METHOD FOR CONTROLLING AN OLEFIN POLYMERIZATION REACTOR SYSTEM

Abstract

Monitoring and control of the polyolefin process. This involves methods for controlling olefin polymerization reactor systems. In some aspects, the methods include: a) selecting n input variables, each input variable corresponding to a process condition for an olefin polymerization process; b) identifying m response variables, each response variable corresponding to a measurable polymer property; c) fitting one of the more than n input variables to a plurality of polymerization reactions using the olefin polymerization reactor system, to provide a plurality of olefin polymers and measuring each of the m response variables as a function of the input variables for each olefin polymer; d) analyzing the change in each of the response variables as a function of the input variables to determine the coefficients;e) Calculate a response surface model (RSM) using general equations for each response variable determined in step d) to correlate any combination of the n input variables with one or more of the m response variables; f) Apply n selected input variables to the calculated response surface model (RSM) to predict one or more of the m target response variables, each target response variable corresponding to a measurable polymer property; g) Use the n selected input variables is1 to isn to operate the olefin polymerization reactor system and provide a polyolefin product.

Description

1 / 52 “METHOD FOR CONTROLLING AN OLEFIN POLYMERIZATION REACTOR SYSTEM” TECHNICAL FIELD OF DISSEMINATION

[0001] This application relates to systems and methods for enhanced reactor control, in particular systems and methods for enhanced control of polyolefin reactors. BACKGROUND

[0002] The properties of polyolefin depend on a number of factors, such as reactor temperature, reaction time, average residence time, olefin concentration, α-olefin comonomer concentration, hydrogen concentration, catalyst type, catalyst concentration, cocatalyst concentration, activator concentration, reactor configuration, reactor volume, and the like. Determining the conditions necessary to produce a polyolefin with the desired properties typically requires time and costly repeated testing to determine whether any particular combination of properties will produce the desired polyolefin properties.

[0003] As the complexity of the resins produced and the complexity of the processes to manufacture them have increased, there is a parallel need for a more advanced systematic method of process control. Determining the key process parameters to monitor and control becomes increasingly difficult when the desired polyolefin is a bimodal polyolefin and when more than one reactor is being used. Bimodal polyolefins with reverse comonomer composition distribution (CCD) have excellent mechanical properties, but are often particularly difficult to determine during manufacture.

[0004] Consequently, improved systems and methods for reactor control are needed. SUMMARY

[0005] This summary is provided to present various concepts in a simplified manner which are described below in the detailed description. This summary is not intended to identify necessary or essential features of the claimed subject matter, nor is it intended to limit the scope of the claimed subject matter.

[0006] This summary and the detailed description below provide Petition 870250053320, dated 06 / 25 / 2025, p. 11 / 80 2 / 52 examples are merely illustrative of the invention. Therefore, the preceding summary and the detailed description below should not be considered restrictive. Additional features or variations thereof may be provided beyond those set forth in this document, such as, for example, various combinations and subcombinations of features described in the detailed description.

[0007] In one aspect, the disclosed processes are applicable to bimodal resins produced in a single reactor using a dual catalyst system, where the production of two distinct polymers in one reactor makes the characterization of each individual polymer extremely difficult. While simple systems can use melt flow and density to control a polymerization process for targeted molecular weight distribution, the current disclosure provides methods based on process sample GPC (gel permeation chromatography), SCB (short chain branching) analysis, and dynamic rheology.

[0008] In one aspect, this disclosure provides methods based on dynamic rheology and rapid GPC to determine which process conditions to adjust to produce the targeted molecular weight distribution for dual catalyst systems in a single reactor, for example, a metallocene dual catalyst system in a single reactor. The methods were developed to input a frequency sweep of the target rheology and / or a rapid GPC of the desired polymer. The rheology and MWD obtained from a current process sample were fed into the disclosed method at regular intervals. The method would then correlate a designed experimental model, for example, a model obtained using previously collected pilot plant data, with the current reaction process conditions. Any minor corrections or deviations can be added to match the current process with the current sample.The method would then compare the current rheology and MWD to the target, calculate a trajectory, and convert that trajectory into a change in the reactor's control parameters. In one aspect, for example, the method could provide a suggestion for new control setting points under the reactor conditions. These steps would be repeated until the process sample rheology and MWD matched the target polymer rheology and MWD.

[0009] In one aspect, for the single reactor double catalyst system, while some essential reactor conditions can be maintained Petition 870250053320, dated 06 / 25 / 2025, page 12 / 80 3 / 52 constants, H2 (hydrogen pressure), temperature, and comonomer (e.g., hexane) can be varied using the disclosed method to obtain a target resin. The same basic methodology is applicable in other resin processes, for example, the Advanced Double Loop (ADL) process, although a different combination of key and manipulated parameters may be used. Therefore, the development of this model involves the use of systematically collected data along with mathematical modeling of the systems to be controlled.

[0010] In one aspect, this disclosure provides a method for controlling an olefin polymerization reactor system, wherein the method includes: a) selecting n input variables I1, I2, I3, ... In, each input variable corresponding to a process condition for an olefin polymerization process; b) identifying m response variables R1, R2, R3, ...Rm, each response variable corresponding to a measurable polymer property, where two of the m response variables are molecular weight distribution (MWD) and short chain branching (SCB); c) fit one of the more than n input variables I1a Inem to a plurality of polymerization reactions using the olefin polymerization reactor system, to provide a plurality of olefin polymers and measure each of the m response variables R1a Rm as a function of the input variables for each olefin polymer; d) analyze the change in each of the response variables R1a Rmem as a function of the input variables I1a In to determine the coefficients according to the following general equation for each response variable R1a Rm:. Ri-m=c0+ V \·(Τϋ 4—1 u = i e) Calculate a Response Surface Model (RSM) using general equations for each response variable R1a Rm(R1- m) determined in step d) to correlate any combination of the n input variables I1a In with one or more of the m response variables R1a Rm; f) Apply n selected input variables Is1, Is2, Is3, ... Isna to the calculated Response Surface Model (RSM) to predict one or more of the m target response variables, Rt1, Rt2, Rt3, ... Rtm, each target response variable corresponding to a measurable polymer property; g) Use the n selected input variables Is1a Isna to operate the olefin polymerization reactor system and provide a polyolefin product. Petition 870250053320, dated 06 / 25 / 2025, page 13 / 80 4 / 52

[0011] According to some aspects, the general equation for each response variable R1a RméRl-m= C0+VU4—iu= i + £VC^tproduct of a unique combination of 2 from I1a ln, selected independently) where ν' is the total number of unique combinations of any 2 from I1a ln, selected independently.

[0012] According to some aspects, the general equation for each response variable R1a RméRl-m= C0+VU4—iu= i + Σ p -1 ( / ''(product of a unique combination of 2 from I1a I, selected independently) + _ i Cw(product of a unique combination of 3 from I1a In, selected independently) where ν' is the total number of unique combinations of any 2 from I1a ln, independently selected; and W is the total number of unique combinations of any 3 from I1a ln, independently selected.

[0013] According to some aspects, the general equation for each response variable R1a RméRl-m= C0+yU4—iu= i + ^“(product of a unique combination of 2 from I1a ln, selected independently) + Σ w -1 (pi'product of a unique combination of 3 from I1a ln, selected independently) + Σ*-! (product of a unique combination of 4 from l1a ln, selected independently)where v' is the total number of unique combinations of any 2 from I1a ln, selected independently; W is the total number of unique combinations of any 3 from I1a ln, selected independently; ex' is the total number of unique combinations of any 4 from I1a ln, selected independently.

[0014] According to another aspect, this disclosure provides a method for controlling an olefin polymerization reactor system, wherein the method comprises: a) selecting one or more of m target response variables, Rt1, Petition 870250053320, dated 06 / 25 / 2025, page 14 / 80 5 / 52 a) Calculate n selected input variables Is1, Is2, Is3, ... Isn using Response Surface Modeling (RSM), according to claim 1, to achieve one or more of the m target response variables, Rt1, Rt2, Rt3, ... Rtm; b) Use the n selected input variables Is1 to Isn to operate the olefin polymerization reactor system and provide a polyolefin product; c) Measure one or more properties of the polyolefin product that correspond to the measured response variables, Rm1, Rm2, Rm3, ... Rmm; d) Repeat steps a) to a) reduce the difference between the target response variables Rt1 to Rtm and the measured response variables Rm1 to Rmm.

[0015] These and other aspects and embodiments in accordance with this disclosure are provided in the drawings, detailed description and claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The patent file or application contains at least one drawing executed in color. Copies of this patent publication or patent application with color drawing(s) will be provided by the Office upon request and payment of the required fee.

[0017] The following figures form part of this descriptive report and are included to demonstrate certain aspects of this disclosure. The invention can be better understood by reference to one or more of these figures in combination with the detailed description of specific aspects presented in this document.

[0018] Figure 1 illustrates a schematic overview of a direct optimization model using a response surface model according to an embodiment of the present disclosure.

[0019] Figure 2 illustrates the predicted and measured molecular weight distribution of an experimental polyolefin.

[0020] Figure 3 illustrates the predicted and measured molecular weight and short-chain branching of an experimental polyolefin.

[0021] Figure 4 illustrates the predicted and experimental viscosity of an experimental polyolefin. Petition 870250053320, dated 06 / 25 / 2025, page 15 / 80 6 / 52

[0022] Figure 5 illustrates the fitting of observed experimental data against predicted RSM values, according to one embodiment of the present disclosure.

[0023] Although the inventions disclosed in this document are susceptible to various modifications and alternative forms, only a few specific embodiments have been shown by way of example in the drawings and are described in detail below. The figures and detailed descriptions of these specific embodiments are not intended to limit the breadth or scope of the inventive concepts or the appended claims in any way. Rather, the figures and detailed written descriptions are provided to illustrate the inventive concepts to a person skilled in the art and to enable such a person to make and use the inventive concepts. DEFINITIONS

[0024] The following definitions are provided to assist those skilled in the art in understanding the detailed description of the present invention. Unless otherwise defined in this document, scientific and technical terms used in connection with the present invention shall have the meanings that are commonly understood by those skilled in the art to whom this invention pertains and, unless otherwise indicated or the context requires otherwise, these definitions apply throughout this disclosure. Furthermore, unless otherwise required by the context, singular terms shall include plurals and plural terms shall include the singular.For example, if a term is used in this disclosure but is not specifically defined in this document, the definition from the IUPAC Compendium of Chemical Terminology, 2nd Ed. (1997) may be applied, provided that such definition does not conflict with any other disclosure or definition applied in this document, or render undefined or ineffective any claim to which such definition applies. To the extent that any definition or usage provided by any document incorporated herein by reference conflicts with the definition or usage provided in this document, the definition or usage provided in this document shall prevail.

[0025] Unless explicitly stated otherwise in defined circumstances, all percentages, parts, ratios and quantities Petition 870250053320, dated 06 / 25 / 2025, page 16 / 80 7 / 52 similar values ​​used in this document are defined by weight.

[0026] Furthermore, in this context, certain features of the invention, which are, for clarity, described in this document in the context of separate aspects, may also be provided in combination in a single aspect. Conversely, several features of the invention, which are, for brevity, described in the context of a single aspect, may also be provided separately or in any subcombination.

[0027] Regarding claim transition terms or expressions, the transition term “comprising,” which is synonymous with “including,” “containing,” or “characterized by,” is inclusive or open-ended and does not exclude additional, unmentioned elements or method steps. The transition expression “consisting of” excludes any element, step, or ingredient not specified in the claim. The transition expression “essentially consisting of” limits the scope of a claim to the materials or steps specified and those that do not materially affect the basic and innovative feature(s) of the claimed invention. A claim of “essentially consisting of” occupies an intermediate ground between closed claims that are written in a “consisting of” format and fully open claims that are written in a “comprising” format.Unless otherwise indicated, when describing a compound or composition "essentially consisting of" should not be interpreted as "comprising," but is intended to describe the cited component which includes materials that do not significantly alter the composition or the method to which the term is applied. For example, an input consisting essentially of material A may include impurities typically present in a commercially produced or commercially available sample of the cited compound or composition.When a claim includes different resources and / or resource classes (for example, a method step, input resources, and / or product resources, among other possibilities), the transition terms that comprise, that essentially consist of, and that consist of apply only to the resource class for which they are used, and it is possible to have different transition terms or expressions used with different resources within a claim. For example, a method may comprise several cited steps (e.g., Petition 870250053320, dated 06 / 25 / 2025, page 17 / 80 8 / 52 other steps not mentioned) but use a catalyst system preparation consisting of specific steps and use a catalyst system comprising both mentioned and unmentioned components. Although compositions and methods are described in terms of “comprising” several components or several steps, compositions and methods may also “consist essentially of” or “consist of” several components or steps.

[0028] The articles “a” and “an” may be employed in connection with various elements and components of compositions, processes, or structures described in this document. This is merely for convenience and to provide a general sense of compositions, processes, or structures. Such a description includes “one or at least one” of the elements or components. Furthermore, as used in this document, the singular articles also include a description of a plurality of elements or components, unless it is evident from a specific context that the plural is excluded.

[0029] “Optional” or “optionally” means that the event or circumstance subsequently described may or may not occur and that the description includes cases in which the event or circumstance occurs and cases in which it does not occur.

[0030] The terms “configured for use” or “adapted for use” and similar language are used in this document to reflect that the particular structure or procedure cited is used in a system or process as disclosed in this document. For example, unless otherwise specified, a particular structure “configured for use” means that it is “configured for use in a reactor system,” including, for example, “configured for use in an olefin polymerization reactor system,” and is therefore designed, shaped, arranged, constructed, and / or adapted to effect olefin polymerization, as would have been understood by those skilled in the art.

[0031] The term “olefin” is used in this document in accordance with the definition specified by IUPAC: acyclic and cyclic hydrocarbons having one or more carbon-carbon double bonds in addition to the formal bonds in aromatic compounds. The class “olefins” includes alkenes and cycloalkenes and the corresponding polyenes. Ethylene, propylene, 1-butene, 2-butene, 1-hexene and the like are non-limiting examples of olefins. Petition 870250053320, dated 06 / 25 / 2025, p. 18 / 80 9 / 52

[0032] The terms polyolefin or polymer, as used in this document, mean a substance produced by polymerization of one or more olefins, alone or in combination with suitable comonomers, catalysts or additives. For example, a polyolefin or polymer, as used in this document, may be produced with a chromium catalyst, a metallocene catalyst, including a double metallocene catalyst, a Ziegler-Natta catalyst or combinations thereof. A polyolefin or polymer, as used in this document, may be produced in a single reactor or in a plurality of reactors in series or parallel. A polyolefin or polymer, as used in this document, may be a monomodal or multimodal polymer.

[0033] The term “about” means that quantities, sizes, formulations, parameters, and other quantities and characteristics are not and need not be exact, but may be approximate and / or larger or smaller, as desired, reflecting tolerances, conversion factors, rounding, measurement error and the like, and other factors known to those skilled in the art. In general, a quantity, size, formulation, parameter, or other quantity or characteristic is “about” or “approximate” whether or not expressly stated to be so. The term “about” also encompasses quantities that differ due to different equilibrium conditions for a composition resulting from a particular initial mixture. Whether or not modified by the term “about,” the claims include equivalents for the quantities. The term “about” may mean within 10% of the reported numerical value, or within 5% of the reported numerical value, or within 2% of the reported numerical value.

[0034] As used in this document, the terms “comprises”, “comprising”, “includes”, “contains”, “has”, “contains”, or “contains”, or any other variation thereof, are intended to encompass a non-exclusive inclusion. For example, a composition, a mixture, a process, a method, an article, or an apparatus comprising a list of elements is not necessarily limited to those elements alone, but may include other elements not expressly listed or inherent in such composition, mixture, process, method, article, or apparatus. Furthermore, unless expressly stated otherwise, “or” refers to an inclusive or and not an exclusive or. Petition 870250053320, dated 06 / 25 / 2025, p. 19 / 80 10 / 52 For example, a condition A or B is satisfied by any 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

[0035] The Figures described above and the written description of the specific structures and functions below are not presented to limit the scope of what the Applicants have invented or the scope of the appended claims. Rather, the Figures and written description are provided to teach anyone skilled in the art how to make and use the inventions for which patent protection is sought. Those skilled in the art will find that not all features of a commercial aspect of the inventions are described or shown for the sake of clarity and understanding. Persons skilled in this art will also find that developing an actual commercial aspect incorporating aspects of the present inventions will require numerous specific implementation decisions to achieve the developer's ultimate goal for the commercial aspect.Such specific implementation decisions may include, and are probably not limited to, compliance with system-related, business-related, government-related, and other constraints that may vary by specific implementation, location, and occasionally. While a developer's efforts may be complex and time-consuming in an absolute sense, such efforts will nevertheless be a routine step for those skilled in the art having the benefit of this disclosure. It should be understood that the inventions disclosed and taught in this document are susceptible to numerous and varied modifications and alternative forms. Finally, the use of a singular term, such as, but not limited to, "a / an," is not intended to limit the number of items.

[0036] In one aspect, this disclosure provides a method for monitoring and controlling a multisite catalyst in a single or multiple reactor system to produce a particular desired product structure and its resulting polymer properties, as illustrated in Figure 1. In some embodiments, these methods allow for more efficient reactor start-ups and adjustments, optimizing for the most desirable possible reactor conditions to produce a Petition 870250053320, dated 06 / 25 / 2025, page 20 / 80 11 / 52 polymer product with specific targets selected again, thus reducing out-of-specification material and maximizing reactor efficiency. In addition to product specifications, reactor specifications such as solids percentage and yield can be optimized by incorporating these parameters as response variables. The main advantage of this invention is that multiple response variables can be optimized simultaneously, thus allowing the ideal operating space for a particular specific product.

[0037] In one aspect, this disclosure provides a method for a systematic approach to a target resin in a faster and more efficient manner than conventional methods. For example, the target resin and the final product can be better defined according to a wider range of characterization parameters. For example, instead of requiring only properties such as melt index (Ml) and density to match the target resin, the entire MWD, rheology frequency scan, SCB distribution and / or LCB content can be targeted. In another aspect, the method utilizes more informative polymer characterization techniques for in-process samples to achieve a faster and more efficient approach to a target resin.

[0038] In one aspect, a method for controlling an olefin polymerization reactor system is provided including: First, a) selecting n input variables I1, I2, I3, ... In, each input variable corresponding to a process condition for an olefin polymerization process; and b) identifying m response variables, R1, R2, R3, ... Rm, each response variable corresponding to a measurable polymer property, wherein two of the m response variables are molecular weight distribution (MWD) and short chain branching (“SCB”). For example, in some embodiments, the input variables may include reactor temperature, reaction time, average residence time, olefin concentration, α-olefin comonomer concentration, hydrogen concentration, catalyst type, catalyst concentration, cocatalyst concentration, activator concentration, reactor configuration, reactor volume, or any combination thereof.For example, in some embodiments, polyolefin is polyethylene and olefin is ethylene.

[0039] In some modalities, the method also includes c) adjusting a Petition 870250053320, dated 06 / 25 / 2025, page 21 / 80 12 / 52 or more of the n input variables I1a ln in a plurality of polymerization reactions using the olefin polymerization reactor system, to provide a plurality of olefin polymers and measure each of the m response variables R1a Rm as a function of the input variables for each olefin polymer; d) analyze the change in each of the response variables R1a Rm as a function of the input variables I1a ln to determine the coefficients according to the following general equation for each response variable R1a Rm: Rl-m= C0+VU 4—lU= 1

[0040] In some modalities, the general equation for each response variable R1a RméRl-m= C0+VU4—iu= i + yP_ Cv(product of a unique combination of 2 from Pa I”, selected independently) where ν' is the total number of unique combinations of any 2 from I1a ln, independently selected.

[0041] In some modalities, the general equation for each response variable R1a RméRl-m= C0+yU4—iu= i ν' + y Cv(product of a unique combination of 2 from I1a I, selected independently) v = iw' + y Cw(product of a unique combination of 3 from I1a I”, selected independently) w = i where ν' is the total number of unique combinations of any 2 from I1a ln, independently selected; and W is the total number of unique combinations of any 3 from I1a ln, independently selected.

[0042] In some modalities, the general equation for each response variable R1a RméRl-m= C0+yU 4—iu= i Petition 870250053320, dated 06 / 25 / 2025, page 22 / 80 13 / 52 + Cp (product of a unique combination of 2 from I1a In, selected independently) V = 1 w' + Cw(product of a unique combination of 3 from I1a I, selected independently) IV = i + ΣχC*(product of a unique combination of 4 from I1a In, selected independently); where V is the total number of unique combinations of any 2 from I1a ln, selected independently; W is the total number of unique combinations of any 3 from I1a ln, selected independently; ex' is the total number of unique combinations of any 4 from I1a ln, selected independently.

[0043] In some modalities, the general equation for each response variable R1a Rm can be expanded to unique combinations of n independently selected I1a ln numbers.

[0044] In some embodiments, the method further includes e) calculating a Response Surface Model (RSM) using general equations for each response variable R1a Rm(R1-m) determined in step d) to correlate any combination of the n input variables I1a ln with one or more of the m response variables R1a Rm; f) applying n selected input variables Is1, Is2, Is3, ... Isna to the calculated Response Surface Model (RSM) to predict one or more of the m target response variables, Rt1, Rt2, Rt3, ... Rtm, each target response variable corresponding to a measurable polymer property; eg) using the n selected input variables Is1a lsn to operate the olefin polymerization reactor system and provide a polyolefin product. For example, in some modalities, the Response Surface Model may be as described 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 entirety of which is incorporated herein by reference.

[0045] For example, in some embodiments, the RSM includes a digital catalyst as described in DesLauriers. As used in this document, digital catalyst is broadly used to refer to models Petition 870250053320, dated 06 / 25 / 2025, p. 23 / 80 14 / 52 mathematical models that can be implemented on a computer to predict catalyst behavior, including the homopolymerization rate of a catalyst, the molar equilibrium for the precatalyst concentration, the rate of change for the total molar concentration of living chains, and the polymerization rate. For example, RSM can include a digital catalyst for a single type of active site or for multiple active sites, such as to model polymerization using more than one metallocene catalyst, Ziegler-Natta, or Phillips.

[0046] In some embodiments, the RSM includes a molecular weight distribution model, for example, a molecular weight distribution model that includes chain transfer reactions based on the Bernoulli model and chain length distribution models based on the Flory most probable distribution. In some embodiments, the RSM includes a short chain branching (SCB) model, for example, in some embodiments, the RSM includes an SCB model based on the Mayo-Lewis equation. In some embodiments, the RSM further includes the temperature dependence of kinetic constants, for example, the RSM may include the temperature dependence for 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 kpi is the propagation constant kp for catalyst i, [M] is the monomer concentration, Kai is the activation rate constant Ka for catalyst i, kdi is the deactivation rate constant kd for catalyst i, t is the time, and Coi is the initial concentration Co of catalyst i. In some embodiments, the polymerization rate, molecular weight, and short-chain branching can be calculated using method-of-moments modeling techniques, which are generally described in Mastan et al., Method of moments: A versatile tool for deterministic modeling of polymerization kinetics, European Polymer J. 68 (2015) 139-160, which is incorporated herein by reference in its entirety. These methods are described in more detail in Example 2 below. Petition 870250053320, dated 06 / 25 / 2025, page 24 / 80 15 / 52

[0047] In some embodiments, the method further includes the steps of: h) measuring one or more properties of the polyolefin product corresponding to the measured response variables, Rm1, Rm2, Rm3, ... Rmm; and i) repeating steps a) and a) to reduce the difference between the target response variables Rt1a and Rtm and the measured response variables Rm1a and Rmm.

[0048] In one aspect, a method for controlling an olefin polymerization reactor system is provided including: First, a) selecting n input variables I1, I2, I3, ... In, each input variable corresponding to a process condition for an olefin polymerization process; b) identifying m response variables, R1, R2, R3, ...Rm, each response variable corresponding to a measurable polymer property, where two of the m response variables are molecular weight distribution (MWD) and short chain branching (“SCB”); c) fit one of the more than n input variables I1a Inem to a plurality of polymerization reactions using the olefin polymerization reactor system, to provide a plurality of olefin polymers and measure each of the m response variables R1a Rm as a function of the input variables for each olefin polymer; d) analyze the change in each of the response variables R1a Rmem as a function of the input variables I1a In to determine the coefficients according to the following general equation for each response variable R1a Rm:. Ri-m=co + yu™cuau); 4—1 u= i e) Calculate a Response Surface Model (RSM) using general equations for each response variable R1a Rm(R1- m) determined in step d) to correlate any combination of the n input variables I1a In with one or more of the m response variables R1a Rm; f) Apply n selected input variables Is1, Is2, Is3, ... Isna to the calculated Response Surface Model (RSM) to predict one or more of the m target response variables, Rt1, Rt2, Rt3, ... Rtm, each target response variable corresponding to a measurable polymer property; g) Use the n selected input variables Is1a Isna to operate the olefin polymerization reactor system and provide a polyolefin product.

[0049] In some embodiments of the above method, step d) analyzing the change in each of the response variables R1a Rm as a function of the input variables I1a Incompensa further includes adding the following sum to Petition 870250053320, dated 06 / 25 / 2025, page 25 / 80 16 / 52 general equation: ν' + Σ Cv (product of a unique combination of 2 from I1a I”, selected independently); V-1 where ν' is the total number of unique combinations of any 2 independently selected from I1a ln, such that the general equation for each response variable R1a Rm is: Rl-m= C0+VU4— <U= 1 vf+ Σ p _! Cv(produto de uma combinação única de 2 dentre Pa I”, selecionadas independentemente).

[0050] In other embodiments of the above method, step d) analyzing the change in each of the response variables R1a Rm as a function of the input variables I1a ln further involves adding the following sum to the general equation: w' Σ _ Cw(product of a unique combination of 3 from I1a In, selected independently); W_1em where W is the total number of unique combinations of any 3 independently selected I1a ln, such that the general equation for each response variable R1a Rmsejam: Rl-m= C0+VU4— <U= 1 v1+ Σ p - i Cv(produto de uma combinação única de 2 dentre I1a I”, selecionadas independentemente) + Σ _ J (produto de uma combinação única de 3 dentre I1a I”, selecionadas independentemente).

[0051] In other embodiments of the above method, step d) analyzing the change in each of the response variables R1a Rm as a function of the input variables I1a ln further involves adding the following sum to the general equation: Σ C* (product of a unique combination of 4 from l1a In, selected independently); where x' is the total number of unique combinations of any 4 independently selected from ln, such that the general equation for each variable Petition 870250053320, dated 06 / 25 / 2025, page 26 / 80 17 / 52 of answer R1a Rmseja: Rl-m= C0+VU 4— <U= 1 + Σ _tC11(produto de uma combinação única de 2 dentre I1a I”, selecionadas independenteniente) + Σ _ j (produto de uma combinação única de 3 dentre Pa In, selecionadas independenteniente) x1+ Σ j CJ(produto de uma combinação única de 4 dentre Pa I, selecionadas independenteniente).

[0052] In some embodiments, the input variables I1a ln include feed rates to the reactor for the catalyst, cocatalyst, activator, ethylene, α-olefin comonomer, hydrogen, reactor solvent, or any combination thereof. For example, in some embodiments, the olefin polymerization reactor system uses two or more catalysts and / or two or more cocatalysts in a single reactor, and the input variables 11a ln comprise the catalyst type and catalyst concentration for each individual catalyst and / or cocatalyst type and cocatalyst concentration for each individual catalyst.

[0053] In some embodiments, the olefin polymerization reactor system is a single-circuit dual catalyst configuration. In some embodiments, the reactor system comprises two or more reactors in series, for example, two reactors in series, three reactors in series, four reactors in series, and so on.

[0054] In some embodiments, the reactor system comprises two or more reactors and each reactor includes its own set of input variables. For example, in some embodiments, the olefin polymerization reactor system is a dual-circuit configuration and each reactor has its own set of input variables |1(Reactor1) to |n(Reactor1) and |1(Reactor2) to |n(Reactor2)

[0055] In some embodiments, the catalyst type is selected from a Ziegler-Natta catalyst, a metallocene catalyst, a Phillips catalyst, or a restricted geometry catalyst.

[0056] In some embodiments, molecular weight distribution (MWD) data (response variable) are [1] measured or [2] generated using the Petition 870250053320, dated 06 / 25 / 2025, page 27 / 80 18 / 52 Bernoulli model.

[0057] In some modalities, short chain branching (SCB) data (response variable) are [1] measured or [2] generated using the Mayo-Lewis equation.

[0058] In some embodiments, the polyolefin product is a copolymer.

[0059] In another aspect, a method is provided for controlling an olefin polymerization reactor system that includes: a) selecting one or more of the m target response variables, Rt1, Rt2, Rt3, ... Rtm, each target response variable corresponding to a measurable property of the polymer; b) calculating n selected input variables Is1, Is2, Is3, ... Isn using the Response Surface Model (RSM) of claim 1, to achieve one or more of the m target response variables, Rt1, Rt2, Rt3, ... Rtm; c) using the n selected input variables Is1 to Isn to operate the olefin polymerization reactor system and provide a polyolefin product; d) measuring one or more properties of the polyolefin product corresponding to the measured response variables, Rm1, Rm2, Rm3, ... Rmm; (ee) Repeat steps (a) and (ad) to reduce the difference between the target response variables Rt1a and Rtme and the measured response variables Rm1a and Rmm.

[0060] In some embodiments, the I1a Ininclude 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, reactor solvent feed rate, or any combination thereof.

[0061] In some embodiments, the olefin polymerization reactor system is a single-circuit dual catalyst configuration using two or more catalysts and / or two or more cocatalysts and the input variables I1a Incomprehend the catalyst type and catalyst concentration for each individual catalyst and / or cocatalyst type and cocatalyst concentration for Petition 870250053320, dated 06 / 25 / 2025, page 28 / 80 19 / 52 each individual catalyst.

[0062] In some embodiments, the olefin polymerization reactor system is a dual-circuit configuration and each reactor comprises its own set of input variables I1(Reactor 1)a In(Reactor 1)e I1(Reactor 2)a In(Reactor 2).

[0063] In some embodiments, the catalyst type is selected from a Ziegler-Natta catalyst, a metallocene catalyst, a Phillips catalyst, or a restricted geometry catalyst.

[0064] In some embodiments, one or more targeted resin properties include molecular weight distribution (MWD), short chain branching (SCB), density, Primary Structure Parameter 2 (PSP2), as described and determined in U.S. Patent No. 8,048,679, the disclosure of which is incorporated by reference in its entirety, weight-average molecular weight (Mw), number-average molecular weight (Mn), polydispersity index (“PDI”, Mw / Mn), viscosity at desired shear rates (frequencies), high-load melt index (HMLI), melt index (MI), MI under a force of 10 kg (I10), Slick Stick Magnitude, Frictional Oscillation Ratio F Magnitude, Young's Modulus, Yield Stress, Yield Effort, Natural Extraction Ratio, Stress Hardening Modulus, environmental stress cracking (“ESCR”), full notched creep test for ESCR test of tubes (“FNCT”), PENT or NPT (Notched Tube Test).

[0065] Molecular weights and molecular weight distributions were obtained using a PL-GPC 220 system (Polymer Laboratory, an Agilent Company) equipped with an IR4 detector (Polymer Carbonization, Spain) and three Styragel HMW-6E GPC columns (Waters, MA) operating at 145 °C. The flow rate of the 1,2,4-trichlorobenzene (TCB) mobile phase containing 0.5 g / l 2,6-di-t-butyl-4-methylphenol (BHT) was set at 1 ml / min and the polymer solution concentrations were in the range of 1.0 to 1.5 mg / ml, depending on the molecular weight. Sample preparation was conducted at 150 °C typically for 4 h, with occasional gentle agitation, before the solutions were transferred to sample vials for injection. An injection volume of approximately 200 µl was used. The integral calibration method was used to deduce molecular weights and molecular weight distributions using a Chevron Phillips Chemical Company HDPE polyethylene resin, MARLEX® BHB5003, as the broad standard.The complete table of the broad standard was... Petition 870250053320, dated 06 / 25 / 2025, page 29 / 80 20 / 52 predetermined in a separate experiment with SEC-MALS. Mn is the number-average molecular weight, Mw is the weight-average molecular weight, Mz is the mean molecular weight, and Mp is the peak molecular weight (location, in molecular weight, of the highest point on the molecular weight distribution curve). The IB parameter was determined from the molecular weight distribution curve (plot of dW / d(Log M) vs. Log M; normalized to an area equal to 1) and is defined as 1 / [dW / d(Log M)]max. PDI is calculated as Mw / Mn.

[0066] The following parameters are measured as specified. SCB is measured by SEC-FTIR. PSP2 is calculated by multiplying the area under the curve of the weighted bonding molecule probability versus molecular weight graph by 100. Polymer density was determined in grams per cubic centimeter (g / cm3) in a compression-molded sample, cooled at approximately 15 °C per hour and conditioned for approximately 40 hours at room temperature according to ASTM D1505 and ASTM D4703.

[0067] The melt index (MI, g / 10 min) was measured by measuring the flow rate of a molten resin through a 0.20955 cm (0.0825 inch) diameter orifice as determined according to ASTM D1238 at 190 °C, weighing 2,160 grams. The melt index under a force of 10 kg (I10, dg / min) represents the flow rate of a molten resin through a 0.20955 cm (0.0825 inch) diameter orifice when subjected to the indicated force (10 kg) at 190 °C, as determined according to ASTM D1238. In some embodiments, polyolefin has an I10 of about 0.5 dg / min. to about 4 dg / min., alternatively about 1 dg / min. to about 3 dg / min. or, alternatively, about 1.5 dg / min. at about 2.5 dg / min.

[0068] The High Load Melting Index (HMLI, dg / min) is measured by measuring the flow rate of a molten resin through a 0.20955 cm (0.0825 inch) diameter orifice when subjected to a force of 21.6 kg at 190 °C according to ASTM D1238. In some embodiments, polyolefin has an HMLI of 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.

[0069] Viscosity is measured by a trace measurement of Petition 870250053320, dated 06 / 25 / 2025, p. 30 / 80 21 / 52 dynamic frequency or by capillary extrusion experiments. For example, for dynamic frequency tracking measurement, polymer pellet samples can be compression molded at 182 °C for a total of about 3 min. The samples can then be melted at a relatively low pressure for 1 min and then subjected to a high molding pressure for an additional 2 min. The molded samples can then be cooled in a cold press (room temperature) and then discs of about 25.4 mm in diameter can be stamped out of the molded slabs for measurement on a rotational rheometer. Measurements can be performed on parallel plates of 25 mm in diameter at 190 °C using a controlled stress rheometer equipped with an air support system, such as the Physica MCR-500, available from Anton Paar. The rheometer test chamber can then be purged with nitrogen to minimize oxidative degradation.After thermal equilibrium, the specimens can be squeezed between the plates to a thickness of 1.6 mm, and the excess trimmed. The dynamic frequency screening test can then be performed with 1 to 10% effort in the LVE regime at angular frequencies from 0.0316 to 316 rad / s.

[0070] Capillary extrusion experiments can be performed at 190 °C using a double-hole capillary rheometer, such as a Rosand RH-7, available near Malvern, operated in constant speed mode. A capillary die with a diameter of 1 mm and a length of 16 mm and a hole die with a diameter of 1 mm can be used. For example, the entry angle for the dies can be about 180 ° and the shrinkage ratio of the reservoir barrel to the die can be about 15. Bagley correction and Rabinowitsch correction can be applied to obtain constant shear stresses as a function of the shear rate.

[0071] The Slick Stick Magnitude and the Friction Oscillation Ratio F Magnitude are measured by the methods detailed in U.S. Patent No. 8,771,816, which is incorporated herein by reference in its entirety. In some embodiments, the Young's Modulus is measured by the slope of a stress-strain curve created during tensile tests conducted on a sample of a material, as determined in accordance with ASTM D638. In some embodiments, the Yield Strength is measured by ASTM D638. In some Petition 870250053320, dated 06 / 25 / 2025, p. 31 / 80 In 22 / 52 embodiments, the natural extraction ratio is measured by ASTM D638. In some embodiments, the stress hardening modulus is measured by ISO 18488, using compression-molded, die-cut tensile specimens that had a nominal thickness of 0.3 mm. In some embodiments, the ESCR is measured by ASTM D1693, condition B, 10% Igepal. In some embodiments, the FNCT is measured by ISO 16770. The PENT (Pennsylvania Notch Test) is measured by ASTM F1473. The NPT (Notch Tube Test) is measured by ISO 13479.

[0072] As described in this document, in some respects, the olefin polymerization reactor system produces more than one component of the olefin polymer and one or more targeted resin properties comprise Mw, Mn, PDI, density and fraction for each polymer component.

[0073] In some embodiments, the viscosity at the desired shear rates (frequencies) includes Eta (0.01), Eta (0.126), Eta (1.585), Eta (19.953) or Eta (251.189). EXAMPLES

[0074] The invention is further illustrated by the following examples, which should in no way be construed as limitations imposed on the scope of this invention. Various other aspects, embodiments, modifications and equivalents thereof may arise for someone skilled in the art after reading the description in this document, without departing from the spirit of the present invention or the scope of the appended claims.

[0075] In each of the examples below, the kinetic input for stage (101) of the schematic overview of the process is shown in Figure 1. The kinetic input for each of the examples below was calculated for a particular Ziegler-Natta catalyst, using both the fundamental equations described above and experimentally derived kinetic data. EXAMPLE 1 - RESPONSE SURFACE METHOD GENERATION FOR A TWO-REACTOR PROCESS

[0076] We used Stat Ease software to generate an optimal seven-factor design of experiments (DoE) and response surface methodology models for a two-reactor process using a specific catalyst with experimentally determined kinetic properties. The input variables Petition 870250053320, dated 06 / 25 / 2025, page 32 / 80 23 / 52 used are shown in Table 1 below: TABLE 1: INPUT VARIABLES AND VALUES Input Variable Description Units Minimum Maximum I1 Catalyst feed to the first reactor (“Cat Feed Rx 1”) kg / h (lb / h) 0.000544 (0.0012) 0.00127 (0.0028) I2 Temperature of the first reactor (“Temp Rx 1”) Degree Celsius (Degree F) 84.4 (184) 97.8 (208) P Feed of 0.5% by weight of triethylaluminum to the first reactor (“0.5% by weight of TEA Rx 1”) kg / h (lb / h) 0.113 (0.25) 0.567 (1.25) I4 Ethylene feed to the first reactor (“C2 Rx 1”) kg / h (lb / h) 13.61 (30) 20.41 (45) I5 Hexene feed weight ratio Ethylene feed ratio for the first reactor (“C6 / C2 Rx 1”) — 0.0025 0.06 I6 Hydrogen feed to ethylene feed weight ratio for the first reactor (“H2 / C2 Rx 1”) — 0 0.0014 r iC4 of the product of the first reactor (“IC4 Rx1”) kg / h (lb / h) 22.68 (50) 32.66 (72) P Temperature of the second reactor (“Temp Rx 2”) Degree Celsius (Degree F) 84.4 (184) 97.8 (208) P Feed of 0,5% by weight of triethylaluminum solution for the second reactor (“0.5% by weight of TEA Rx 2”) kg / h (lb / h) 0.2268 (0.5) 0.567 (1.25) I10 Ethylene feed for the first reactor (“C2 Rx 2”) kg / h (lb / h) 13.61 (30) 20.41 (45) I11 Weight ratio of hexene feed to ethylene feed for the second reactor (“C6 / C2 Rx 2”) — 0 0.020 I12 Weight ratio of hydrogen feed to ethylene feed for the second reactor (“H2 / C2 Rx 2”) — 0.0002 0.0038 I13 iC4 of the product of the second reactor (“iC4 Rx 2”) kg / h (lb / h) 22.68 (50) 32.66 (72)

[0077] Throughout these examples, any reference to the input variables I1a I13se refers to the detailed descriptions and units in Table 1.

[0078] The calculated response variables (30 illustrated), based on experimentally derived kinetic data, fundamental kinetic equations and various property models described above, together with the inlet reactor variables are shown in Table 2 below, along with the associated typical error. Petition 870250053320, dated 06 / 25 / 2025, page 33 / 80 24 / 52 for each variable. TABLE 2: RESPONSE VARIABLES Response Variables Description Units Typical Error + / - R1 Ethylene gas concentration in the first reactor (“C2gas1”) % by mol 1% R2 Hexene gas concentration in the first reactor (“C6gas1”) % by mol 1% R3 Hydrogen gas concentration in the first reactor (“H2gas1”) % by mol 2% R4 Ethylene gas concentration in the second reactor (“C2gas2”) % by mol 1% R5 Hexene gas concentration in the second reactor (“C6gas2”) % by mol 1% R6 Hydrogen gas concentration in the second reactor (“H2gas2”) % by mol 1% R7 Mw of the product from the first reactor (“Mw RX-T”) g / mol 8% R8 Mn of the product from the first reactor (“Mn RX-T”) g / mol 8% R9 Density of the product from the first reactor (“density RX-1”) g / cm3 0.002 R10 Weight fraction of the product from the second reactor that is from the first reactor (“Weight fraction RX-1”) _ 0.001 R11 Mw of the product from the second reactor (“Mw Mixture”) g / mol 8% R12 Mn of the product from the second reactor (“Mn Mixture”) g / mol 8% R13 PDI of the product from the second reactor (“PDI Mixture”) — 1 R14 Density of the product from the second reactor (“Mixture Density”) g / cm3 0.002 R15 % of solids in the first reactor (“Solids RX-1”) % by weight 0.2 R16 % of solids in the second reactor (“Solids RX-2”) % by weight 0.2 RI7 % yield of the first reactor (“% Yield RX-1”) % 0.2 R18 % yield of the second reactor (“% Yield RX-2”) % 0.2 R19 Flow rate of the product from the first reactor (“Productivity RX-1”) kg / h (lbs / h) 0.181 (0.4) R20 Product flow rate of the second reactor (“Productivity RX-2”) kg / h (lbs / h) 0.181 (0.4) R21 Catalyst activity polymer in g / catalyst in g 1% R22 PSP2 0.7 R23 HLMI 21.6 g / min 22% R24 110 10 g / min 22% R25 Ml 2.16 g / min 30% R26 Reo pt 1 0.01 radians / s 22% R27 Reo pt 2 0.126 radians / s 20% R28 Reo pt 3 1.585 radians / s 20% R29 Reo pt 4 19,953 radians / s 20% R30 Reo pt 5 251,189 radians / s 20%,

[0079] Reo pt 1, Reo pt 2, Reo pt 3, Reo pt 4 and Reo pt 5 each refer to points along a rheology or viscosity curve, where viscosity is measured against the oscillation frequency in radians per second. The units Petition 870250053320, dated 06 / 25 / 2025, p. 34 / 80 25 / 52 provided refer to the particular oscillation frequency at which viscosity is measured. Throughout these examples, any reference to the response variables R1 to R30 refers to the detailed descriptions and units in Table 2.

[0080] Without intending to be limited to any particular theory, it is believed that the use of RSM allows one versed in the technique to minimize the number of experiments in the DoE, while retaining an acceptable predictive capacity. EXAMPLE 2 - GENERATION OF ADVANCED MODELS AND OPTIMIZATION PROCESS USING RESPONSE SURFACE METHODS

[0081] Next, reactor conditions and product spaces were determined using the RSM ranges given in Example 1. First, as described in Example 1 above, and the schematic overview given in Figure 1, specific catalyst kinetic data (101) as previously described, reactor conditions (103) are used as input variables for the Response Surface Method (109) and polymer microstructures (105) and polymer properties (107) are used as response variables for the Response Surface Method (109). The Response Surface Method (109) is then used to determine predicted polymer microstructures and properties (111). In order to optimize the selected RSM input variables, specific product targets (113) were fed into the optimization and desirability functions (115) to arrive at the selected ideal reactor targets (117).

[0082] A sample DoE of 115 was constructed as shown in Table 3 and analyzed. This DoE is for polymerization conditions and primary responses for a one-catalyst, two-reactor process. This table shows the individual levels for the 13 input variables provided in Table 1. Changes in the calculated response variables listed in Table 2 for each (run) condition were then correlated to the change in the input response level. All responses were modeled independently (30 models in this case), and ANOVA tables and DoE equations were used to predict the responses.

[0083] The optimization conditions were determined by calculating the desired function provided in the Stat Ease software. As will be understood by one versed in the technique, the general desirability function (D) is calculated by assigning each Petition 870250053320, dated 06 / 25 / 2025, page 35 / 80 26 / 52 response Yi(x), a desirability function di(Yi) that varies between di(Yi) = 0, indicating an undesirable response, and di(Yi) = 1, indicating a highly desirable response. A response transformation based on Nominal-O-Best was used.

[0084] The polymerization conditions and primary responses for the initial ideal DoE IV (calibration set) are shown in Table 3 below, using the input variables from Table 1. TABLE 3: POLYMERIZATION CONDITIONS AND PRIMARY RESPONSES Petition 870250053320, dated 06 / 25 / 2025, page 36 / 80 27 / 52 I1 I2 P I4 P P I7 P P I10 I I12 I’3 EXECUÇÃO X103 x102 X103 X102 X10·4 1 2.80 184.0 1,5 50 6.70 1.40 50,0 185.4 1,5 37,85 0.10 0.02 50,0 2 2.80 184.0 0.25 50 6.70 0.00 50,0 208.0 0.25 50 2.00 0.02 52,0 3 1.90 187.1 0.25 33.8 4.73 0.00 50,0 185.3 0.25 30 2.00 0.38 71,7 4 2.80 208.0 1,5 44 0.65 1.40 50,0 184.0 0.25 30 0.00 0.02 72,0 5 1,67 197,2 1,19 30,3 0,65 0,55 72,0 191,6 0,98 46,2 0,00 0,02 64,4 6 1.20 197.2 0.25 30 0.65 1.40 72,0 202.1 1,5 30 2.00 0.25 55,1 7 2.80 185.6 1.11 30 6.70 0.28 72,0 184.0 0.25 34.6 0.00 0.27 72,0 8 1.20 208.0 1,5 30 6.70 0.00 50,0 184.0 0.25 44.2 2.00 0.38 56,3 9 2.49 194.6 1,5 30 3.68 0.00 54,0 204.8 0.66 33 0.00 0.38 50,0 10 2.80 198.9 1,5 40,61 6.70 0.64 60,0 189.4 0.76 50 1.94 0.10 50,0 11 2.80 184.0 1,5 50 0.65 1.40 72,0 208.0 1,5 30 2.00 0.38 50,0 12 2.80 208.0 1,5 50 1.86 0.92 50,0 208.0 0.25 50 1.30 0.38 61,4 13 2.80 204.6 0.44 47.9 5.70 0.71 65,1 184.0 1,5 49 0.00 0.02 61,1 14 2.38 208.0 1,5 30,6 6.70 1.40 54,4 196.0 0.97 50 0.00 0.38 72,0 15 1.20 208.0 0.25 30 6.70 0.00 50,0 206.1 0.71 30 2.00 0.19 50,0 16 1.20 208.0 0.25 50 6.70 1.40 50,0 184.0 1,5 50 1.90 0.38 72,0 17 1,20 208,0 1,23 50 0,65 0,00 72,0 184,3 0,25 30 2,00 0,34 72,0 18 1.20 184.0 0.25 50 0.65 1.04 72,0 184.0 0.25 30 0.05 0.02 72,0 19 2.80 208.0 1,5 30 6.70 0.00 72,0 208.0 0.25 50 2.00 0.38 72,0 20 1.20 184.0 1,5 50 6.70 0.00 72,0 184.0 0.25 50 0.46 0.02 72,0 21 2.80 208.0 1,5 30 0.95 1.40 72,0 192.6 1,5 42.2 0.98 0.18 51,1 22 1.53 208.0 1.46 39.8 2.16 1.15 52,2 201.1 1,5 30 1.92 0.38 59,5 23 1.90 202.0 0.25 50 4.19 1.40 50,0 208.0 0.83 50 0.00 0.06 72,0 24 2.60 184.0 0.25 38.4 0.65 0.63 53,4 184.0 0.25 41 1.12 0.02 50,0 25 2.80 194.6 0.41 48.5 0.65 1.40 72,0 198.9 0.25 50 1.31 0.02 50,0 26 2.76 208.0 1,5 50 0.65 0.00 54,3 203.0 1,5 49.3 2.00 0.02 72,0 27 2.80 184.0 1.12 48 4.28 0.84 63,9 194.8 0.25 38.3 2.00 0.02 72,0 28 1.89 208.0 1.05 30 6.70 0.06 63,6 185.1 1.09 30 1.73 0.02 72,0 29 2.11 208.0 0.25 42.5 0.65 1.09 59,4 208.0 0.25 34 2.00 0.07 65,3 30 1,28 208,0 1,5 50 0,65 0,13 50,0 184,0 1,5 50 0,00 0,38 50,0 31 2.80 196.5 0.25 50 0.65 0.59 50,0 191.9 1.47 30 1.53 0.20 72,0 32 1.20 184.0 0.25 50 4.95 0.09 72,0 208.0 1.19 38 2.00 0.38 72,0 33 1.20 190.2 1.46 40.4 0.65 1.40 60,5 196.0 0.25 39,2 0.00 0.18 50,0 34 2.80 208.0 0.25 50 6.70 1.40 72,0 184.0 0.25 30 2.00 0.02 50,0 35 1.20 184.0 0.25 38 0.65 1.40 50,0 208.0 0.25 50 2.00 0.38 72,0 36 1.34 196.8 1,5 50 0.65 1.40 71,8 208.0 1,5 39.2 0.86 0.16 72,0 37 2.34 206.8 0.69 34.9 0.65 0.00 66,5 208.0 0.84 50 2.00 0.36 50,4 38 2.61 197.5 1,5 50 6.70 0.28 72,0 184.0 1,5 34,97 2.00 0.38 70,6 39 2.80 208.0 0.98 50 0.65 0.99 53,1 208.0 1.16 30 0.00 0.02 50,0 40 1.92 184.0 0.84 39,7 0.65 0.60 65,7 184.0 1,5 30 0.93 0.38 50,0 41 2.80 188.3 1.36 50 5.85 1.40 72,0 184.0 0.25 50 0.00 0.38 50,0 42 2,80 198,4 1,37 30 0,65 0,21 50,0 193,8 0,25 30 2,00 0,03 53,0 43 2.80 184.0 0.25 30 0.65 1.33 50,0 184.0 0.25 50 0.00 0.38 50,0 44 2.80 208.0 0.25 30 6.70 1.40 64,3 208.0 0.25 50 0.00 0.02 51.8 45 2.38 208.0 1.5 30.6 6.70 1.40 54.4 196.0 0.97 50 0.00 0.38 72.0 46 1.20 184.0 1.15 32 6.70 0.28 50.0 184.0 0.25 30 0.00 0.02 50.0 47 2.48 205.1 0.79 32 4.89 0.96 72.0 200.1 0.25 30 1.07 0.38 50.0 48 2.80 208.0 0.25 40 3.25 1.40 50.0 184.0 1.5 50 2.00 0.38 50.0 49 2.80 208.0 0.25 30 0.65 0.00 72.0 193.0 1.5 30 0.00 0.38 72.0 50 2.80 208.0 0.25 40 3.25 1.40 50.0 184.0 1.5 50 2.00 0.38 50.0 51 2.80 184.0 1.5 50 1.01 0.00 62.1 184.0 0.56 42.3 0.30 0.02 53.3 52 2.50 184.0 0.25 41.5 3.89 0.66 72.0 199.0 0.9 36.4 0.00 0.19 50.0 53 2.80 184.0 1.38 50 6.70 0.00 72.0 208.0 1.5 50 0.00 0.09 65.1 54 1.31 195.9 0.86 50 4.22 0.00 63.1 191.2 1.5 30 0.00 0.17 63.1 55 2.80 184.0 0.25 30 0.65 0.00 72.0 184.0 201.6 0.25 37.6 0.65 0.19 50.0 184.0 1.17 43.3 1.43 0.02 61.6. Petition 870250053320, dated 06 / 25 / 2025, p. 37 / 80 28 / 52 58 2.80 193.0 1.28 30 3.83 0.00 50,0 184.0 1,5 50 1.04 0.24 69,3 59 1.72 184.0 1,5 50 6.70 0.00 72,0 197.4 0.25 30 1.30 0.38 50,0 60 1.98 206.9 0.25 40.2 6.70 0.48 72,0 207.5 0.25 42.4 2.00 0.02 50,0 61 1.98 208.0 1,5 50 6.70 0.58 72,0 207.0 0.25 37.5 0.00 0.13 60,7 62 1.20 192.6 1,5 38.8 6.70 1.40 72,0 184.0 0.32 30 1.93 0.26 69,3 63 1.20 208.0 1,4 50 3.68 1.19 69,6 184.0 0.99 36 1.12 0.02 50,6 64 1,99 188,0 1,02 50 0,65 1,40 50,0 184,0 0,58 50 1,80 0,14 62,9 65 1.20 208.0 1,5 30 6.70 1.35 50,0 208.0 1,5 47 0.00 0.02 59,1 66 1.20 195.4 0.25 50 4.40 0.79 58,9 184.0 0.25 39.3 1.89 0.31 50,0 67 1.20 208.0 0.88 49.4 6.70 1.40 72,0 200.8 0.77 50 2.00 0.30 56,2 68 1.20 184.0 0,6 30 2.22 0.00 66,2 203.2 0.26 44 1.28 0.14 59,9 69 1.20 196.0 1,5 50 6.70 0.00 50,0 208.0 0.25 30 2.00 0.02 72,0 70 1.20 196.0 0.25 30 6.70 0.00 72,0 184.0 1.33 49.6 0.32 0.38 50,0 71 1.55 197.0 0.67 30 6.61 0.75 65,1 206.2 1,5 50 2.00 0.14 71,7 72 2.16 199.1 0.34 30 5.52 1.40 51,9 184.0 1.34 30 0.15 0.22 57,6 73 2.80 208.0 0.71 45.3 6.70 0.00 50,0 185.2 0.72 36 0.52 0.33 58,0 74 1.20 208.0 1,5 30 6.70 1.35 50,0 208.0 1,5 47 0.00 0.02 59,1 75 1.92 208.0 0.25 30 0.65 0.00 66,5 184.0 0.25 30 0.00 0.02 50,0 76 1,20 184,0 0,25 47,18 6,70 1,37 55,9 202,5 1,34 30 1,67 0,02 59,0 77 1.20 184.0 0.96 47.8 5.61 0.00 50,0 194.8 1.34 50 2.00 0.27 50,0 78 2.17 202.8 0.25 50 6.70 0.89 59,9 208.0 1,5 40.5 0.87 0.35 50,0 79 1.50 184.0 1,5 34.8 1.26 0.78 72,0 193.8 1,5 50 2.00 0.38 60,6 80 1.20 184.0 0.25 45 5.67 1.40 50,0 184.0 0.63 50 0.00 0.02 50,0 81 1.50 184.0 1,5 34.8 1.26 0.78 72,0 193.8 1,5 50 2.00 0.38 60,6 82 1.20 208.0 1,5 42 4.52 0.00 67,4 208.0 1.27 49.4 0.37 0.38 69,8 83 2.31 191.6 0.52 48.5 0.65 0.00 61,0 194.8 0.38 49.4 0.15 0.38 72,0 84 1.59 184.0 0.51 30 6.70 1.40 72,0 184.0 0.26 50 2.00 0.02 50,0 85 2.10 184.0 1.14 36.9 6.28 1.40 50,0 208.0 0.46 39 1.63 0.26 50,0 86 2.53 208.0 0.49 33,3 4.34 0.00 50,0 208.0 1.28 37,8 1.71 0,38 72,0 87 1.20 190.4 0.56 40.2 6.70 0.56 54,4 208.0 0.25 50 0.00 0.38 59,2 88 1.20 184.0 1,5 30 6.70 1.31 72,0 208.0 1,5 30 0.00 0.38 50,0 89 1,20 208,0 0,25 39 6,70 1,40 72,0 203,7 1,5 30 0,00 0,02 72,0 90 2.80 198.9 0.87 30 0.65 1.40 60,8 184.0 0.87 38.4 1.94 0.38 72,0 91 1.20 184.0 1,5 30 6.70 1.31 72,0 208.0 1,5 30 0.00 0.38 50,0 92 2.80 208.0 0.75 33,3 6.70 1.40 50,0 208.0 1.5 30 2.00 0.02 72,0 93 1.20 197.2 0.56 30 6.64 1.40 50,4 192.1 0.25 40.6 1.01 0.02 72,0 94 1.20 208.0 0.81 30 0.65 0.53 50,0 208.0 0.47 36 0.28 0.28 72,0 95 2.80 198.0 0,3 44 4.22 0.00 72,0 208.0 0.68 30 0.84 0.02 69,1 96 2.09 184.0 0.74 30 0.74 0.92 55,2 208.0 1,5 50 1.00 0.02 50,0 97 1.28 184.0 1,5 50 3.61 0.82 50,0 191.7 0.78 36.2 0.25 0.38 69,8 98 2.29 184.0 1,5 30 4.49 1.40 63,9 202.5 0.49 30 0.50 0.02 63,1 99 2.80 184.0 0.25 50 6.70 1.40 55,7 208.0 0.25 30 0.00 0.38 72,0 100 2.80 184.0 0.72 30 6.70 0.00 62,2 202.1 1,5 30 2.00 0.38 50,0 101 2,40 184,0 1,5 36,4 0,65 0,04 67,5 208,0 1,16 30 1,41 0,28 72,0 102 2.00 208.0 0.25 35 2.95 0.75 72,0 184.0 0.25 50 1.34 0.22 66,5 103 1.20 184.0 1,5 30 0.65 1.40 50,0 184.0 1,5 30 2.00 0.02 72,0 104 1.69 195.3 1.32 38.9 4.31 0.00 72,0 208.0 1,5 37.3 2.00 0.02 50,0 105 1.95 184.0 1 30 1.35 1.40 72,0 208.0 0.25 48.7 0.00 0.38 72,0 106 2.80 184.0 0.25 38.1 6.70 1.40 66,7 192.5 0.94 48.2 1.32 0.34 66,9 107 1.20 184.0 0.42 37.5 2.47 1.40 62,8 184.0 1,5 50 0.00 0.20 72,0 108 1.20 208.0 1,5 30 0.65 1.40 72,0 208.0 0.25 50 2.00 0.02 50,0 109 1.20 208.0 0.25 50 0.65 0.00 72,0 208.0 1,5 50 0.00 0.02 50,0 110 1.20 208.0 1,5 37.6 3.83 0.41 62,2 199.1 0.25 30 2.00 0.16 55,0 111 1.58 208.0 0.25 50 0.65 1.40 72,0 188.8 0.78 34 0.00 0.38 57,7 112 2.10 184.0 0.25 30 6.70 0.00 50,0 204.9 1,5 38 0.00 0.02 72,0 113 1.90 208.0 0.85 39.9 3.83 0.00 50,0 196.5 0.25 50 0.58 0.02 50,0 114 2,80 184,0 1,5 35 0,65 0,63 50,0 208,0 0,25 50 0,00 0,02 72,0 115 1.20 184.0 0.25 50 0.65 0.00 50,0 208.0 0.25 30 0.22 0.38 50,0.

[0085] The resulting response variable ranges obtained from the input data, transformations used, and equation forms to fit the data, Petition 870250053320, dated 06 / 25 / 2025, page 38 / 80 29 / 52 as well as the resulting predictive R-squared obtained from ANOVA are shown in Table 4 below. As can be seen in this table, excellent fits were obtained for all response variables. Response Variable Minimum Maximum Transformation Model Fit Predicted R-squared ANOVA R1 1.21 7.00 Base 10 Log Quadratic R 0.9992 R2 0.07 1.58 Square Root Quadratic R 0.9991 R3 0.00 1.94 Square Root Quadratic R 0.9704 R4 3.02 12.70 None Quadratic R 0.9988 R5 0.02 0.98 None Quadratic R 0.9992 R6 0.07 2.92 None Quadratic R 0.9997 R7 16.872 945.957 Inverse Square Quadratic R 0.9958 R8 2.925 149.836 Inverse Square Quadratic R 0.9956 R9 0.919 0.981 None QuadraticR 0.985 R10 0.394867 0.66209 None QuadraticR 0.9998 R11 16.573 738.314 Logarithmic Base 10 QuadraticR 0.9868 R12 2.770 98.782 Logarithmic Base 10 QuadraticR 0.9805 R13 5 45 Logarithmic Base 10 QuadraticR 0.8913 R14 0.927 0.983 None QuadraticR 0.9936 R15 28 49.5 None QuadraticR 0.9999 R16 28.1 48.3 None QuadraticR 0.9998 R17 95 99.1 None QuadraticR 0.994 R18 90.3 98 None QuadraticR 0.9985 R19 28.4 49.5 None LinearR 0.9995 R20 54.8 97.5 None LinearR 0.9987 R21 2.15E + 05 8.17E + 05 Log of Base 10 QuadraticR 0.9999 R22 0.3 22.3 Power QuadraticR 0.9886 R23 9.60E - 02 8.03E + 04 Log of Base 10 QuadraticR 0.9864 R24 2.27E - 02 5.00E + 04 Log of Base 10 QuadraticR 0.989 R25 1.96E-03 1.53E + 04 Log of Base 10 QuadraticR 0.9838 R26 1.60E + 01 1.91E + 06 Log of Base 10 QuadraticR 0.9856 R27 1.60E + 01 7.86E + 05 Log of Base 10 QuadraticR 0.9865 R28 1.56E + 01 1.88E + 05 Logarithmic Base 10 QuadraticR 0.9886 R29 1.19E + 01 2.99E + 04 Logarithmic Base 10 QuadraticR 0.9908 R30 5.88E + 00 4.18E + 03 Logarithmic Base 10 QuadraticR 0.9914. TABLE 4: GENERAL ADJUSTMENTS FOR RESPONSE VARIABLES

[0086] The adjustment for particular properties of a polyethylene produced in a bench-scale process using 0.0106 grams of Cat B Ziegler Natta catalyst (TZ300 Ziegler Natta catalyst available from Total), 1 ml of a 1 M triethylaluminum (TEA) solution, 0.8970 kg / m3 (0.056 lbmol / ft3) ethylene concentration, a hexene to ethylene weight 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 still Petition 870250053320, dated 06 / 25 / 2025, p. 39 / 80 30 / 52 illustrated in Figures 2 to 4. First, Figure 2 illustrates the process of Figure 1 from stage (101) to (105) for a specific catalysis performed under a set of reactor conditions for an experimental multisite catalyst in a single reactor. Specifically, Figure 2 illustrates the measured molecular weight distribution (SCB data) under particular reactor conditions against the fit (shown as a solid line) generated by the four sites generated from known kinetic equations. As Figure 2 illustrates, the kinetic equations offer an excellent fit to the experimental data. The catalyst site fractions used to model the molecular weight distribution and short chain branching are shown below: TABLE 5: CATALYST SITE FRACTIONS Catalyst Site Number | Site Fraction | 1 | 0.100 | 2 | 0.483 | 3 | 0.298 | 4 | 0.088 | 5 | 0.031

[0087] Secondly, Figure 3 illustrates the process of Figure 1 from stage (101) to (105) for a specific catalysis performed under a set of reactor conditions for an experimental multisite catalyst in a double reactor system, as detailed in Table 4 below. TABLE 6: REACTOR CONDITIONS Input variable Value I1 1.270 kg / h (2.8 lb / h) (dry basis) I2 86.67 °C (188 °F) I7 34,020 kg / h (75,000 lb / h) I3 50 ppm I4 24,490 kg / h (54,000 lb / h) I5 16.7829 kg / Mkg (37 lb / Mlb) I6 0.003629 kg / Mkg (0.008 lb / Mlb) I8 86.67 °C (188 °F) I13 22,680 kg / h (50,000 lb / h) I9 50 ppm I10 22,000 kg / h (48,500 lb / h) In 0.02041kg / Mkg (0.045 lb / Mlb) I12 0.907185 kg / Mkg (2.0 lb / Mlb) Petition 870250053320, dated 06 / 25 / 2025, pp. 40 / 80 31 / 52

[0088] Specifically, Figure 3 illustrates the measured molecular weight and short-chain branching (shown in circles) against the five sites generated from kinetic equations. For this multi-site double reactor model, the equations were based on the method of moments modeling techniques, which are generally described in Mastan et al., Method of moments: A versatile tool for deterministic modeling of polymerization kinetics, European Polymer J. 68 (2015) 139-160, which is incorporated herein by reference in its entirety. More specifically, for this model, a Bernoulli-type model was assumed for the reaction equations. A variety of deactivation types were included in the overall formulation that can be differentiated or considered equal to each other for each catalyst site type.The quantity of each type of site in a catalyst was considered an adjustable parameter, as was the fraction of potential sites relative to the catalyst weight.

[0089] The specific kinetic equations used are described in more detail below. For a single site, we include an activation reaction, where Cc is the non-activated catalyst site, T is the alkyl group, and C is the activated site; Cc + T ^ C (activation) kka

[0090] Deactivation (termination) reactions were modeled using the equations below, where PnA is an active chain, n monomer units long, last added with monomer A or B (denoted by the superscript). Cd is a deactivated site. PnD is a dead polymer chain, n monomer units long. C is as defined above. Ch and Ct are active catalyst sites originating from a hydrogen transfer or an alkyl transfer; +, ^Cd + P° (deactivation) kda +. ^Cd + P° (deactivation) kdb C ^ Cd (deactivation) kd Ch ^ Cd (deactivation) kdh C ^ Cd (deactivation) kdt

[0091] The initiation reactions were modeled using the equations below, where A and B are different olefin monomers, and Pia and Pib are the initial growth of the polymer with the last monomer added to A and B. Petition 870250053320, dated 06 / 25 / 2025, page 41 / 80 32 / 52 C + A ^Pf (initiation) ka C + B ^ P. (initiation) kb Ch + A ^ Pj (initiation) kah Ch + B ^ Pi (initiation) kbh Ct + A ^ Pf (initiation) kat Ct + B ^ Pl (initiation) kbt

[0092] The propagation reactions were modeled using the equations below. Pn + A ^ P„+i (propagation of monomer A at the A-terminated site) kpAA Pn + B ^ Pj21 (propagation of monomer B at the A-terminated site) kpAB Pj + A ^ P*+ 1 (propagation of monomer A at the B-terminated site) kpBA Pj + B ^ Pj21 (propagation of monomer B at the B-terminated site) kpBB

[0093] Beta hydride transfer and elimination reactions were modeled using the equations below. Pn + A ^ Pi, + Pj (Transfer to monomer A at the A-terminated site) ktAA Pn + B ^ Pj + Pj (Transfer to monomer B at the A-terminated site) ktAB Pn + A ^ Pj + Pj (Transfer to monomer A at the B-terminated site) ktBA Pj + B ^ P[' + Pj (Transfer to monomer B at the B-terminated site) ktBB Pj· + H ^ Ch + Pj (Transfer to H at the A-terminated site) ktAH Pj + H ^ Ch + Pj (Transfer to H at site ending in B) ktBH Pj- + T ^ Ct + Pj (Transfer to Al at the site ending in A) ktAT Pj + T ^ Ct + Pj (Transfer to Al at site ending in B) ktBT Pj ^ Ch + Pj (Beta hydride elimination at the A-terminated site) ktA(p> Pj ^ Ch + Pj (Beta hydride elimination at the B-terminated site) ktB(p>

[0094] In these equations, the initial reactants include: the unactivated catalyst (Cc), ethylene (monomer A), olefin comonomer (monomer B), hydrogen (H), alkyl (T). As the reaction proceeds, the polymer chains grow and become a reactant as well. The carrier solvent used in these reactions is isobutane (iC4). Differential rate equations for individual species can be written based on the concentration of the species, the concentration of the species with which they are reacting (if appropriate), and a Petition 870250053320, dated 06 / 25 / 2025, page 42 / 80 33 / 52 reaction rate constant, in general form: d[species] dt = (rate constant) ^^(rea=concentration)

[0095] For polymer chains, there are many species, since each time a monomer is added, a monomeric unit grows. Tracking each chain individually would be a very arduous task. At the same time, to obtain structural information, the distribution of the chains needs to be tracked. This is handled by considering the momenta for the distribution of the chains and formulating them in differential rate equations. Below are shown the momenta equations for each polymer in the reaction, the last monomer added being A or B, or a dead polymer (site no longer active), D, denoted by the superscript. The index, n, denotes the number of monomeric units in the chain, eq denotes the momenta (in our case, we are interested in the 0°, 1° and 2°, as these will allow the determination of the number-average molecular weight (Mn = H1 / H0) and mass-average weight (Mw = H2 / H1). The equations for these momenta are shown below: Hp = ^nq[+A] n HPb= £nqMn H@D= ^ + n

[0096] The differential with respect to time can be expressed for momenta, and on the right-hand side the differentiation can be brought into the sum. Below, the moment for PnA is shown as an example: dEG _ y „ qd[AB] dt =Lnndt

[0097] The expression can then be written for dPnA / dt, dPnB / dt, and dPnD / dt, incorporating the individual species, summed according to the moment equations and reformulated. These formulations are shown in detail in Appendix A. The result is a set of rate expressions involving each of the concentrations of individual species, Cc, C, Ch, Ct, A, B, H, T, and the 0°, 1°, and 2° moment for polymer chains last reacted with A, B, or dead chains, D (H0A, HiAe H2A, H0B, HiBe H2B, H0D, HiDe H2D). These equations are Petition 870250053320, dated 06 / 25 / 2025, page 43 / 80 34 / 52 provided below. = — ka[T][Cc] — ka[C][A] - kb[C][B] - kd[C ] + ka[T][Cc] = -kah[Ch][A] - kbh[Ch][B] - kdh[Ch]+ kath[HaO][H ] + kbth[HbO][H] + kats[O] kt =[Hb][H][H] [A] - kbt[Ct][B]- kdt[Ct] + katt[HaO][T] + kbtt[HbO][T] + kd[C] + kdh[Ch] + kdt[Ct] + kda[HaO] + kdb[HbO] ^ = — ka[C][A] - kah[Ch[A]-[A][A] bwa[HaO][A] - kpba[HbO][A] - kata[HaO][A] - kbta[HbO][A] ^ = - kb[C][B] - kbh[Ch][B] - kbt[Ct][B] - kpab[HaO][B] - kpbb[HbO][B][B]-[B][B] kbtb[HbO][B] — kath[HaO][H] - kbth[HbO][H] % = - katt[HaO][T] - kbtt[HbO][T] - ka [T] [Cc] = +ka[C][A] + kab[Ch][A] + kat[Ct][A][B][Hab][O] kpba[A][WbO] - katb[B][HaO] + kbta[HbO] — kath[W][ / 7aO] - &αΓί[7Ί(ΗαΟ] - kats[HaO] - kda[WaO] = + kb[C][B] + kbh[Ch][B] + kb[C][B] + kbh[Ch][B] + kb[B][H][H] + kpnb[B][BaO] - kbta[A][HbO] + katb[B][BaO] - kbth[H][HbO] - kbtt[T][Bb0] — kbts[WbO] - kdb[HbO] = + kata[ / faO][A] + kbta[HbO] [AbO][A +[A] kbtb[HbO] [B] + kath[#aO] [W] + katt[HaO][T] + kats[WaO] + kda[BaO] + kbth[HbO][W] + kbtt[27bO][T] +kbts[HbO] + kdb[WbO] = + ka[C][A] + kah[Cb][A] + kat[Ct][A] + kpaa[HaO][A] - kpab[Hal][B] + kpba[A][[Hbl] + [BbO]] + kata[A](—[Wal] + [BnO]) + Arbta[A][ / 7bO] - katb[B][Hal] - katb[B][Hal] - katt[T][Hal] - kats[ / 7al] - kda[Hal] = + kb[C][B] + W>ft[Ch][B] + kbt[Ct][B] + kpbb[HbO][B] - kpba[Hbl][A] + kpab[B]([Hal] + [HaO]) + kbtb[B](— [Hbl] + [WbO]) + katb[B][HaO] - kbta[A][Hbl] — kbtb[H][ / 7bl] - kbtt[T][27bl] — kbts[Hbl] - kdb[Hbl] + kata[Wal][A] + kbta[Hbl][A] + katb[Wal][A] + kbtb[Hbl][B] + kathp / al] [W] + katt[Hal][T] + kats[Hal] + / cda[Hal] + kbtb[Hbl][ / 7] + kbtt[ / 7bl] [T] + kbts[Hbl] + kdb[Hbl] = +ka[C][A] + kab[Ch][A] + kat[Ct][A] + kpaa[A][(2[Wal] + [HaO]) - kpab[B][ / 7a2] + kpba[A]([Hb2] + 2[Hbl] + [HbO]) - kata[A]([Ha2] - [WaO]) + kbta[A][WbO] - katb[B][Ha2] - kath[H][Ha2] - katt[T][Ha2] - kats[HA2] - kda[Ha2] = + kb[C][B] + kbft[Ch][B] + kbt[Ct][B] + kpbb[B][(2[Hbl] + [WbO]) - kpba[A][Hb2] + kpab[B]([Ha2] + 2[Hal] + [HaO]) - / cbtb[B][([Hb2] - [HbO]) + katb[B][BaO] - kbta[A][Hb2]- kbth[H][Hb2] - kbtt[T][Hb2] - kbts[Hb2] - kdb[Hb2] = + kata[Ha2][A] + kbta[Hb2][A] + katb[Ha2][A] + kbtb[Hb2][B] + kath[Ha2] [H] + katt[Ha2][T] + kats[Wa2] + kda[Ha2] + / cbtft[Hb2][ / 7] + kbtt[Hb2][T] + kbts[Hb2] + kdb[Hb2]

[0098] As one skilled in the art will readily understand, with each formulated species reaction rate, one can arrive at a molecular equilibrium equation for each species given the reactor system. With the set of initial conditions, the resulting set of equations can then be solved numerically simultaneously to obtain the concentrations of the species as a function of time.

[0099] For a batch reactor, the relevant equations are simply those written above, without additional terms. For a bench-scale semi-batch reactor, the same is true, except for the Petition 870250053320, dated 06 / 25 / 2025, p. 44 / 80 35 / 52 components that are continuously fed to the reactor to maintain a constant concentration (e.g., C2=). For these, the differential with respect to time is defined as equal to zero.

[0100] For an ideal CSTR, it is necessary to add terms for component input and output. An example for the generic component “X” is provided below: ^M = (reaction rates) + N (XF0— O) (6)

[0101] Where τ is the average residence time = V / uo (V = reactor volume and u0 = volume flow rate).

[0102] For multiple sites, we arrived at 5 sites (resulting in 5 Shultz-Flory distributions) as a best fit of the MWD for the ZN catalyst we used (as shown in Figure 2), adding differential equations for each additional site. Therefore, for each site, there would be a set of differential equations as provided above. These equations, coupled with differential mass balances, were solved simultaneously using a MATLAB program to obtain the quantities of each species and the momenta associated with each site. (The method provides the species as a function of time.) From the different momenta, one can then obtain the quantity of each Shultz-Flory and its number-average molecular weight. The resulting equations also allow the calculation of the comonomer quantity in each, which also allows the calculation of the SCB for each SF. At this point, we can linearly add the quantity of each SF to obtain the overall MWD and SCB.

[0103] This method obtains the same results as the closed-form equation method (described in DesLauriers) if one uses multisite reactors there, but for certain reactor configurations (namely, a double-circuit reactor configuration), this momentum method may be easier to implement. To obtain the kinetic coefficients, we performed several laboratory reactions (set up in a designed experiment), developed the resulting MWD and SCB from the experiments, and fitted the model parameters to the data. We then verified this model by running different reactor conditions in the pilot plant in ADL mode. This data was used as input in stage (101) in Figure 1. Petition 870250053320, dated 06 / 25 / 2025, page 45 / 80 36 / 52

[0104] In Figure 3, the fit for the molecular weight distribution is shown as a solid line, while the fit for the short-chain branching distribution is shown as a dashed line. As Figure 3 illustrates, the kinetic equations provide an excellent fit to the experimental data.

[0105] Third, Figure 4 illustrates the process of Figure 1 from stage (105) to (107) for a viscosity curve of a model that uses molecular weight distribution compared to data as input. In this figure, the molecular weight distribution predicted from the Soares-type method of moment models was used as input to the rheology model to obtain the viscosity curve properties. As one versed in the art will readily understand, models can be obtained that use molecular weight distribution and short-chain branching input to obtain a variety of predictions for properties such as density, PSP2, PSP3*, HLMI, I-10, MI and the like. Specifically, Figure 4 illustrates the experimental viscosity data (shown as circles) and the predicted viscosity curve (shown as a solid line). As Figure 4 illustrates, the viscosity model exhibited an excellent fit to experimental viscosity data.

[0106] There is a substantial body of work reported in the literature describing the dependence of the rheological properties of entangled melts on their molecular weight distribution, as described, for example, in (1) M. Rubinstein and RH Colby, J. Chem. Phys., Vol. 89, No. 8, p. 5,291, 1988; (2) d. Cloizeaux, Macromolecules, Vol. 23, p. 4,678, 1990; (3) SH Wasserman and WW Graessley, J. Rheol., Vol. 36, No. 2, p. 543, 1992; (4) JS Fodor, Ph. Thesis: Application of Normal-Mode Microdielectrometry Towards Investigation of Diffusion and Flow-Induced Phenomena in Polymer Melts, Notre Dame, IN: University of Notre Dame, 1995; and (5) JS Fodor, JR Huljak and DA Hill, Relaxation of normal dielectric and viscoelastic modes in blended, polydisperse cis-polyisoprene melts, The Journal of Chemical Physics, vol. 103, no. 13, pp. 5725-5734, 1995; each of which.The theory and modeling have been developed allowing for a fairly reasonable prediction of the rheological properties of a melt based on knowledge of its molecular weight distribution and the correlation between the polymer relaxation time and molecular weight. Several models have been developed based on this. Petition 870250053320, dated 06 / 25 / 2025, page 46 / 80 37 / 52 some form of creep theory and mixing rules that explain the polydispersity of the system (references). It has been found that very reasonable predictions can be obtained using a double creep model for relaxation and a Tsenoglou mixing rule, as described in C. Tsenoglou, Macromolecules, vol. 24, p. 1792 and 1991, which is incorporated by reference in this document in its entirety. This combination can be used to obtain predictions for the rheology based on the molecular weight distribution.

[0107] The shear relaxation modulus, G(t), knowing the autocorrelation function for the momentum in a polymer melt, Ψφ, is given by, where GPé is the plateau modulus, = Ψφ (25)

[0108] The storage-loss modulus can then be calculated, f 00 β'(ω) = ω IG(t) 5εη(ωϋ) dt Jo f 00 β(ω) = ω IG(t) εο5(ωϋ) dt Jo

[0109] As will be readily understood by one skilled in the art, Tsenoglou's mixing rule takes into account the interaction of molecular weight mixing and chain relaxation dynamics, and is given by the following, where, ζj, are the fraction of molecular weight species, is the relaxation function for each species as a function of its characteristic relaxation time, η. ψ(0= ELiW-rp1'2]2) (j = MogM · MWD(Mj)

[0110] Next, hhi is defined as a ratio of the molecular weight of the species to a reference molecular weight, M*. hhj = -4 j M

[0111] Without intending to be limited to any particular theory, it is believed, based on literature data, that the relaxation time varies with molecular weight for a given power. For polyethylene, and in this work, 3.4 was considered appropriate, (t* = 0.00013 s, M* = 40,000 g / mol, Gp = 1.34 x 106 Pa). Petition 870250053320, dated 06 / 25 / 2025, p. 47 / 80 38 / 52 Tj = τ* · hhj3'4

[0112] Double creep attempts to explain the creep of individual chains within the fusion, as constrained by the entanglements of the fusion, as well as the relaxation of the entanglements themselves. This yields the following form for the autocorrelation function of individual species, ^))=(^-^^ \ odd /

[0113] The equations for G'(w) and G(w) can be transformed into the following, which is easier to integrate: G'(w) = / “F^sin^dz G(w) = í[ F^cos^dz

[0114] These equations can then be evaluated given the molecular weight distribution and by choosing appropriate values ​​for the adjustable parameters, M* and τ*. The methods used to simplify the integration are described elsewhere, such as in JS Fodor, Ph.D. Thesis: Application of Normal-Mode Microdielectrometry Towards Investigation of Diffusion and Flow-Induced Phenomena in Polymer Melts, Notre Dame, IN: University of Notre Dame, 1995.

[0115] Once G' and G” are calculated, the complex viscosity can be obtained, {*(w)

[0116] Next, the properties of the melting index were predicted using the viscosity curve results discussed above. Although there are known correlations between average molecular weight and melting index measurement, there is no rigid theoretical basis for these correlations and, without being constrained by any particular theory, it is believed that these correlations may lose accuracy as the molecular distribution changes from the standard distribution form that was used when the correlation was developed.

[0117] In order to retain as much of the viscosity prediction as possible, melt index predictions can be obtained by first fitting the viscosity curves to a Careau-Yasada model and then using that model in a computational fluid dynamics simulation (such as with COMSOL). Petition 870250053320, dated 06 / 25 / 2025, pp. 48 / 80 39 / 52 Multiphysics®) to model the flow in a melt index device. Having the flow profile and melt density at the outlet, a skilled technician could then integrate over the outlet surface to obtain the amount of material leaving the surface in 10 minutes. Changing the driving force of the pressure in the model to match the weights used in the machine allows different melt index values ​​to be predicted.

[0118] The geometry of the melt index die was reproduced in the CFD simulation according to the dimensions provided in ASTM D1238-13. The die diameter was set at 2.095 mm and its length was set at 8 mm. The barrel diameter was set slightly smaller than the barrel foot dimension at 9 mm. (The given dimension was 9.4742 mm, but it was slightly adjusted in an attempt to obtain a prediction that better matched the initial adjustments.) The barrel length dimensions were considered less critical. Without intending to be limited to any particular theory, it was believed that the length needed to be long enough for a steady-state flow to develop through the die inlet, so 10 mm was chosen as the die length. We tested values ​​greater and less than 10 mm, and demonstrated that the prediction is minimally sensitive to this dimension.

[0119] The pressure that imparts the flow was calculated from the knowledge of the weight used in the measurement divided by the surface area, Pmi = Weight * (-7.77-) \ n*-o / 4 /

[0120] The weight used in this document dictates the type of melt index: 2.16 kg for MI, 21.6 kg for HLMI, for example. The weight and geometry can be manipulated to match any desired type of melt index measurement.

[0121] The melt index machine typically operates at 190 °C for polyethylene; however, we add temperature dependence if we want to model an index at a different temperature. The following expression was used for the melt density, pm, where T is the temperature in degrees Celsius in the matrix, pm = 863.79 - 0.5126 * (7)

[0122] The modeling required a constitutive equation relating the Petition 870250053320, dated 06 / 25 / 2025, pp. 49 / 80 40 / 52 Fluid stress behavior. For this, the Careau-Yasada (CY) model was fitted to the viscosity curve for the sample under consideration. In general, a reasonable fit was found for the generated curves. If necessary or desired, several CY models could be used. (The parameter, n, in the model was set to 0.1818. This produced reasonable fits, but removed a parameter from the fitting routine. If desired, it can be left as an adjustable parameter when fitting the viscosity curve), n - 1 η = η0* (1 + (ωτ,,)0) “

[0123] The melt index measurement was then predicted by integrating the velocity profile over the matrix surface, multiplying by the density and setting the units to g / 10 min.

[0124] A series of validation experiments were conducted using various weight ratios of 1-hexene to ethylene and ethylene concentrations, as illustrated in Figure 4. The model was found to fit the data well for both primary and derived responses (within a 95% predictive range limit) for 7 of the 9 samples. Response surface models are illustrated in Figures 6 and 7. For both Figures 6 and 7, the 1-hexene to ethylene ratio, temperature, and time were set to 0.4, 130 °C, and 4 minutes, respectively.

[0125] Several examples using a dual reactor system to evaluate the direct response surface method on a wide variety of variables and conditions are provided below. The input variables and selected values ​​for these experiments are shown in Tables 7 and 8 below. TABLE 7: INPUT VARIABLES Input Variable Experiment 1 Experiment 2 Experiment 3 Experiment 4 Experiment 5 I1 184 184 184 184 184 I2 0 0 0 0 0 P 0 1 1 1 1 I4 45 45 30 45 30 P 0.067 0.007 0.007 0.007 0.007 I6 0 0 0 0 0 I7 72 50 50 50 72 P 184 184 184 190 208 P 0.620 0.5 0.5 1.25 0.5 I10 30 30 45 45 30 I11 0.015 0 0 45 30 I12 0.0002 0.0002 0.0002 0.001 0.0008 I13 72 72 50 50 72

[0126] The response variables selected for these experiments Petition 870250053320, dated 06 / 25 / 2025, pages 50 / 80 41 / 52 included the weight-average molecular weight of the first reactor (MwRX-1), molar weight-average molecular weight of the first reactor (MnRX-1), density of the product of the first reactor (density RX-1) in g / cm3, the weight fraction of the final product (the product of the second reactor) emerging from the first reactor (weight fraction RX-1), the weight-average molecular weight of the product of the second reactor (Mescla Mw), the molar weight-average molecular weight of the product of the second reactor (Mescla Mn), the PDI of the product of the second reactor (Mescla PDI), the density of the product of the second reactor (Mescla Density) in g / cm3, High Load Melting Index (HLMI) of the product of the second reactor, melt flux index (110) of the product of the second reactor and the melt flux index (Ml) in g / ml. TABLE 8: RESPONSE VARIABLES AND VALUES FOR EXPERIMENT 1 Response Variable Observed Value Predicted Value RSM 95% Low PI 95% High PI R7 52,160 29,966 27,494 32,788 R8 5,710 5,712 5,175 6,339 R9 0.962 0.964 0.959 0.969 R10 - 0.610 0.608 0.611 R11 58,730 36,681 29,060 46,301 R12 5,930 7,951 6,341 9,969 R13 9.9 7.0 5.0 10.0 R14 0.961 0.959 0.957 0.961 R23 > 500 > 500 - - R24 > 500 > 500 - - R25 > 500 127 43.5 370 TABLE 9: RESPONSE VARIABLES AND VALUES FOR THE EXPERIMENT 2 Response Variable Observed Value Predicted Value RSM 95% Low PI 95% High PI R7 96,950 50,012 45,010 55,898 R8 13,650 9,092 8,078 10,309 R9 -0.966 0.962 0.970 R10 -0.617 0.616 0.619 R11 119,240 91,192 72,471 114,749 R12 14,000 13,455 10,802 16,761 R13 8.5 6.0 4.0 9.0 R14 0.955 0.961 0.959 0.963 R23 190.5 297 133 665 R24 48.18 47.2 21.9 102 R25 4.67 3.83 1.38 10.6 Petition 870250053320, dated 06 / 25 / 2025, pp. 51 / 80 42 / 52 TABLE 10: RESPONSE VARIABLES AND VALUES FOR EXPERIMENT 3 Response Variable Observed Value Predicted Value RSM 95% Low PI 95% High PI R7 177,900 120,554 102,294 144,179 R8 27,940 23,323 19,298 28,753 R9 0.953 0.951 0.946 0.955 R10 - 0.421 0.420 0.423 R11 184,830 200,870 159,133 253,553 R12 35,730 25,027 20,022 31,284 R13 5.2 9.0 6.0 13.0 R14 0.956 0.955 0.953 0.957 R23 11.34 16.1 7.15 36.3 R24 3.08 2.28 1.05 4.99 R25 0.34 0.14 0.05 0.39 TABLE 11: RESPONSE VARIABLES AND VALUES FOR THE EXPERIMENT 4 Response Variable Observed Value Predicted Value RSM 95% Low PI 95% High PI R7 140,590 132,076 111,581 158,782 R8 20,100 23,083 19,180 28,311 R9 0.960 0.951 0.947 0.956 R10 -0.522 0.521 0.524 R11 100,330 156,140 125,110 194,868 R12 11,100 19,693 16,066 24,140 R13 9.0 8.0 6.0 11.0 R14 0.964 0.957 0.955 0.959 R23 342.8 117 54.9 250 R24 88.5 12.5 5.89 26.6 R25 9.32 0.35 0.13 0.90 TABLE 12: RESPONSE VARIABLES AND VALUES FOR THE EXPERIMENT 5 Response Variable Observed Value Predicted Value RSM 95% Low PI 95% High PI R7 578,100 516,451 372,039 764,714 R8 114,500 98,964 68,058 156,923 R9 0.922 0.924 0.919 0.928 R10 -0.604 0.602 0.605 R11 429,610 318,559 252,428 402,015 R12 13,960 25,881 20,761 32,264 R13 -12.0 8.0 18.0 R14 0.944 0.940 0.938 0.942 R23 - 8.78 3.84 20.1 R24 - 0.687 0.311 1.52 R25 0.94 0.06 0.02 0.16 Petition 870250053320, dated 06 / 25 / 2025, page 52 / 80 43 / 52

[0127] The excellent correlations between the observed experimental values ​​and the predicted RSM values ​​of these response variables are illustrated in Figure 5.

[0128] Next, using RSM, an inverse model was generated to select response targets and solve the polymerization conditions needed to meet those targets, using numerical optimization functions contained in the RSM software (step (113) in Figure 1). EXAMPLE 3 - INVERSE MODEL USING THE RESPONSE SURFACE METHOD WITH A VIRTUAL REACTOR

[0129] Next, an optimization / inverse prediction was conducted for a virtual double reactor system using the RSM model and desirability functions (step (115) in Figure 1). First, a set of defined reactor variables was selected, as shown below. These variables indicate that the desired reactor temperatures are 86.6667 °C (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 any hexene to the second reactor. TABLE 13: DEFINED REACTOR VARIABLES AND VALUES Defined Variable Description Targeted Value I2 Reactor 1 Temperature 86.67 °C (188 °F) I8 Reactor 2 Temperature 86.67 °C (188 °F) I6 Hydrogen to Ethylene Weight Ratio in Reactor 1 minimum I11 Hexene to Ethylene Weight Ratio in Reactor 2 0

[0130] Next, a set of desired polymer properties was assembled, including the weight-average molecular weight of the first reactor (Mw RX-1), the molar-average molecular weight of the first reactor (Mn RX-1), the density of the product from the first reactor (density RX-1) in g / cm3, the weight fraction of the final product (the product of the second reactor) emerging from the first reactor (weight fraction RX-1), the weight-average molecular weight of the product from the second reactor (Mixture Mw), the molar-average molecular weight of the product from the second reactor (Mixture Mn), the PDI of the product from the second reactor (Mixture PDI), the density of the product from the second reactor (Mixture Density) in g / cm3, and the productivity of the second reactor (Productivity RX-2), as detailed in the table below. Petition 870250053320, dated 06 / 25 / 2025, page 53 / 80 44 / 52 TABLE 14: PROPERTIES AND DESIRED VALUES OF THE POLYMER Selected Input Variable Description Desired Value R7 Mn RX-1 (g / mol) 114,000 R8 Mw RX-1 (g / mol) 619,000 R9 Density RX-1 (g / cm3) 0.926 R10 Weight Fraction RX-1 0.53 R12 Mixture Mn 8,200 R11 Mixture Mw 41,500 R14 Mixture Density (g / cm3) 0.948 R20 Productivity RX-2 kq / h (lb / h) 44,950 (99,100)

[0131] The system inputs in Table 15 above were all set to remain within a model range. The desired polymer properties and values ​​were then entered into the MATLAB® and Stat-Ease® models, which returned a variety of possible solutions for the reactor parameters, ranked by desirability. The most desirable values ​​of the targeted variables are shown below: TABLE 15: CALCULATED VALUES OF THE REACTOR PARAMETER VARIABLES Targeted Input Variable Description Calculated value of the inverse RSM from MATLAB Calculated value of the inverse RSM from Stat-Ease I2 Reactor 1 Temperature 86.67 °C (188 °F) 86.67 °C (188 °F) I8 Reactor 2 Temperature 86.67 °C (188 °F) 87.22 °C (189 °F) I8 Hydrogen to Ethylene Weight Ratio in Reactor 1 2.0 0.7 I11 Hexene to Ethylene Weight Ratio in Reactor 2 0.045 2.44

[0132] Although the disclosed method is adaptable to any system, it can be particularly useful in systems with a higher level of complexity. For example, the disclosed method is also applicable in the ADL system, where it can eliminate the need for a fluff sample in the first reactor for normal process monitoring and decrease the time to reach specification. The fluff sample from the purge column outlet (a normal safe sampling point for fluff) can be analyzed with dynamic rheology to determine what adjustments are needed to the process to move the molecular weight distribution in the desired direction. The HMW (high molecular weight) polymer will dominate the low pure region of the rheology curve and the low molecular weight polymer will dominate the high molecular weight region of the dynamic rheology. The differences in Petition 870250053320, dated 06 / 25 / 2025, pp. 54 / 80 45 / 52 dynamic rheology of the target across the entire pure rate range provides insights into deficiencies in molecular weight and composition ratio. Since each polymer is produced in a separate reactor, adjustments to the overall bimodal polymer are made in the respective reactor producing the portion of the polymer requiring adjustment. In another aspect, this methodology can be used to improve property control of chromium resin systems by linking process parameters to changes in the amount of LCB in the resin along with the normally monitored resin properties, all combined into a method as described above.

[0133] In a further aspect, the disclosed method can be used to manage the transition from one resin type to a different resin type in a plant. For example, this method can be applied to manage the direct transition from a bimodal ADL film resin to a bimodal ADL tube resin or from a bimodal ADL tube resin to a bimodal ADL film resin. This transition may require, for example, making small adjustments to the molecular weight distribution, and the disclosed technique can reduce transition times because a model can be adapted to specific transitions. Such methods can provide more system flexibility, reduce the amount of resin outside specifications, and provide a significant impact on financial performance at the scale of a system. ASPECTS

[0134] The invention is described above with reference to numerous specific aspects and examples. Many variations will arise for those skilled in the art in light of the above detailed description. All such obvious variations are within the full intended scope of the appended claims. Other aspects of the invention may include, but are not limited to, the following (aspects are typically described as “comprising”, but alternatively, may “essentially consist of” or “consist of”, unless specifically stated otherwise).

[0135] According to a first aspect of the present disclosure, a method for controlling an olefin polymerization reactor system is provided, wherein the method comprises: a) selecting n input variables I1, I2, I3, ... In, each input variable corresponding to a process condition for an olefin polymerization process; b) identifying m response variables, R1, R2, R3, ... Rm, Petition 870250053320, dated 06 / 25 / 2025, pages 55 / 80 46 / 52 each response variable corresponding to a measurable polymer property, where two of the m response variables are molecular weight distribution (MWD) and short chain branching (SCB); c) fit one or more of the n input variables I1a ln in a plurality of polymerization reactions using the olefin polymerization reactor system, to provide a plurality of olefin polymers and measure each of the m response variables R1a Rm as a function of the input variables for each olefin polymer; d) analyze the change in each of the response variables R1a Rm as a function of the input variables I1a ln to determine the coefficients according to the following general equation for each response variable R1a Rm: Rl-m= C0+VU 4—iu= ie ) calculate a Response Surface Model (RSM) using general equations for each response variable R1a Rm(R1- m) determined in step d) to correlate any combination of the n input variables 11a ln with one or more of the m response variables R1a Rm; f) apply n selected input variables Is1, Is2, Is3, ... Isn to the calculated Response Surface Model (RSM) to predict one or more of the m target response variables, Rt1, Rt2, Rt3, ... Rtm, each target response variable corresponding to a measurable polymer property; eg) use the n selected input variables Is1a lnn to operate the olefin polymerization reactor system and provide a polyolefin product.

[0136] According to a second aspect of the present disclosure, a method according to the first aspect is provided, in which the general equation for each response variable R1a RméRl-m= C0+VU 4—iu= i + £v_ Cv(product of a unique combination of 2 from I1a In, selected independently) where ν' is the total number of unique combinations of any 2 from I1a ln, selected independently.

[0137] According to a third aspect of the present disclosure, a method according to the first aspect is provided, in which the general equation for each response variable R1a Rmé Petition 870250053320, dated 06 / 25 / 2025, pages 56 / 80 47 / 52Rl-m= C0+VU 4—iu= i + Σ p -! C'Cproduct of a unique combination of 2 from I1a I, selected independently) + V'V_ Cw(product of a unique combination of 3 from I1a In, selected independently) where ν' is the total number of unique combinations of any 2 from I1a ln, selected independently; and W is the total number of unique combinations of any 3 from I1a ln, selected independently.

[0138] In accordance with a fourth aspect of the present disclosure, a method in accordance with the first aspect is provided, in which the general equation for each response variable R1a RméRl-m= C0+VU 4—iu= i + Σ p -1 c1'(product of a unique combination of 2 from I1a ln, selected independently) + Σ^_ i Cw(product of a unique combination of 3 from I1a ln, selected independently) + V * _ Cx(product of a unique combination of 4 from Pa I, selected independently) where ν' is the total number of unique combinations of any 2 from I1a ln, selected independently; W is the total number of unique combinations of any 3 from I1a ln, selected independently; ex' is the total number of unique combinations of any 4 from I1a ln, selected independently.

[0139] According to a fifth aspect of the present disclosure, a method according to any one of the first to fourth aspects is provided, which further comprises the steps of: h) measuring one or more properties of the polyolefin product corresponding to the measured response variables, Rm1, Rm2, Rm3, ... Rmm; and i) repeating steps a) and a) to reduce the difference between the target response variables Rt1a Rtm and the measured response variables Rm1a Rmm.

[0140] According to a sixth aspect of the present disclosure, a method according to any one of the first to fifth aspects is provided, wherein the step of d) analyzing the change in each of the response variables R1a Rm as a function of the input variables I1a ln further comprises adding the following sum to the general equation: Petition 870250053320, dated 06 / 25 / 2025, pp. 57 / 80 48 / 52 ν' + Cv(product of a unique combination of 2 from I1a ln, selected independently) v=i where ν' is the total number of unique combinations of any 2 from I1a ln, independently selected, such that the general equation for each response variable R1a Rm is: + Συ-1 (product of a unique combination of 2 from I1a In, selected independently).

[0141] In accordance with a seventh aspect of the present disclosure, a method in accordance with the sixth aspect is provided, wherein the step of d) analyzing the change in each of the response variables R1a Rm as a function of the input variables I1a ln further comprises adding the following sum to the general equation: W(product of a unique combination of 3 from I1a I, selected independently); where W is the total number of unique combinations of any 3 independently selected I1a ln, such that the general equation for each response variable R1a Rm is: Σ p -1 (product of a unique combination of 2 from Pa In, selected independently) + Σ^ - i (product of a unique combination of 3 from I1a In, selected independently).

[0142] According to an eighth aspect of the present disclosure, a method according to the seventh aspect is provided, wherein the step of d) analyzing the change in each of the response variables R1a Rm as a function of the input variables I1a ln further comprises adding the following sum to the general equation: _ Cx(product of a unique combination of 4 from I1a I”, selected independently) where x' is the total number of unique combinations of any 4 from I1a ln, independently selected, such that the general equation for each variable Petition 870250053320, dated 06 / 25 / 2025, pages 58 / 80 49 / 52 of the answer R1a Rmseja: Rl-m= C0+VU4—iu= i + y ” _ Cv(product of a unique combination of 2 from I1a I”, selected independently) + 2w_ j Cw(product of a unique combination of 3 from I1a I, selected independently) + (product of a unique combination of 4 from I1a I, selected independently)

[0143] According to a ninth aspect of the present disclosure, a method according to any one of the first to eighth aspects is provided, wherein the input variables I1a lncomprise 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, or any combination thereof.

[0144] According to a tenth aspect of the present disclosure, a method according to any one of the first to ninth aspects is provided, wherein the input variables 11a lncomprise feed rates to the reactor for the catalyst, cocatalyst, activator, ethylene, α-olefin comonomer, hydrogen, reactor solvent or any combination thereof.

[0145] According to an eleventh aspect of this disclosure, a method according to any one of the first to tenth aspects is provided, 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 11a comprise catalyst type and catalyst concentration for each individual catalyst and / or cocatalyst type and cocatalyst concentration for each individual catalyst.

[0146] According to a twelfth aspect of the present disclosure, a method according to any one of the first to eleventh aspects is provided, wherein the olefin polymerization reactor system is a single-circuit double catalyst configuration.

[0147] In accordance with a thirteenth aspect of this disclosure, a method in accordance with any one from the first to the eleventh. Petition 870250053320, dated 06 / 25 / 2025, pp. 59 / 80 50 / 52 aspects are provided, where the reactor system comprises two or more reactors in series.

[0148] According to a fourteenth aspect of the present disclosure, a method according to any one of the first to eleventh or thirteenth aspects is provided, wherein the olefin polymerization reactor system is a double-circuit dual configuration and each reactor comprising its own set of input variables I1(Reactor 1)a In(Reactor 1)e I1(Reactor 2)a In(Reactor 2) .

[0149] According to a fifteenth aspect of the present disclosure, a method according to any one of the first to fourteenth aspects is provided, wherein the type of catalyst is selected from a Ziegler-Natta catalyst, a metallocene catalyst, a Phillips catalyst or a restricted geometry catalyst.

[0150] According to a sixteenth aspect of the present disclosure, a method according to any one of the first to fifteenth aspects is provided, wherein molecular weight distribution (MWD) data (response variable) are [1] measured or [2] generated using the Bernoulli Model.

[0151] According to a seventeenth aspect of the present disclosure, a method according to any one of the first to sixteenth aspects is provided, wherein short chain branching (SCB) data (response variable) are [1] measured or [2] generated using the Mayo-Lewis equation.

[0152] According to an eighteenth aspect of the present disclosure, a method according to any one of the first to seventeenth aspects is provided, wherein the polyolefin product is a copolymer.

[0153] According to a nineteenth aspect of the present disclosure, a method for controlling an olefin polymerization reactor system, wherein the method comprises: a) selecting one or more of the m target response variables, Rt1, Rt2, Rt3, ... Rtm, each target response variable corresponding to a measurable polymer property; b) calculating n selected input variables Is1, Is2, Is3, ... Isn using the Response Surface Model (RSM) of claim 1 to achieve one or more of the m target response variables, Rt1, Rt2, Rt3, ... Rtm; c) using the n selected input variables Is1 to Isn to operate the reactor system. Petition 870250053320, dated 06 / 25 / 2025, pages 60 / 80 51 / 52 polymerization of olefin and provide a polyolefin product; d) measure one or more properties of the polyolefin product that correspond to the measured response variables, Rm1, Rm2, Rm3, ... Rmm; ee) repeat steps a) and d) to reduce the difference between the target response variables Rt1a Rtm and the measured response variables Rm1a Rmm.

[0154] According to a twentieth aspect of the present disclosure, a method according to the nineteenth aspect is provided, wherein the input variables I1a Incompensate 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, reactor solvent feed rate, or any combination thereof.

[0155] According to a twenty-first aspect of this disclosure, a method according to either the nineteenth or twentieth aspects is provided, wherein the olefin polymerization reactor system is a single-circuit dual catalyst configuration using two or more catalysts and / or two or more cocatalysts and the input variables I1a comprise a catalyst type and catalyst concentration for each individual catalyst and / or cocatalyst type and cocatalyst concentration for each individual catalyst.

[0156] According to a twenty-second aspect of the present disclosure, a method according to either the nineteenth or twentieth aspects is provided, wherein the olefin polymerization reactor system is a dual double-circuit configuration and each reactor comprises its own set of input variables |1(Reactor 1)a |n(Reactor 1)e |1(Reactor 2)a |n(Reactor 2).

[0157] According to a twenty-third aspect of the present disclosure, 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 restricted geometry catalyst. Petition 870250053320, dated 06 / 25 / 2025, pp. 61 / 80 52 / 52

[0158] According to a twenty-fourth aspect of this disclosure, a method according to any one of the nineteenth to twenty-third aspects is provided, wherein one or more targeted resin properties comprise molecular weight distribution (MWD), short chain branching (SCB), density, PSP2, Mw, Mn, PDI, viscosity at desired shear rates (frequencies), HMLI, I10, MI, Slick Stick Magnitude, Frictional Oscillation Ratio F Magnitude, Young's Modulus, Yield Stress, Yield Effort, Natural Extraction Ratio, Effort Hardening Modulus, ESCR, FNCT, PENT or NPT.

[0159] According to a twenty-fifth aspect of the present disclosure, a method according to the twenty-fourth aspect is provided, wherein the olefin polymerization reactor system produces more than one olefin polymer component and one or more targeted resin properties comprise Mw, Mn, PDI, density and fraction for each polymer component.

[0160] According to a twenty-sixth aspect of the present disclosure, a method according to either the twenty-fourth or twenty-fifth aspect is provided, wherein the viscosity at the desired shear rates (frequencies) comprises Eta (0.01), Eta (0.126), Eta (1.585), Eta (19.953) or Eta (251.189).

[0161] According to a twenty-seventh aspect of this disclosure, a method according to any one of the nineteenth to twenty-sixth aspects is provided, wherein the polyolefin product is a copolymer. Petition 870250053320, dated 06 / 25 / 2025, pp. 62 / 80

Claims

1 / 7 CLAIMS 1. A method for controlling an olefin polymerization reactor system, wherein the method is characterized in that it comprises: a) selecting n input variables I1, I2, I3, ... In, each input variable corresponding to a process condition for an olefin polymerization process; b) identifying m response variables, R1, R2, R3, ... Rm, each response variable corresponding to a measurable polymer property, wherein two of the m response variables are molecular weight distribution (MWD) and short chain branching (SCB); c) fitting one or more of the n input variables I1 to In in a plurality of polymerization reactions using the olefin polymerization reactor system, to provide a plurality of olefin polymers and measuring each of the m response variables R1 to Rm as a function of the input variables for each olefin polymer;d) Analyze the change in each of the response variables R1 to Rm as a function of the input variables I1 to In to determine the coefficients C0 and Cu (for u = 1 an) according to the following general equation for each response variable R1 to Rm: Ri-m = C° + ^ V'C) 4—1 u= ie) Calculate a Response Surface Model (RSM) using general equations for each response variable R1 to Rm (R1-m) determined in step d) to correlate any combination of the n input variables I1 to In with one or more of the m response variables R1 to Rm; f) Apply n selected input variables Is1, Is2, Is3, ... Isn to the calculated Response Surface Model (RSM) to predict one or more of the m target response variables, Rt1, Rt2, Rt3, ... Rtm, each target response variable corresponding to a measurable polymer property; e.g.) Use the n selected input variables Is1 to Isn to operate the olefin polymerization reactor system and provide a polyolefin product.

2. Method, according to claim 1, characterized in that the general equation for each response variable R1 to Rm is Petition 870260074641, dated 07 / 27 / 2026, page 10 / 23 2 / 7 R1-m = C0 + VU 4— <U= 1 + Σ x C”(produto de uma combinação única de 2 dentre I1 a In, selecionadas independentemente) em que ν' é o número total de combinações únicas de quaisquer 2 dentre I1 a ln, independentemente selecionadas.

3. Method, according to claim 1, characterized in that the general equation for each response variable R1 to Rm is R1-m = C0 + VU 4— <U= 1 + Σρ - χ Cv(produto de uma combinação única de 2 dentre I1 a I, selecionadas independentemente) + Σ^-! (produto de uma combinação única de 3 dentre I1 a In,selecionadas independentemente) em que ν' é o número total de combinações únicas de quaisquer 2 dentre I1 a ln, independentemente selecionadas; e W é o número total de combinações únicas de quaisquer 3 dentre I1 a ln, selecionadas independentemente.

4. Method, according to claim 1, characterized in that the general equation for each response variable R1 to Rm is R1-m = C0 + yU 4—iu= i + Σ p - i Cv(product of a unique combination of 2 from I1 to I, selected independently) + Σ^ -1 (product of a unique combination of 3 from I1 to I, selected independently) + _ Cx(product of a unique combination of 4 from I1 to I, selected independently); where ν' is the total number of unique combinations of any 2 from I1 to ln, selected independently; W is the total number of unique combinations of any 3 from I1 to ln, selected independently; ex' is the total number of unique combinations of any 4 from I1 to ln, selected independently.

5. Method according to claim 1, characterized in that it further comprises the steps of: h) measuring one or more properties of the polyolefin product corresponding to the measured response variables, Rm1, Rm2, Rm3, ... Rmm; and i) repeating steps a) and a) to reduce the difference between the target response variables Rt1 to Rtm and the measured response variables Rm1 to Rmm. Petition 870260074641, dated 27 / 07 / 2026, p. 11 / 23 3 / 7 6. Method according to claim 1, characterized in that step d) analyzing the change in each of the response variables R1 to Rm as a function of the input variables I1 to ln further comprises adding the following sum to the general equation: + £ _ Cv(product of a unique combination of 2 from I1 to ln, selected independently); where ν' is the total number of unique combinations of any 2 from I1 to ln, selected independently, such that the general equation for each response variable R1 to Rm is: R1-m = C0 + VU 4— <U= 1 + C1'(produto de uma combinação única de 2 dentre I1 a In,selecionadas independentemente).

7. Method according to claim 6, characterized in that the step d) analyzing the change in each of the response variables R1 to Rm as a function of the input variables I1 to ln further comprises adding the following sum to the general equation: _ Cw(product of a unique combination of 3 from I1 to I”, selected independently); where W is the total number of unique combinations of any 3 from I1 to ln, independently selected, such that the general equation for each response variable R1 to Rm is: R1-m = C0 + VU nCuQU) 4— <U= 1 + Σ p - i (produto de uma combinação única de 2 dentre I1 a I”, selecionadas independentemente) + Σ^-! (produto de uma combinação única de 3 dentre I1 a In,selecionadas independentemente).

8. Method, according to claim 7, characterized in that the step d) analyzing the change in each of the response variables R1 to Rm as a function of the input variables I1 to ln further comprises adding the following sum to the general equation: _ 1 C*(product of a unique combination of 4 from I1 to ln, selected independently); Petition 870260074641, dated 07 / 27 / 2026, p. 12 / 23 4 / 7 where / is the total number of unique combinations of any 4 from I1 to ln, independently selected, such that the general equation for each response variable R1 to Rm is: R1-m = C0 + VU 4—iu= i + Σ v - i Cv(product of a unique combination of 2 from I1 to ln, independently selected) + Cw(product of a unique combination of 3 from I1 to ln, independently selected) + _ C*(product of a unique combination of 4 from I1 to ln, independently selected).

9. Method according to claim 1, characterized in that the input variables 11 to ln comprise 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, or any combination thereof.

10. Method according to claim 1, characterized in that the input variables I1 to ln comprise feed rates to the reactor for the catalyst, cocatalyst, activator, ethylene, α-olefin comonomer, hydrogen, reactor solvent, or any combination thereof.

11. Method, according to claim 1, characterized in that the olefin polymerization reactor system uses two or more catalysts and / or two or more cocatalysts in a single reactor and the input variables I1 to ln comprise a catalyst type and catalyst concentration for each individual catalyst and / or cocatalyst type and cocatalyst concentration for each individual catalyst.

12. Method according to claim 1, characterized in that the olefin polymerization reactor system is a single-circuit dual catalyst configuration.

13. A method according to claim 1, characterized in that the reactor system comprises two or more reactors in series.

14. Method according to claim 1, characterized in that the olefin polymerization reactor system is a double-circuit configuration and each reactor comprises its own set of input variables I1(Reactor 1) to |n(Reactor 1) and |1(Reactor 2) to |n(Reactor 2) 15. Method according to claim 9, characterized in that the type of catalyst is selected from a Ziegler-Natta catalyst, a metallocene catalyst, a Phillips catalyst or a restricted geometry catalyst.

16. Method according to claim 1, characterized in that the molecular weight distribution (MWD) data (response variable) are [1] measured or [2] generated using the Bernoulli model.

17. Method according to claim 1, characterized in that the short chain branching (SCB) data (response variable) are [1] measured or [2] generated using the Mayo-Lewis equation.

18. Method according to claim 1, characterized in that the polyolefin product is a copolymer.

19. Method for controlling an olefin polymerization reactor system, wherein the method is characterized in that it comprises: a) selecting one or more of the m target response variables, Rt1, Rt2, Rt3, ... Rtm, each target response variable corresponding to a measurable polymer property; b) calculating n selected input variables Is1, Is2, Is3, ... Isn using the Response Surface Model (RSM) calculated from claim 1, to achieve one or more of the m target response variables, Rt1, Rt2, Rt3, ... Rtm; c) using the n selected input variables Is1 to Isn to operate the olefin polymerization reactor system and provide a polyolefin product; d) measuring one or more properties of the polyolefin product corresponding to the measured response variables, Rm1, Rm2, Rm3, ... Rmm; (ee) Repeat steps (a) and (ad) to reduce the difference between the target response variables Rt1 to Rtm and the measured response variables Rm1 to Rmm.

20. Method according to claim 19, characterized in that the input variables I1 to In comprise 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, reactor solvent feed rate, or any combination thereof.

21. Method according to claim 19, characterized in that the olefin polymerization reactor system is a single-circuit dual catalyst configuration using two or more catalysts and / or two or more cocatalysts and the input variables I1 to In comprise a catalyst type and catalyst concentration for each individual catalyst and / or individual cocatalyst type and cocatalyst concentration for each individual catalyst.

22. Method according to claim 19, characterized in that the olefin polymerization reactor system is a dual-circuit configuration and each reactor comprises its own set of input variables I1(Reactor 1) to In(Reactor 1) and I1(Reactor 2) to In(Reactor 2) 23. Method according to claim 20, characterized in that the type of catalyst is selected from a Ziegler-Natta catalyst, a metallocene catalyst, a Phillips catalyst or a restricted geometry catalyst.

24. Method according to claim 19, characterized in that one or more targeted resin properties comprise molecular weight distribution (MWD), short chain branching (SCB), density, PSP2, Mw, Mn, PDI, viscosity at desired shear rates (frequencies), HMLI, I10, MI, Slick Stick Magnitude, Frictional Oscillation Ratio F Magnitude, Young's Modulus, Yield Stress, Yield Effort, Natural Extraction Ratio, Effort Hardening Modulus, ESCR, FNCT, PENT or NPT.

25. Method according to claim 24, characterized in that the olefin polymerization reactor system produces more than one olefin polymer component and one or more targeted resin properties comprise Mw, Mn, PDI, density and fraction for each polymer component. Petition 870260074641, dated 07 / 27 / 2026, p. 15 / 23 7 / 7 26. Method according to claim 24, characterized in that the viscosity at desired shear rates (frequencies) comprises Eta (0.01), Eta (0.126), Eta (1.585), Eta (19.953) or Eta (251.189).

27. Method according to claim 19, characterized in that the polyolefin product is a copolymer. Petition 870260074641, dated 07 / 27 / 2026, pp. 16 / 23

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