This invention relates generally to thermal processing of liquid hydrocarbons in a fluidized bed coking reactor.
Fluidized bed technologies have been applied to a type of hydrocarbon processing known as “coking”. In a commercial coking process a hydrocarbon feed is reacted at temperatures greater than approximately 350° C., and typically greater than 430° C., but typically less than 580° C. The targeted chemical species of the coking process reside for the most part in the “pitch” fraction of the feed, typically defined as the fraction of the oil that boils above 524° C., based on standard industry test methods. A number of fluid bed coking reactors have appeared in the patent literature since the 1940s, an example of which is disclosed in U.S. Pat. No. 2,895,904. The term “Fluid Coking” has become synonymous with the coking reactor described in this patent.
Another example of a conventional Fluid Coking reactor 15 having a fluidized bed 23 is shown in
In the conventional Fluid Coking reactor shown in
An operational challenge that exists with fluidized beds is to maintain fluidized conditions. When a bed “defluidizes” the drag force imparted by the movement of the gas relative to the solid particles is no longer able to support the weight of the solid particles. The bed then “slumps”, and intimate contact between the solid particles is re-established as the bed is no longer fluidized. A bed that is defluidized is said to be a “packed bed” of solids. Defluidization of a fluid bed during operation constitutes a serious operational challenge, since loss of bed fluidity results in a system that behaves in a manner that is inconsistent with a continuous fluid.
For a petroleum oil application in which the fluidized solid particles provide the energy required to convert a liquid hydrocarbon feed into lower boiling products and a condensed coke byproduct, the situation only worsens following a defluidization event. Any liquid present in the system at the time of the defluidization incident will continue to react. The coke formed will bridge the adjacent solids together, essentially cementing the entire bed together as a single cohesive unit. This problem is magnified if fresh feed addition is continued after the defluidization event. The end result is that the processing unit has to be shut down for maintenance, which requires the solid mass to be cut out of the reactor using water lasers, or other mechanical means. This activity is taken at considerable expense, with implications both upstream and downstream in the refinery.
The mechanism by which defluidization is initiated by the agglomeration of wet particles is of particular importance in a fluidized bed coking process. When a fluidized bed coking reactor defluidizes due to the introduction of too much liquid feed, the bed is said to have “bogged”, and the processes leading to the bogged bed is referred to as “bogging”. British patent 759,720 discloses operational guidelines for feeding a Fluid Coking process for converting a heavy hydrocarbon feed to lower boiling products, and in particular, defines a maximum feed rate below which defluidization by bogging will be avoided. In this patent, a Fluid Coking process is disclosed wherein hot fluidized solids are fed continuously into a fluid bed coking reactor, with cool solids withdrawn at the same rate. As described in the patent, the bulk of the data were obtained in a laboratory-scale fluidized bed unit in which the fluidized solids were not added or withdrawn from the reactor; this mode of operation is referred to in the basic chemical engineering literature as a “fed batch” reactor. Data from the fed batch reactor were used to empirically formulate a mathematical relationship used to calculate the maximum possible feed rate at which fluidized conditions could be maintained. The inputs to the model were: the reactor temperature, and the amount of coke forming material in the fresh feed, as determined by the standard “Conradson Carbon Number (CCR)” test. It is well known within the industry that the “Micro Carbon Residue (MCR)” test or equivalent could be applied effectively in place of the CCR. An empirical factor was included that captures the impact of scale-up, the efficiency of feed distribution on the particles, the characteristics of the fluidized solids, and the fluidization gas rate.
While British patent 759,720 discloses a method to feed a Fluid Coking process, the data accumulated for the model were acquired using a fed batch reactor. A fed batch reactor configuration substantially differs from the Fluid Coking process, the most significant difference being no circulation of solids in a fed batch reactor. Therefore, it is unclear whether it is accurate to base the prediction of defluidization in a fluid bed coking reactor from data obtained from a fed batch reactor. Further, British patent 759,720 does not provide any insight into how to efficiently operate a fluidized bed reactor exhibiting mixing characteristics that are not well mixed with respect to the fluidized solids. In particular, it is not clear how applicable the method disclosed in British patent 759,720 is for feeding a fluidized bed reactor with primarily plug flow characteristics, such as a cross-flow fluidized bed reactor as disclosed in Applicant's own PCT publication no. WO 2005/040310.
According to one aspect of the invention, there is a provided a fluidized bed coking reactor apparatus comprising: a reaction vessel having a feed material inlet, a solids inlet, a solids outlet and a fluidization gas inlet; a temperature sensor inside the reaction vessel for measuring a reactor temperature profile; a solids feed mechanism in communication with the solids inlet for feeding solid particles into the reactor vessel; a feed material feed mechanism in communication with the feed material inlet for feeding feed material into the reactor; and a supervisory controller. The controller is communicative with the temperature sensor to monitor the reactor temperature profile, the solids feed mechanism to monitor and control a mass flow rate of the solid particles, and the feed material feed mechanism to control a rate of feeding feed material into the reactor. The controller has a memory encoded with steps and instructions executable by the controller to determine an upper feed material feed rate which is a feed material feed rate that causes defluidization in the reactor when the reactor is operating under conditions having a selected degree of backmixing in the fluidized bed and wherein the upper feed material feed rate is a function of the solid particles mass flow rate, the reactor temperature profile, mixing characteristics of the reactor, and properties of: the feed material, the solid particles, and a fluidization gas fed into the reactor. The memory is further enclosed with executable steps and instructions to compare the feed material set point feed rate to the determined upper feed material feed rate and when the feed material set point feed rate is greater than the upper feed material feed rate, to control the feed material feed mechanism to feed material at a set point feed rate FSP or control the solids feed mechanism to feed solid particles at a mass flow rate S so that the feed material set point feed rate is at or below the upper feed material feed rate.
According to another aspect of the invention, there is provided a method of operating a fluidized bed coking reactor comprising:
According to yet another aspect of the invention, there is provided a computer readable medium encoded with steps and instructions executable by a controller to determine an upper feed material feed rate of a fluidized bed coking reactor operating at a reactor temperature profile and receiving solid particles at a mass flow rate, wherein the upper feed material feed rate is defined as a feed rate of feed material deposited onto a selected fraction of a fluidized bed of solid particles in the reactor that causes defluidization in the reactor when the reactor is operating under conditions having a selected degree of backmixing in the fluidized bed, and wherein the upper feed material feed rate is a function of the solid particles mass flow rate, the reactor temperature profile, mixing characteristics of the reactor, and properties of: the feed material, the solid particles, and a fluidization gas fed into the reactor.
Introduction and Terminology
The embodiments described herein relate to an improved coking process for converting a feed material (“feed”) into various product materials (“products”) using a fluidized bed coking reactor (“primary upgrading reactor” or “reactor”) at feed rates that avoids defluidization of solid particles (otherwise known simply as “solids”) that are fluidized by a fluidization gas in the reactor.
The feed in these embodiments is a liquid-phase hydrocarbon stream of which at least a fraction undergoes a chemical reaction in the primary upgrading reactor. The feed can consist of a pitch stream received from a fractionator apparatus, along with some gas oil material, wherein “gas oil” refers to the fraction of oil that boils below 524° C., but above 177° C., measured using standard industry test methods. The feed may be comprised of a single substance or may be comprised of a plurality of substances. The liquid products may be comprised of a single product or substance, or a plurality of products or substances, and are typically the commercially desired products from the fluidized bed coking process.
When the feed is fed into the primary upgrading reactor, some of the liquid-phase pitch is vaporized without reacting (“volatile pitch”), and the remainder of the pitch remains on the solid particles and is eventually reacted to form coke, non-condensable gases, and liquid product (“reacting pitch”).
All gaseous material exiting the fluidized bed coking reactor is referred to as the “reactor vapour” or “reactor gases”, and include the liquid products, non-condensable gases, fluidization gas, and the volatile pitch. A component of the reactor gases known as “reactor product” refers to all of the hydrocarbon vapours exiting the reactor (liquid products, non-condensable gases, and volatile pitch) and in particular does not include the fluidization gas.
Apparatus
Referring now to
As shown in
The solids feed mechanism 106 can be one of several solids transfers systems as known in the art; for example, the solids feed mechanism can be a standpipe/riser arrangement used in commercial fluid coking and which comprises a slide valve to regulate solids flow. The solids flow rate in such a mechanism can be measured by measuring the pressure drop across the valve. Other types of solids feed mechanism do not use a slide valve and instead can use a loop seal or a rotary or “star” valve. In systems with a loop seal, the solids flow is modulated by changing the rate of aeration gas introduced into the seal. As such the rate of solids transfer can be calculated by determining the amount of gas added to the loop seal, and the pressure drop through the loop seal; in systems that use a rotary valve the solids flow rate can be determined by the rotational speed of the rotary valve. Still another approach to determining solids flow rate is by heat balance, wherein measuring the temperature at key locations with the system can be used to determine the heat properties of the flowing system and thus the flow rate of solids within the system.
The feed material 40 is introduced into the reactor 20 at a feed material inlet 42 by a feed material feed mechanism (not shown in this Figure but shown schematically as item 110 in
Referring again to
At typical reactor operating conditions about 65% by weight of the pitch contacting the solids is reacting pitch that coats the solids and is eventually converted into either coke or liquid or non-condensable gas products in the reactor 20. The remaining 35% of the liquid pitch material is volatile pitch which vaporizes without reacting or coating the solids and exits the reactor 20 with other the reactor products; after exiting the reactor 20, the volatile pitch in the reactor product is condensed and separated from the liquid products in the fractionator apparatus 18 and then is recycled back to the reactor 20 along with fresh feed material 40.
Referring again to
Referring again to
Determining Feed Rate in an Improved Coking Process for a Generalized Fluidized Bed Reactor
The improved coking process of the present embodiments operates a fluidized bed reactor to process as much feed, and hence produce as much commercially useful product as possible without causing the fluidized bed to defluidize, or worse still, to bog. To determine the maximum feed rate that can be sustained before defluidization by a bogging mechanism occurs, the mixing characteristics and the solid particle throughput of the fluidized bed must be considered. The following concepts and definitions are used as part of this derivation:
With these concepts the desired relationships governing the feeding of a fluidized bed coking reactor to avoid defluidization can be developed and is described below.
In a fed-batch process, liquid feed is continually added to a fluidized bed of solids, but no fresh solids are added, and no solids are removed. It is understood in this case that an external heat source is required to add energy to the fluidized solids in order to initiate the chemical reactions. This energy can be provided by an electrical heater, as disclosed in British patent 759,720. At steady state, a mass balance on the reactor dictates that the rate at which the pitch liquid fraction is added to the reactor must equal the sum of the rate at which the volatile pitch leaves the reactor and the rate at which the reacting pitch is converted due to chemical reaction. This is shown mathematically in equation (1), where FK is the rate at which the reacting pitch fraction is added to the reactor (lb/hr), VK is the rate at which the volatile pitch exits the reactor as vapour (lb/hr), rK is the rate of disappearance of the reacting pitch fraction (lb liquid/lb dry fluidized bed material-hr), and mb is the inventory of fluidized solids in the bed prior to feed introduction (lb).
FK=VK+rKmb equation (1)
The coke forming propensity of a liquid hydrocarbon under standardized conditions can be determined using industry-standard characterizations, such as the Conradson Carbon Residue (CCR) test. The actual amount of coke produced is related the standardized coking propensity through the “coke producing factor” (CPF), defined as the mass of coke produced in the actual coking environment per mass of coke produced by the same feed under the standardized environment. With this definition the rate of accumulation of coke in the reactor is given by the expression (FCF−PCP)π=FΔCCRπ where F is the total feed rate of hydrocarbon feed to the reactor (lb/hr), CF is the amount of coke formed from the feed under standardized coking conditions (lb coke/lb hydrocarbon), P is the rate of condensable liquid products exiting the reactor (lb/hr), CP is the amount of coke formed from the condensable liquid products under standardized coking conditions (lb coke/lb hydrocarbon), π is the CPF, defined above, and ΔCCR is the fraction of coke forming material in the feed to the reactor, determined under standardized conditions destroyed in the reactor (lb CCR/lb feed). From the expression above ΔCCR is implicitly defined as ΔCCR=CF−(P/F)CP.
The rate of reacting pitch fraction deposited on the bed is related to the rate of coke production through stoichiometry by the expression:
where αKC is the stoichiometric coefficient associated with the formation of coke from the reacting pitch sub-fraction (lb coke produced/lb liquid reacted). Substituting this expression into equation (1) and expanding the rate equation in equation (1):
where kK is the first order rate constant associated with the disappearance of the reacting pitch fraction of the feed by chemical reaction (hr−1), and mK is the mass of the reacting pitch fraction in the reactor at steady state.
The bed has a natural capacity to resist defluidization, determined by the degree of shear in the bed, and other factors that will be discussed. At a particular operating condition, as the feed rate of the reacting pitch to the reactor is increased, this natural capacity is exceeded and the bed defluidizes by the bogging mechanism described above. The critical concentration of the reacting pitch at which this occurs is given by the quantity (mK/mb)*. With this definition the maximum allowable feed rate of the feed to the reactor in order to prevent defluidization is given by equation (4) as:
This equation states that the amount of reacting pitch fraction that can be added at steady state is limited by the rate at which it is converted to non-condensable gas and liquid products and coke in the reactor. From chemical reaction theory, the rate constant is temperature dependent, and can be expressed by the well known Arrhenius relationship as:
kK=Δ exp(−Ea/RT) equation (5)
Where A is the pre-exponential factor (hr−1), Ea is the activation energy (cal/mol), R is the universal gas constant (cal/mol-K), and T is the temperature (K) of the reactor. Since a fed batch reactor is well-mixed, this temperature is uniform throughout the reactor.
Combining this temperature dependence with equation (4) yields the desired final result governing the safe operation of a fed batch reactor.
This equation relates the amount of feed that can be fed to a fluidized bed of particles, if no particles are added to or removed from the reactor. Here the subscript “FB” is used to identify that the constraint is specific to the fed batch reactor system. In descriptive terms, the rate at which a fed-batch reactor can accept feed is limited by the rate at which the tacky particles dry out by chemical reaction.
The results of this derivation are comparable to the findings disclosed in British patent 759,720 for the fed batch reactor disclosed in that patent, except with respect to three important and relevant distinctions:
The appropriate formulation for a continuous, well-mixed fluid bed coking reactor considers the fact that the process is continuous with respect to coke addition and removal, and that the solid particles in the fluid coking reactor are well mixed. With these considerations, at steady state the net rate at which the reacting pitch fraction is deposited on the bed must equal the rate at which it is advected out of the reactor on the withdrawn solids, and the rate at which the reacting pitch fraction reacts. Mathematically this is given by the equation:
Making the same substitutions as introduced above, and rearranging, the following condition to avoid defluidization is derived:
where S is the rate at which solids are continuously introduced into the reactor (lb/hr), and the subscript “CSTR” is used to identify the steady state operation of a reactor configuration in which solids are continuously introduced into the reactor and the mixing characteristics of the solids within the reactor are well-mixed. Comparing equation (6) and equation (8) associated with the fed-batch and continuous processes, respectively, two additional deficiencies to the proposal in British patent 759,720 to relate the fed batch process findings to a continuous well-mixed fluid bed coking process can be identified, in addition to the three stated above.
In a continuous reactor where the mixing characteristics are plug flow there is no mixing in the direction of flow of the solid particles. For a plug flow reactor of length L (ft) in which the feed is introduced instantaneously at the point of entry of the solids into the reactor, the concentration of the reacting pitch fraction at any location Z (ft) along the length of the reactor is given by the equation:
where (mK/mb)z is the concentration at any location z in the reactor, and (mK/mb)0 is the concentration at the entrance location. Note that unlike the continuous or fed batch arrangements, the temperature is not uniform in the plug flow reactor, and drops continuously in the direction of flow. Hence kK|z is used to refer to the rate constant at any position in the reactor. The details of the derivation is known in the art, and for example, can be found in Fogler, H. S., “Elements of Chemical Reaction Engineering”, Prentice-Hall, Englewood, N.J., 1986, or Smith, J. M., “Chemical Engineering Kinetics”, Third Ed., McGraw-Hill Book Company, New York, N.Y., 1981.
From inspection of this equation the concentration of the heavy reacting material is largest at the location Z=0. Hence the risk of defluidization is greatest in a plug flow reactor at the location where the feed is introduced.
At the location Z=L the mass of coke per mass of fresh bed solids is necessarily given by quantity FΔCCRπ/S. This quantity of coke is related to the mass of the reacting pitch fraction introduced onto the solids at the location Z=0 through stoichiometry, yielding the equality:
Therefore to avoid defluidization
where the subscript “PLUG” is used to differentiate the plug flow reactor type.
Some observations can be made when comparing the continuous plug flow and well mixed systems to which fresh solids are continually advected. First, the well mixed CSTR system has the ability to accept more feed, since the tacky solids that are dried out are back mixed in with the rest of the bed solids, providing an additional mechanism to reduce the concentration of tacky solids in the bed. The incremental amount of feed that can be added in the well mixed system is dependent upon temperature. Second, the maximum amount of feed that can be accepted by the plug flow reactor is not dependent upon temperature, whereas the well mixed reactor contains a temperature-dependent termed as described. Third, the temperature independent term in the CSTR formulation is the same as that for the plug flow.
This result brings to light further issues with the findings disclosed in British patent 759,720.
The maximum feed rate that a plug flow reactor can accept is not dependent upon temperature, or on the mass of fluidized solids in the bed. Therefore, while the findings in British patent 759,720 would provide a conservative operating condition for the continuous, well mixed system, the findings in this patent would have no relevance whatsoever to a plug flow arrangement.
Comparing the results above, it is apparent that there are two factors that impact the maximum concentration of tacky material in the reactor, and hence the ability of the particular reactor configuration to resist defluidization by bogging. The first is the backmixing of dry solids in the reactor, and the second is the advection of dry solids into the reactor. The FB configuration relies solely on the backmixing of solid within the reactor to resist bogging, while the PLUG configuration relies solely on the advection of fresh solids. The CSTR configuration incorporates both backmixing and advection. Mathematically the maximum feed rate that can be fed to the CSTR to avoid bogging is the sum of the fed batch and plug flow derivations, and equation (8) is equal to the sum of equation (6) and equation (11).
While the extremes of no backmixing (plug flow) and complete backmixing (CSTR) are useful concepts, there are cases in real processes where the degree of backmixing lies somewhere in between these two extremes. By definition plug flow represents the case where the reactor volume consists of a series of CSTR units, each occupying the full cross section of the reactor, but each of infinitesimal volume. At the other extreme, in contrast to the infinite number of well-mixed subunits that formulate the plug flow reactor, the CSTR reactor can be viewed as comprising a single CSTR unit. Therefore, reactor configurations with degrees of backmixing between the PLUG and CSTR cases can be modeled by considering the reactor as being as a number of CSTR units in series, where the number is between unity and infinity. This concept has indeed found utility in practice in describing the mixing characteristics of various reactor configurations (see, for instance, Fogler, supra).
In practice it may not be possible or desirable to introduce the desired quantity of feed into only the first volume element of a particular reactor configuration. If the mixing condition of the solids in the reactor is characterized by n elements of equal volume using the CSTR-in-series description, and the feed is introduced over the first p volume elements, where p≦n, the maximum concentration will occur in the final element of this subset. Assuming each of the n elements receives the same amount of feed, which is practically the case in commercial applications, the total amount of feed that can be introduced without bogging can be derived by considering a series of volume elements, and constraining the exit concentration of element p to be less than αKC(mK/mb)*. The solution to this problem must consider the fact that although the temperature is uniform within each of the n elements, the temperature will drop along the length of the reactor due to process requirements and heat losses to the surroundings, so that Ti+1<T, where Ti is the temperature in any given volume element. Considering these temperature differences, the amount of feed that can be introduced to each of the p equal volume elements so that the maximum concentration does not exceed α(mK/mb)* is given by the equation:
where C1=αKC(mK/mb)*, C2=Ea/R, and kK|i is the first order rate constant (hr−1) associated with volume element i, related to temperature by the expression kK|i=A exp(−C2/Ti. The quantity (mK/mb)0 represents the amount of the reacting liquid pitch fraction contained on the fluidized solids entering the reactor.
The parameter C1 represents the quantity of coke that will be formed from the reacting pitch fraction feed residing on the fluidized solids at the point of bogging, expressed as a concentration (kg coke produced/kg bed solids). Any incremental feed introduced to the fluidized bed under these conditions will cause the bed to defluidize. This parameter is determined experimentally, as will be described.
The parameter C2 represents the activation energy for the reaction of the heavy hydrocarbon liquids. This value has been found to be relatively constant for heavy petroleum fractions, varying less than ˜7% about a value of 53 kcal/mol for a wide range of gasoils, light hydrocarbon fractions, and asphalt. (Raseev, S., “Thermal and Catalytic Processes in Petroleum Refining”, Marcel Dekker, Inc., New York, 2003).
With these definitions it is clear that the fraction of the fluidized bed that has been characterized by the parameter n that is receiving feed is given by the ratio ε=p/n. With ε as the independent variable, p can be determined by the integer value of the product of ε and n, given mathematically as p=INT(εn).
The above relationship captures the complete range of mixing conditions, and is illustrated in
Methods for determining the mixing characteristics “n” and “p” of a reactor vessel are well known in the art. One approach is described below:
where n represents the total number of volume elements that represent the fluidized bed.
The derivation of equation (14) can be found in standard reaction engineering text books, including those authored by Smith, and by Fogler. Evaluation of equation (14) is carried out using the data generated as described above, and standard numerical methods.
An example of this approach has been applied to the applicant's own cross flow coking bed process described in 2,505,632. A 0.5 scale model was constructed and a phosphorescent particles energized with ultraviolet light were injected into the bed. The presence of the tracer particles were detected at various locations. Applying the equations provided above the parameter n associated with the reactor was found to have a value of 15.
Generalized Feeding Strategy
As noted previously, it is desirable to operate a fluidized bed coking reactor to process as much feed material, and hence produce as much product as possible without causing the fluidized bed to defluidize, or worse still, to bog. The improved coking process therefore comprises an upper feed rate limit of feed material for the reactor that is defined from the derivations described previously. In particular, the upper feed rate limit of feed material is determined from equation (12), which is reproduced below as equation 18, except with feed rate F defined as “FMAX”:
The reactor can be operated safely at any feed material feed rate that is lower than the upper feed rate limit. However, it may be desirable to supply the feed material to the reactor at a rate that is within an optimal range which is safe but yet outputs product at an acceptably productive rate, and in such cases the improved coking process can include a lower feed rate limit. Because the reactor can ideally approach a pure plug flow state, the lower limit of the optimal feed rate range is determined for the plug flow case from equation (12), with p=1 and n=∞. Under these conditions equation (12) collapses to equation (11), which is reproduced below as equation 19 except with “FPLUG” replaced with “FMIN”:
The lower feed rate limit determined in this manner represents the most conservative feed material feed rate required to avoid defluidization. Lower rates will avoid defluidization, but may penalize process economics.
Determining the variables for equation (15) and equation (16) were previously discussed and are summarized below:
It is recognized that equation (17) represents the special case of equation (12), where the terms S and (mK/mb)0 are equal to zero, and n=p=1. While the fed-batch configuration is a convenient means of determining the parameter C1 as described, it is recognized that any reactor can be used for this purpose, provided that the mixing characteristics are known. A discussion on how to determine the mixing characteristics is described above.
The generalized feeding strategy of the improved coking process as described above can be implemented as a program executed by an automated supervisory controller that controls certain subsystems of a fluidized bed coking reactor, such as the cross-flow fluidized bed reactor 20 shown in
A supervisory controller is a controller that controls a number of individual subsystem controllers. The supervisory controller has information on how a number of sub-systems interact. Based on the status of these subsystems, and other measured inputs, the supervisory controller interacts with the controllers of the various sub-systems usually by adjusting the set-points of variables controlled by the sub-system controllers. In this embodiment, the supervisory controller is a programmable logic controller 100 as shown in
The subsystems controlled by the supervisory controller 100 in this embodiment are the functional elements of the reactor, namely the solids feed mechanism 106, the fluidization gas injector 108, and the feed material feed mechanism 110. The supervisory controller 100 manipulates the set points of these subsystems 106, 108, 110 to make sure that the upper feed rate limit FMAX is never exceeded. This is accomplished typically by adjusting a feed material set point feed rate FSP of the feed material feed mechanism 110. The solids rate S set point of the solids feed mechanism 106 can also be adjusted, but the adjustability of this rate can be constrained by the typical requirement that the solids be dry upon exiting the reactor 20. The fluidization gas set point of the fluidization gas injector 108 can also be adjusted, but the adjustability of this rate can be constrained by certain equipment in the hydrocarbon processing system 10, such as gas/solids separation equipment (not shown).
The supervisory controller 100 has a memory encoded with the generalized feeding strategy program which is executable by the controller 100 to carry out the generalized feeding strategy in the following manner:
It is understood that the controller parameters associated with proportional, derivative, and integral action will have to be optimized as would be known to one skilled in the art.
While exemplary embodiments of the invention have been illustrated and described, it will be appreciated that various changes can be made therein without departing from the scope and spirit of the invention.
Filing Document | Filing Date | Country | Kind | 371c Date |
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PCT/CA2011/001392 | 12/23/2011 | WO | 00 | 9/6/2013 |
Publishing Document | Publishing Date | Country | Kind |
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WO2012/083431 | 6/28/2012 | WO | A |
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2788312 | Moser, Jr. | Apr 1957 | A |
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Number | Date | Country |
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101911275 | Dec 2010 | CN |
759720 | Oct 1956 | GB |
768209 | Feb 1957 | GB |
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20130341174 A1 | Dec 2013 | US |
Number | Date | Country | |
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61426870 | Dec 2010 | US |