Claims:1. A method for controlling superheat of a molten metal during a continuous casting process, the method comprising:
detecting, by a control unit, arrival of a ladle to an online purging [OLP] station, wherein the ladle is adapted to transport the molten metal from a secondary metallurgical process to a casting unit;
determining, by the control unit, an OLP lifting temperature of the molten metal, based on temperature parameters and time parameters associated with the molten metal and the ladle; and
indicating, by the control unit, the OLP lifting temperature to an operator,.

2. The method as claimed in claim 1, wherein the OLP lifting temperature is used as a controlling variable to control the superheat of the molten metal during the continuous casting process.

3. The method as claimed in claim 1, wherein the OLP lifting temperature is determined by an empirical expression as an algebraic sum of a liquidus temperature of the molten metal, the superheat of the molten metal, change in a normal temperature drop during the continuous casting process, and a product of change in a thermal stratification temperature and a factor dependent on a turn-around-time of the ladle.

4. The method as claimed in claim 3, wherein the empirical expression is derived by a computational fluid dynamics methodology.

5. The method as claimed in claim 3, wherein the change in the normal temperature drop during the continuous casting process is a function dependent on the turn-around-time of the ladle, a holding time of the ladle, and a casting duration.

6. The method as claimed in claim 3, wherein the change in the thermal stratification temperature is a function dependent on the holding time of the ladle.

7. The method as claimed in claim 3, wherein the turn-around-time of the ladle is in the range of about 40 minutes to about 120 minutes.

8. The method as claimed in claim 5, wherein the holding time of the ladle is in the range of about 15 minutes to about 40 minutes.

9. The method as claimed in claim 1, wherein the ladle is adapted to transport the molten metal in the range of about 150 tonne to about 220 tonne.

10. The method as claimed in claim 1, the OLP lifting temperature is indicated on an indication unit associated with the control unit.

11. The method as claimed in claim 1, wherein the molten metal is a steel.

12. The method as claimed in claim 1, wherein the method is applicable for a steel plant. , Description:TECHNICAL FIELD
Present disclosure relates to a field of material science and metallurgy. Particularly, but not exclusively, the present disclosure relates to a continuous casting process. Further, embodiments of the present disclosure discloses a method for controlling superheat of a molten metal during the continuous casting process, for improvising efficiency of a metallurgical plant.

BACKGROUND OF THE DISCLOSURE
A continuous casting process is a metallurgical process involving continuous supply of a liquid metal, also referred to as a molten metal, into a mold. The molten metal may be solidified into a semi-finished billet, bloom, or slab in the mold, and may be subjected for subsequent rolling in the finishing mills. The mold may be adapted with a shape, configuration, dimension, and the like, so that, a billet obtained from the continuous casting process resembles a predefined profile. Further, the molten metal may be directly transferred from a secondary metallurgical processes to the continuous casting unit via one or more a ladles. The ladles may be adapted to teem the molten metal into the mold, through one or more tundish provided therein, to continuously cast the molten metal.

To increase productivity of a metallurgical plant, there is a need to maintain a constant rate of the continuous casting process, in order to minimize manufacturing meantime and production losses. Several factors may be involved in regulating the rate of continuous casting process such as, but not limited to, heat losses, abrupt solidification of the molten metal during casting process, spillage of molten metal, and the like. One of the controllable factors for enhancing the productivity of the metallurgical plant may be a superheat of the molten metal. The superheat of the molten metal may be defined as the difference in temperature of the molten metal between the teeming process and solidification of the molten metal, during the continuous casting process.

However, in the conventional continuous casting process, the ladle may be released from an online purging station at high temperature to avoid low superheat problem during the casting of the molten metal. Nonetheless, the high superheat of the molten metal may compel operators at the metallurgical plant to reduce the rate of continuous casting process, which may eventually lead to production loss.

The present disclosure is directed to overcome one or more limitations stated above or any other limitation associated with the prior arts.
SUMMARY OF THE DISCLOSURE

One or more shortcomings of the prior art are overcome by a method as disclosed and additional advantages are provided through the method as described in the present disclosure.

Additional features and advantages are realized through the techniques of the present disclosure. Other embodiments and aspects of the disclosure are described in detail herein and are considered a part of the claimed disclosure.

In one non-limiting embodiment of the disclosure, a method for controlling superheat of a molten metal during a continuous casting process is disclosed. The method comprises firstly detecting, by a control unit, arrival of a ladle to an online purging [OLP] station. The ladle is adapted to transport a molten metal from a secondary metallurgical process to a casting unit. Then, determining, by the control unit, an OLP lifting temperature of the molten metal, based on temperature parameters and time parameters associated with the molten metal and the ladle. The method further includes indicating, by the control unit, the OLP lifting temperature to an operator,. The OLP lifting temperature is used as a controlling variable to control the superheat of the molten metal during the continuous casting process.

In an embodiment, the OLP lifting temperature is determined by an empirical expression as an algebraic sum of a liquidus temperature of the molten metal, the superheat of the molten metal, change in a normal temperature drop during the continuous casting process, and a product of change in a thermal stratification temperature and a factor dependent on a turn-around-time of the ladle. The empirical expression is derived by a computational fluid dynamics methodology.

In an embodiment, the change in the normal temperature drop during the continuous casting process is a function dependent on the turn-around-time of the ladle, a holding time of the ladle, and a casting duration. Further, the change in the thermal stratification temperature is a function dependent on the holding time of the ladle.

In an embodiment, the turn-around-time of the ladle is in the range of about 40 minutes to about 120 minutes. Further, the holding time of the ladle is in the range of about 15 minutes to about 40 minutes. Also, the ladle is adapted to transport the molten metal in the range of about 150 tonne to about 220 tonne.
In an embodiment, the OLP lifting temperature is indicated on an indication unit associated with the control unit.

In an embodiment, the molten metal is a steel, and the method is applicable for a steel plant.

It is to be understood that the aspects and embodiments of the disclosure described above may be used in any combination with each other. Several of the aspects and embodiments may be combined together to form a further embodiment of the disclosure.

The foregoing summary is illustrative only and is not intended to be in any way limiting. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features will become apparent by reference to the drawings and the following detailed description.

BRIEF DESCRIPTION OF THE ACCOMPANYING FIGURES

The novel features and characteristics of the disclosure are set forth in the appended description. The disclosure itself, however, as well as a preferred mode of use, further objectives and advantages thereof, will best be understood by reference to the following detailed description of an illustrative embodiment when read in conjunction with the accompanying figures. One or more embodiments are now described, by way of example only, with reference to the accompanying figures wherein like reference numerals represent like elements and in which:
Figure. 1 illustrates a schematic process route of a ladle cycle during a continuous casting process, in accordance with an embodiment of the disclosure.

Figure. 2 illustrates a schematic representations of the ladle operations in the process route of the ladle cycle, during the continuous casting process, in accordance with an embodiment of the disclosure.

Figure. 3 illustrates a graphical representation of a variation of a bulk temperature of a liquid steel with respect to time spent by the ladle during the continuous casting process, predicted by a computational fluid dynamics [CFD] methodology, in accordance with an embodiment of the disclosure.

Figure. 4 illustrates a graphical representation of a variation of the bulk temperature of the liquid steel with respect to the time spent by the ladle during the continuous casting process, predicted by the CFD methodology for different slag layer thicknesses, in accordance with an embodiment of the present disclosure.

Figure. 5 illustrates a graphical representation of a variation of the bulk temperature of the liquid steel with respect to the time spent by the ladle during the continuous casting process, predicted by the CFD methodology for variations in ladle life, in accordance with an embodiment of the disclosure.

Figures. 6a-6c illustrates a graphical representation of a variation of hot face temperature of the ladle with turn-around-time [TAT] for a green ladle and the ladle in circulation i.e. after 45 Heats, in accordance with an embodiment of the present disclosure.

Figure. 7 illustrates a graphical representation of a steel plant trial results of an online purging [OLP] lifting temperature with respect to the OLP lifting temperature predicted by the empirical expression, in accordance with an embodiment of the present disclosure.

The figures depict embodiments of the disclosure for purposes of illustration only. One skilled in the art will readily recognize from the following description that alternative embodiments of the methods illustrated herein may be employed without departing from the principles of the disclosure described herein.

DETAILED DESCRIPTION

The foregoing has broadly outlined the features and technical advantages of the present disclosure in order that the detailed description of the disclosure that follows may be better understood. Additional features and advantages of the disclosure will be described hereinafter which form the subject of the description of the disclosure. It should also be realized by those skilled in the art that such equivalent methods do not depart from the scope of the disclosure. The novel features which are believed to be characteristic of the disclosure, as to method of operation, together with further objects and advantages will be better understood from the following description when considered in connection with the accompanying figures. It is to be expressly understood, however, that each of the figures is provided for the purpose of illustration and description only and is not intended as a definition of the limits of the present disclosure.
In the present document, the word "exemplary" is used herein to mean "serving as an example, instance, or illustration." Any embodiment or implementation of the present subject matter described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments.

While the disclosure is susceptible to various modifications and alternative forms, specific embodiment thereof has been shown by way of example in the drawings and will be described in detail below. It should be understood, however that it is not intended to limit the disclosure to the particular forms disclosed, but on the contrary, the disclosure is to cover all modifications, equivalents, and alternative falling within the spirit and the scope of the disclosure.

The terms “comprises”, “comprising”, or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a method that comprises a list of acts does not include only those acts but may include other acts not expressly listed or inherent to such method. In other words, one or more acts in a method proceeded by “comprises… a” does not, without more constraints, preclude the existence of other acts or additional acts in the method.

Embodiments of the present disclosure disclose a method for controlling a superheat of a molten metal during a continuous casting process. The superheat is a difference in temperature between a pouring and/or teeming temperature and a solidification temperature of the molten metal. In the continuous casting process such as, but not limiting to, a steel plant, superheat of the molten steel plays a major role to determine the quality of a cast. Controlling of the superheat within the desired limit may be required during casting for producing the cast of high quality, while minimizing production losses. In the conventional continuous casting processes the ladle may be released at high temperature from an online purging [OLP] station to avoid low superheat problem, which may leads to high superheat cases during the casting process. The high superheat compels operators to reduce the rate of casting, which in-turn leads to production losses.

Accordingly, the embodiments of the present disclosure disclose a method of controlling the superheat of a molten metal during a continuous casting process. In the method of the present disclosure, an online purging [OLP] lifting temperature is used as a controlling variable to control the superheat of the molten metal, during the continuous casting process. The OLP lifting temperature may be defined as the temperature at which a ladle should be released and/or dislodged from the OLP station, during a ladle cycle. The method of the present disclosure includes detecting, by a control unit, arrival of the ladle to the OLP station. Then, determining, by the control unit, the OLP lifting temperature of the molten metal, based on temperature parameters and time parameters associated with the molten metal and the ladle. The method further includes indicating, by the control unit, the OLP lifting temperature to an operator, to dislodge the ladle from the OLP station.

In an embodiment, the OLP lifting temperature may be determined by an empirical model or expression. The empirical model is an expression for the OLP lifting temperature with parameters identified as contributors towards heat transfer mechanism. A Computational Fluid Dynamics [CFD] methodology based investigation may be performed for a complete process cycle of the ladle, to identify these parameters. The CFD methodology based simulations may be further performed by varying the identified parameter to notice and/or observe sensitivity and trend of the identified parameters on the superheat of the molten metal.

Henceforth, the present disclosure is explained with the help of figures of a method of controlling the superheat of the molten metal during continuous casting process. However, such exemplary embodiments should not be construed as limitations of the present disclosure, since the method may be used on other types of steels where such need arises. A person skilled in the art can envisage various such embodiments without deviating from scope of the present disclosure.

Figure 1 is an exemplary embodiment of the present disclosure which illustrates a schematic process route of a ladle cycle traced by a ladle, in a metallurgical plant, during a continuous casting process. The ladle, prior commencing with the continuous casting process, may be cleaned and inspected for cracks and/or any defects in its refractory, at a green ladle unit. Further, the ladle employed in the continuous casting process for the first time may be referred to as a green ladle. The refractory of the green ladle may be manufactured with suitable lining material such as, but not limited to, dolomite bricks, magnesia chrome bricks, magnesia carbon bricks, high alumina bricks, aluminum carbon bricks, and the like, in order to enhance properties of the green ladle. The properties may be including, but not limited to, withstand service conditions and chemical heating, high thermal resistance, and the like.

The green ladle, on inspection, may then be transported to a pre-heating chamber, where the green ladle may be subjected to a heating process such that, the refractory of the green ladle may be heated up to a temperature of about 1000ºC. This pre-heating of the ladle may be performed to assist in mitigating thermal shocks, which in-turn may damage the refractory of the ladle. Additionally, the ladles, particularly the green ladles, on pre-heating assists in curbing conventional and radiational heat losses therein. Further, upon pre-heating, the green ladle, or the ladle, may be transported to a tapping station. At the tapping station, a molten metal which is derived from a secondary metallurgical process may be tapped into the ladle and secured therein. In an embodiment, the molten metal may be tapped from a blast furnace. It may be noted that the molten metal may be at an elevated temperature of about 1750ºC to about 1850ºC, during the tapping. Additionally, during tapping of the molten metal, other regents and/or reactants such as, but not limited to, ferroalloy additions and/or additives, may be introduced. In an embodiment, the ferroalloy additions and/or additives may include, but may not be limited to, high Carbon FeMn, SiMn, Ferro Silicon, aluminium, lime, coke, and the like. Once a predefined quantity of the molten metal may be collected in the ladle, the ladle may then be transported to an online purging [OLP] station. As an example, the ladle may transport the molten metal ranging from about 170 tonne to 220 tonne.

At the OLP station, the molten metal in the ladle may be churned and/or purged by supplying pressurized gases. The pressurized gases may be at least one of the inert gases, whereby purging the inert gas may generate turbulence to enhance thermal homogenization in the molten metal. Further, during purging of the molten metal, similar to the tapping, the ferroalloy additions and/or additives may be introduced. It may be noted that the purging of the molten metal may be performed in order to attain uniform temperature and consistency in chemical composition of the molten metal, in the ladle. In an embodiment, upon purging the molten metal for a predefined time and/or a predetermined temperature, the ladle may be held at a particular position of the metallurgical plant for a pre-calculated time, also referred to as a holding time. During this holding time, the ladle, and in-turn the molten metal, may be held idle, with or without a cover member being placed over the ladle for enclosure.

Once the ladle, and in-turn the molten metal, lapses the holding time, the ladle may then be transported to a teeming unit. At the teeming unit, the ladle may be tilted to continuously teem and/or pour the molten metal on to a one or more tundish, thereafter to a casting mold, or also referred to as a caster, for producing a continuous cast product. In an embodiment, the ladle, upon completely teeming the molten metal, may be configured to dump slag in the ladle at a slag dumping unit, where the slag may be formed during traversing of the ladle at various process route of the ladle cycle in the metallurgical plant. Post dumping of the slag, the ladle may be transported to an inspection and repair unit, where the ladle may be inspected for any defects and/or repairs that may be required. Upon completion of the inspection and/or repairs, the ladle may be adapted to be re-aligned for receiving the molten metal, at the tapping unit.

Referring now to Figure.2, which is a schematic representation of the ladle operation in the process route of the ladle cycle in the metallurgical plant, which in the exemplary embodiment is a steel plant. The ladle operation may be regulated in order to improve efficiency of the steel plant. Here, upon transporting the ladle from the tapping station to the OLP station, superheat of the molten metal may be controlled, by regulating movement and/or transportation of the ladle therefrom. In an embodiment, the molten metal referred herein is steel. Further, an OLP lifting temperature may be determined, to indicate an operator to dislodge the ladle from the OLP station, in order to transport the ladle to the teeming station, for maintaining the superheat of the molten metal.

The OLP lifting temperature may be determined by considering various parameters such as temperature parameters and time parameters, during the continuous casting process, of a molten steel, herein also referred to as the molten metal.

In an embodiment, thermal profile of the molten metal may be derived, during movement and/or transportation of the ladle from the tapping station to the OLP station and thereafter for the holding time period of the ladle, through a computational fluid dynamics [CFD] methodology stored in a control unit. Additionally, reduction in the temperature of the molten metal, due to the addition of the ferroalloy additions and/or additives, during the tapping process and the purging process, may also be considered as a parameter for the CFD methodology. In an embodiment, the one or more sensors may be provided in the ladle, where the one or more sensors may be configured to determine the temperature parameters and the time parameters therein. Further, the temperature parameters and the time parameters, of the molten steel and the ladle, sensed by the one or more sensors, may be communicated to the control unit, as signals. The control unit may then derive an empirical model, based on the CFD methodology therein, to determine and/or predict the OLP lifting temperature, for improving the efficiency and/or productivity of the steel plant.
Here, one skilled in the art would recognize that the temperature parameters and the time parameters employed for deriving various graphical representations depicted hereafter, are sensed by the one or more sensors and analysed by the control unit, based on the CFD methodology.
Referring now to Figure. 3, which depicts a plot of a bulk temperature of a molten steel as a function of the time spent by the ladle at various process routes of the ladle cycle, in the steel plant. It may be noted that a linear variation of the bulk temperature with respect to the time spent is achieved, during movement and/or transportation of the ladle from the tapping station to beginning of the teeming station.

Further, thickness of the slag formed during the transportation of the ladle, and in-turn the molten steel, was considered for reduction of the heat loss at a top surface of the molten steel. In view of this, a plot of the bulk temperature of the molten steel as a function of the time spent by the ladle in the various process route of the ladle cycle may be generated through the CFD methodology. Figure.4 depicts the plot for three different slag thicknesses on the molten steel. However, due to minor variations in slopes for each of the three different slag thicknesses therein. It may be noticed that the thickness of the slag may be effective in controlling the heat loss from the ladle.

Also, ladle life may be considered as one of the parameters controlling the superheat of the molten metal. It may be noted that the refractory of the ladle may be eroded with increase in the ladle life. The reduction in thickness of the refractory may enhance heat transfer from an outer surface of the ladle to its inner surface. In view of this, the ladle life may be considered as a parameter for the CFD methodology. As an example, five different life of the ladle may be considered. The ladle life may be 15 heats, 30 heats, 45 heats, 60 heats, and 75 heats, where the heat may be referred to as a number of times the ladle is filled with the molten steel, or a number of cycles performed by the ladle at the tapping station. Figure. 5 illustrates variation of the bulk temperature of the molten metal as a function of the time spent by the ladle at various process route of the ladle cycle, for different life of the ladle. It may be noted from the slopes of each of the five different life of the ladle that, no significant drop in the bulk temperature of the molten steel is observed with change in the ladle life. In addition, drop in the bulk temperature of the molten metal in the green ladle in comparison with the five different life of the ladle may also be observed. Moreover, it may also be noted that, maintaining a comparatively high initial refractory temperature may lead to low temperature drop of the molten steel in the green ladle. Thus, it can be derived from these plots that the role of ladle life with respect to the bulk temperature of the molten steel is minor.
Furthermore, it is noted that the time spent by the ladle at the slag dumping station and the repair and/or inspection may be comparatively high before re-aligning at the tapping station. Here, the heat loss from the refractory of the ladle may be increased with increase in the time spent by the ladle at the slag dumping unit and at the repair and/or inspection unit. Figures. 6a to 6c depicts plots with various zones of the ladle as a function of a turn-around-time [TAT] of the ladle. The TAT may be defined as a complete time spent by the ladle in the process route of the ladle cycle. Further, each of the plots in Figures. 6a to 6c depicts comparison of the green ladle with that of the ladle in circulation, in the steel plant. It may be noticed that the temperature drop in the molten steel after 90 minutes of the TAT becomes minor, but, is still significant.
In view of the above parameters, the control unit by employing the CFD methodology, may establish a relation between the temperature parameters and the time parameters, in order to derive the thermal profile. Here, with the thermal profile and the empirical model developed from the CFD methodology, the control unit may determine the temperature at which the ladle may be dislodged from the OLP station, i.e. the OLP lifting temperature, such that the superheat of the molten metal may be controlled.

In an embodiment, the empirical model, or also referred to as an empirical expression, may be developed through regression analysis of data pre-fed to the control unit, for CFD methodology, may also incorporate a chill factor of the ferroalloy additions and/or additives given in Table 1.
SI. No. Ferro Alloy Added oC Change for one Kg of addition per MT of steel
1 High Carbon FeMn -2.26
2 SiMn -1.58
3 Ferro Silicon -1.73
4 Aluminium +0.16
5 Lime -0.14
6 Coke -5.96
Table 1
Further, on accumulating the temperature parameters and the time parameters, the control unit may be configured to determine the OLP lifting temperature, by the CFD methodology, for a predefined condition of the ladle and the molten steel, in the steel plant. The OLP lifting temperature, determined vide the empirical expression of the CFD methodology, may be defined as an algebraic sum of a liquidus temperature of the molten metal, the superheat of the molten metal, change in a normal temperature drop during the continuous casting process, and a product of change in a thermal stratification temperature and a factor dependent on a turn-around-time of the ladle.

The expression for the OLP lifting temperature is given as:

OLP lifting temperature = f ------------- (1)

where,
OLP lifting temperature: determined OLP lifting temperature (in OC)
: Liquidus temperature (in OC)
: Change in normal temperature drop (in OC)
: Change in temperature drop due to thermal stratification (in OC).

Super heat: Desired super heat at the caster for a current heat of the ladle (in OC).
Here, the thermal stratification temperature may be deduced by the expression,

------- (2)
where,
: Estimated time (in minutes) between OLP end to casting start. In an embodiment, the holding time of the ladle is in the range of about 15 minutes to about 40 minutes.

Further, the normal temperature drop may be deduced by the expression,

--------- (3)
where,
TAT : Turn Around Time (in minutes) is the amount of time spent by the ladle in inspection, repairing and slag dumping, in previous heat of the ladle. In an embodiment, the TAT of the ladle is in the range of about 40 minutes to about 120 minutes.

: Estimated Casting duration (in minutes) of current heat of the ladle, till the first superheat reading of the molten steel is recorded.

Furthermore, the factor dependent on the TAT of the ladle, which influences the OLP lifting temperature may be deduced by the expression,

f = a9 TAT-a10 TAT2 --------- (4)

Here, the value of coefficient a0 to a10 of the expression 1 to the expression 4 may be derived from the Table 2 mentioned below.

SI. No. Coefficients/Constants Range
1 a0 3-4
2 a1 2-3
3 a2 0.09-0.1
4 a3 0.001-0.003
5 a4 .00025-.00035
6 a5 0.5-0.6
7 a6 0.05-0.06
8 a7 1.5-2.5
9 a8 0.1-0.2
10 a9 0.01-0.03
11 a10 0.00005-0.00007

Table 2.

Further, in the Figure.7, regression of a practical OLP lifting temperature as a function of a determined output OLP lifting temperature, by the control unit, for life of the ladle at 40 heats in a direct route is depicted. It may be observed that the regression exhibits that about 92% of the determination output OLP lifting temperature shows variation in the range of about ±10OC with that of the practical OLP lifting temperature. It was further noticed that about 71% of the determined OLP lifting temperature exhibits variation of about + 5 OC with the practical OLP lifting temperature. Thus it is evident that, the OLP lifting temperature determined and/or predicated by the control unit, based on the empirical expression derived from the CFD methodology, is within acceptable ranges, and thus, can be construed to assist in controlling the superheat of the molten steel, during the continuous casting process.

The CFD methodology is developed by formulation of governing equations for all the processes aforementioned. The equations are then solved for the computational domain of the ladle and that of the molten steel, for each ladle cycle.

In an embodiment, the OLP lifting temperature is indicated on an indication unit associated with the control unit. The indication unit may be at least one of a visual indication unit, audio indication unit, audio-visual indication unit, and the like.

In an embodiment of the disclosure, the method of the present disclosure determines OLP lifting temperature, which may be used as variable for controlling the superheat during continuous casting process. The controlling of the super heat improves productivity of the casting process, and reduces the downtime.

EQUIVALENTS:

With respect to the use of substantially any plural and/or singular terms herein, those having skill in the art can translate from the plural to the singular and/or from the singular to the plural as is appropriate to the context and/or application. The various singular/plural permutations may be expressly set forth herein for sake of clarity.

It will be understood by those within the art that, in general, terms used herein, and especially in the appended claims (e.g., bodies of the appended claims) are generally intended as "open" terms (e.g., the term "including" should be interpreted as "including but not limited to," the term "having" should be interpreted as "having at least," the term "includes" should be interpreted as "includes but is not limited to," etc.). It will be further understood by those within the art that if a specific number of an introduced claim recitation is intended, such an intent will be explicitly recited in the claim, and in the absence of such recitation no such intent is present. For example, as an aid to understanding, the following appended claims may contain usage of the introductory phrases "at least one" and "one or more" to introduce claim recitations. However, the use of such phrases should not be construed to imply that the introduction of a claim recitation by the indefinite articles "a" or "an" limits any particular claim containing such introduced claim recitation to inventions containing only one such recitation, even when the same claim includes the introductory phrases "one or more" or "at least one" and indefinite articles such as "a" or "an" (e.g., "a" and/or "an" should typically be interpreted to mean "at least one" or "one or more"); the same holds true for the use of definite articles used to introduce claim recitations. In addition, even if a specific number of an introduced claim recitation is explicitly recited, those skilled in the art will recognize that such recitation should typically be interpreted to mean at least the recited number (e.g., the bare recitation of "two recitations," without other modifiers, typically means at least two recitations, or two or more recitations). Furthermore, in those instances where a convention analogous to "at least one of A, B, and C, etc." is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., "a system having at least one of A, B, and C" would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and/or A, B, and C together, etc.). In those instances where a convention analogous to "at least one of A, B, or C, etc." is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., "a system having at least one of A, B, or C" would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and/or A, B, and C together, etc.). It will be further understood by those within the art that virtually any disjunctive word and/or phrase presenting two or more alternative terms, whether in the description, claims, or drawings, should be understood to contemplate the possibilities of including one of the terms, either of the terms, or both terms. For example, the phrase "A or B" will be understood to include the possibilities of "A" or "B" or "A and B."

While various aspects and embodiments have been disclosed herein, other aspects and embodiments will be apparent to those skilled in the art. The various aspects and embodiments disclosed herein are for purposes of illustration and are not intended to be limiting, with the true scope and spirit being indicated by the following claims.