprising the steps of: producing at least two under different reaction conditions

ES 2 347 802 T3 polymer compositions, each composition comprising at least two different polymers, each polymer having at least one different monomer or reactant incorporation; determining for each polymer composition: the incorporation of at least one monomer or reactant, a corresponding reactor production rate and reactor fractionation; and determining a linear equation defined by the reactor fractionations and the corresponding monomer or reactant incorporation ratios divided by the production rate of the corresponding reactor. In one embodiment of the invention, the technique used to estimate a reactor split is a chromatographic procedure such as gel permeation or size exclusion chromatography. It will be appreciated by understanding this aspect of the invention that the production of additional compositions can be performed, their reactor fractionation, incorporation and production rates measured, such as to produce a more precise and accurate linear correlation between fractionation and incorporation as described. Furthermore, the order of the steps is not especially critical and in understanding the invention, variations in the steps are considered within the scope of the invention.

In another aspect of the invention, a process is provided for controlling reactor fractionation in a multimodal polymerization reaction, comprising the steps of: applying a predetermined linear relationship between reactor fractionation, incorporation and production rate, to control a reaction of polymerization in a reactor, polymerizing at least one monomer in the presence of at least two catalysts in the reactor; obtain periodic data of incorporation and production speed of the reactor; and periodically adjusting at least one reaction variable to maintain a desired reactor split in accordance with the predetermined linear relationship. In one embodiment of this inventive aspect, the reactor process variable is a ratio of the catalyst that produces a first resin to the catalyst that produces a second resin. In another embodiment, the reaction variable is the ratio between the delivery rate of the catalyst that produces a first resin and the delivery rate of the catalyst that produces a second resin. In another embodiment, the method further comprises the step of controlling the concentration of the at least one reactant to maintain a desired reactor fractionation. In another embodiment of the invention, the reactant is hydrogen. In another embodiment of the invention, a first catalyst is a metallocene catalyst and a second catalyst is a Zeigler-Natta catalyst. In yet another embodiment of the invention, fractionation is controlled by rates of addition relative to a reaction of at least two monomers. In a preferred embodiment, a monomer is an alpha-olefin monomer that has at least two carbon atoms and can

ES 2 347 802 T3 is selected from the group consisting of ethylene, propene, butene, hexene, octene, or mixtures thereof. In an especially preferred embodiment, one monomer is butene or hexene and a second monomer is ethylene.

In another embodiment, a manipulated process variable may be a selective catalyst promoter or inhibitor, reactor temperature, gas composition in the reactor, or other reaction variable. In another aspect of the process the step is provided to control the concentration of the at least one reactant to maintain a desired reactor fractionation and in one embodiment, the reactant may be hydrogen or another reactant that affects the preferred addition to or affects the polymers produced. The method allows to control the production balance between multiple polymeric components in a polymerization where the polymers have different molecular parameters (for example, molecular weights, mass fractions and different incorporations of at least one monomer or other reactant). Process variables can be used analogously to control fractionation of the reactor and thus the product produced. In certain embodiments, these include, but are not limited to, reactant and monomer addition rates, temperature, pressure, gas compositions, and other variables that can be used to vary the incorporation of reactant or monomer into a polymer composition.

In another especially preferred embodiment of the invention, ethylene can be reacted with two catalysts such as those described herein: the product produced is bimodal polyethylene and hydrogen is the selectively incorporated reactant.

In a further aspect of the invention, the fractionation of the reactor is determined and subsequently controlled in the same reactor or in a different one after knowing the correlation or relationship or linear equation that relates the fractionation of the reactor and the incorporation. The reaction can be controlled by intermittently or periodically monitoring the reaction variables and adjusting them according to the estimated fractionation determined by the predetermined linear relationship to maintain the desired reactor fractionation.

In another embodiment of the invention, the catalyst may be combinations of a bis-amide-based catalyst, Zeigler-Natta catalyst, metallocene catalyst, or similar olefin polymerization catalysts, as long as the catalysts produce polymeric species that are useful and discernible from each other in the combinations. That is, each contemplated catalyst combination responds differently to changes in reaction conditions, monomer incorporation, reactant incorporation, and the like, so that at least two different values ​​of incorporation and / or production rates can be obtained. and fractionation of the reactor

ES 2 347 802 T3 can be proportional to some physical quantity related to reactor fractionation, so that a linear equation with a non-zero slope can be determined or estimated according to the procedure. The catalysts can be added to a reactor as supported, separately supported, or single supported catalysts; one catalyst can be a supported catalyst and the other a catalyst prepared in solution and added to the reactor; both catalysts can be prepared in solutions and the solutions added separately or together. Furthermore the catalysts, as solutions or supported, can be added to different parts of the reactor and at different rates, as desired. Variations in catalyst addition schemes are considered within the scope of the invention.

In another aspect of the invention, a process is provided for producing a polymer composition by controlling reactor fractionation in a multimodal polymerization, comprising the steps of: determining a desired reactor fractionation for a multimodal polymer composition based on a physical property of the polymer composition; polymerizing at least one monomer in the presence of at least two catalysts under conditions that produce the desired reactor fractionation; and periodically adjusting at least one reaction variable according to a predetermined linear relationship to maintain the desired reactor fractionation. In one embodiment, the composition is a film grade bimodal high density polyethylene (which is a high molecular weight / lower molecular weight composition with improved processability due to the different (typically lower) molecular weight fraction of the composition. , when a product with high film strength is required) and at least one monomer is ethylene and the at least two catalysts are dry co-supported Zeigler-Natta and metallocene catalysts. In another embodiment, the composition is a bimodal, high-density pipe grade polyethylene (which is a composition that can be manufactured into a thicker cross-sectional product that has relatively high impact resistance, for example liquid transport pipes. such as water pipes, commercial or residential) and at least one monomer is ethylene and the at least two catalysts are a spray-dried bisamide catalyst and a metallocene catalyst. In preferred embodiments, at least one monomer is selected from the group consisting of ethylene, propylene, butene, hexene, octene, or mixtures thereof, and in an especially preferred embodiment of this aspect of the invention, one monomer is hexene and a second The monomer is ethylene and the catalysts are selected from the group consisting of bisamide, metallocene, Zeigler-Natta, or mixtures thereof.

With a view to the various aspects of the invention, the characteristics of the product

ES 2 347 802 T3 of a bimodal or multimodal resin / polymer system depend on the distribution of molecular species. The present invention allows the online estimation of the reactor fractionation (which is the fraction by weight of a primary component of the resin) of resins or polymers produced by binary or ternary catalytic systems in a single or multistage reactor, without depending on the periodic physical measurement of reactor fractionation by analytical procedure. The invention allows the timely manipulation of the process conditions to control the fractionation of the reaction and, in this way, the quality of the product, making use of simple, fundamental models for the estimation / prediction of fractionation. The estimation and prediction of fractionation does not depend on any ongoing physical measurement of fractionation: it depends on mathematical relationships obtained from material balance models and a component or components (for example, monomers or reactants) that are consumed unevenly by the two polymeric constituents in the production of a bi- or multi-modal resin. Furthermore, the methodology does not depend on meaningful use of specific model parameters other than knowing that each catalyst produces a resin that incorporates at least one monomer reactant in different fractions. For example, hexene can contribute 10 weight percent to a polymerized by a first catalyst versus 20 percent by weight to a second polymerized by a second catalyst. The process is effective with bi- or multimodal catalyst systems in which a reactant (such as hydrogen) or a particular monomer (such as hexene) is selectively consumed relative to the generation of a particular component of the resin generated with a particular catalyst. The method is used to directly predict and control the instantaneous fractionation of a bimodal or multi-modal polymerization reaction to a target value. Instant splitting is controlled to provide a desired cumulative splitting.

The method provides an improved measurement of reactor conditions. For example, a typical industry practice is to determine reactor fractionation by intermittent measurements of accumulated fractionation (the gross average property) using an analytical technique, such as size exclusion chromatography, for products with bimodal molecular weight distributions. But the effectiveness of this procedure depends on sampling the resin, sample preparation, generating the CEM data, and reducing the data to an estimate of fractionation (ie, chromatogram deconvolution). This procedure is generally not effective in controlling a reactor due to the substantial delay in providing feedback to the operation of the process. In addition, this procedure is quite expensive and susceptible to errors.

ES 2 347 802 T3 due to the complexities involved. In contrast, the present invention allows a more direct estimation of resin quality in a mixed catalyst polymerization process.

The present inventive process is based on the discovery that instantaneous fractionation is linearly related to the incorporation, as defined above, of any particular reactant (such as hydrogen), a monomer or a comonomer (such as ethylene or hexene, etc. .), in a polymer or resin where this particular reactant or monomer is most likely to react with a particular catalyst under a particular set of reaction conditions (constant temperature, pressure and gas composition). The change in the amount of a reactant or monomer in the reactor is measurable or calculable and, by changing any factor that affects the rate of production of a particular component, along with the knowledge of the output or rate of production of the reactor, can be obtained a readily available estimate of instantaneous fractionation.

For any component, monomer, or other reactant that is materially incorporated into the polymers by the different catalysts in different measurable amounts, (H₂, C₆, C₂, etc. under the same or different reaction conditions, incorporation may occur in which Cx is the component of interest, and the two polymeric species differ in their average molecular weight (or relative mass fraction in a sample) or other molecular property such as :

IC = X^Cb^XPRB + ^XTO^XpRA where: / C^x is the incorporation (rate) of the monomer Cx or, alternatively, another reactant; xC^X is the fraction by weight of comonomer or reactant incorporated in a first component of the catalyst, X'C is the fraction by weight of the comonomer in the resin produced by the other component of the catalyst. PRb and PR_to are the production rates of the two polymeric components

Therefore.

PRTot. = PRa + PRb, Eq. 2 then

I^Cx = X, (PR_Tot - PR_TO) + X PR

Eq. 3

ES 2 347 802 T3 applying the definition of instantaneous fractionation, Si as:

S_i = PR_to / PRroty substituting in the above equation, gives:

PR_T = X_B^Cx (1 - S) + X_TO^Cx Yes

Eq. 4 which can be solved for Si to produce the following relationship for fractionation:

(jCx Λ

--X^CBI _S = l ^pr ¡'(xC^x - xC)

Eq. 5

Si = A + B x

Cx

PR_T

Eq. 6 in which xC^x

XCx and Cx

TO ^{- X}B

Eq. 7 with the condition that:

Cx and Cx

TO ^{- X}B

Eq. 8 xC^x - x^c_B^x φ or

Eq. 9

ES 2 347 802 T3

In this way, during a reaction under constant conditions (temperature, gas composition and pressure), instantaneous fractionation can be obtained knowing the total polymer production rate, and the incorporation of the component or components of interest because Eq. 6 shows that there is a linear relationship between fractionation and incorporation rate and production rates and measured or proportional fractionation values. The procedure is based on the condition that the weight fractions of Cx are different in the two constituent polymers and only a single reactant or monomer must satisfy the above criteria. It is only relevant that the slope and cutoff of Eq. 6 are functions of the relative mass fractions of the at least two basic polymers produced. The type or class of species distribution is not critical. That is, the molecular weight, the branching of the chains, the relative density, etc. they are not critical to the fractionation calculation by the present procedure.

Data on multiple cleavages are obtained when more than two resin components are present (ie multimodal cleavages). The associated fractionations are used analogously to control the reactor and thus control the properties of the resin. Multimodal fractionations are calculated in a similar way to the bimodal case but using vector and matrix relationships (instead of scalars), as shown below. The following mathematical relationships are denoted Eq. For convenience and those skilled in the art will realize that they refer to vectors and matrices.

For multi-modal systems (i.e. 'n' modal), the fractionation can be described as a vector quantity as follows:

Eq. 10 in which:

<td>s =</td><td>V</td><td></td><td>Λ</td><td>·, Β =</td><td> 1______</td><td>5j2^Β22</td><td>^Β\ η</td><td> ;/ =</td><td>I₂/ PR</td>

<td></td><td>s „.</td><td></td><td>Λ.</td><td></td><td></td><td></td><td> --------------------1 § «3</td><td></td><td>J_n/ PR_</td>

Eq. 11

Si = (Mass of component 'i' / Total mass of resin) for i = 1,2, 3, ... n

Ii = (Incorporation of component 'i') for i = 1,2, 3, ... n

PR = total production rate of the reactor

Because these various amounts are available by estimate or are

ES 2 347 802 T3 measurable, instantaneous values ​​of the individual product component fractionations can be obtained and once these quantities are known they can be used with the linear relationship as shown in equation 6 for the bimodal case and the equation 10 for the multimodal case to monitor the reaction by periodic measurements of the reactor / monomer / reactant conditions, followed by appropriate adjustments to a desired value. Consequently, the properties of the product are controlled. Production rates are available using material balance and / or heat balance data, and incorporation data is similarly available using material consumption and recovery data. As the fractionation is proportional to the proportion of the incorporation of a reactant or monomer in the final product and the production rate to obtain at least two experimental values ​​of this proportion and determine the fractionation experimentally for those values, or an amount that is proportional to fractionation (reflecting a change in composition of a bi- or multi-modal sample) a linear correlation between fractionation and incorporation can be obtained. Accordingly, the fractionations can be obtained in the subsequent reaction or periodically in a continuous reaction, as long as the reaction conditions affecting the individual resin incorporation fractions are the same.

Finally, during the transition of a reactor between two different products that have different fractionations, the incorporation parameters, similarly, would also change and this would be predictable by means of a resin properties model, for example a description of the physical properties attributed to a resin comprising multiple types of polymers synthesized together, where the incorporation parameters are known. In this way, the transition of reactor conditions between the desired products can be performed and the process under the desired reactor conditions can be controlled with the processes according to the present invention.

Fluidized Bed Reactors

Fluidized bed reactors are well known in the art and are preferred for applying the processes according to the present invention. A particular non-limiting example of a fluidized bed reactor is described herein, in Figure 1, for illustrative purposes only. Those skilled in the art will recognize that numerous modifications and improvements can be made, as desired, to the fluidized bed reactor for the practical implementation of the processes of the present invention. Furthermore, as those skilled in the art will recognize, other polymerization reactors will be useful in practicing the inventive process of the present invention.

Figure 1 illustrates a gas phase fluidized bed reactor 20 useful in performing

ES 2 347 802 T3 certain non-limited examples of the process of the present invention. Reactor 20 has a reactor body 22, which is generally a vertical cylinder having a fluidization grid 24 located in its lower region. The reactor body 22 encloses a fluidized bed zone 26 and a velocity reduction zone 28 that is generally larger in diameter, compared to the diameter of the fluidized bed zone 26 of the reactor body 22.

The gaseous reaction mixture exiting the top of the reactor body 22, called the recycle gas stream, contains primarily unreacted monomer, unreacted hydrogen gas, inert condensable gases such as isopentane, and inert non-condensable gases such as nitrogen. The recycle gas stream is transferred through line 30 to compressor 32, and from compressor 32 to heat exchanger 34. A gas analyzer 38 can be used to sample the recycle gas stream to determine the concentrations of the various components. Typically, the gas analyzer is a gas chromatograph (GC), or a spectrograph such as a near infrared (NIR) spectrometer or a Fourier transform near infrared (FT-NIR) spectrometer. An additional heat exchanger (not shown) can also be used, if desired, preferably upstream of compressor 32.

The cooled recycle gas stream exits heat exchanger 34 through line 40. As discussed above, the cooled recycle gas stream can be gaseous, or it can be a mixture of gas and liquid phases. This stream connects to the reactor together with the monomer preparation stream 60.

Those skilled in the art will understand that less gas is required to maintain fluidization when the reactor employed is a stirred bed reactor. In a preferred embodiment, a stirred bed reactor is used for the practical implementation of the embodiments of the present invention, with or without the addition of a so-called condensate mode of operation.

An optional compressor may be provided to ensure that a sufficient velocity is imparted to the gases flowing to the bottom of the reactor. The gas stream entering the bottom of the reactor may contain condensed liquid, if desired.

All or part of the liquid phase separated from the recycle stream in a separator would be transferred to a manifold 50 located at or near the top of the reactor. If desired, an in-line pump can be provided to facilitate liquid transfer to manifold 50. Liquid entering manifold 50 flows downwardly to manifold 54 through a plurality of conduits 56 which have good heat exchange properties and which are in heat exchange contact with the wall of the reactor. The passage of

ES 2 347 802 T3 liquid through conduits 56 cools the inner wall of the reactor and heats the liquid to a greater or lesser degree, depending on the temperature differential and the duration and extent of the heat exchange contact. In this way, by the time the liquid entering the manifold 50 reaches the manifold 54, it has become a heated fluid which may have remained in a completely liquid state or may have partially or fully vaporized.

The monomer preparation can be introduced into the reactor in liquid or gaseous form through line 60.

A gas that is inert to the catalyst, such as nitrogen or argon, is preferably used to bring the catalyst to the bed.

The catalysts can be introduced in the form of supported catalysts, or a supported catalyst and a solution of another catalyst; or a solution of two catalysts added separately or in combination. Solutions can be gaseous or liquid. Furthermore, the catalysts can be in the form of dry catalysts.

The polymeric product particles can be removed from the reactor through line 62 in the conventional manner, such as, for example, by the method and apparatus described in US Patent No. 4,621,952.

Catalysts and Polymers

Catalysts for bimodal or multimodal polymerizations can be injected continuously or intermittently into the reactor using a catalyst feed tube (not shown), such as the device described in US Patent No. 3,779,712. In one embodiment, the catalysts are preferably introduced into the reactor at a point 20 to 40 percent of the diameter of the reactor, away from the reactor wall and at a height of about 5 to about 30 percent of the height of the bed. , although these relationships are not critical to the practical realization of the present invention. Suitable catalysts are any combination of catalysts that preferably produces a bimodal or multimodal polymeric product that contains at least one monomer that can be accurately measured as it is added to a reactor and incorporated into the polymers that are produced. The catalyst combinations can preferably be metallocene and Zeigler-Natta (ie, Zeigler catalysts) as is known in the art, or other catalysts such as amide-based catalysts that produce different polymeric species. In other preferred embodiments, an amide-based catalyst can be prepared in accordance with the teachings of Published United States Patent Applications US 2003 / 0171206A1 and US 2003 / 0191012A1: can be used in an especially preferred embodiment with a metallocene catalyst or ZeiglerES 2 347 802 T3

Natta to produce a bimodal homo- or copolymer system, for example, bimodal polyethylene or a bimodal polyethylene-co-hexene copolymer.

In the processes of the present invention, the fluidized bed reactor is operated to form polyolefins having at least one bimodal physical property distribution (eg, mass fraction) and in copolymers, at least one bimodal comonomer distribution . Such polyolefins include, but are not limited to, polyethylene (s), polypropylene, polyisobutylene, polybutylenes, polyhexenes, polyoxules, and copolymers thereof.

In one embodiment, the at least one polyolefin includes poly (ethylene-cohexene) copolymers. In another, a bimodal polyethylene is produced. Other low density polyethylenes (LDPE) can be prepared in the gas phase process using Zeigler-Natta or vanadium catalysts, and typically have a density in the range of 0.916-0.940 g / cm³. Polyethylene in the same density range, i.e. 0.916 to 0.940 g / cm³, which is linear and does not contain long chain branches is known as linear low-density polyethylene (LLDPE) and can be produced with conventional Ziegler-Natta catalysts or with metallocene catalysts. Relatively higher density LDPE, typically in the range 0.928 to 0.940 g / cm³, is sometimes called medium density polyethylene (MDPE). Polyethylenes that have an even higher density are high-density polyethylenes (HDPE), that is, polyethylenes that have densities greater than 0.940 g / cm³, and are generally prepared with Ziegler-Natta catalysts. Very low density polyethylene VLDPE is also known. VLDPEs can be produced by numerous different procedures, producing polymers with different properties, but which are generally described as polyethylenes having a density of less than 0.916 g / cm³, typically 0.890 to 0.915 g / cm³ or 0.900 to 0.915 g / cm³.

Polymers that have more than two types of monomers, such as terpolymers, are also included within the scope of the term copolymer, as used herein. Suitable comonomers include α-olefins, such as α-olefins C₃-C₂₀ or α-olefins C₃-C₁₂. The α-olefin comonomer can be linear or branched, and two or more comonomers can be used, if desired. Examples of suitable comonomers include α-olefins C₃-Ci₂ linear, and α-olefins, and α-olefins having one or more C1-C3 alkyl branches, or an aryl group. Specific examples include propylene; 3-methyl-1-butene;

3,3-dimethyl-1-butene; 1-pentene; 1-pentene with one or more methyl, ethyl or propyl substituents;

1-hexene with one or more methyl, ethyl or propyl substituents; 1-heptene with one or more methyl, ethyl or propyl substituents; 1-octene with one or more methyl, ethyl or propyl substituents;

1-nonene with one or more methyl, ethyl or propyl substituents; ethyl, 1-decene substituted with

ES 2 347 802 T3 methyl or dimethyl; 1-dodecene; and styrene. It should be appreciated that the above list of comonomers is merely exemplary, and is not intended to be limiting. Preferred comonomers include propylene, 1-butene, 1-pentene, 4-methyl-1-pentene, 1-hexene, 1-octene, styrene, and the like.

Other useful comonomers include polar vinyl monomers, conjugated and unconjugated dienes, acetylene, and aldehyde, which can be included in minor amounts in terpolymer compositions. Unconjugated dienes useful as comonomers are preferably straight chain hydrocarbon diolefins or cycloalkenyl substituted alkenes having 6 to 15 carbon atoms. Suitable unconjugated dienes include, for example: (a) straight chain acyclic dienes, such as 1,4-hexadiene and 1,6-octadiene; (b) branched chain acrylic dienes, such as 5-methyl-1,4-hexadiene; 3,7-dimethyl-1,6-octadiene; and 3,7-dimethyl-1,7-octadiene; (c) single ring alicyclic dienes, such as 1,4-cyclohexadiene; 1,5-cyclo-octadiene and 1,7-cyclododecadiene; (d) linked ring and fused multi-ring alicyclic dienes, such as tetrahydroindene; norbornadiene; methyl-tetrahydroindene; dicyclopentadiene (DCPD); bicyclo- (2,2,1) -hepta-2,5diene; alkenyl, alkylidene, cycloalkenyl and cycloalkylidene norbornenes, such as 5-methylene-2-norbornene (MNB), 5-propenyl-2-norbornene, 5-isopropylidene-2-norbornene, 5- (4-cyclopentenyl) -2-norbornene, 5-cyclohexylidene- 2-norbornene, and 5-vinyl-2-norbornene (VNB); and (e) cycloalkenyl substituted alkenes, such as vinyl cyclohexene, allyl cyclohexene, vinyl cyclooctene, 4-vinyl cyclohexene, allyl cyclodecene, and vinyl cyclododecene. Of the unconjugated dienes typically used, the preferred dienes are dicyclopentadiene, 1,4-hexadiene, 5-methylene-2-norbornene, 5-ethylidene-2-norbornene, and tetracyclo- (A-11,12) -5,8-dodecene. . Particularly preferred diolefins are 5-ethylidene-2-norbornene (ENB), 1,4-hexadiene, dicyclopentadiene (DCPD), norbornadiene, and 5-vinyl-2-norbornene (VNB).

In a preferred embodiment at least two catalysts are a combination of a metallocene catalyst and a Ziegler or Ziegler-Natta catalyst that will produce a relatively higher and relatively lower molecular weight blended polymer blend. In another preferred embodiment, an amide catalyst can be used in conjunction with a metallocene or a Ziegler catalyst. In yet another preferred embodiment a combination of three catalysts is used to prepare a multi-modal polymer system.

Examples

The following non-limiting Examples are provided to illustrate some specific embodiments of the present invention.

Example 1. Preparation of a hexene copolymer resin in a pilot plant reactor to obtain data for estimation of fractionation.

ES 2 347 802 T3

A copolymerization was carried out using hexene monomer and ethylene monomer. The reactor was a pilot plant reactor that can produce approximately 50 to 70 pounds of polymer or resin per hour. The basic reactor is approximately 30.5 cm (one foot) in diameter and 3.1 m (10 feet) high. There is a transition to a conical section, where the diameter of the reactor approximately quadruples. There is a third section at the top that is approximately 1.2 m (4 ft) in diameter. The total height of the reactor is approximately 9.1 m (30 ft). A recycle gas stream loops from the top of the reactor and is reintroduced to the bottom of the reactor. There are two main pieces of equipment attached to the recycle section: the first is a compressor that compresses the gas to maintain a flow of gas through the recycle stream and into the reactor. The second is a heat exchanger that removes heat from the reactor thereby controlling the reaction temperature. The product is removed from the fluidized bed using a product discharge tank, separated from the reactor by a cycled automatic valve. The discharge system works by keeping the discharge tank at a lower pressure than in the reactor and the resin is pneumatically forced into the tank when the valve is opened. The valve closes and the tank is vented and purged. Subsequently, after sufficient purging, the resin falls through another valve into the storage drum.

The procedure was carried out by varying the proportions of the catalyst supply rate (one catalyst was a metallocene catalyst, the other a ZeiglerNatta catalyst) to obtain different values ​​for incorporation for each monomer (ethylene and 1-hexen) and reactant (hydrogen) used to determine fractionation. The incorporation information for ethylene, hexene, and hydrogen was obtained by calculating the mass flow rate to the reactor and subtracting the measured loss terms, as defined above. These data are shown in Table 1, divided by the production speed. The fractionation EMF data corresponding to the different catalyst feed rate values ​​were determined using a conventional procedure to obtain resolution of mass fractions of the sample of the polymer produced in the reactor. The calculated fractionation data was determined from the linear equation drawn for ethylene, hexene, and hydrogen, as shown in Figures 2-5 inclusive. These data illustrate the generally good agreement between the cumulative CEM-measured splits and the calculated instantaneous splits, determined by the method of the present invention.

ES 2 347 802 T3

Table 1 - Pilot Reactor - Fractionation Data Set 1

<td>Moment</td><td>Incorp. C2 / PR</td><td>Incorp. C6 / PR</td><td>Incorp. H2 / PR</td><td>CEM fractionation</td><td>Fractionation of lncorp. by C2H4</td><td>Fractionation of Incorp. by C6H12</td><td>Fractionation of Incorp. by H2</td><td>Proportion Supply Cat</td>

<td>Day 1 12:00:00 P.M</td><td> 0,9914</td><td> 0,0077</td><td>8.48 E-04</td><td> 60,97</td><td> 57,0</td><td> 57,0</td><td> 56,2</td><td> 5,6</td>

<td>Day 1 13:00:00 P.M</td><td> 0,9910</td><td> 0,0082</td><td>8.29 E-04</td><td> 60,97</td><td> 56,8</td><td> 56,8</td><td> 56,4</td><td> 5,6</td>

<td>Day 2 9:00:00 A.M</td><td> 0,9891</td><td> 0,0102</td><td>7.51 E-04</td><td> 58,54</td><td> 55,8</td><td> 55,7</td><td> 57,1</td><td> 5,6</td>

<td>Day 2 10:00:00 A.M</td><td> 0,9899</td><td> 0,0094</td><td>7.66 E-04</td><td> 58,54</td><td> 56,2</td><td> 56,1</td><td> 57,0</td><td> 5,6</td>

<td>Day 3 6:00:01 A.M</td><td> 0,9902</td><td> 0,0091</td><td>7.76 E-04</td><td> 60,90</td><td> 56,3</td><td> 56,3</td><td> 56,9</td><td> 5,6</td>

<td>Day 3 7:00:01 A.M</td><td> 0,9871</td><td> 0,0121</td><td>7.73 E-04</td><td> 60,90</td><td> 54,7</td><td> 54,7</td><td> 56,9</td><td> 5,6</td>

<td>Day 4 12:00:01 P.M</td><td> 0,9924</td><td> 0,0070</td><td>6.07 E-04</td><td> 50,00</td><td> 57,5</td><td> 57,4</td><td> 58,6</td><td> 5,6</td>

<td>Day 4 1:00:01 P.M</td><td> 0,9920</td><td> 0,0074</td><td>5.88 E-04</td><td> 50,00</td><td> 57,3</td><td> 57,2</td><td> 58,8</td><td> 5,6</td>

<td>Day 5 12:00:01 P.M</td><td> 0,9904</td><td> 0,0090</td><td>6.42 E-04</td><td> 52,26</td><td> 56,5</td><td> 56,4</td><td> 58,3</td><td> 5,6</td>

ES 2 347 802 T3

<td>Moment</td><td>Incorp. C2 / PR</td><td>Incorp. C6 / PR</td><td>Incorp. H2 / PR</td><td>CEM fractionation</td><td>Fractionation of lncorp. by C2H4</td><td>Fractionation of Incorp. by C6H12</td><td>Fractionation of Incorp. by H2</td><td>Proportion Supply Cat</td>

<td>Day 5 1:00:01 P.M</td><td> 0,9951</td><td> 0,0041</td><td>7.78 E-04</td><td> 52,26</td><td> 58,9</td><td> 58,9</td><td> 56,9</td><td> 5,6</td>

<td>Day 14 12:00:00 P.M</td><td> 0,9938</td><td> 0,0055</td><td>6.39 E-04</td><td> 63,26</td><td> 58,3</td><td> 58,1</td><td> 58,3</td><td> 5,6</td>

<td>Day 14 1:00:00 P.M</td><td> 0,9959</td><td> 0,0035</td><td>6.45 E-04</td><td> 63,26</td><td> 59,4</td><td> 59,2</td><td> 58,2</td><td> 5,6</td>

<td>Day 15 12:00:00 P.M</td><td> 0,9944</td><td> 0,0051</td><td>4.72 E-04</td><td> 66,94</td><td> 58,6</td><td> 58,4</td><td> 60,0</td><td> 5,5</td>

<td>Day 15 1:00:00 P.M</td><td> 0,9966</td><td> 0,0029</td><td>5.06 E-04</td><td> 66,94</td><td> 59,7</td><td> 59,5</td><td> 59,6</td><td> 5,5</td>

<td>Day 19 12:00:00 P.M</td><td> 0,9935</td><td> 0,0059</td><td>6.02 E-04</td><td> 68,62</td><td> 58,1</td><td> 58,0</td><td> 58,7</td><td> 5,5</td>

<td>Day 19 1:00:00 P.M</td><td> 0,9935</td><td> 0,0059</td><td>6.47 E-04</td><td> 68,62</td><td> 58,1</td><td> 58,0</td><td> 58,2</td><td> 5,5</td>

<td>Day 20 3:00:00 P.M</td><td> 0,9879</td><td> 0,0113</td><td>8.13 E-04</td><td> 55,33</td><td> 55,1</td><td> 55,1</td><td> 56,5</td><td> 4,2</td>

<td>Day 20 4:00:00 P.M</td><td> 0,9884</td><td> 0,0108</td><td>7.80 E-04</td><td> 55,33</td><td> 55,4</td><td> 55,4</td><td> 56,9</td><td> 4,2</td>

<td>Day 24 6:00:00 A.M</td><td> 0,9766</td><td> 0,0220</td><td>1.33 E-03</td><td> 51,76</td><td> 49,2</td><td> 49,5</td><td> 51,3</td><td> 4,2</td>

ES 2 347 802 T3

<td>Moment</td><td>Incorp. C2 / PR</td><td>Incorp. C6 / PR</td><td>Incorp. H2 / PR</td><td>CEM fractionation</td><td>Fractionation of lncorp. by C2H4</td><td>Fractionation of Incorp. by C6H12</td><td>Fractionation of Incorp. by H2</td><td>Proportion Supply Cat</td>

<td>Day 24 7:00:00 A.M</td><td> 0,9808</td><td> 0,0180</td><td>1.20 E-03</td><td> 51,76</td><td> 51,4</td><td> 51,6</td><td> 52,6</td><td> 4,2</td>

<td>Day 25 3:00:00 P.M</td><td> 0,9967</td><td> 0,0022</td><td>1.17 E-03</td><td> 53,46</td><td> 59,8</td><td> 59,9</td><td> 52,9</td><td> 4,2</td>

<td>Day 25 4:00:00 P.M</td><td> 0,9986</td><td> 0,0001</td><td>1.31 E-03</td><td> 53,46</td><td> 60,8</td><td> 61,0</td><td> 51,5</td><td> 4,2</td>

<td>Day 26 9:00:00 A.M</td><td> 0,9916</td><td> 0,0077</td><td>6.83 E-04</td><td> 51,45</td><td> 57,1</td><td> 57,0</td><td> 57,8</td><td> 4,2</td>

<td>Day 26 10:00:00 A.M</td><td> 0,9921</td><td> 0,0072</td><td>7.10 E-04</td><td> 51,45</td><td> 57,4</td><td> 57,3</td><td> 57,6</td><td> 4,2</td>

<td>Day 27 12:00:00 P.M</td><td> 0,9888</td><td> 0,0106</td><td>6.38 E-04</td><td> 51,83</td><td> 55,6</td><td> 55,5</td><td> 58,3</td><td> 4,2</td>

<td>Day 27 1:00:00 P.M</td><td> 0,9906</td><td> 0,0086</td><td>7.21 E-04</td><td> 51,83</td><td> 56,6</td><td> 56,5</td><td> 57,5</td><td> 4,2</td>

<td>Day 28 9: 00:01 A.M</td><td> 0,9813</td><td> 0,0177</td><td>9.90 E-04</td><td> 50,79</td><td> 51,7</td><td> 51,7</td><td> 54,7</td><td> 4,2</td>

<td>Day 28 10:00:01 A.M</td><td> 0,9824</td><td> 0,0160</td><td>1.55 E-03</td><td> 50,79</td><td> 52,3</td><td> 52,7</td><td> 49,0</td><td> 4,2</td>

<td>Day 30 6:00:01 P.M</td><td> 0,9871</td><td> 0,0117</td><td>1.20 E-03</td><td> 51,08</td><td> 54,7</td><td> 54,9</td><td> 52,6</td><td> 4,2</td>

ES 2 347 802 T3

<td>Moment</td><td>Incorp. C2 / PR</td><td>Incorp. C6 / PR</td><td>Incorp. H2 / PR</td><td>CEM fractionation</td><td>Fractionation of lncorp. by C2H4</td><td>Fractionation of Incorp. by C6H12</td><td>Fractionation of Incorp. by H2</td><td>Proportion Supply Cat</td>

<td>Day 30 7:00:01 P.M</td><td> 0,9856</td><td> 0,0130</td><td>1.47 E-03</td><td> 51,08</td><td> 53,9</td><td> 54,2</td><td> 49,9</td><td> 4,2</td>

<td>Day 33 9:00:01 A.M</td><td> 0,9801</td><td> 0,0188</td><td>1.05 E-03</td><td> 51,46</td><td> 51,1</td><td> 51,2</td><td> 54,2</td><td> 4,2</td>

<td>Day 33 10:00:01 A.M</td><td> 0,9898</td><td> 0,0096</td><td>6.59 E-04</td><td> 51,46</td><td> 56,1</td><td> 56,0</td><td> 58,1</td><td> 4,2</td>

<td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td>

<td>Slope (B of Eq. 6)</td><td> 526,22</td><td> 524,94</td><td> 10.142,26</td><td></td><td></td><td></td><td></td><td></td>

<td>Ordered at the origin (A of Eq. 6)</td><td> -464,70</td><td> 61,06</td><td> 64,77</td><td></td><td></td><td></td><td></td><td></td>

Example 2. Application of the Calculated Fractions to the Commercial Scale Production of Bimodal Polyethylene.

A commercial scale production of bimodal polyethylene-co-hexene was carried out using the same catalyst systems as in Example 1 and relative proportions of similar monomers, and hydrogen (gas composition). The calculated instantaneous splits (using the slope and cuts for hydrogen that were calculated in Example 1) are shown in Table 2, along with the calculated cumulative splits (based on a moving average). A comparison of the instantaneous fractionation data calculated together with the cumulative fractionation data calculated from CEM is shown in Figure 6.

ES 2 347 802 T3

Table 2 - Production Reactor Fractionation Data Set, Example 2

<td>Moment</td><td>Incorp. C2 / PR</td><td>Incorpo C6 / PR</td><td>Incorpo H2 / PR</td><td>H2 fractionation estimation</td><td>Division Accumulated</td>

<td>Day 1 3:00 AM</td><td> 0,983</td><td> 0,015</td><td> 0,00062</td><td> 63,213</td><td></td>

<td>Day 1 3:05 AM</td><td> 0,984</td><td> 0,016</td><td> 0,00015</td><td> 69,733</td><td></td>

<td>Day 1 3:10 AM</td><td> 0,984</td><td> 0,015</td><td> -0,00049</td><td> 60,806</td><td></td>

<td>Day 1 3:15 AM</td><td> 0,984</td><td> 0,015</td><td> 0,00039</td><td> 63,327</td><td></td>

<td>Day 1 3:20 AM</td><td> 0,985</td><td> 0,015</td><td> 0,00014</td><td> 58,477</td><td></td>

<td>Day 1 3:25 AM</td><td> 0,984</td><td> 0,015</td><td> 0,00062</td><td> 74,729</td><td></td>

<td>Day 1 3:30 AM</td><td> 0,984</td><td> 0,017</td><td> -0,00098</td><td> 58,957</td><td></td>

<td>Day 1 3:35 AM</td><td> 0,985</td><td> 0,014</td><td> 0,00057</td><td> 64,252</td><td></td>

<td>Day 1 3:40 AM</td><td> 0,984</td><td> 0,015</td><td> 0,00005</td><td> 60,276</td><td></td>

<td>Day 1 3:45 AM</td><td> 0,983</td><td> 0,016</td><td> 0,00044</td><td> 67,617</td><td></td>

<td>Day 1 3:50 AM</td><td> 0,985</td><td> 0,014</td><td> -0,00028</td><td> 61,480</td><td> 64,135</td>

<td>Day 1 3:55 AM</td><td> 0,983</td><td> 0,016</td><td> 0,00032</td><td> 62,529</td><td> 64,078</td>

<td>Day 1 4:00 AM</td><td> 0,984</td><td> 0,016</td><td> 0,00022</td><td> 62,850</td><td> 64,045</td>

<td>Day 1 4:05 AM</td><td> 0,985</td><td> 0,015</td><td> 0,00019</td><td> 61,583</td><td> 64,020</td>

<td>Day 1 4:10 AM</td><td> 0,985</td><td> 0,014</td><td> 0,00031</td><td> 70,013</td><td> 63,968</td>

<td>Day 1 4:15 AM</td><td> 0,984</td><td> 0,015</td><td> -0,00052</td><td> 60,809</td><td> 64,098</td>

ES 2 347 802 T3

<td>Moment</td><td>Incorp. C2 / PR</td><td>Incorpo C6 / PR</td><td>Incorpo H2 / PR</td><td>H2 fractionation estimation</td><td>Division Accumulated</td>

<td>Day 1 4:20 AM</td><td> 0,984</td><td> 0,015</td><td> 0,00039</td><td> 62,160</td><td> 64,029</td>

<td>Day 1 4:25 AM</td><td> 0,985</td><td> 0,014</td><td> 0,00026</td><td> 66,027</td><td> 63,989</td>

<td>Day 1 4:30 AM</td><td> 0,984</td><td> 0,016</td><td> -0,00012</td><td> 64,715</td><td> 64,033</td>

<td>Day 1 4:35 AM</td><td> 0,984</td><td> 0,015</td><td> 0,00001</td><td> 61,078</td><td> 64,048</td>

<td>Day 1 4:40 AM</td><td> 0,984</td><td> 0,015</td><td> 0,00036</td><td> 60,979</td><td> 63,984</td>

<td>Day 1 4:45 AM</td><td> 0,984</td><td> 0,015</td><td> 0,00037</td><td> 69,746</td><td> 63,920</td>

<td>Day 1 4:50 AM</td><td> 0,985</td><td> 0,015</td><td> -0,00049</td><td> 63,599</td><td> 64,043</td>

<td>Day 1 4:55 AM</td><td> 1,000</td><td> 0,000</td><td> 0,00012</td><td> 64,770</td><td> 64,034</td>

<td colspan="5">Pending</td><td> -10142,260</td>

<td colspan="5">Ordered at the origin</td><td> 64,770</td>

Although the present invention and its advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the invention as defined by the appended claims. 5 Furthermore, the scope of the present application is not intended to be limited to the particular embodiments of the method, machine, manufacture, and composition of matter, means, procedures, and steps described in the specification. As will be readily appreciated from the disclosure, methods, machines, fabrication, compositions of matter, media, procedures, or steps, currently existing or to be developed later, may be used that perform substantially the same function or achieve substantially the same result as corresponding embodiments described herein. Accordingly, the appended claims are intended to include within their scope such processes, machines, fabrication, compositions of matter, media, procedures, or steps.