US20030144432A1 - Method for reducing sheeting and agglomerates during olefin polymerisation - Google Patents
Method for reducing sheeting and agglomerates during olefin polymerisation Download PDFInfo
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- US20030144432A1 US20030144432A1 US10/220,040 US22004002A US2003144432A1 US 20030144432 A1 US20030144432 A1 US 20030144432A1 US 22004002 A US22004002 A US 22004002A US 2003144432 A1 US2003144432 A1 US 2003144432A1
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- polymerisation
- temperature
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- agglomerates
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- C—CHEMISTRY; METALLURGY
- C08—ORGANIC MACROMOLECULAR COMPOUNDS; THEIR PREPARATION OR CHEMICAL WORKING-UP; COMPOSITIONS BASED THEREON
- C08F—MACROMOLECULAR COMPOUNDS OBTAINED BY REACTIONS ONLY INVOLVING CARBON-TO-CARBON UNSATURATED BONDS
- C08F10/00—Homopolymers and copolymers of unsaturated aliphatic hydrocarbons having only one carbon-to-carbon double bond
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- C—CHEMISTRY; METALLURGY
- C08—ORGANIC MACROMOLECULAR COMPOUNDS; THEIR PREPARATION OR CHEMICAL WORKING-UP; COMPOSITIONS BASED THEREON
- C08F—MACROMOLECULAR COMPOUNDS OBTAINED BY REACTIONS ONLY INVOLVING CARBON-TO-CARBON UNSATURATED BONDS
- C08F2/00—Processes of polymerisation
- C08F2/002—Scale prevention in a polymerisation reactor or its auxiliary parts
-
- C—CHEMISTRY; METALLURGY
- C08—ORGANIC MACROMOLECULAR COMPOUNDS; THEIR PREPARATION OR CHEMICAL WORKING-UP; COMPOSITIONS BASED THEREON
- C08F—MACROMOLECULAR COMPOUNDS OBTAINED BY REACTIONS ONLY INVOLVING CARBON-TO-CARBON UNSATURATED BONDS
- C08F210/00—Copolymers of unsaturated aliphatic hydrocarbons having only one carbon-to-carbon double bond
- C08F210/16—Copolymers of ethene with alpha-alkenes, e.g. EP rubbers
Definitions
- the present invention relates to a method for reducing/suppressing sheeting or agglomerates during polymerisation of olefins, especially during the fluidised bed gas phase polymerisation of olefins.
- the present invention relates to a method for reducing/suppressing sheeting or agglomerates during the product grade transition and/or catalyst transitions occurring during polymerisation of olefins.
- Processes for the co-polymerisation of olefins in the gas phase are well known in the art. Such processes can be conducted for example by introducing the gaseous monomer and comonomer into a stirred and/or gas fluidised bed comprising polyolefin and a catalyst for the polymerisation.
- the polymerisation is conducted in a fluidised bed reactor wherein a bed of polymer particles is maintained in a fluidised state by means of an ascending gas stream comprising the gaseous reaction monomer.
- the start-up of such a polymerisation generally employs a bed of polymer particles similar to the polymer which it is desired to manufacture.
- fresh polymer is generated by the catalytic polymerisation of the monomer, and polymer product is withdrawn to maintain the bed at more or less constant volume.
- An industrially favoured process employs a fluidisation grid to distribute the fluidising gas to the bed, and to act as a support for the bed when the supply of gas is cut off.
- the polymerisation of olefins is an exothermic reaction and it is therefore necessary to provide means to cool the bed to remove the heat of polymerisation. In the absence of such cooling the bed would increase in temperature and, for example, the catalyst becomes inactive or the bed commences to fuse.
- the preferred method for removing the heat of polymerisation is by supplying to the polymerisation reactor a gas, the fluidising gas, which is at a temperature lower than the desired polymerisation temperature, passing the gas through the fluidised bed to conduct away the heat of polymerisation, removing the gas from the reactor and cooling it by passage through an external heat exchanger, and recycling it to the bed.
- the temperature of the recycle gas can be adjusted in the heat exchanger to maintain the fluidised bed at the desired polymerisation temperature.
- the recycle gas generally comprises the monomer and comonomer olefins, optionally together with, for example, an inert diluent gas such as nitrogen or a gaseous chain transfer agent such as hydrogen.
- an inert diluent gas such as nitrogen or a gaseous chain transfer agent such as hydrogen.
- the recycle gas serves to supply the monomer to the bed, to fluidise the bed, and to maintain the bed at the desired temperature.
- Monomers consumed by the polymerisation reaction are normally replaced by adding make up gas or liquid to the polymerisation zone or reaction loop.
- a gas fluidised bed polymerisation reactor is typically controlled to achieve a desired melt index and density for the polymer at an optimum production.
- Conditions within the polymerisation reactor have to be carefully controlled to reduce the risk of agglomerate and/or sheet formation which may ultimately lead to bed instabilities and a need to terminate the reaction and shut down the reactor. This is the reason why commercial scale reactors are designed to operate well within proven stable operating zones and why the reactors are used in a carefully circumscribed fashion.
- An embodiment of the present invention finds its source in the study of the properties of reacting polymer particles. It has been found that sheeting or agglomeration do not occur when instantaneous particle properties (mechanical, physical, dielectric . . . ) are maintained in a bounded window.
- Industrial operation usually requires the production of different grades.
- Product transition usually corresponds to a variation in particle properties.
- agglomerates or sheeting varies widely in size and aspect but they are usually similar in most respects.
- One of the most probable cause of agglomeration or sheeting is the accumulation of powder at the reactor walls.
- the layer formed at the wall can be as thin as a few micrometers and up to several centimetres.
- the corresponding sheet or agglomerates have comparable thickness.
- the length of agglomerates can vary between a few centimetres and several meters.
- a visual inspection at the outlet of the reactor can be used in order to monitor the presence of sheets or agglomerates.
- Temperature probes can also monitor the formation of the sheets or agglomerates.
- the probes can be anywhere between the insulation of the reactor (when used) to the centre of the reactor.
- the analysis of temperature probes is believed to be an excellent indication of the formation of sheets or agglomerates.
- a surprising lowering of the temperature at the wall indicates that particles adhere, causing a probable insulating effect from the bulk temperature. Deviations of a few degrees up to more than 20° C. (sometimes 35° C.) have been commonly observed. When skin temperatures start to rise, it indicates the presence of a reacting layer of powder at the wall.
- Another very advantageous monitoring tool consists in optical fibres located on the surface of the reactor; examples thereof can be found in French patent application n o 0007196 filed on Jun. 6, 2000 by BP Chemicals SNC.
- the present invention indicates that the problem of agglomeration or sheeting can be solved regardless of static electricity considerations.
- the present invention provides a process for reducing/suppressing sheeting or agglomerates during polymerisation of olefins, especially during the fluidised bed gas phase polymerisation of olefins.
- the present invention relates to a method for reducing/suppressing sheeting or agglomerates during start-up, transitioning and steady state olefin polymerisation.
- the behaviour of a representative set of 10 million particles is simulated in order to evaluate the amount of overheating particles, i.e. those particles for which the surface temperature is higher than sintering temperature, i.e. the temperature which is slightly inferior below the melting temperature and which is representative of the temperature at which the polymer powder starts to agglomerate.
- the sintering temperature of the polymer powder under reactor operating conditions is the temperature at which a bed of said polymer powder in contact with a gas having the same composition as the reactor recycle gas used in producing the polymer powder will sinter and form agglomerates when fluidization velocity is at maximum taking into account the fine particle entrainment limitation.
- the sintering temperature is decreased by decreasing the resin density, by increasing the melt index and by increasing the amount of dissolved monomers.
- the particle temperature is estimated by solving heat transfer equations at the level of the particle.
- the fundamental mechanisms involved in that process can be divided in 2 categories: mechanisms responsible for heat generation (polymerisation reaction depending on well quantified kinetics) and equations governing heat transfer.
- Heat generation is well quantified based on well known reaction kinetics and the stochastic approach allows us to describe the complexity of the fluid bed reactor using statistical dispersion of key parameters (such as partial pressure of reactants, initial concentration of active sites, level of impurities, . . . ) around their quasi-steady state average values. This process allowed us to generate a representative set of reacting particles in the reactor (10 7 ).
- FIG. 2 illustrates the typical results obtained for gas phase polymerisation process wherein the mass percentage of overheating particles is given for increasing polymerisation temperature.
- the typical Overheating/Temperature curve also indicates that agglomerates can be formed at lower temperature and points out the existence of a local minimum where temperature is still high but the risk of agglomeration or sheeting is very low.
- Resin properties are predicted from resin molecular structure which is relatively simple in the case of simple polymers such as polyethylene or polypropylene.
- LLDPE Linear Low Density Polyethylene
- HDPE High Density Polyethylene
- the simple molecular structure in that case can be described by the average polymer chain length, the dispersion of the chain lengths (polydispersity), the type of short chain branching (type of comonomer), the amount of short chain branching, the short chain branching distribution, and the size and amount of long chain branching.
- the model has been built from measurements of Tensile Strength performed on injection moulded samples (ASTM n o D638-89). Over 150 samples have been tested covering a wide range of densities and Melt-Indexes. The comparison between predictions and measurements is given in FIG. 1 for RIGIDEXTM product types.
- another embodiment of the present invention is to provide an effective process for reducing/suppressing sheeting or agglomerates during polymerisation of olefins, process characterised in that the above criteria “Crit” is maintained in a bounded window which corresponds to the high temperature optimised operating window.
- the optimum operating window can be reached by controlling instantaneous particle properties, preferably mechanical properties, e.g. tensile strength as described hereabove.
- the instantaneous properties of the growing polymer particles are predicted by using a structure/property model.
- the instantaneous properties are mechanical properties of the growing polymer.
- step 2 just before or just after step 2, if the sheet formation process can not be effectively controlled, proceed with a complete polymerisation stop process and restart the polymerisation at a temperature which is at least equal to T X1 .
- the process according to the present invention is particularly suitable for the manufacture of polymers in a continuous gas fluidised bed process.
- Illustrative of the polymers which can be produced in accordance with the invention are the following:
- SBR polymer of butadiene copolymerised with styrene
- ABS polymer of acrylonitrile, butadiene and styrene
- nitrile polymer of butadiene copolymerised with acrylonitrile
- EPR polymer of ethylene with propylene
- copolymer of ethylene and vinyltrimethoxy silane copolymer of ethylene and one or more of acrylonitrile, maleic acid esters, vinyl acetate, acrylic and methacrylic acid esters and the like
- the polymer is a polyolefin preferably copolymers of ethylene and/or propylene and/or butene.
- Preferred alpha-olefins used in combination with ethylene and/or propylene and/or butene in the process of the present invention are those having from 4 to 8 carbon atoms.
- small quantities of alpha olefins having more than 8 carbon atoms, for example 9 to 40 carbon atoms (e.g. a conjugated diene) can be employed if desired.
- the preferred alpha-olefins are but-1-ene, pent-1-ene, hex-1-ene, 4-methylpent-1-ene, oct-1-ene and butadiene.
- Examples of higher olefins that can be copolymerised with the primary ethylene and/or propylene monomer, or as partial replacement for the C 4 -C 8 monomer are dec-1-ene and ethylidene norborene.
- the process of the present invention preferably applies to the manufacture of polyolefins in the gas phase by the copolymerisation of ethylene with but-1-ene and/or hex-1-ene and/or 4MP-1.
- LLDPE linear low density polyethylene
- HDPE high density polyethylene
- the polymerisation is preferably carried out continuously in a vertical fluidised bed reactor according to techniques known in themselves and in equipment such as that described in European patent application EP-0 855 411, French Patent No. 2,207,145 or French Patent No. 2,335,526.
- the process of the invention is particularly well suited to industrial-scale reactors of very large size.
- a high-activity catalyst consisting essentially of a chromium oxide activated by a beat treatment and associated with a granular support based on a refractory oxide.
- the following examples were conducted in a conventional fluidised bed reactor.
- the catalyst used was a Ziegler type, titanium based catalyst (supported or pre-polymerised).
- the products made in the examples were copolymers of ethylene and butene, and ethylene and 4-methyl-pentene-1.
- Hydrogen was used as a chain transfer agent to control the melt-index of the polymer.
- the second example is an illustration of the optimum control of particle properties to avoid sheeting and agglomerates.
- This example is a product transition similar to the case of example 1. In this second case, temperature is adjusted to compensate for final resin property changes.
- This second example is an illustration of continuous operation in the sheeting/agglomerates-free operating window.
- the third example is taken from WO99/02573. It is similar to the second example in terms of particle properties and final resin properties. This example is an illustration of particle properties moving outside the optimum window during grade transitioning. In this example, the meta-stable window has been chosen: the powder accumulation problem is not solved but polymerisation temperature is decreased such that the layer of powder at the wall does not melt.
- a fluidised bed reactor was transitioned from a 0.926 density, 0.6 melt index ethylene/4-methyl-pentene-1 copolymer to a 0.935 density, 0.5 melt index ethylene/4-methyl-pentene-1 copolymer.
- the prepolymer Ziegler titanium based catalyst
- the bed temperature was slightly decreased from 86° C. to 83° C. during transition to the higher density product.
- the tensile strength criteria is used to monitor instantaneous reacting particle properties: the first product operating conditions correspond to particle properties in the optimum operating window (no sheeting nor agglomerates). During grade transitioning, the criteria started to increase from 5.6 to 6.5 which is outside the optimum window. The polymer instantaneously formed in the reactor became too brittle and fines and micro-fines started to form. Powder then accumulated at wall leading to overheating as it was observed on skin temperature probes and sheeting.
- a fluidised bed reactor was transitioned from a 0.919 density, 0.9 melt index ethylene/butene copolymer to a 0.926 density, 0.75 melt index ethylene/butene copolymer.
- the prepolymer (Ziegler titanium based catalyst) was the same as the one used in comparative example 1.
- the bed temperature was increased from 86° C. to 96° C. during transition to the higher density product with a rate such that the tensile strength criteria is maintained at 5.6.
- Polymerisation temperature is increased to maintain particle properties in the optimum window: not too close to sintering and not too brittle/crystalline. For comparison, if polymerisation temperature had been maintained at 86° C. during transition, the criteria would have reached 6.7 indicating that particle properties were far above the upper limit of the optimum window (similar to example 1).
- a fluidised bed reactor was transitioned from a 0.917 density (instead of 0.919 for example 2), 0.6 melt index (instead of 0.9 for example 2) ethylene/hexene copolymer to a 0.925 density (instead of 0.926 for example 2), 0.5 melt index (instead of 0.75 for example 2) ethylene/hexene copolymer.
- the catalyst Ziegler titanium-based was the same for both products.
- the bed temperature was increased from 86° C. to 91° C. during the transition to the higher density product.
- the first product is made at 86° C. which corresponds to a criteria of 5.5. This product is therefore in its optimum operating window thus explaining that neither sheeting nor agglomerates have been experienced in this case.
- the criteria reaches 6.2 which is outside the optimum window for particle properties. In fact, the value of 5.6 would require us to operate at 97° C. (comparable to the similar case reported in the previous example).
- particle properties are too brittle and crystalline leading to the formation of a layer of powder at the wall.
- the temperature is high enough so the layer of powder can fuse and sheets start to form. Lowering operating temperature prevents the fusion of the layer but does not solve the problem of inadapted particle properties.
- the catalyst used was 2,6-diacetylpyridinebis(2,4,6-trimethylanil)FeCl 2 activated with methylaluminoxane (MAO) and supported on silica (Crosfield grade ES70X).
- MAO methylaluminoxane
- silica Silica
- the polymerization was carried out in a conventional fluidized bed gas phase polymerization reactor.
- the catalyst injection rate was set such as to maintain the production rate constant at the desired level.
- the polymerization temperature was consequently increased to 96° C. and, within a short period of time, disappearance of cold bands could be observed which is synonymous of having reached the optimum operating window.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
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US12/923,840 US20110224394A1 (en) | 2000-03-06 | 2010-10-08 | Method for reducing sheeting and agglomerates during olefin polymerisation |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
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EP00430010.9 | 2000-03-06 | ||
EP00430010 | 2000-03-06 |
Related Child Applications (1)
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US11/014,901 Continuation US7812103B2 (en) | 2000-03-06 | 2004-12-20 | Method for reducing sheeting and agglomerates during olefin polymerisation |
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US20030144432A1 true US20030144432A1 (en) | 2003-07-31 |
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US10/220,040 Abandoned US20030144432A1 (en) | 2000-03-06 | 2001-03-02 | Method for reducing sheeting and agglomerates during olefin polymerisation |
US11/014,901 Expired - Fee Related US7812103B2 (en) | 2000-03-06 | 2004-12-20 | Method for reducing sheeting and agglomerates during olefin polymerisation |
US12/923,840 Abandoned US20110224394A1 (en) | 2000-03-06 | 2010-10-08 | Method for reducing sheeting and agglomerates during olefin polymerisation |
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US11/014,901 Expired - Fee Related US7812103B2 (en) | 2000-03-06 | 2004-12-20 | Method for reducing sheeting and agglomerates during olefin polymerisation |
US12/923,840 Abandoned US20110224394A1 (en) | 2000-03-06 | 2010-10-08 | Method for reducing sheeting and agglomerates during olefin polymerisation |
Country Status (14)
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US (3) | US20030144432A1 (pt) |
EP (2) | EP1263809B1 (pt) |
JP (1) | JP5568701B2 (pt) |
KR (1) | KR100721746B1 (pt) |
CN (1) | CN1181104C (pt) |
AT (2) | ATE481428T1 (pt) |
AU (2) | AU2001235847B2 (pt) |
BR (1) | BR0108743B1 (pt) |
CA (1) | CA2402072C (pt) |
DE (2) | DE60143099D1 (pt) |
MX (1) | MXPA02008717A (pt) |
PL (1) | PL200428B1 (pt) |
WO (1) | WO2001066610A1 (pt) |
ZA (1) | ZA200206809B (pt) |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20050192764A1 (en) * | 2004-03-01 | 2005-09-01 | Holland Richard A. | Computation of radiating particle and wave distributions using a generalized discrete field constructed from representative ray sets |
WO2007015074A1 (en) * | 2005-08-02 | 2007-02-08 | Ineos Europe Limited | Diene polymerisation |
Families Citing this family (9)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
DE60143099D1 (de) * | 2000-03-06 | 2010-10-28 | Ineos Europe Ltd | Verfahren zur Reduzierung von Belagbildung und Verklumpung während der Olefinpolymerisation |
US7598327B2 (en) | 2004-11-10 | 2009-10-06 | Chevron Phillips Chemical Company Lp | Method for polymerizing olefins in a gas phase reactor using a seedbed during start-up |
EP1840140A1 (en) * | 2006-03-30 | 2007-10-03 | Total Petrochemicals Research Feluy | Method for making a transition between polymer grades |
JP5292754B2 (ja) * | 2007-09-27 | 2013-09-18 | 住友化学株式会社 | オレフィン重合体の製造方法 |
US7718743B2 (en) | 2008-08-01 | 2010-05-18 | Exxonmobil Chemical Patents Inc. | Methods for monitoring reactor passivation for gas phase polymerization |
WO2010014371A1 (en) * | 2008-08-01 | 2010-02-04 | Exxonmobil Chemical Patents Inc. | Methods for monitoring reactor passivataion for gas phase polymerization |
BRPI1015130B1 (pt) | 2009-07-28 | 2019-11-26 | Univation Tech Llc | processo de polimerização usando um catalisador de geometria limitada suportado |
EP3418308B1 (en) * | 2017-06-20 | 2020-03-11 | Borealis AG | A method, an arrangement and use of an arrangement for olefin polymerisation |
CN112135845A (zh) * | 2018-06-14 | 2020-12-25 | 博里利斯股份公司 | 用于在具有改善的热均质性的气相反应器中聚合烯烃的方法 |
Family Cites Families (10)
Publication number | Priority date | Publication date | Assignee | Title |
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US532178A (en) | 1895-01-08 | Brick-drier | ||
FR2660926B1 (fr) * | 1990-04-11 | 1992-07-31 | Bp Chemicals Snc | Prepolymere d'alpha-olefine contenant un metal de transition et procede de polymerisation d'alpha-olefine en phase gazeuse mettant en óoeuvre le prepolymere. |
FR2661297B1 (fr) * | 1990-04-18 | 1993-02-12 | Alcatel Radiotelephone | Circuit de multiplexage de signaux d'horloge. |
US5672666A (en) * | 1995-06-05 | 1997-09-30 | Exxon Chemical Patents Inc. | Process for transitioning between incompatible polymerization catalysts |
US5627242A (en) * | 1996-03-28 | 1997-05-06 | Union Carbide Chemicals & Plastics Technology Corporation | Process for controlling gas phase fluidized bed polymerization reactor |
US5866661A (en) * | 1996-12-13 | 1999-02-02 | Phillips Petroleum Company | Ethylene polymerization processes and products thereof |
AU8382698A (en) | 1997-07-08 | 1999-02-08 | Union Carbide Chemicals & Plastics Technology Corporation | Method for reducing sheeting during olefin polymerization |
AU8488198A (en) * | 1997-07-16 | 1999-02-10 | Union Carbide Chemicals & Plastics Technology Corporation | Low bed-level transition, start-up, and reactor residence time control using sound waves |
US6300429B1 (en) * | 1998-12-31 | 2001-10-09 | Union Carbide Chemicals & Plastics Technology Corporation | Method of modifying near-wall temperature in a gas phase polymerization reactor |
DE60143099D1 (de) * | 2000-03-06 | 2010-10-28 | Ineos Europe Ltd | Verfahren zur Reduzierung von Belagbildung und Verklumpung während der Olefinpolymerisation |
-
2001
- 2001-03-02 DE DE60143099T patent/DE60143099D1/de not_active Expired - Lifetime
- 2001-03-02 AU AU2001235847A patent/AU2001235847B2/en not_active Ceased
- 2001-03-02 BR BRPI0108743-6A patent/BR0108743B1/pt not_active IP Right Cessation
- 2001-03-02 AU AU3584701A patent/AU3584701A/xx active Pending
- 2001-03-02 KR KR1020027011618A patent/KR100721746B1/ko not_active IP Right Cessation
- 2001-03-02 AT AT06076117T patent/ATE481428T1/de active
- 2001-03-02 EP EP01907983A patent/EP1263809B1/en not_active Expired - Lifetime
- 2001-03-02 CA CA002402072A patent/CA2402072C/en not_active Expired - Fee Related
- 2001-03-02 WO PCT/GB2001/000920 patent/WO2001066610A1/en active IP Right Grant
- 2001-03-02 JP JP2001565774A patent/JP5568701B2/ja not_active Expired - Fee Related
- 2001-03-02 DE DE60120125T patent/DE60120125T2/de not_active Expired - Lifetime
- 2001-03-02 PL PL356964A patent/PL200428B1/pl unknown
- 2001-03-02 MX MXPA02008717A patent/MXPA02008717A/es active IP Right Grant
- 2001-03-02 AT AT01907983T patent/ATE328013T1/de active
- 2001-03-02 EP EP06076117A patent/EP1688444B1/en not_active Expired - Lifetime
- 2001-03-02 US US10/220,040 patent/US20030144432A1/en not_active Abandoned
- 2001-03-02 CN CNB018040039A patent/CN1181104C/zh not_active Expired - Fee Related
-
2002
- 2002-08-26 ZA ZA200206809A patent/ZA200206809B/xx unknown
-
2004
- 2004-12-20 US US11/014,901 patent/US7812103B2/en not_active Expired - Fee Related
-
2010
- 2010-10-08 US US12/923,840 patent/US20110224394A1/en not_active Abandoned
Cited By (9)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US20050192764A1 (en) * | 2004-03-01 | 2005-09-01 | Holland Richard A. | Computation of radiating particle and wave distributions using a generalized discrete field constructed from representative ray sets |
US7197404B2 (en) * | 2004-03-01 | 2007-03-27 | Richard Andrew Holland | Computation of radiating particle and wave distributions using a generalized discrete field constructed from representative ray sets |
US20080021682A1 (en) * | 2004-03-01 | 2008-01-24 | Holland Richard A | Computation of radiating particle and wave distributions using a generalized discrete field constructed from representative ray sets |
AU2005220732B2 (en) * | 2004-03-01 | 2010-06-17 | Applied Computational Technologies, Llc | Computation of radiating particle and wave distributions using a generalized discrete field constructed from representative ray sets |
US8145459B2 (en) * | 2004-03-01 | 2012-03-27 | Applied Computational Technologies, Llc | Computation of radiating particle and wave distributions using a generalized discrete field constructed from representative ray sets |
US8972227B2 (en) | 2004-03-01 | 2015-03-03 | Varian Medical Systems, Inc. | Computation of radiating particle and wave distributions using a generalized discrete field constructed from representative ray sets |
US10921756B2 (en) | 2004-03-01 | 2021-02-16 | Varian Medical Systems, Inc. | Computation of radiating particle and wave distributions using a generalized discrete field constructed from representative ray sets |
WO2007015074A1 (en) * | 2005-08-02 | 2007-02-08 | Ineos Europe Limited | Diene polymerisation |
US8124698B2 (en) | 2005-08-02 | 2012-02-28 | Ineos Europe Limited | Diene polymerisation |
Also Published As
Publication number | Publication date |
---|---|
KR100721746B1 (ko) | 2007-05-25 |
CN1181104C (zh) | 2004-12-22 |
EP1263809B1 (en) | 2006-05-31 |
US20050165179A1 (en) | 2005-07-28 |
BR0108743B1 (pt) | 2011-04-05 |
CA2402072C (en) | 2009-12-29 |
DE60120125T2 (de) | 2006-10-26 |
CA2402072A1 (en) | 2001-09-13 |
AU2001235847B2 (en) | 2006-01-12 |
WO2001066610A1 (en) | 2001-09-13 |
CN1425029A (zh) | 2003-06-18 |
BR0108743A (pt) | 2004-06-29 |
PL200428B1 (pl) | 2009-01-30 |
JP5568701B2 (ja) | 2014-08-13 |
EP1688444A3 (en) | 2009-03-18 |
AU3584701A (en) | 2001-09-17 |
US20110224394A1 (en) | 2011-09-15 |
KR20020079939A (ko) | 2002-10-19 |
DE60120125D1 (de) | 2006-07-06 |
ATE481428T1 (de) | 2010-10-15 |
ATE328013T1 (de) | 2006-06-15 |
DE60143099D1 (de) | 2010-10-28 |
PL356964A1 (en) | 2004-07-12 |
MXPA02008717A (es) | 2004-09-06 |
EP1263809A1 (en) | 2002-12-11 |
EP1688444B1 (en) | 2010-09-15 |
ZA200206809B (en) | 2004-02-25 |
EP1688444A2 (en) | 2006-08-09 |
US7812103B2 (en) | 2010-10-12 |
JP2003525983A (ja) | 2003-09-02 |
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