RU2811191C2 - Control and management of polyolefin production process - Google Patents

Abstract

FIELD: olefin polymerization.

SUBSTANCE: invention is related to a method for controlling an olefin polymerization reactor system and includes a) selecting n input variables, each input variable corresponding to a technological condition of the olefin polymerization process; b) defining m output variables, each output variable corresponding to a measurable property of the polymer; c) adjusting one or more of the n input variables in a plurality of polymerization reactions using an olefin polymerization reactor system to produce a plurality of olefin polymers and measuring each of the m output variables as a function of the input variables for each olefin polymer; d) analysing the change in each of the output variables as a function of the input variables to determine the coefficients; f) calculating a response surface model (RSM) using general equations for each output variable defined in step d) to correlate any combination of n input variables with one or more of m output variables; f) applying the n selected input variables to the calculated response surface model (RSM) to predict one or more of the m target output variables, each target output variable corresponding to a measurable property of the polymer; and g) applying n selected input variables I^sl - I^sn to operate the olefin polymerization reactor system and produce a polyolefin product. The invention is also related to an embodiment of a method for controlling an olefin polymerization reactor system.

EFFECT: improvement of process control.

27 cl, 3 ex, 15 tbl, 5 dwg

Description

TECHNICAL FIELD

[1] This application relates to systems and methods for improved reactor control, in particular, to systems and methods for improved control of polyolefin production reactors.

BACKGROUND OF THE ART

[2] Polyolefin properties depend on many factors such as reactor temperature, reaction time, average residence time, polyolefin concentration, α-olefin comonomer concentration, hydrogen concentration, catalyst type, catalyst concentration, cocatalyst concentration, activator concentration, design reactor, reactor volume, etc. Determining the necessary conditions to produce a polyolefin having the desired properties typically requires time and expensive repeated testing to determine whether a particular combination of conditions will produce the desired properties of the polyolefin.

[3] As the complexity of manufactured resins and the complexity of their production processes increases, there is a parallel need for an improved, systematic way to control the process. Determining key process parameters for monitoring and control becomes increasingly complex if the required polyolefin is a bimodal polyolefin and if more than one reactor is involved. Bimodal reverse comonomer distribution (CCD) polyolefins have excellent mechanical properties, but their production is often difficult to determine.

[4] Accordingly, improved reactor control systems and methods are needed.

SUMMARY OF THE INVENTION

[5] The summary of the invention is presented to introduce various concepts in a simplified form, which are further described below in the following detailed description. The summary of the invention is not intended to define the required or necessary features of the claimed subject matter of the invention, nor is the summary of the invention intended to limit the claimed subject matter of the invention.

[6] The Summary of the Invention and the following Detailed Description provide examples and are merely illustrative of the present invention. Accordingly, the above summary and the following detailed invention should not be construed as limiting. Additional features or variations thereof may be provided beyond those set forth herein, such as, for example, various combinations and subcombinations of the features presented in the detailed description.

[7] In one aspect, the described methods are applicable to bimodal resins produced in a single reactor using a dual catalyst system, where the production of two different polymers in a single reactor makes it extremely difficult to characterize each individual polymer. Although simple systems can use flow rate and melt density to control the polymerization process to the desired molecular weight distribution, methods based on GPC (gel permeation chromatography) of the process sample, SBC (short chain branching) analysis, and dynamic rheology are proposed herein. .

[8] In one aspect of the present disclosure, dynamic rheology and fast GPC-based methods are provided for determining process conditions to be adjusted to obtain a desired molecular weight distribution for dual single-reactor catalyst systems, for example, a dual metallocene single-reactor catalyst system. Methods have been developed to enter the required rheological values during frequency scanning and/or fast GPC of the desired polymer. The rheological data and MWD obtained for a given process sample were introduced into the described method at regular intervals. The proposed method then correlates the developed experimental model, for example, a model obtained using data previously collected in an experimental setup, with the actual conditions of the reaction process. Any minor corrections or amendments may be made to ensure that the actual process conforms to this template. Then, in the proposed method, the actual rheology and MWD are compared with the target value, the trajectory is calculated, and the resulting trajectory is translated into changing the reactor control parameters. In one aspect, for example, the proposed method may enable the development of new setpoints to control reactor conditions. These steps are repeated until the rheology and MWD of the technological sample match the rheology and MWD values of the required polymer.

[9] In one aspect, for a dual catalyst system in a single reactor, while maintaining certain key reactor conditions at a constant value, using the described method, it is possible to vary H (hydrogen pressure), temperature, and comonomer (eg, hexane) to produce the desired resin. The same basic methodology applies to other resin processes, such as the Advanced Dual Loop (ADL) process, although a different combination of key and controllable parameters may be used. Thus, the development of the said model involves the use of data collected in a systematic manner, along with mathematical modeling of the systems to be controlled.

[10] In accordance with one aspect, provided herein is a method for controlling an olefin polymerization reactor system, comprising: a) selecting n input variables I ¹ , I ² , I ³ , ... I ⁿ , each input variable corresponding to a process condition of the olefin polymerization process ; b) defining t output variables, R ¹ , R ² , R ³ , ... R ^m , each output variable corresponding to a measurable property of the polymer, with two of the t output variables being molecular weight distribution (MWD) and short chain branching (SCB); c) adjusting one or more of the n input variables I ¹ - I ⁿ in a plurality of polymerization reactions using an olefin polymerization reactor system to produce a plurality of olefin polymers and measuring each of the m output variables R ¹ - R ^m as a function of the input variables for each olefin polymer; d) analyzing the change in each of the output variables R ¹ - R ^m as a function of the input variables I ¹ - I ⁿ to determine the coefficients in accordance with the following general equation for each output variable R ¹ - R ^m :

e) calculation of a response surface model (RSM) using general equations for each output variable R ¹ - R ^m (R ^1-m ) defined in step d), to correlate any combination of n input variables I ¹ - I ⁿ with one or more of m output variables R ¹ - R ^m ; f) applying n selected input variables I ^s1 , I ^s2 , I ^s3 , … I ^sn to the estimated response surface model (RSM) to predict one or more of the m target output variables, R ^t1 , R ^t2 , R ^t3 , … R ^tm , each target output variable corresponds to a measurable property of the polymer; and g) applying n selected input variables I ^s1 - I ^sn to operate the olefin polymerization reactor system and produce a polyolefin product.

[11] According to some aspects, the general equation for each output variable R ¹ - R ^m is

(the product of the unique combination of 2 of I ¹ - I ⁿ , independently selected), where v' represents the total number of unique combinations of any 2 of I ¹ - I ⁿ , selected independently.

[12] According to some aspects, the general equation for each output variable R ¹ - R ^m is

(product of a unique combination of 2 from I ¹ - I ⁿ , chosen independently)

(product of a unique combination of 3 of I ¹ - I ⁿ , chosen independently),

where v' represents the total number of unique combinations of any 2 of I ¹ - I ⁿ selected independently; and w' represents the total number of unique combinations of any 3 of I ¹ - I ⁿ independently selected.

[13] According to some aspects, the general equation for each output variable R ¹ - R ^m is

(product of a unique combination of 2 from I ¹ - I ⁿ , chosen independently)

(product of a unique combination of 3 from I ¹ - I ⁿ , chosen independently)

(product of a unique combination of 4 from I ¹ - I ⁿ , chosen independently),

where v' represents the total number of unique combinations of any 2 of I ¹ - I ⁿ selected independently; and w' represents the total number of unique combinations of any 3 of I ¹ - I ⁿ independently selected; and x' represents the total number of unique combinations of any 4 of I ¹ - I ⁿ independently selected.

[14] In another aspect, provided herein is a method for controlling an olefin polymerization reactor system, comprising: a) selecting one or more m target output variables, R ^t1 , Rt ² , R ^t3 , ... R ^tm , each target output the variable corresponds to a measurable property of the polymer; b) calculating n selected input variables I ^s1 , F ^s2 , I ^s3 , … I ^sn using the response surface model (RSM) of claim 1 to achieve one or more of the m target output variables, R ^t1 , R ^t2 , R ^t3 , … R ^tm ; c) using n selected input variables I ^s1 - I ^sn to operate the olefin polymerization reactor system and produce a polyolefin product; d) measuring one or more properties of the polyolefin product corresponding to m measured output variables, R ^m1 , R ^m2 , R ^m3 , ... R ^mm ; and e) repeating steps a) to d) to reduce the difference between the target output variables R ^t1 and R ^tm and the measured output variables

[15] These and other aspects and embodiments of the present disclosure are set forth in the drawings, detailed description and claims.

BRIEF DESCRIPTION OF GRAPHIC MATERIALS

[16] The proposed set of patent or application materials contains at least one graphic material made in color. Copies of the publication of this patent or patent application with color graphic material(s) will be made available to the Office upon request and upon payment of the required fee.

[17] The following figures form a part of the present description and are included to further demonstrate certain aspects of the present description. The invention may be better understood by reference to one or more of the provided figures in conjunction with the detailed description of specific aspects presented herein.

[18] FIG. 1 provides a schematic overview of a proposed optimization model using a response surface model in accordance with one embodiment of the present disclosure.

[19] Figure 2 shows the predicted and measured molecular weight distribution of the experimental polyolefin.

[20] Figure 3 shows the predicted and measured molecular weight and short chain branching of the experimental polyolefin.

[21] Figure 4 shows the predicted and experimental viscosity of the experimental polyolefin.

[22] FIG. 5 illustrates smoothing of observed experimental data against predicted RSM values, in accordance with one embodiment of the present disclosure.

[23] Although the present invention described herein may be subject to various modifications and alternative forms, only a few specific embodiments are shown in the drawings by way of example and are described in detail below. The drawings and detailed description of these specific embodiments are in no way intended to limit the scope or spirit of the concepts of the present invention or the appended claims. Instead, the proposed drawings and detailed written description are presented to illustrate the concepts of the present invention to one skilled in the art and to enable said person skilled in the art to make and use the concepts of the present invention.

DEFINITIONS

[24] The following definitions are presented to facilitate the understanding of the detailed description of the present invention by one skilled in the art. Unless otherwise specified herein, scientific and technical terms used in connection with the present invention have the meanings commonly understood by one skilled in the art to which the present invention pertains, unless otherwise indicated or the context indicates otherwise. , the above definitions apply to the entire description. In addition, unless the context otherwise requires, terms in the singular form include plural forms, and terms in the plural form include singular forms. For example, if a term is used in this specification but is not specifically defined, the definition from the IUPAC Compendium of Chemical Terminology, 2nd edition (1997) may be used unless such definition conflicts with any other specification or definition provided herein. or if it does not result in uncertainty or impossibility of any claim to which the definition applies. If any definition or application of terminology provided in any document incorporated by reference herein is inconsistent with the definition or application of terminology provided herein, the definition or application of terminology provided herein shall govern.

[25] Except where specifically stated otherwise in certain circumstances, all percentages, fractions, ratios and similar amounts used herein are by weight.

[26] In addition, in this regard, certain features of the present invention, which for clarity are described in the context of individual aspects, may also be presented in combination within a single aspect. Conversely, various features of the present invention, which for brevity are described in the context of a single aspect, may also be presented individually or in any subcombination.

[27] With respect to the description of transitional terms or expressions, the transitional term “comprising,” which is synonymous with the terms “comprising,” “having,” or “characterized,” is inclusive or open-ended and does not exclude additional, unlisted elements or process steps. The transitional expression "consisting of" excludes any element, step or ingredient not specifically listed in the claim. The transitional expression "consisting essentially of" limits the scope of the claim to specific materials or steps, and those that do not significantly affect the essential and novel feature(s) of the claimed invention. The "consisting essentially of" claim occupies an intermediate group between closed claims, which are written in the "consisting of" format, and fully open claims, which are written in the "comprising" format. Unless otherwise stated, when describing a compound or composition, “consisting essentially of” is not to be construed as “comprising” and is intended to describe said component containing materials that do not substantially alter the composition or method in respect of which the term is used. . For example, a feedstock consisting essentially of Material A may contain impurities typically found in a commercially produced or commercially available sample of the compound or composition. If a claim includes various features and/or classes of features (for example, a process step, raw material features, and/or product features, among other possibilities), then the transition terms “comprising,” “consisting essentially of,” and “consisting of” refer to only to the class of characteristics in relation to which they are used, and in one paragraph different transitional terms or expressions for different characteristics can be used. For example, the method may include several listed steps (and other unlisted steps), but it uses the preparation of a catalyst system consisting of certain steps, and uses a catalyst system containing the listed components and other unlisted components. Although the compositions and methods are described as “including” various components or steps, the compositions and methods may also “consist essentially of” or “consist of” various components and steps.

[28] The singular terms may be used to refer to various elements and components of the compositions, methods, or structures described herein. This is for convenience only and to provide a general understanding of the compositions, methods or structures. Such description includes "one or at least one" of the specified elements or components. In addition, as used herein, the singular forms also include descriptions of a plurality of elements or components, unless it is obvious from the particular context that the plural form is excluded.

[29] “Optional” or “optional” means that the event or circumstance described below does not necessarily have to occur, and that the description includes cases in which the specified event or circumstance occurs and cases in which it does not.

[30] The terms “capable of being used” or “adapted for use” and similar expressions are used in this context to reflect that the particular structure or technique specified is used in the system or method described herein. For example, unless otherwise indicated, a particular design of “configured for use” means “constructed for use in a reactor system,” including, for example, “constructed for use in an olefin polymerization reactor system,” and therefore designed, shaped, arranged , designed and/or adapted to effect polymerization of an olefin, as understood by those skilled in the art.

[31] The term "olefin" is used herein in accordance with the IUPAC definition: acyclic and cyclic hydrocarbons having one or more carbon-carbon double bonds, other than the formal bonds in aromatic compounds. The class "olefins" includes alkenes and cycloalkenes, as well as the corresponding polyenes. Non-limiting examples of olefins include ethylene, propylene, 1-butene, 2-butene, 1-hexene and the like.

[32] The terms "polyolefin" or "polymer" as used herein mean a substance produced by the polymerization of one or more olefins, alone or in combination with suitable comonomers, catalysts or additives. For example, a "polyolefin" or "polymer" as used herein may be produced with a chromium catalyst, a metallocene catalyst, including a dual metallocene catalyst, a Ziegler-Natta catalyst, or combinations thereof. "Polyolefin" or "polymer" as used herein may be produced in a single reactor or in multiple reactors arranged in series or parallel. "Polyolefin" or "polymer" as used herein may be a monomodal or multimodal polymer.

[33] The term “about” means that the quantity, size, composition, parameters and other quantitative values and characteristics are not and should not be exact, but may be approximate and/or larger or smaller, as desired, reflecting tolerances, conversion factors , rounding, measurement error, etc., as well as other factors known to those skilled in the art. In general, quantity, size, composition, parameter or other quantitative value or characteristic is prefixed with "about" or "approximately" whether or not it is explicitly stated. The term “about” also includes those quantities that differ due to different equilibrium conditions for the composition obtained from a particular initial mixture. Regardless of whether the term "about" is modified, the claims include quantitative equivalents. The term "about" may mean within 10% of a specified numerical value, or within 5% of a specified numerical value, or within 2% of a specified numerical value.

[34] As used herein, the terms “comprises”, “containing”, “includes”, “comprising”, “has”, “having”, “contains” or “comprising”, or any variation thereof, is intended to imply non-exclusive inclusion. For example, a composition, mixture, process, method, article or device that contains a certain list of elements is not necessarily limited to only the specified elements, but may include other elements not explicitly listed or not inherent in the specified composition, mixture, process, method, product or device. Also, unless specifically stated otherwise, “or” refers to an inclusive “or,” not an exclusive “or.” For example, state A or B is satisfied by one or more of the following: A is true (or present), and B is false (or not present), A is false (or not present), and B is true (or present), and both A and B are true (or present).

DETAILED DESCRIPTION

[35] The figures described above and the written description of specific structures and functions set forth below are not intended to limit the scope of what the inventors of this application believe to be an invention or the scope of the appended claims. Rather, the figures and written description are intended to enable any person skilled in the art to make and use the proposed inventions for which patent protection is sought. Those skilled in the art will understand that not all features of the commercial aspect of the present invention are described or shown for the sake of clarity and understanding. It will also be appreciated by those skilled in the art that the development of an actual commercial aspect incorporating aspects of the present invention will require many implementation-specific decisions to be made to achieve the developer's ultimate goal in the commercial aspect. Such implementation-specific decisions may include, and are likely not limited to, compliance with system, commercial, governmental, and other restrictions, which may vary by implementation, location, and change from time to time. Although the development efforts may be complex and time consuming in absolute terms, such efforts are nonetheless common practice for those skilled in the art to benefit from the present disclosure. It should be understood that the inventions disclosed and described herein are susceptible to numerous and various modifications and alternative forms. Finally, the use of a term in its singular form is not intended to limit the number of elements.

[36] In accordance with one aspect, the present description provides a method for monitoring and controlling a multisite catalyst in a single or multiple reactor system to obtain a specific desired product structure and resulting polymer properties, as shown in FIG. 1. In some embodiments, the proposed methods provide the ability to more efficiently run reactors and regulate reactors by optimizing the most desirable possible reactor conditions to produce a polymer product with reselected specific target values, thereby reducing the amount of off-spec material and maximizing reactor efficiency. In addition to product characteristics, by implementing these parameters as output variables, reactor characteristics such as percent solids and yield can be optimized. The main advantage of the present invention is the ability to simultaneously optimize several output variables, which allows for an optimal workspace for a particular specified product.

[37] In accordance with one aspect, the present description provides a method for a systematic approach to obtaining the desired resin in a faster and more efficient manner than conventional methods. For example, the required resin and final product can be more precisely defined according to a wider range of characteristic parameters. For example, instead of specifying only a few properties such as melt index (MI) and density, a full range of MWD, frequency scan rheology, MCR distribution, and/or DPR content can be specified to match a desired resin. In one aspect, the proposed method utilizes more informative polymer characterization techniques for samples obtained without stopping the process to achieve a faster and more efficient approach to obtaining the desired resin.

[38] In one aspect, a method is provided for controlling an olefin polymerization reactor system, comprising: First, a) selecting n input variables I ¹ , I ² , I ³ , ... I ⁿ , each input variable corresponding to a process condition for the olefin polymerization process; and b) defining m output variables, R ¹ , R ² , R ³ , … R ^m , each output variable corresponding to a measurable property of the polymer, with two of the m output variables being molecular weight distribution (“MWD”) and short chain branching ( "KCR") For example, in some embodiments, input variables may include reactor temperature, reaction time, average residence time, olefin concentration, α-olefin comonomer concentration, hydrogen concentration, catalyst type, catalyst concentration, catalyst concentration, activator concentration, reactor configuration, reactor volume or any combination thereof. For example, in some embodiments, the polyolefin is polyethylene and the olefin is ethylene.

[39] In some embodiments, the proposed method further includes c) adjusting one or more n input variables I ¹ - I ⁿ in a plurality of polymerization reactors using a polymerization reactor system to produce a plurality of olefin polymers and measuring each of the m output variables R ¹ - R ^m as a function of the input variables for each olefin polymer; d) analyzing the change in each of the output variables R ¹ - R ^m as a function of the input variables I ¹ - I ⁿ to determine the coefficients in accordance with the following general equation for each output variable R ¹ - R ^m :

[40] In some embodiments, the general equation for each output variable R ¹ - R ^m is

(product of a unique combination of 2 from I ¹ - I ⁿ , chosen independently),

where v' represents the total number of unique combinations of any 2 of I ¹ - I ⁿ , independently selected.

[41] In some embodiments, the general equation for each output variable R ¹ - R ^m is

(product of a unique combination of 2 from I ¹ - I ⁿ , chosen independently)

(product of a unique combination of 3 of I ¹ - I ⁿ , chosen independently),

where v' represents the total number of unique combinations of any 2 of I ¹ - I ⁿ selected independently; and w' represents the total number of unique combinations of any 3 of I ¹ - I ⁿ independently selected.

[42] In some embodiments, the general equation for each output variable R ¹ - R ^m is

(product of a unique combination of 2 from I ¹ - I ⁿ , chosen independently)

(product of a unique combination of 3 from I ¹ - I ⁿ , chosen independently)

(product of a unique combination of 4 from I ¹ - I ⁿ , chosen independently),

where v' represents the total number of unique combinations of any 2 of I ¹ - I ⁿ selected independently; and w' represents the total number of unique combinations of any 3 of I ¹ - I ⁿ independently selected; and x' represents the total number of unique combinations of any 4 of I ¹ - I ⁿ independently selected.

[43] In some embodiments, the general equation for each output variable R ¹ - R ^m can be extended to unique combinations of n pieces I ¹ - I ⁿ selected independently.

[44] In some embodiments, the proposed method further includes e) calculating a Response Surface Model (RSM) using general equations for each output variable R ¹ - R ^m (R ^{1 - m} ) defined in step d), to correlate any combination of n input variables I ¹ - I ⁿ with one or more of m output variables R ¹ - R ^m ; f) applying n selected input variables I ^s1 , I ^s2 , I ^s3 , … I ^sn to the estimated response surface model (RSM) to predict one or more of the m target output variables, R ^t1 , R ^t2 , R ^t3 , … R ^tm , each target output variable corresponds to a measurable property of the polymer; and g) applying n selected input variables I ^s1 - I ^sn to operate the olefin polymerization reactor system and produce a polyolefin product. For example, in some embodiments, the response surface model may be as in DesLauriers et al., Mapping the Structure-Property Space of Bimodal Polyethylenes Using Response Surface Methods. Part 1: Digital Data Investigation, Macromol. React. Eng. 2018, 170066 (“DesLauriers”), the entire contents of which are incorporated herein by reference.

[45] For example, in some embodiments, the RSM includes a digital catalyst described in DesLauriers. In this context, "digital catalyst" is widely used to describe mathematical models that can be implemented on a computer to predict catalyst performance, including the rate of homopolymerization on the catalyst, the molar balance for precatalyst concentration, the rate of change of the total molar concentration of living chains, and the rate of polymerization. For example, RSM can include a digital catalyst for one type of active site or for multiple active sites, for example, to simulate polymerization using more than one metallocene catalyst, Ziegler-Natta catalysts, or Phillips catalysts.

[46] In some embodiments, RSM includes a molecular weight distribution model, such as a molecular weight distribution model including chain transfer reactions based on the Bernoulli model, and chain length distribution models based on the Flory most likely distribution. In some embodiments, the RSM includes a short-chain branching (SCB) model, for example, in some embodiments, the RSM includes a SCB model based on the Mayo-Lewis equation. In some embodiments, the RSM further includes a temperature dependence of the kinetic constants, for example, the RSM may include a temperature dependence for the kinetic constants based on the Arrhenius equation. For example, in some embodiments, the polymerization rate for a system of n single-site catalysts can be calculated using the following equation:

where k _pi represents the chain growth constant k _p for catalyst i, [M] represents the monomer concentration, K _ai represents the activation rate constant K _a for catalyst i, k _di represents the deactivation rate constant k _d for catalyst i, t represents is time, and _C0i is the initial concentration _C0 of catalyst i. In some embodiments, polymerization rate, molecular weight, and short-chain branching can be calculated using "method of moments" modeling techniques, which are described generally in Mastan et al., Method of moments: A versatile tool for deterministic modeling of polymerization kinetics , European Polymer J. 68 (2015) 139-160, the entire contents of which are incorporated herein by reference. These methods are described in more detail below in example 2.

[47] In some embodiments, the proposed method further includes the steps of: h) measuring one or more properties of the polyolefin product corresponding to m measured output variables, R ^m1 , R ^m2 , R ^m3 , … R ^mm ; and i) repeating steps a) h) to reduce the difference between the target output variables R ^t1 - R ^tm and the measured output variables R ^m1 - R ^mm .

[48] In one aspect, a method for controlling an olefin polymerization reactor system is provided, including: First, a) selecting n input variables I ¹ , I ² , I ³ , ... I ⁿ , each input variable corresponding to a process condition of the olefin polymerization process; b) defining m output variables, R ¹ , R ² , R ³ , ... R ^m , each output variable corresponding to a measurable property of the polymer, with two of the m output variables being molecular weight distribution ("MWD") and short-chain branching ("KCR"); c) adjusting one or more of the n input variables I ¹ - I ⁿ in a plurality of polymerization reactions using an olefin polymerization reactor system to produce a plurality of olefin polymers and measuring each of the m output variables R ¹ - R ^m as a function of the input variables for each olefin polymer; d) analyzing the change in each of the output variables R ¹ - R ^m as a function of the input variables I ¹ - I ⁿ to determine the coefficients in accordance with the following general equation for each output variable R ¹ - R ^m :

e) calculation of a response surface model (RSM) using general equations for each output variable R ¹ - R ^m (R ^1-m ) defined in step d), to correlate any combination of n input variables I ¹ - I ⁿ with one or more of m output variables R ¹ - R ^m ; f) applying n selected input variables I ^s1 , I ^s2 , I ^s3 , … I ^sn to the estimated response surface model (RSM) to predict one or more of the m target output variables, R ^t1 , R ^t2 , R ^t3 , … R ^tm , each target output variable corresponds to a measurable property of the polymer; and g) applying n selected input variables I ^s1 - I ^sn to operate the olefin polymerization reactor system and produce a polyolefin product.

[49] In some embodiments of the method described above, step d) analyzing the change in each of the output variables R ¹ - R ^m as a function of the input variables I ¹ - I ⁿ further includes adding to the general equation the following sum:

(product of a unique combination of 2 from I ¹ - I ⁿ , chosen independently);

where v' represents the total number of unique combinations of any 2 of I ¹ - I ⁿ , chosen independently, so that the general equation for each output variable R ¹ - R ^m is:

(product of a unique combination of 2 from I ¹ - I ⁿ , chosen independently).

[50] In other embodiments of the method described above, step d) analyzing the change in each of the output variables R ¹ - R ^m as a function of the input variables I ¹ - I ⁿ further includes adding to the general equation the following sum:

(product of a unique combination of 3 of I ¹ - I ⁿ , independently selected);

where w' represents the total number of unique combinations of any 3 of I ¹ - I ⁿ , chosen independently, so that the general equation for each output variable R ¹ - R ^m is:

(product of a unique combination of 2 from I ¹ - I ⁿ , chosen independently)

(product of a unique combination of 3 from I ¹ - I ⁿ , chosen independently).

[51] In other embodiments of the method described above, step d) of analyzing the change in each of the output variables R ¹ - R ^m as a function of the input variables I ¹ - I ⁿ further includes adding to the general equation the following sum:

(product of a unique combination of 4 from I ¹ - I ⁿ , chosen independently);

where x' represents the total number of unique combinations of any 4 of 1' - I ⁿ chosen independently, so that the general equation for each output variable R ¹ - R ^m is:

(product of a unique combination of 2 from I ¹ - I ⁿ , chosen independently)

(product of a unique combination of 3 from I ¹ - I ⁿ , chosen independently)

(product of a unique combination of 4 from I ¹ - I ⁿ , chosen independently).

[52] In some embodiments, the input variables I ¹ - I ⁿ include reactor feed rates of catalyst, cocatalyst, activator, ethylene, α-olefin comonomer, hydrogen, reactor solvent, or any combination thereof. For example, in some embodiments, an olefin polymerization reactor system uses two or more catalysts and/or two or more cocatalysts in a single reactor, and the input variables I ¹ - I ⁿ include catalyst type and catalyst concentration for each individual catalyst and/or cocatalyst type and cocatalyst concentration for each individual catalyst.

[53] In some embodiments, the olefin polymerization reactor system has a single-loop, dual-catalyst configuration. In some embodiments, the reactor system comprises two or more reactors in series, such as two reactors in series, three reactors in series, four reactors in series, etc.

[54] In some embodiments, a reactor system includes two or more reactors, and each reactor has its own set of input variables. For example, in some embodiments, the olefin polymerization reactor system has a dual-loop, dual-catalyst configuration, and each reactor has its own set of input variables I ^{1 (reactor 1)} - I ^{n (reactor 1)} and I ^{1 (reactor 2)} - I ^{n (reactor 2 )} .

[55] In some embodiments, the catalyst type is selected from a Ziegler-Natta catalyst, a metallocene catalyst, a Phillips catalyst, and a constrained geometry catalyst.

[56] In some embodiments, molecular weight distribution (MWD) data (output variable) [1] is measured or [2] obtained using a Bernoulli model.

[57] In some embodiments, short chain branching (SCB) data (output variable) [1] is measured or [2] obtained from the Mayo-Lewis equation.

[58] In some embodiments, the polyolefin product is a copolymer.

[59] In another aspect, a method is provided for controlling an olefin polymerization reactor system, comprising: a) selecting one or more m target output variables, R ^t1 , R ^t2 , R ^t3 , … R ^tm , each target output variable corresponding to a measurable property of the polymer; b) calculating n selected input variables I ^s1 , I ^s2 , I ^s3 , … I ^sn using the response surface model (RSM) of claim 1 to achieve one or more of the t target output variables, R ^t1 , R ^t2 , R ^t3 , … R ^tm ; c) using n selected input variables I ^s1 - I ^sn to operate the olefin polymerization reactor system and produce a polyolefin product; d) measuring one or more properties of the polyolefin product corresponding to m measured output variables, R ^m1 , R ^m2 , R ^m3 , ... R ^mm ; and e) repeating steps a) - d) to reduce the difference between the target output variables R ^t1 and R ^tm and the measured output variables R ^m1 - R ^mm .

[60] In some embodiments, the input variables I ¹ - I ⁿ include reactor temperature, reaction time, average residence time, ethylene concentration, α-olefin comonomer concentration, hydrogen concentration, catalyst type, catalyst concentration, cocatalyst concentration, activator concentration, configuration reactor, reactor volume, catalyst feed rate, cocatalyst feed rate, activator feed rate, ethylene feed rate, α-olefin comonomer feed rate, hydrogen feed rate, reactor solvent feed rate, or any combination thereof.

[61] In some embodiments, the olefin polymerization reactor system has a single-loop, dual-catalyst configuration in which two or more catalysts and/or two or more cocatalysts are used, and the input variables I ¹ - I ⁿ include catalyst type and catalyst concentration for each individual catalyst and/or the type of cocatalyst and the concentration of cocatalyst for each individual catalyst.

[62] In some embodiments, the olefin polymerization reactor system has a dual-loop, dual-catalyst configuration, and each reactor has its own set of factor input variables I ^{1 (reactor 1)} - I ^{n (reactor 1)} and I ^{1 (reactor 2)} - I ^{n ( reactor 2)}

[63] In some embodiments, the catalyst type is selected from a Ziegler-Natta catalyst, a metallocene catalyst, a Phillips catalyst, and a constrained geometry catalyst.

[64] In some embodiments, one or more of the desired resin properties include molecular weight distribution (MWD), short chain branching (SCB), density, Primary Structure Parameter 2 (PSP2), as described and defined in US Pat. No. 8,048,679, the full disclosure of which is incorporated herein by reference, weight average molecular weight ( _Mw ), number average molecular weight ( _Mn ), polydispersity index (“PDI”, Mw _{/ Mn} ), viscosity at given speeds (frequencies) shear, melt index at high load (MI-HI), melt index (“MI”), MI at 10 kg load (I ₁₀ ), smooth sliding value, F ratio of stick-slip value, Young’s modulus, yield strength, yield strain, cold draw ratio, strain hardening modulus, environmental stress cracking (“ESCR”), notch creep test for ESCR pipe testing (“FNCT”), PENT or NPT (notched pipe testing).

[65] Molecular weight and molecular weight distribution were determined using a PL-GPC 220 gel permeation chromatograph system (Polymer Labs, Agilent Company) equipped with an IR4 detector (Polymer Char, Spain) and three Styragel HMW-6E GPC columns (Waters, Massachusetts , USA), operating at 145°C. The flow rate of the mobile phase of 1,2,4-trichlorobenzene (TCB) containing 0.5 g/L 2,6-di-tert-butyl-4-methylphenol (BNT) was set to 1 ml/min, and the concentrations of the solutions polymer was 1.0-1.5 mg/ml, depending on the molecular weight. The sample was prepared at 150 degrees C for 4 hours with periodic and gentle stirring, then the solutions were transferred to sample flasks for sample injection. A sample injection volume of approximately 200 μL was used. To determine molecular weights and molecular weight distribution, an internal calibration method was used using Chevron Phillips Chemical Company's HDPE polyethylene resin MARLEX® BHB5003 as a broad range standard. The integral table of broad standards was determined in advance in a separate experiment using size exclusion chromatography with multi-angle laser light scattering (SEC-MLS). _Mn is the number-average molecular weight, _Mw is the weight-average molecular weight, _Mz is the z-average molecular weight, and Mp is the peak molecular weight (the position, by molecular weight, of the highest point on a molecular weight distribution curve). The IB parameter was determined from the molecular weight distribution curve (plot of dW/d(Log M) versus Log M; normalized to an area of 1) and was defined as 1/[dW/d(Log M)] _MAX . PDI was calculated as M _w /M _n .

[66] The following parameters are measured as specified. CCR is measured using Fourier transform SEC-IR. PSP2 is calculated by multiplying the area under the curve of a graph of the weighted probability of a bound molecule versus molecular weight by 100. The density of the polymer is determined in grams per cubic centimeter (g/cm ³ ) on a direct compression sample cooled at about 15°C per hour and conditioned for approximately 40 hours at room temperature, in accordance with ASTM D1505 and ASTM D4703.

[67] Melt index (MI, g/10 min) is measured by measuring the flow rate of molten resin through a 0.0825 inch (2.1 mm) diameter orifice, in accordance with ASTM D1238 at 190° C., weighing 2.160 grams. Melt index under 10 kg load (I ₁₀ , dg/min) reflects the rate of flow of molten resin through a 0.0825 inch (2.1 mm) diameter hole under a specified load (10 kg) at 190°C, measured in accordance with ASTM D1238. In some embodiments, the polyolefin has an I ₁₀ of from about 0.5 dg/min to about 4 dg/min, alternatively from about 1 dg/min to about 3 dg/min, or alternatively from about 1.5 dg/min to about 2 dg/min. .5 dg/min.

[68] High Load Melt Index (HL-HI, dg/min) is measured by measuring the flow rate of molten resin through a 0.0825 inch (2.1 mm) diameter orifice under a 21.6 kg load at 190°C, at in accordance with ASTM D1238. In some embodiments, the polyolefin has an IR-VH of from about 5 dg/min to about 15 dg/min, alternatively less than about 15 dg/min, alternatively less than about 12 dg/min, or alternatively less than about 10 dg/min.

[69] Viscosity is measured by dynamic frequency measurements or capillary extrusion experiments. For example, for dynamic frequency measurements, samples of polymer beads can be pressed into a mold at 182° C. for a total of about 3 minutes. The samples can then be left to melt at relatively low pressure for 1 minute and then subjected to high molding pressure for a further 2 minutes. The molded specimens can then be quenched in a cold press (room temperature) and the cast plates can then be stamped into discs of approximately 25.4 mm in diameter for measurement on a rotary rheometer. Measurements can be made on parallel plates with a diameter of 25 mm at 190°C using a load-controlled rheometer equipped with an aerostatic support system, such as the Physica MCR-500 from Anton Paar. The rheometer chamber can then be purged with nitrogen to minimize oxidative decomposition. After thermal equilibration, the samples can be clamped between plates to a thickness of 1.6 mm and the excess trimmed off. Testing can then be carried out under dynamic frequency variation with 1-10% stretch in LVE mode at angular frequencies from 0.0316 to 316 rad/s.

[70] Capillary extrusion experiments can be carried out at 190°C using a double-barrel capillary rheometer such as the Rosand RH-7 from Malvern, operating in constant speed mode. You can use a capillary head with a diameter of 1 mm and a length of 16 mm and a mouthpiece with a diameter of 1 mm. For example, the entry angle for the heads may be approximately 180°, and the taper ratio from the tank to the head may be approximately 15. The Bagley correction and the Rabinowitz correction can be used to obtain the constant shear stress as a function of the shear rate.

[71] The smooth slip value and the F ratio of the stick slip value are measured by methods described in detail in US Pat. No. 8,771,816, the entire contents of which are incorporated herein by reference. In some embodiments, Young's modulus is measured from the slope of a stress-strain curve generated during tensile tests performed on a sample of the material, as determined in accordance with ASTM D638. In some embodiments, yield strain is measured according to ASTM D638. In some embodiments, the cold draw ratio is measured according to ASTM D638. In some embodiments, the strain hardening modulus is measured according to ISO 18488 using pressed tensile specimens having a nominal thickness of 0.3 mm. In some embodiments, ESCR is measured according to ASTM D1693, Condition B, 10% Igepal. In some embodiments, FNCT is measured per ISO 16770. PENT (Pennsylvania Notch Test) is measured per ASTM F1473. NPT (notched pipe test) is measured according to ISO 13479.

[72] As described herein, in some aspects, the olefin polymerization reactor system produces more than one olefin polymer component, and one or more target resin properties include _Mw , _Mn , PDI, density, and proportion of each polymer component.

[73] In some embodiments, the viscosity at desired shear rates includes Eta(.01), Eta(.126), Eta(1.585), Eta(19.953), or Eta(251.189).

EXAMPLES

[74] The present invention is further illustrated by the following examples, which should in no way be construed as limiting the scope of the present invention. Various other aspects, embodiments, modifications, and equivalents thereof may become apparent to those skilled in the art upon reading the description herein without departing from the spirit of the present invention or the scope of the appended claims.

[75] In each of the examples below, the kinetic input variable for step 101 represented in the process diagram is shown in FIG. 1. The kinetic input variable for each of the examples below was calculated for a specific Ziegler-Natta catalyst using both the fundamental equations described above and the kinetic data obtained experimentally.

Example 1: Creating a Response Surface Method for a Two-Reactor Process

[76] Used Stat Ease software to generate seven-factor optimal design of experiments (DoE) and response surface methodology models for a two-pot process using a specific catalyst with experimentally determined kinetic properties. The input variables used are presented below in Table 1:

[77] In the above examples, any mention of input variables I ¹ - I ¹³

refers to the descriptions and units specified in Table 1.

[78] Calculated output variables (30 presented) based on

The experimentally derived kinetic data, fundamental kinetic equations, and models for the various properties described above, along with the reactor input variables, are presented below in Table 2, along with the typical uncertainty associated with each variable.

[79] Reol. vol. 1, reol. vol. 2, reol. vol. 3, reol. v. 4 and reol. v. 5 refer to points on a rheology or viscosity curve when plotting viscosity versus vibration frequency in radians per second. The values shown refer to the specific oscillation frequency when measuring viscosity. In these examples, any reference to the output variables R ¹ - R ³⁰ refers to the descriptions and units specified in Table 2.

[80] Without being limited to any particular theory, it is believed that the use of RSM allows one skilled in the art to minimize the number of experiments in a DoE while maintaining acceptable predictive ability.

Example 2: Creating Forward Models and Optimization Process Using Response Curve Methods

[81] Reactor conditions and product areas were then determined using the RSM ranges presented in Example 1. First, as described above in Example 1 and shown in the schematic representation in FIG. 1, kinetic data 101 of a particular catalyst was used as described above. reactor conditions 103 as input variables to the response surface method 109, and polymer microstructure 105 and polymer properties 107 were used as output variables to the response surface method 109. The response surface method 109 was then used to determine the predicted microstructures and properties 111 of the polymer. To optimize the selected RSM input variables, specific product targets 113 were entered into the optimization and desirability functions 115 to achieve the selected optimal reactor targets 117.

[82] 115 experimental DoEs were obtained and analyzed, presented in Table 3. The resulting DoEs are provided for polymerization conditions and primary responses for a single-catalyst, two-reactor process. This table shows individual values for the 13 input variables presented in Table 1. The change in the calculated output variables listed in Table 2 for each condition (cycle) was then correlated with the change in the value of the input response. All responses were modeled independently (30 models in this case) and ANOVA tables and DoE equations were used to predict responses.

[83] Optimization conditions were determined by calculating the desirability function provided in Stat Ease software. As will be understood by those skilled in the art, the overall desirability function (D) is calculated by assigning to each response Y _i (x) a desirability function d _i (Yi), which ranges from d _i (Y _i )=0, which means an undesirable response, to d _i (Y _i )=1, which means a very desirable response. Response transformation based on the nominal best result was used.

[84] Polymerization conditions and primary responses for the initial IV - optimal DoE (calibration setting) are presented below in Table 3, using the input variables from Table 1.

[85] The resulting ranges of output variables obtained from the presented input data, the transformations and equation forms used to smooth the data, and the resulting R-squared predictive coefficients of determination obtained by the ANOVA analysis are presented below in Table 4. The presented table shows what was obtained excellent fit for all output variables.

[86] Matching the specific properties of polyethylene produced on a laboratory scale using 0.0106 g Ziegler-Natta Cat B catalyst (Ziegler-Natta TZ300 catalyst from Total), 1 ml of 1 M triethylaluminum (TEA) solution, 0.056 lb ethylene concentration mol/ft ³ , a hexene to ethylene mass ratio of 0.69, a hydrogen to ethylene molar ratio of 0.091, and 2 L of isobutane at a reactor temperature of 90° C. (outside the DOE study) are further illustrated in FIGS. 2-4. First, FIG. 2 illustrates the process depicted in FIG. 1 from steps 101 to 105 for a specific catalysis run under a set of reactor conditions for a pilot multisite catalyst in a single reactor. In particular, FIG. 2 shows the measured molecular weight distribution (QCR data) at specific reactor conditions relative to a smooth curve (shown as a solid line) based on four centers obtained from known kinetic equations. Figure 2 shows that the kinetic equations provide excellent agreement with experimental data. The proportions of catalyst sites used to model molecular weight distribution and short-chain branching are presented below:

[87] Secondly, FIG. 3 illustrates the process depicted in FIG. 1 from steps 101 to 105 for a specific catalysis run under a set of reactor conditions for a pilot multisite catalyst in a two-reactor system detailed below in Table 4.

[88] In particular, Figure 3 shows the measured molecular weight and short-chain branching (shown in circles) relative to the five sites obtained from the kinetic equations. For this multisite dual reactor model, the equations are based on “method of moments” modeling techniques, which are described generally in Mastan et al., Method of moments: A versatile tool for deterministic modeling of polymerization kinetics, European Polymer J. 68 (2015 ) 139-160, the entire contents of which are incorporated herein by reference. More specifically, in this model, a Bernoulli-type model was adopted for the reaction equations. The overall problem included different types of deactivation, which can be distinguished or assumed to be equal to each other, for each type of catalytic site. The number of each type of center in the catalyst was considered an adjustable parameter, as was the proportion of potential centers relative to the mass of the catalyst.

[89] The specific kinetic equations used are described in more detail below. For one site, one activation reaction was included, where Cc represents a non-activated site of the catalyst, T represents an alkyl, and C represents an activated site;

[90] Deactivation (termination) reactions were modeled using the equations below, where P _n ^A represents the active chain of length n monomer units last attached to monomer A or B (indicated by a superscript). _Cd represents the deactivated center. P _n ^D is a “dead” polymer chain with a length of n monomer units. C is as described above. C _h and C _t represent the active sites of the catalyst formed by hydrogen transfer or alkyl transfer;

[91] Initiation reactions were modeled using the equations below, where A and B represent the different olefin monomers, and P ₁ ^A and P ₁ ^B represent the initial growth of the polymer with the last monomer, either A or B, attached.

[92] Chain propagation reactions were modeled using the equations below.

[93] Transfer reactions and beta-hydride elimination reactions were modeled using the equations below.

[94] In the equations presented, the starting reactants include: non-activated catalyst (Cc), ethylene (monomer A), olefin comonomer (monomer B), hydrogen (H), alkyl (T). As the reaction proceeds, the polymer chains grow and also become a reactant. The solvent carrier used in these reactions is isobutane (iC4). Differential rate equations for individual particles can be written based on the concentration of the particles, the concentration of the particles with which they react (if possible), and the reaction rate constant in general form:

[95] For polymer chains, there are many particles, since each time a monomer is added, they grow by one monomer unit. Tracking each circuit individually would be a very difficult task. At the same time, to obtain structural information, it is necessary to monitor the distribution of chains. This is solved by considering the chain distribution moments and substituting them into the differential velocity equations. Below are the moment equations for each polymer in the reaction, the last monomer added being either A or B, or the "dead" (no longer containing active sites) polymer D, indicated by a superscript. The indicator n denotes the number of monomer units in the chain, and q denotes the moment (in this case, ^{the 0th} , ^1st and 2nd ^are of interest, since they provide the ability to determine the number-average molecular weight ( _Mn = _H1 / _H0 ) and the weight-average molecular weight (M _w = H ₂ /H ₁ ) Below are the equations for the indicated moments:

[96] For moments, a differential with respect to time can be expressed, and the right-hand side of the differentiation can be placed in a sum. The moment for P _n ^A is presented below as an example:

[97] Expressions for dP _n ^A /dt, dP _n ^B /dt and dP _n ^D /dt can then be written down involving individual particles, summed according to the moment equations and rewritten. Such records are presented in more detail in Appendix A. The result is a set of rate expressions including the concentrations of each individual particle, Cc, C, Ch, Ct, A, B, H, T, as well as ^{the 0th} , ^1st and ^2nd moments for polymers chains that last reacted with A, B or “dead chains”, D (H ₀ ^A , H ₁ ^A and H ₂ ^A , H ₀ ^B , H ₁ ^B and H ₂ ^B , H ₀ ^D , H ₁ ^D and H _2D ⁾ . The said equations are presented below.

[98] Those skilled in the art will appreciate that by recording the reaction rate of each species of particle, one can arrive at a molecular balance equation for each species of particle in a given reactor system. Given a set of initial conditions, the resulting system of equations can then be solved numerically simultaneously to obtain particle concentrations as a function of time.

[99] For a batch reactor, the relative equations are those written above, without additional conditions. For a semi-batch laboratory reactor, the same is true, except when components are continuously added to the reactor to maintain a constant concentration (for example, C2=). In this case, the time differential is taken equal to zero.

[100] For an ideal continuously stirred reactor (CSTR), it is necessary to add conditions for loading and unloading components. Below is an example of a generic "X" component:

[101] Where τ represents the average residence time = V/υ ₀ (V = reactor volume, and υ0 = volume flow).

[102] For multiple sites, the inventors arrived at 5 centers (resulting in 5 Schultz-Flory distributions) that best matched the MWD for the Ziegler-Natta catalyst used (as shown in FIG. 2) and added differential equations for each additional center . Thus, for each center there is a set of differential equations presented above. The presented equations, along with the differential mass balance, were solved simultaneously using MATLAB to obtain the number of each particle species and the moments associated with each site. (In the proposed method, the particles depend on time). Then, from different points, the amount of each Schultz-Flory component and its average and spruce molecular weight can be obtained. The resulting equations also provide the ability to calculate the amount of comonomer in each component, which also allows the calculation of the CCR for each SF. At this point, the amount of each SF can be added linearly to obtain the total MMR and CCR values.

[103] The proposed method gives the same results as the near-form equation method (described in DesLauriers) when using multiple centers, but for certain reactor configurations (namely the two-loop reactor configuration) this method of moments may be simpler for implementation. To obtain the kinetic coefficients, the authors of the invention carried out several laboratory reactions (set up in a planned experiment), deconvoluted the MWD and CCR values obtained in the experiments, and fitted the model parameters to the data. The inventors then tested the proposed model using different reactor conditions in a pilot plant in ADL mode. The resulting data is used as input variables at step 101 in FIG. 1.

[104] In FIG. 3, the solid line shows the correspondence of the molecular weight distribution, and the correspondence of the short-chain branching distribution is shown by the dotted line. Figure 3 shows that the kinetic equations provide excellent agreement with the experimental data.

[105] Third, FIG. 4 depicts the method presented in FIG. 1, from steps 105 to 107, for the viscosity curve obtained from the model using the molecular weight distribution compared to the data used as input variables. In the figure shown, the molecular weight distribution predicted by Soares-type moment models was used as input to the rheology model to obtain the viscosity curve characteristics. Those skilled in the art will appreciate that models can be generated that use molecular weight distribution and short-chain branching inputs to produce various predictions for properties such as density, PSP2, PSP3*, IR-BH, I-10, IR, etc. Specifically, FIG. 4 shows the experimental viscosity data (shown as circles) and the predicted viscosity curve (shown as a solid line). As shown in Figure 4, the viscosity model shows excellent agreement with the experimental viscosity data.

[106] The literature contains a significant amount of work describing the dependence of the rheological properties of intertwined melts on their molecular weight distribution, as described, for example, in (1) M. Rubinstein and R. H. Colby, J. Chem. Phys., vol. 89, no. 8, p. 5291, 1988; (2) d. Cloizeaux, Macromolecules, vol. 23, p. 4678, 1990; (3) S. H. Wasserman and W. W. Graessley, J. Rheol, vol. 36, no. 2, p. 543, 1992; (4) J. S. Fodor, Ph.D. Thesis: Application of Normal-Mode Microdielectrometry Towards hivestigation od Diffusion and Flow-Induced Phenomena in Polymer Melts, Notre Dame, IN: University of Notre Dame, 1995; and (5) J. S. Fodor, J. R. Huljak and D. A. Hill, “Dielectric and viseoelastic normal-mode relaxation in entangle 4 polydisperse cis-polyisoprene melts,” The Journal of Chemical Physics, vol. 103, no. 13, cc. 5725-5734,1995. A theory and modeling method have been developed that allows a very reasonable prediction of the rheological properties of the melt based on the known molecular weight distribution and the correlation between relaxation time and molecular weight of the polymer. Several models have been developed based on some form of reptation theory and mixing rules that take into account the polydispersity of the system (links). It has been found that very reasonable predictions can be obtained using the double reptation model for relaxation and Tsenoglou's mixing rule, as described in S. Tsenoglou, Macromolecules, vol. 24, p. 1792,1991, the full description of which is incorporated herein by reference. This combination can be used to make predictions of rheological properties based on molecular weight distribution.

[107] The shear relaxation modulus, G(t), a known autocorrelation function for the moment in a polymer melt, Ψ(t), is represented by the following expression, where G _p is the plateau modulus,

[108] The storage modulus and loss modulus can then be calculated,

[109] As understood by those skilled in the art, Tsenoglow's mixing rule takes into account the interaction of a mixture of molecular weights and the dynamics of chain relaxation, it is defined by the following expression, where represents the fraction of particles with a certain molecular weight, and ψ(t, τ _j ,) represents the relaxation function for each type of particle depending on the characteristic relaxation time, τ _j .

[110] Then h _i is determined as the ratio of the molecular mass of the particles to the reference molecular mass M*:

[111] Without being limited to any particular theory, it is believed from the literature that the relaxation time varies depending on the molecular weight to a certain extent. For polyethylene and in this work, a suitable value of 3.4 was established (τ* = 0.00013 s, M* = 40000 g/mol, Gp = 1.34 × 10 ⁶ Pa).

[112] An attempt has been made to explain the reptation of individual chains in the melt by double reptation due to the restrictions caused by the weaves in the melt, as well as the relaxation of the weaves themselves. As a result, the following form is obtained for the autocorrelation function of individual particles:

[113] The equations for G'(ω) and G''(ω) can be transformed into the following equations, which are easier to integrate:

[114] These equations can then be evaluated taking into account the molecular weight distribution and selecting appropriate values for the controlled parameters, M* and τ*. Methods used to facilitate integration are described elsewhere, for example in J. S. Fodor's PhD thesis: Application of Normal-Mode Microdielectrometry Towards Investigation of Diffusion and Flow-Induced Phenomena in Polymer Melts, Notre Dame, Indiana: University of Notre Dame, 1995.

[115] After calculating G' and G'', the complex viscosity can be obtained,

[116] Melt index properties were then predicted using the viscosity curve results discussed above. Although there are known correlations between average molecular weight and measured melt index values, there is no strict theoretical basis for these correlations, and without being limited to any particular theory, it is believed that such correlations may become inaccurate as the molecular distribution deviates from the standard distribution shape. which was used to construct the correlation.

[117] To retain as much as possible from the viscosity prediction, melt index predictions can be obtained by first fitting the viscosity curves to the Karo-Yasada model, then using said model in a CFD simulation (e.g., using COM SOL Multiphysics®) for the simulation. flow in the device for determining the melt index. Knowing the flow profile and melt density at the exit, one skilled in the art can then perform an integral over the exit surface to obtain the amount of material leaving the surface in 10 minutes. Changing the pressure driving force in this model to match the masses used in the instrument provides the ability to predict different melt index values.

[118] The melt index die geometry was reproduced in CFD simulations according to the dimensions specified in ASTM D1238-13. The diameter of the head was set at 2.095 mm, and its length was 8 mm. The barrel diameter was set at a level slightly less than the diameter of the barrel support, at 9 mm. (The given size was 9.4742 mm, but was adjusted slightly in an attempt to obtain a prediction that better matched the original match.) The dimensions of the barrel length were considered less critical. Without being bound by any particular theory, it was believed that the length should be long enough for the flow through the head inlet to be considered steady, so 10 mm was chosen as the head length. We tested values greater and less than 10 mm and showed that the prediction was minimally sensitive to this size.

[119] The pressure created by the flow was calculated from the known mass used in the measurement divided by the surface area,

[120] The mass used determines the type of melt index: for example, 2.16 kg for IR, 21.6 kg for IR-VN. The mass and geometry can be changed to suit any type of melt index measurement required.

[121] The melt index apparatus is typically operated at 190°C for polyethylene, but the inventors added a temperature dependence in the event that it was necessary to simulate the index at a different temperature. The following expression was used for the melt density, ρ _m , where T represents the die temperature in degrees Celsius,

[122] The modeling required a composite equation relating the characteristics of the fluid under stress and strain. To do this, the Caro-Yasad (CY) model was fitted to the viscosity curve for the sample under consideration. In general, reasonable agreement was observed for the plotted curves. Multiple CY models can be used if necessary or desired. (The n parameter in this model was set to 0.1818. As a result, a sufficient match was obtained, and one parameter was removed from the fitting procedure. If necessary, it can be left as a variable parameter when fitting the viscosity curve),

[123] The measured melt index was then predicted by integrating the velocity profile over the die surface, multiplying by the density, and converting the units to g/10 min.

[124] A series of validation experiments were performed using various 1-hexene to ethylene weight ratios and ethylene concentrations as shown in FIG. 4. The model was found to fit the data well for both primary and derived responses (within the 95% limit of the prediction interval) for 7 of the 9 samples. The response surface models are shown in Figures 6 and 7. For both Figures 6 and 7, the ratio of 1-hexene to ethylene, temperature and time were set to 0.4, 130°C and 4 minutes, respectively.

[125] Below are several examples of using a two-reactor system to evaluate the direct response surface method under a wide range of variables and conditions. The input variables and values selected for these experiments are presented below in Tables 7 and 8.

[126] Output variables selected for these experiments included weight average molecular weight in the first reactor (M _w RX-1), molar average molecular weight in the first reactor (M _n RX-1), density of the first reactor product (density RX-1) in g/cm ³ , mass fraction of the final product (product of the second reactor) that leaves the first reactor (ppm RX-1), weight-average molecular weight of the product of the second reactor (M _w mixture), average molar molecular weight of the product of the second reactor ( Mn _of the mixture), PDI of the product of the second reactor (PDI of the mixture), density of the product of the second reactor (mixture density) in g/cm ³ , melt index at high load (MI-HI) of the product of the second reactor, melt flow index (MF) of the product of the second reactor and melt flow index (MI) in g/ml.

[127] The excellent correlation between observed experimental values and RSM predicted values for the reported output variables is illustrated in Figure 5.

[128] An inverse model was then created using RSM to select targets and determine the necessary polymerization conditions to achieve the targets using the numerical optimization functions contained in the RSM software (step 113 in FIG. 1).

Example 3: Inverse model using response surface method with virtual reactor

[129] Optimization/backward prediction was then performed for the two-reactor virtual system using the RSM model and desirability functions (step 115 in FIG. 1). First, a set of custom reactor variables was selected, as shown below. These variables indicate that the desired reactor temperature is 188°F, that it is desirable to minimize the amount of hydrogen added to the first reactor, and that it is desirable not to add hexene to the second reactor.

[130] A set of desired polymer properties was then obtained, including the weight average molecular weight in the first reactor (M _w RX-1), the molar average molecular weight in the first reactor (M _n RX-1), the density of the first reactor product (density RX-1) in g/cm ³ , mass fraction of the final product (product of the second reactor) that leaves the first reactor (ppm RX-1), weight-average molecular weight of the product of the second reactor (M _w mixture), average molar molecular weight of the product of the second reactor (M _n mixture), second reactor product PDI (mixture PDI), second reactor product density (mixture density) in g/cm ³ and second reactor capacity (RX-2 capacity), as detailed in the following table.

[131] All system inputs listed in Table 15 above were adjusted to remain within the model range. The desired polymer properties and their values were then entered into MATLAB® and Stat-Ease® models, which produced a variety of possible solutions for reactor parameters, ranked by desirability. The most desirable values for the target variables are shown below:

[132] Although the described method can be adapted to any system, it may be particularly useful in systems that have a higher level of complexity. [134] For example, the described method is also applicable in an ADL system, where it can eliminate the need for floc sampling in the first reactor for normal process control and reduce the time to achieve required specifications. The floc sample at the outlet of the purge column (the normal safe sampling point) can be analyzed using dynamic rheology to determine the necessary adjustments in the production process to change the molecular weight distribution in the desired direction. In dynamic rheology, the HMM (high molecular weight) polymer will dominate the low shear region of the rheology curve, and the low molecular weight polymer will dominate the high shear region. Differences in dynamic rheology relative to target across the shear rate range provide insight into molecular weight and compositional ratio uncertainties. Since each polymer is produced in a separate reactor, adjustments to the overall bimodal polymer are made in the corresponding reactor in which the portion of the polymer that requires adjustment is produced. In another aspect, the proposed methodology can be used to improve control of the properties of chromium resin systems by relating process parameters to changes in the amount of long chain branching (LCB) in the resin along with typically controlled properties of the resin, and all of these parameters are combined in the method described above.

[133] In an additional aspect, the proposed method can be used in a plant to control the transition from one type of resin to another type of resin. For example, the proposed method can be used to control a direct transition from a bimodal ADL film resin to a bimodal ADL pipe resin or from a bimodal ADL pipe resin to a bimodal ADL film resin. Such a transition may require, for example, small adjustments to the molecular weight distribution, and the proposed method may reduce switching times since the model can be tailored to specific transitions. Such methods can provide greater system flexibility, reduce the amount of substandard resin, and have a significant impact on system-wide financial performance.

ASPECTS

[134] The present invention has been described above with reference to numerous aspects and specific examples. Many variations thereof will become apparent to those skilled in the art in light of the above detailed description. All such obvious variations are included within the full intended scope of the appended claims. Other aspects of the present invention may include, but are not limited to, the following (aspects generally described as “including,” but alternatively they may “consist essentially of” or “consist of” unless specifically stated otherwise).

[135] In accordance with the first aspect of the present description, there is provided a method for controlling a polymerization reactor system, including: a) selecting n input variables I ¹ , I ² , I ³ , … I ⁿ , each input variable corresponding to a process condition of an olefin polymerization process; b) defining t output variables, R ¹ , R ² , R ³ , ... R ^m , each output variable corresponding to a measurable property of the polymer, with two of the t output variables being molecular weight distribution (MWD) and short chain branching (SCB); c) adjusting one or more of the n input variables I ¹ - I ⁿ in a plurality of polymerization reactions using an olefin polymerization reactor system to produce a plurality of olefin polymers and measuring each of the m output variables R ¹ - R ^m as a function of the input variables for each olefin polymer; d) analyzing the change in each of the output variables R ¹ - R ^m as a function of the input variables I ¹ - I ⁿ to determine the coefficients in accordance with the following general equation for each output variable R ¹ - R ^m :

e) calculation of a response surface model (RSM) using general equations for each output variable R ¹ - R ^m (R ^1-m ) defined in step d), to correlate any combination of n input variables I ¹ - I ⁿ with one or more of m output variables R ¹ - R ^m ; f) applying n selected input variables I ¹ , I ^s2 , I ^s3 , … I ^sn to the estimated response surface model (RSM) to predict one or more of the m target output variables, R ^t1 , R ^t2 , R ^t3 , … R ^tm , each target output variable corresponds to a measurable property of the polymer; and g) applying n selected input variables I ^s1 - I ^sn to operate the olefin polymerization reactor system and produce the polyolefin product

[136] In accordance with the second aspect of the present description, a method according to the first aspect is provided, characterized in that the general equation for each output variable R ¹ - R ^m is

(product of a unique combination of 2 from I ¹ - I ⁿ , chosen independently)

where v' represents the total number of unique combinations of any 2 of I ¹ - I ⁿ , independently selected.

[137] In accordance with the third aspect of the present description, a method according to the first aspect is provided, characterized in that the general equation for each output variable R ¹ - R ^m is

(product of a unique combination of 2 from I ¹ - I ⁿ , chosen independently)

(product of a unique combination of 3 of I ¹ - I ⁿ , chosen independently),

where v' represents the total number of unique combinations of any 2 of I ¹ - I ⁿ selected independently; and w' represents the total number of unique combinations of any 3 of I ¹ - I ⁿ independently selected.

[138] In accordance with the fourth aspect of the present description, a method according to the first aspect is provided, characterized in that the general equation for each output variable R ¹ - R ^m is

(product of a unique combination of 2 from I ¹ - I ⁿ , chosen independently)

(product of a unique combination of 3 from I ¹ - I ⁿ , chosen independently)

(product of a unique combination of 4 from I ¹ - I ⁿ , chosen independently),

where v' represents the total number of unique combinations of any 2 of I ¹ - I ⁿ selected independently; and w' represents the total number of unique combinations of any 3 of I ¹ - I ⁿ independently selected; and x' represents the total number of unique combinations of any 4 of I ¹ - I ⁿ independently selected.

[139] In accordance with the fifth aspect of the present description, there is provided a method according to any of the first to fourth aspects, further comprising the steps of: h) measuring one or more properties of the polyolefin product corresponding to the measured output variables, R ^m1 , R ^m2 , R ^m3 , … R ^mm ; and i) repeating steps a) - h) to reduce the difference between the target output variables R ^t1 - R ^tm and the measured output variables R ^m1 - R ^mm .

[140] In accordance with the sixth aspect of the present specification, a method according to any one of the first to fifth aspects is provided, characterized in that the step d) of analyzing the change in each of the output variables R ¹ - R ^m as a function of the input variables I ¹ - I ⁿ is additionally involves adding the following sum to the general equation:

(product of a unique combination of 2 from I ¹ - I ⁿ , chosen independently)

where v' represents the total number of unique combinations of any 2 of I ¹ - I ⁿ , chosen independently, so that the general equation for each output variable R ¹ - R ^m is:

(product of a unique combination of 2 from I ¹ - I ⁿ , chosen independently)

[141] In accordance with the seventh aspect of the present description, a method according to the sixth aspect is proposed, characterized in that step d) analyzing the change in each of the output variables R ¹ - R ^m as a function of the input variables I ¹ - I ⁿ further includes adding to the total equation of the following sum:

(product of a unique combination of 3 from I ¹ - I ⁿ , chosen independently)

where w' represents the total number of unique combinations of any 3 of I ¹ - I ⁿ , chosen independently, so that the general equation for each output variable R ¹ - R ^m is:

(product of a unique combination of 2 from I ¹ - I ⁿ , chosen independently)

(product of a unique combination of 3 from I ¹ - I ⁿ , chosen independently).

[142] In accordance with the eighth aspect of the present description, a method according to the seventh aspect is proposed, characterized in that step d) of analyzing the change in each of the output variables R ¹ - R ^m as a function of the input variables I ¹ - I ⁿ further includes adding to the total equation of the following sum:

(product of a unique combination of 4 from I ¹ - I ⁿ , chosen independently),

where x ¹ represents the total number of unique combinations of any 4 of I ¹ - I ⁿ , chosen independently, so that the general equation for each output variable R ¹ - R ^m is:

(product of a unique combination of 2 from I ¹ - I ⁿ , chosen independently)

(product of a unique combination of 3 from I ¹ - I ⁿ , chosen independently)

(product of a unique combination of 4 from I ¹ - I ⁿ , chosen independently).

[143] In accordance with the ninth aspect of the present description, there is provided a method according to any of the first to eighth aspects, characterized in that the input variables I ¹ - I ⁿ include reactor temperature, reaction time, average residence time, ethylene concentration, α-olefin concentration comonomer, hydrogen concentration, catalyst type, catalyst concentration, cocatalyst concentration, activator concentration, reactor configuration, reactor volume, or any combination thereof.

[144] In accordance with the tenth aspect of the present description, there is provided a method according to any of the first through ninth aspects, characterized in that the input variables I ¹ - I ⁿ include feed rates into the reactor of catalyst, cocatalyst, activator, ethylene, α-olefin comonomer, hydrogen, reactor solvent, or any combination thereof.

[145] According to an eleventh aspect of the present specification, a process according to any of the first to tenth aspects is provided, characterized in that the olefin polymerization reactor system uses two or more catalysts and/or two or more cocatalysts in one reactor, and the input variables I ¹ - I ⁿ include the catalyst type and catalyst concentration for each individual catalyst and/or the cocatalyst type and cocatalyst concentration for each individual catalyst.

[146] According to a twelfth aspect of the present specification, there is provided a process according to any one of the first to eleventh aspects, characterized in that the olefin polymerization reactor system has a single loop dual catalyst configuration.

[147] According to a thirteenth aspect of the present specification, a method according to any one of the first to eleventh aspects is provided, wherein the reactor system comprises two or more reactors arranged in series.

[148] According to a fourteenth aspect of the present specification, there is provided a process according to any one of the first through eleventh or thirteenth aspects, characterized in that the olefin polymerization reactor system has a dual-loop dual-catalyst configuration and each reactor has its own set of ^reactor input variables ¹⁾ - I ^{n (reactor 1)} and I ^{1 (reactor 2)} - I ^{n (reactor 2)}

[149] According to the fifteenth aspect of the present specification, there is provided a process according to any one of the first to fourteenth aspects, characterized in that the type of catalyst is selected from a Ziegler-Natta catalyst, a metallocene catalyst, a Phillips catalyst, or a constrained geometry catalyst.

[150] According to a sixteenth aspect of the present specification, a method according to any one of the first to fifteenth aspects is provided, characterized in that molecular weight distribution (MWD) data (output variable) [1] is measured or [2] obtained using a model Bernoulli.

[151] In accordance with the seventeenth aspect of the present specification, there is provided a method according to any one of the first to sixteenth aspects, characterized in that the short chain branching (SCB) data (output variable) [1] is measured or [2] obtained using the Mayo equation Lewis.

[152] According to the eighteenth aspect of the present specification, there is provided a method according to any one of the first to seventeenth aspects, characterized in that the polyolefin product is a copolymer.

[153] In accordance with the nineteenth aspect of the present description, there is provided a method for controlling a polymerization reactor system, comprising: a) selecting one or more m target output variables, R ^t1 , R ^t2 , R ^t3 , ... R ^tm , each target output variable corresponding to a measurable properties of the polymer; b) calculating n selected input variables I ^s1 , I ^s2 , I ^s3 , … I ^sn using the response surface model (RSM) of claim 1 to achieve one or more of the m target output variables, R ^t1 , R ^t2 , R ^t3 , … R ^tm ; c) using n selected input variables I ^s1 - I ^sn to operate the olefin polymerization reactor system and produce a polyolefin product; d) measuring one or more properties of the polyolefin product corresponding to the measured output variables, R ^m1 , R ^m2 , R ^m3 , ... R ^mm ; and e) repeating steps a) - d) to reduce the difference between the target output variables R ^t1 and R ^tm and the measured output variables R ^m1 - R ^mm .

[154] In accordance with the twentieth aspect of the present description, there is proposed a method according to the nineteenth aspect, characterized in that the input variables I ¹ - I ⁿ include reactor temperature, reaction time, average residence time, ethylene concentration, α-olefin comonomer concentration, hydrogen concentration , catalyst type, catalyst concentration, cocatalyst concentration, activator concentration, reactor configuration, reactor volume, catalyst feed rate, cocatalyst feed rate, activator feed rate, ethylene feed rate, α-olefin comonomer feed rate, hydrogen feed rate, solvent feed rate for reactor or any combination thereof.

[155] According to the twenty-first aspect of the present specification, there is provided a process according to any of the nineteenth or twentieth aspects, wherein the olefin polymerization reactor system has a single-loop, dual-catalyst configuration in which two or more catalysts and/or two or more cocatalysts in one reactor, and the input variables I ¹ - I ⁿ include catalyst type and catalyst concentration for each individual catalyst and/or cocatalyst type and cocatalyst concentration for each individual catalyst.

[156] In accordance with the twenty-second aspect of the present description, there is provided a method according to any of the nineteenth or twentieth aspects, characterized in that the olefin polymerization reactor system has a dual-loop dual-catalyst configuration and each reactor has its own set of input variables I ^{1 (reactor 1 )} - I ^{n (reactor 1)} and I ^{1 (reactor 2)} - I ^{n (reactor 2)} .

[157] According to the twenty-third aspect of the present specification, a method according to any one of the nineteenth to twenty-second aspects is provided, wherein the type of catalyst is selected from a Ziegler-Natta catalyst, a metallocene catalyst, a Phillips catalyst, or a constrained geometry catalyst.

[158] According to the twenty-fourth aspect of the present specification, there is provided a method according to any one of the nineteenth to twenty-third aspects, characterized in that one or more of the target properties of the resin include molecular weight distribution (MWD), short chain branching (SCB), density, PSP2, M _w , M _n , PDI, viscosity at given shear rates (frequencies), IR-VN, I ₁₀ , IR, smooth sliding value, stick-slip value ratio F, Young's modulus, yield strength, yield strain, cold drawing degree , strain hardening modulus, ESCR, FNCT, PENT or NPT.

[159] According to the twenty-fifth aspect of the present specification, there is provided a method according to the twenty-fourth aspect, characterized in that more than one olefin polymer component is produced in the olefin polymerization reactor system, and one or more of the desired resin properties include _Mw , _Mn , PDI , density and proportion of each polymer component.

[160] In accordance with the twenty-sixth aspect of the present description, there is provided a method according to any of the twenty-fourth or twenty-fifth aspects, characterized in that the viscosity at given shear rates (frequencies) includes Eta(.01), Eta(.126), Eta (1.585), Eta(19.953) or Eta(251.189).

[161] According to the twenty-seventh aspect of the present specification, there is provided a method according to any one of the nineteenth to twenty-sixth aspects, wherein the polyolefin product is a copolymer.

Claims (69)

1. A method for controlling an olefin polymerization reactor system, comprising: a) selection of n input variables I ¹ , I ² , I ³ , ... I ⁿ , with each input variable corresponding to the technological condition of the olefin polymerization process; b) defining m output variables R ¹ , R ² , R ³ , ... R ^m , each output variable corresponding to a measurable property of the polymer, two of the m output variables being molecular weight distribution (MWD) and short chain branching (SCB); c) adjusting one or more of the n input variables I ¹ - I ⁿ in a plurality of polymerization reactions using an olefin polymerization reactor system to produce a plurality of olefin polymers and measuring each of the m output variables R ¹ - R ^m as a function of the input variables for each olefin polymer; d) analysis of the change in each of the output variables R ¹ - R ^m as a function of the input variables I ¹ - I ⁿ to determine the coefficients C ⁰ and C ^u for u=1-n in accordance with the following general equation for each output variable R ¹ - ^Rm : e) calculating a response surface model (RSM) using the general equations for each output variable R ¹ - R ^m (R ^1-m ) defined in step d), to correlate any combination of n input variables I ¹ - I ⁿ with one or more of m output variables R ¹ - R ^m ; f) applying n selected input variables I ^s1 , I ^s2 , I ^s3 , … I ^sn to the calculated response surface model (RSM) to predict one or more of the m target output variables R ^t1 , R ^t2 , R ^t3 , … R ^tm , wherein each target output variable corresponds to a measurable property of the polymer; And g) applying n selected input variables I ^s1 - I ^sn to operate the olefin polymerization reactor system and produce a polyolefin product. 2. The method according to claim 1, in which the general equation for each output variable R ¹ - R ^m is (product of a unique combination of 2 of I ¹ - I ⁿ , chosen independently), where v' represents the total number of unique combinations of any 2 of I ¹ - I ⁿ , chosen independently. 3. The method according to claim 1, in which the general equation for each output variable R ¹ - R ^m is (product of a unique combination of 2 of I ¹ - I ⁿ , chosen independently) (product of a unique combination of 3 of I ¹ - I ⁿ , chosen independently), where v' represents the total number of unique combinations of any 2 of I ¹ - I ⁿ , independently selected; and w' represents the total number of unique combinations of any 3 of I ¹ - I ⁿ , independently selected. 4. The method according to claim 1, in which the general equation for each output variable R ¹ - R ^m is (product of a unique combination of 2 of I ¹ - I ⁿ , chosen independently) (product of a unique combination of 3 of I ¹ - I ⁿ , chosen independently) (product of a unique combination of 4 of I ¹ - I ⁿ , independently selected), where v' represents the total number of unique combinations of any 2 of I ¹ - I ⁿ , independently selected; w' represents the total number of unique combinations of any 3 of I ¹ - I ⁿ , independently selected; and x' represents the total number of unique combinations of any 4 of I ¹ - I ⁿ selected independently. 5. The method according to claim 1, additionally including the steps: h) measuring one or more properties of the polyolefin product corresponding to m measured output variables R ^m1 , R ^m2 , R ^m3 , ... R ^mm ; And i) repeating steps a) - h) to reduce the difference between the target output variables R ^t1 - R ^tm and the measured output variables R ^m1 - R ^{m tn} . 6. The method according to claim 1, in which step d) analyzing the change in each of the output variables R ¹ - R ^m as a function of the input variables I ¹ - I ⁿ additionally includes adding the following sum to the general equation: (product of a unique combination of 2 of I ¹ - I ⁿ , independently selected); where v' represents the total number of unique combinations of any 2 of I ¹ - I ⁿ , chosen independently, so that the overall equation for each output variable R ¹ - R ^m is (product of a unique combination of 2 of I ¹ - I ⁿ , chosen independently). 7. The method according to claim 6, in which step d) analyzing the change in each of the output variables R ¹ - R ^m as a function of the input variables I ¹ - I ⁿ additionally includes adding the following sum to the general equation: (product of a unique combination of 3 of I ¹ - I ⁿ , independently selected); where w' represents the total number of unique combinations of any 3 of I ¹ - I ⁿ , chosen independently, so that the general equation for each output variable R ¹ - R ^m is (product of a unique combination of 2 of I ¹ - I ⁿ chosen independently) (product of a unique combination of 3 of I ¹ - I ⁿ , chosen independently). 8. The method according to claim 7, in which step d) analyzing the change in each of the output variables R ¹ - R ^m as a function of the input variables I ¹ - I ⁿ additionally includes adding to the general equation the following sum: (product of a unique combination of 4 of I ¹ - I ⁿ , independently selected); where x' represents the total number of unique combinations of any 4 of I ¹ - I ⁿ , chosen independently, so that the overall equation for each output variable R ¹ - R ^m is (product of a unique combination of 2 of I ¹ - I ⁿ , chosen independently) (product of a unique combination of 3 of I ¹ - I ⁿ , chosen independently) (product of a unique combination of 4 of I ¹ - I ⁿ , chosen independently). 9. The method of claim 1, wherein the input variables I ¹ - I ⁿ include reactor temperature, reaction time, average residence time, ethylene concentration, α-olefin comonomer concentration, hydrogen concentration, catalyst type, catalyst concentration, cocatalyst concentration, concentration activator, reactor configuration, reactor volume, or any combination thereof. 10. The method of claim 1, wherein the input variables I ¹ - I ⁿ include rates of catalyst, cocatalyst, activator, ethylene, α-olefin comonomer, hydrogen, reactor solvent, or any combination thereof. 11. The method of claim 1, wherein the olefin polymerization reactor system uses two or more catalysts and/or two or more cocatalysts in a single reactor, and the input variables I ¹ - I ⁿ include catalyst type and catalyst concentration for each individual catalyst and /or the type of cocatalyst and the concentration of cocatalyst for each individual catalyst. 12. The method of claim 1, wherein the olefin polymerization reactor system has a single-loop, dual-catalyst configuration. 13. The method according to claim 1, wherein the reactor system contains two or more reactors arranged in series. 14. The method according to claim 1, wherein the olefin polymerization reactor system has a two-loop configuration with a dual catalyst, and each reactor has its own set of input variables I ^{1 (Reactor 1)} - I ^{n (reactor 1)} and I ^{1 (reactor 2)} - I ^{n(reactor 2)} . 15. The method of claim 9, wherein the catalyst type is selected from a Ziegler-Natta catalyst, a metallocene catalyst, a Phillips catalyst, or a constrained geometry catalyst. 16. The method of claim 1, wherein the molecular weight distribution (MWD) data as an output variable is [1] measured or [2] obtained using a Bernoulli model. 17. The method of claim 1, wherein the short chain branching (SCB) data as an output variable is [1] measured or [2] obtained using the Mayo-Lewis equation. 18. The method of claim 1, wherein the polyolefin product is a copolymer. 19. A method for controlling an olefin polymerization reactor system, comprising: a) selecting one or more of m target output variables R ^t1 , R ^t2 , R ^t3 , ... R ^tm , each target output variable corresponding to a measurable property of the polymer; b) calculating n selected input variables I ^s1 , I ^s2 , I ^s3 , … I ^sn using the calculated response surface model (RSM) of claim 1 to achieve said one or more of the m target output variables R ^t1 , R ^t2 , R ^t3 , … R ^tm ; c) applying n selected input variables I ^s1 - I ^sn to operate the olefin polymerization reactor system and produce a polyolefin product; d) measuring one or more properties of the polyolefin product corresponding to m measured output variables R ^m1 , R ^m2 , R ^m3 , ... R ^mm ; And e) repeating steps a) - d) to reduce the difference between the target output variables R ^t1 - R ^tm and the measured output variables R ^m1 - R ^mm . 20. The method of claim 19, wherein the input variables I ¹ - I ⁿ include reactor temperature, reaction time, average residence time, ethylene concentration, α-olefin comonomer concentration, hydrogen concentration, catalyst type, catalyst concentration, cocatalyst concentration, concentration activator, reactor configuration, reactor volume, catalyst feed rate, cocatalyst feed rate, activator feed rate, ethylene feed rate, α-olefin comonomer feed rate, hydrogen feed rate, reactor solvent feed rate, or any combination thereof. 21. The method of claim 19, wherein the olefin polymerization reactor system has a single-loop, dual-catalyst configuration using two or more catalysts and/or two or more cocatalysts, and the input variables I ¹ - I ⁿ include catalyst type and catalyst concentration for each individual catalyst and/or the type of cocatalyst and the concentration of cocatalyst for each individual catalyst. 22. The method according to claim 19, wherein the olefin polymerization reactor system has a two-loop configuration with a dual catalyst, and each reactor has its own set of input variables I ^{1 (reactor 1)} - I ^{n (reactor 1)} and I ^{1 (reactor 2)} - I ^{n(reactor 2)} . 23. The method of claim 20, wherein the catalyst type is selected from a Ziegler-Natta catalyst, a metallocene catalyst, a Phillips catalyst, or a constrained geometry catalyst. 24. The method of claim 19, wherein said one or more target properties of the resin include molecular weight distribution (MWD), short chain branching (SCB), density, primary structure parameter 2 (PSP2), weight average molecular weight (M _w ), number average molecular weight ( _Mn ), polydispersity index (PDI), viscosity at required shear rates, melt index at high load (MI-HI), melt index (MI), MI at 10 kg load (I ₁₀ ), smooth sliding value , F-ratio Stick Slip Values, Young's Modulus, Yield Strength, Strain at Yield, Cold Draw Ratio, Strain Hardening Modulus, Environmental Cracking (ESCR), Notch Creep Test for ESCR Pipe Test (FNCT), C Test Pennsylvania Notched Pipe Test (PENT) or Notched Pipe Test (NPT). 25. The method of claim 24, wherein the olefin polymerization reactor system produces more than one olefin polymer component, and said one or more target resin properties include _Mw , _Mn , PDI, density, and proportion of each polymer component. 26. The method of claim 24, wherein the viscosity at the desired shear rates includes Eta(.01), Eta(.126), Eta(1.585), Eta(19.953) or Eta(251.189). 27. The method of claim 19, wherein the polyolefin product is a copolymer.

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