Patent Application
20250012270
Examples described herein generally relate to pumps. More specifically, the examples described herein generally relate to positive displacement pumps. Even more specifically, the examples described herein relate to positive displacement pumps having direct load wrist pins.
Positive displacement reciprocating pumps pump fluid at high pressure and constant flow. Positive displacement reciprocating pumps can be used for various applications within oil and gas, such as, for example, drilling, fracking, or the like. Positive displacement reciprocating pumps have multiple moving parts and are heavy and large. The inventors of the present disclosure have discovered a need to make a direct load path, which can decrease the weight and size of the pump and can reduce the number of parts required in manufacturing and maintaining the pump.
In examples, a positive displacement reciprocating pump can include a crank member, a wrist pin assembly, a plunger assembly, and a pump section. The crank member can be rotatable about a central axis. The wrist pin assembly can be pivotably coupled to the crank member. The wrist pin assembly can be operable to translate in a first direction and a second direction as the crank member rotates. The plunger assembly can be directly coupled to the wrist pin assembly. The plunger assembly can translate along a central axis in the first direction and the second direction as the crank member rotates. The pump section can be pressurized by the plunger assembly moving in the first direction and depressurized by the plunger assembly moving in the second direction.
In examples, a wrist pin assembly can include a connecting rod, a housing, a crosshead, a wrist pin, and a plunger assembly. The connecting rod can be pivotably attached to a crank member. The housing can extend between a crank member end and a piston rod end. The connecting rod can extend from the crank member and into the housing through the crank member end. The crosshead can be installed within the housing. The crosshead can be operable to translate within the housing between the crank member end and the piston rod end. The wrist pin can be installed within the crosshead. The connecting rod can be pivotably attached to the wrist pin to translate the wrist pin and the crosshead within the housing in a first direction and a second direction as the crank member rotates. The plunger assembly can be directly coupled to the wrist pin and extend from the wrist pin through the piston rod end. The plunger assembly can translate along a central axis in the first direction and the second direction as the crank member rotates.
Various examples are illustrated in the figures of the accompanying drawings. Such examples are demonstrative and not intended to be exhaustive or exclusive embodiments of the present subject matter.
Positive displacement reciprocating pumps can include single or multiple plungers or pistons in single or multiple cylinders, respectively. A slider-crank mechanism can drive the plunger and piston. The slider-crank mechanism can convert the rotational motion of crankshafts into a reciprocating motion of the plunger and piston. The generated reciprocating motion can create a suction phenomenon in a pump section while the plunger or piston is traveling in one direction and a discharge phenomenon while the plunger or piston is traveling in an opposite direction. In the discharge direction, the pump can experience high axial loads on the plunger and piston rod, which can be transferred through a wrist pin, a crosshead, and a connecting rod assembly. The inventors of the present disclosure have created a wrist pin assembly that can be used in positive displacement reciprocating pumps. In some examples, the wrist pin can be effective to decrease the size of reciprocating pumps, decrease the weight of reciprocating pumps, and reduce the loads imposed on the crosshead via the cranking member. The direct load wrist pin will be discussed in more detail with reference to
The crank member 110 can be configured to translate a rotational motion from a rotary member 114 to the wrist pin assembly 120. The crank member 110 can be installed within a crank member housing 112. A rotary member 114 can extend through the crank member housing 112 to couple the crank member 110 to a power source. The rotary member 114 can be a shaft coupled to the crank member 110, via a cam, or any other device that can transfer rotational motion from a shaft rotating about a first axis to a gear, disc, sprocket, or the like rotating about a second axis. In examples, the crank member 110 can be rotatable about a central axis CA such that the rotational energy of the rotary member 114 can rotate the crank member 110. For example, a perimeter surface 116 of the crank member 110 can be in direct contact with the rotary member 114 such that the rotary member 114 rotates the crank member 110 about the central axis CA. The crank member 110 can include cast iron, carbon steel, alloy steel, forged steel, billet steel, nodular iron, any combination or alloy thereof, or the like. The function of the crank member 110 will be discussed in more detail herein with reference to
The wrist pin assembly 120 can be configured to transfer axial load from the crank member 110 to the plunger assembly 140. The wrist pin assembly 120 can be pivotably coupled to the crank member 110. The wrist pin assembly 120 can be operable to translate in a first direction A and a second direction B as the crank member 110 rotates. The wrist pin assembly 120 will be discussed in more detail with reference to
The plunger assembly 140 can be configured to receive the axial load from the wrist pin assembly 120 and translate in the first direction A and the second direction B into and out of the pump section 150, respectively. The plunger assembly 140 can be directly coupled to the wrist pin assembly 120. The plunger assembly 140 can translate along a longitudinal axis LA in the first direction A and the second direction B as the crank member 110 rotates. The plunger assembly 140 will be discussed in more detail with reference to
The pump section 150 can be configured to use the energy provided by the plunger assembly 140 to pump the fluid through the positive displacement pump 100. The pump section 150 can be pressurized by the plunger assembly 140 moving in the first direction A and depressurized by the plunger assembly 140 moving in the second direction B. In examples, as the pump section 150 is depressurized, the pump section 150 can draw a working fluid within the pump section 150 (e.g., from a fluid supply source), and as the pump section 150 is pressurized, the pump section 150 can expel the working fluid from the pump section 150 (e.g., to a pressurized side such as to a wellhead for fracking or other operations) to move the working fluid through the pump section 150.
The connecting rod 122 can be configured to convert rotational motion of the crank member 110 to longitudinal motion. In one or more examples, the connecting rod 122 can be an elongated member that can be at least partially hollow. The connecting rod 122 can be pivotably attached to and extend from the crank member 110 into the housing 124 and be pivotably attached to the wrist pin 132 within the housing 124 and the crosshead 130. In one or more examples, the connecting rod can be connected to the crank member near an outer peripheral edge such that the end of the connecting rod coupled to the crank member follows a circular path as the crank member rotates.
The housing 124 can be configured to provide a reciprocation chamber in which the crosshead 130 can articulate back and forth in directions A and B. The housing 124 can, thus, maintain the lateral position of the crosshead 130. The housing 124 can extend between a crank member end 126 and a piston rod end 128. The connecting rod 122 can extend into the housing 124 via the crank member end 126. The housing can define a reciprocation chamber having circular, interrupted circular, oval, square, or the like cross-section adapted to receive and control the motion of the crosshead. In one or more examples, the chamber can have a diameter slightly larger than the crosshead.
The crosshead 130 can be configured for arrangement in the chamber of the housing 124 to articulate back and forth within the chamber in the directions A and B. The crosshead 130 can interface with the housing 124 to control the lateral motion of the end of the connecting rod connected thereto. The crosshead 130 can be generally cylindrically shaped and extend along a central axis CA. The crosshead 130 can have a cylindrical, interrupted circular, oval, square, or the like cross-section. The crosshead 130 can include steel, iron, stainless steel, aluminum, titanium, non-metallic composites, any alloys or combinations thereof, or the like. The crosshead 130 can be hollow such as to permit coupling of the connecting rod 122 to the wrist pin 132 arranged therewithin. The crosshead 130 can be installed within the housing 124. The crosshead 130 can be operable to translate within the housing 124 between the crank member end 126 and the piston rod end 128 of the housing 124.
The wrist pin 132 can be configured for coupling to the connecting rod 122 to receive longitudinal forces in both directions A and B and transfer those forces to the plunger assembly 140. Notably, the present wrist pin may do so directly. The wrist pin 132 can be a pin, rod, or another linkage that is elongated and can extend across an internal diameter of the hollow portion of the crosshead 130. In examples, the wrist pin 132 can be hollow to reduce material and reduce the weight of the wrist pin 132. The wrist pin 132 can include steel, iron, stainless steel, aluminum, titanium, non-metallic composites, any alloys or combinations thereof, or the like. The wrist pin 132 can be installed within the crosshead 130. In examples, the connecting rod 122 can be pivotably attached to the wrist pin 132 to translate the wrist pin 132 and the crosshead 130 within the housing 124 in the first direction A and the second direction B as the crank member 110 rotates. The connecting rod 122, the housing 124, the crosshead 130, and the wrist pin 132 will be discussed in more detail with reference to
The connecting rod 122 can be an elongated member extending between a crank side section 160 and a wrist pin side section 164. The crank side section 160 can include a crank side attachment 162. The crank side attachment 162 can be configured to attach to the connecting rod 122 to the crank member 110. In examples, the crank side attachment 162 can be a clamp, such as, for example, a two-piece clamp, or any other connecting interface that can connect the connecting rod 122 to the crank member 110. In particular, the connecting interface may be adapted to clamp around a pin with a bearing, for example, so that the crank side section 160 of the connecting rod 122 may pivotally couple to a pin on the surface of the crank member and may follow the pin around a circular path of the crank member. The wrist pin side section 164 can be opposite the crank side section 160. The wrist pin side section 164 can include a wrist pin side attachment interface 166.
The wrist pin side attachment interface 166 can be an aperture, clamp, or any other mechanism that can attach the wrist pin side section 164 of the connecting rod 122 to the wrist pin 132. In examples, the wrist pin 132 can be installed into the wrist pin side attachment interface 166 to couple the wrist pin 132 to the crosshead 130.
As discussed herein, the crosshead 130 can be hollow such as to permit the wrist pin side section 164 of the connecting rod 122 can fit within the crosshead 130. The crosshead 130 can include a first aperture 134 and a second aperture 136 (shown in phantom in
The wrist pin 132 can be installed into the wrist pin side attachment interface 166 of the connecting rod 122 within the crosshead 130. For example, at least a portion of the wrist pin 132 can extend into the first aperture 134 and the second aperture 136 when the wrist pin 132 is installed within the crosshead 130. As such, the wrist pin 132 can transfer axial loads to the crosshead 130 while reducing, minimizing, or avoiding transfer of the non-axial loads transferred from the wrist pin 132 to the crosshead 130. The crosshead 130 can engage with the housing 124 (first shown in
The plunger assembly 140 can be directly connected to the wrist pin 132 such that, the axial load transferred to the wrist pin 132 from the connecting rod 122 can be directly transferred to the plunger assembly 140. The connection between the wrist pin 132 and the plunger assembly 140 will be discussed in more detail with reference to
The plunger assembly 140 can include a pony rod 170. The pony rod 170 can be coupled to the wrist pin 132 such that the pony rod 170 translates with the connecting rod 122, the crosshead 130, and the wrist pin 132 due to rotation of the crank member 110. The pony rod 170 can be a hollow shaft, rod, or another elongated member that can transfer force between the wrist pin 132 and the piston rod 174.
The wrist pin 132 can include a pony rod attachment interface 172 that can extend radially therefrom the wrist pin 132. The pony rod attachment interface 172 can be configured to couple the pony rod 170 to the wrist pin 132. in examples, the pony rod attachment interface 172 can include a threaded surface that can be complementary to a threaded surface on the pony rod 170, such as to removably couple the pony rod attachment interface 172 to the wrist pin 132. In examples, the pony rod attachment interface 172 can include a threaded pin and aperture, tongue and groove, or any other coupling mechanism that can be complementary with the pony rod 170 to removably secure, attach, or couple the pony rod 170 to the wrist pin 132.
In examples, the pony rod attachment interface 172 can extend from the wrist pin 132 such that the pony rod attachment interface 172 can be secured within (i.e., inserted within) the pony rod 170 as the pony rod 170 is attached to the pony rod attachment interface 172. In examples, the pony rod attachment interface 172 can be formed within the wrist pin 132 such that the pony rod 170 has an appendage that inserts within the pony rod attachment interface 172 to secure the pony rod 170 to the wrist pin 132. In examples, the wrist pin 132 and the pony rod 170 can have multiple attachment interfaces that are engaged as the pony rod 170 is attached to the wrist pin 132.
Because the pony rod 170 is directly secured, attached, or coupled to the wrist pin 132, the pony rod 170 can translate in the first direction A and the second direction B along a longitudinal axis LA of the pony rod 170 as the crank member 110 rotates. The pony rod attachment interface 172 can directly attach the pony rod 170 or the piston rod 174 to the wrist pin 132, which can reduce the parts and reduce the length of the wrist pin assembly 120 and the plunger assembly 140. The decreased length of the wrist pin assembly 120 and the plunger assembly 140, compared to standard reciprocating pumps, can help reduce the weight of the positive displacement pump 100 and permit the positive displacement pump 100 to fit within smaller envelopes while maintaining the same pumping capacity as comparable reciprocating pumps. Moreover, as the connecting rod 122 can be pivotably attached to the wrist pin 132, the connecting rod 122 can mainly only transfer the axial loads to the wrist pin 132, which can reduce the radial loading of the crosshead 130. Thus, the crosshead 130 can be thinner and made from less material, which can reduce the weight of the crosshead 130.
The plunger assembly 140 can include a piston rod 174. The piston rod 174 can be removably coupled to the pony rod 170 opposite the pony rod attachment interface 172 of the wrist pin 132. The piston rod 174 can extend into the pump section 150 of the positive displacement pump 100 to pressurize and depressurize the pump section 150 as the piston rod 174 translates in the first direction A and the second direction B, respectively.
The plunger assembly 140 can also include a clamp 176. The clamp 176 can be configured to removably couple the piston rod 174 to the pony rod 170. The clamp 176 enables the piston rod 174 to be replaced without tearing into the rest of the positive displacement pump 100. For example, the clamp 176 can be removed, and the piston rod 174 can be replaced. As the piston rod 174 can become worn during the operation of the positive displacement pump 100, the clamp 176 helps reduce downtime of the positive displacement pump 100 while performing repairs, preventative maintenance, or the like. In examples of the plunger assembly 140, the pony rod 170 and the piston rod 174 can be a single unitary rod that directly connects to the pony rod attachment interface 172 of the wrist pin 132 and extends into the pump section 150.
In examples, such as the example shown in
The housing 124 can be fluidically sealed. For example, the piston rod end 128 can include one or more seals 125 to help maintain lubricating fluid (e.g., oil, graphite, or the like) within the housing 124. The crank member end 126 can also include one or more seals to isolate the lubricating fluid within the housing 124. In examples, the housing 124 can be fluidically connected to the crank member housing 112 such that a single lubricating fluid can be used to lubricate the crank member 110, at least a portion of the rotary member 114, the connecting rod 122, the crosshead 130, and the wrist pin 132.
As discussed herein, the crank member 110 can be pivotably coupled to the wrist pin assembly 120, and more specifically, the crank member 110 can be pivotably coupled to the crank side section 160 of the connecting rod 122. As such, as the crank member 110 rotates, the wrist pin assembly 120 can translate between the crank member end 126 and the piston rod end 128 of the housing 124.
For example, the crank member 110 can rotate counterclockwise to move the wrist pin assembly 120 from the first position 600 (as shown in
In another example, the crank member 110 can rotate clockwise to move the wrist pin assembly 120 from the first position 600 to the fourth position 900. As the wrist pin assembly 120 is in the fourth position 900, the crank member 110 can rotate clockwise to move the wrist pin assembly 120 into the third position 800. As the wrist pin assembly 120 is in the third position 800, the crank member 110 can rotate clockwise to move the wrist pin assembly 120 into the second position 700. As the wrist pin assembly 120 is in the second position 700, the crank member 110 can rotate clockwise to move the wrist pin assembly 120 into the first position 600.
The first position 600, the second position 700, the third position 800, and the fourth position 900 are not the only positions of the wrist pin assembly 120. For example, the crank member 110 can rotate such as to put the wrist pin assembly 120 in any position between any of the first position 600, the second position 700, the third position 800, and the fourth position 900.
In each of the above examples, the connecting rod 122, the crosshead 130, the wrist pin 132, and the plunger assembly 140 can translate within the housing 124 with respect to the rotation of the crank member 110. For example, when the crank member 110 moves the wrist pin assembly 120 into the second position 700, the connecting rod 122, the crosshead 130, the wrist pin 132, and the plunger assembly 140 can translate to a maximum position in the first direction A. For example, when the crank member 110 is in the fourth position 900, the connecting rod 122, the crosshead 130, the wrist pin 132, and the plunger assembly 140 can translate to a maximum position in the second direction B.
As discussed herein, the connecting rod 122 is pivotably attached to the crank member 110 and the wrist pin 132 on opposite ends of the connecting rod 122. As the crank member 110 rotates, the connecting rod 122 can traverse in the first direction A and the second direction B as the crank member end 126 of the connecting rod 122 moves about the central axis CA of the crank member 110. The wrist pin 132 can engage with the first aperture 134 and the second aperture 136 of the crosshead 130 to translate the crosshead 130 in the first direction A and the second direction B as the connecting rod 122 moves in the first direction A and the second direction B, respectively.
As discussed herein, the plunger assembly 140 can be attached directly to the connecting rod 122. For example, the pony rod 170 can be attached directly to the pony rod attachment interface 172 of the wrist pin 132. As the wrist pin 132 translates in the first direction A and the second direction B, the plunger assembly 140 also translates in the first direction A and the second direction B, respectively. The piston rod 174 can be directly coupled to the pony rod attachment interface 172 such that the piston rod 174 translates in the first direction A and the second direction B as the pony rod attachment interface 172 translates in the first direction A and the second direction B, respectively. Therefore, as the crank member 110 rotates, the piston rod 174 can pressurize and depressurize the pump section 150 as the piston rod 174 moves in the first direction A and the second direction B, respectively.
The following, non-limiting examples, detail certain aspects of the present subject matter to solve the challenges and provide the benefits discussed herein, among others.
Example 1 is a positive displacement reciprocating pump comprising: a crank member rotatable about a central axis; a wrist pin assembly pivotably coupled to the crank member, the wrist pin assembly operable to translate in a first direction and a second direction as the crank member rotates; a plunger assembly directly coupled to the wrist pin assembly, the plunger assembly translates along a central axis in the first direction and the second direction as the crank member rotates; and a pump section pressurized by the plunger assembly moving in the first direction and depressurized by the plunger assembly moving in the second direction.
In Example 2, the subject matter of Example 1 includes, wherein the wrist pin assembly comprises: a connecting rod pivotably attached to the crank member; a housing extending between a crank member end and a piston rod end, the connecting rod extending from the crank member and into the housing through the crank member end; a crosshead installed within the housing, the crosshead operable to translate within the housing between the crank member end and the piston rod end; and a wrist pin installed within the crosshead, the connecting rod pivotably attached to the wrist pin to translate the wrist pin and the crosshead within the housing in the first direction and the second direction as the crank member rotates.
In Example 3, the subject matter of Example 2 includes, wherein the connecting rod comprises: a crank side section comprising: a crank side attachment interface configured to attach the connecting rod to the crank member; and a wrist pin side section, the wrist pin side section opposite the crank side section, the connecting rod extending longitudinally between the crank side section and the wrist pin side section, the wrist pin side section comprising: a wrist pin side attachment interface.
In Example 4, the subject matter of Example 3 includes, wherein the wrist pin is installed into the wrist pin side attachment interface to couple the wrist pin to the crosshead.
In Example 5, the subject matter of Example 4 includes, wherein the crosshead is hollow such that the wrist pin side section of the connecting rod can fit within the crosshead, the crosshead comprising: a first aperture; and a second aperture, the first aperture concentrically aligned with the second aperture such that a vertical axis of the first aperture and the second aperture are orthogonal to the central axis of the crosshead.
In Example 6, the subject matter of Example 5 includes, wherein at least a portion of the wrist pin extends into the first aperture and the second aperture when the wrist pin is installed within the crosshead.
In Example 7, the subject matter of Example 6 includes, wherein the wrist pin comprises: a pony rod attachment interface extending radially therefrom.
In Example 8, the subject matter of Example 7 includes, wherein the plunger assembly comprises: a pony rod coupled to the pony rod attachment interface of the wrist pin, the pony rod operable to translate in a first direction and a second direction along a longitudinal axis of the pony rod as the crank member rotates.
In Example 9, the subject matter of Example 8 includes, wherein the plunger assembly comprises: a piston rod removably coupled to the pony rod opposite the pony rod attachment interface, the piston rod extending into the pump section to pressurize and depressurize the pump section; and a clamp configured to couple the piston rod to the pony rod.
In Example 10, the subject matter of Examples 2-9 includes, wherein the connecting rod, the housing, the crosshead, and the plunger assembly are installed substantially horizontally.
Example 11 is a wrist pin assembly comprising: a connecting rod pivotably attached to a crank member; a housing extending between a crank member end and a piston rod end, the connecting rod extending from the crank member and into the housing through the crank member end; a crosshead installed within the housing, the crosshead operable to translate within the housing between the crank member end and the piston rod end; a wrist pin installed within the crosshead, the connecting rod pivotably attached to the wrist pin to translate the wrist pin and the crosshead within the housing in a first direction and a second direction as the crank member rotates; and a plunger assembly directly coupled to the wrist pin and extending from the wrist pin through the piston rod end, the plunger assembly translates along a central axis in the first direction and the second direction as the crank member rotates.
In Example 12, the subject matter of Example 11 includes, wherein the connecting rod comprises: a crank side section, the crank side section comprising: a crank side attachment interface configured to attach the connecting rod to the crank member; and a wrist pin side section, the wrist pin side section opposite the crank side section, the connecting rod extending longitudinally between the crank side section and the wrist pin side section, the wrist pin side section comprising: a wrist pin side attachment interface.
In Example 13, the subject matter of Example 12 includes, wherein the wrist pin is installed into the wrist pin side attachment interface to couple the wrist pin to the crosshead.
In Example 14, the subject matter of Example 13 includes, wherein the crosshead is hollow such that the wrist pin side section of the connecting rod can fit within the crosshead, the crosshead comprising: a first aperture; and a second aperture, the first aperture being concentrically aligned with the second aperture such that a vertical axis of the first aperture and the second aperture are orthogonal to the central axis of the crosshead.
In Example 15, the subject matter of Example 14 includes, wherein at least a portion of the wrist pin extends into the first aperture and the second aperture when the wrist pin is installed within the crosshead.
In Example 16, the subject matter of Examples 11-15 includes, wherein the wrist pin comprises: a pony rod attachment interface extending radially therefrom.
In Example 17, the subject matter of Example 16 includes, wherein the plunger assembly comprises: a pony rod directly coupled to the pony rod attachment interface of the wrist pin, the pony rod operable to translate in the first direction and the second direction along a longitudinal axis of the pony rod as the crank member rotates.
In Example 18, the subject matter of Example 17 includes, wherein the plunger assembly comprises: a piston rod removably coupled to the pony rod opposite the pony rod attachment interface of the wrist pin, the piston rod extending and retracting with the pony rod; and a clamp configured to couple the piston rod to the pony rod.
In Example 19, the subject matter of Examples 11-18 includes, wherein the connecting rod, the housing, the crosshead, and the plunger assembly are installed substantially horizontally.
In Example 20, the subject matter of Examples 11-19 includes, wherein the housing is fluidically sealed.
Example 21 is an apparatus comprising means to implement of any of Examples 1-20.
Example 22 is a system to implement of any of Examples 1-20.
Example 23 is a method to implement of any of Examples 1-20.
Example 24 is a device, apparatus, system, or method of any element of any of Examples 1-20.
The above-detailed description includes references to the accompanying drawings, which form a part of the detailed description. The drawings show, by way of illustration, specific embodiments that may be practiced. These embodiments are also referred to herein as “examples.” Such examples may include elements in addition to those shown or described. However, the present inventors also contemplate examples in which only those elements shown or described are provided. Moreover, the present inventors also contemplate examples using any combination or permutation of those elements shown or described (or one or more aspects thereof), either with respect to a particular example (or one or more aspects thereof), or with respect to other examples (or one or more aspects thereof) shown or described herein.
All publications, patents, and patent documents referred to in this document are incorporated by reference herein in their entirety, as though individually incorporated by reference. In the event of inconsistent usages between this document and those documents so incorporated by reference, the usage in the incorporated reference(s) should be considered supplementary to that of this document; for irreconcilable inconsistencies, the usage in this document controls.
In this document, the terms “a” or “an” are used, as is common in patent documents, to include one or more than one, independent of any other instances or usages of “at least one” or “one or more.” In this document, the term “or” is used to refer to a nonexclusive or, such that “A or B” includes “A but not B,” “B but not A,” and “A and B,” unless otherwise indicated. In the appended claims, the terms “including” and “in which” are used as the plain-English equivalents of the respective terms “comprising” and “wherein.” Also, in the following claims, the terms “including” and “comprising” are open-ended, that is, a system, device, article, or process that includes elements in addition to those listed after such a term in a claim are still deemed to fall within the scope of that claim. Moreover, in the following claims, the terms “first,” “second,” and “third,” etc. are used merely as labels, and are not intended to impose numerical requirements on their objects.
The term “about,” as used herein, means approximately, in the region of, roughly, or around. When the term “about” is used in conjunction with a numerical range, it modifies that range by extending the boundaries above and below the numerical values set forth. In general, the term “about” is used herein to modify a numerical value above and below the stated value by a variance of 10%. In one aspect, the term “about” means plus or minus 10% of the numerical value of the number with which it is being used. Therefore, about 50% means in the range of 45%-55%. Numerical ranges recited herein by endpoints include all numbers and fractions subsumed within that range (e.g. 1 to 5 includes 1, 1.5, 2, 2.75, 3, 3.90, 4, 4.24, and 5). Similarly, numerical ranges recited herein by endpoints include subranges subsumed within that range (e.g. 1 to 5 includes 1-1.5, 1.5-2, 2-2.75, 2.75-3, 3-3.90, 3.90-4, 4-4.24, 4.24-5, 2-5, 3-5, 1-4, and 2-4). It is also to be understood that all numbers and fractions thereof are presumed to be modified by the term “about.”
The above description is intended to be illustrative, and not restrictive. For example, the above-described examples (or one or more aspects thereof) may be used in combination with each other. Other embodiments may be used, such as by one of ordinary skill in the art upon reviewing the above description. The Abstract is to allow the reader to quickly ascertain the nature of the technical disclosure and is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. Also, in the above Detailed Description, various features may be grouped together to streamline the disclosure. This should not be interpreted as intending that an unclaimed disclosed feature is essential to any claim. Rather, inventive subject matter may lie in less than all features of a particular disclosed embodiment. Thus, the following claims are hereby incorporated into the Detailed Description, with each claim standing on its own as a separate embodiment. The scope of the embodiments should be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled.
