Patent Application
20210047917
Wellbores drilled into subterranean formations may enable recovery of desirable fluids (e.g., hydrocarbons) using a number of different techniques. A logging tool may be employed in subterranean operations to determine wellbore and/or formation properties. Formation evaluation further from a wellbore is a critical step in reservoir characterization and monitoring. Logging tools typically measure the “near-field,” or in the proximity of the wellbore. Logging tools are evolving to measure the “far-field,” or large distances from the wellbore.
One formation parameter of interest may be the true dip angle of a formation. The term “true dip angle” refers to the steepest angle of descent of a tilted bed or other formation feature relative to a horizontal plane. True dip angle is the dip angle measured in a 2-dimensional (2D) plane oriented perpendicular to the formation's strike line (i.e., a line marking the intersection of the bed or feature with a horizontal plane). True dip angle may also be expressed as the angle between the vertical axis and a vector normal to the formation bedding plane. More generally, the true dip of a formation or other feature is simply characterized as the dip. The term “dip,” without any other qualifiers, will mean “true dip”. A related parameter is the relative dip angle, which is the angle between the wellbore axis and the vector normal to the formation bedding plane, measured in their common plane. It may be desirable to know the true dip angle both in the near-field and in the far-field. Currently, logging tools typically may be wellbore pad tools that generate images for dip analysis from current measurements. However, while these logging tools may be used to measure dip angle at the wellbore wall, they typically cannot provide dip angles at a given distance away from the wellbore. While other logging tools may be able to provide measurements at larger distances from the wellbore, they typically do not provide images suitable for dip analysis.
These drawings illustrate certain aspects of some examples of the present disclosure, and should not be used to limit or define the disclosure.
The present disclosure relates generally to borehole sonic logging and, more particularly to, improved reflection imaging of formation structures away from the wellbore. These images may be used by a geologist and/or geophysical interpreter for a number of things. For example, one may observe abrupt shifts in bedding features as might be caused by a fault plane, or in some cases, directly image the fault plane itself. Other uses may relate to changes in bedding dip away from the well, for example, as might be caused by an overturned fold structure. Those skilled in the art will realize that there may be many more potential geological structures that may be of interest to the skilled practitioner. By way of example, borehole sonic data may be gathered to construct a structure-guided velocity model to determine the relative dip angle of a formation bed from borehole sonic logging tools. In examples, the relative dip angle may be further manipulated to determine the true dip angle of the formation bed, with knowledge of the wellbore deviation and direction.
In contrast to prior logging tools, the present techniques may enable accurate determination of the dip angles in the near-field and the far-field. For example, the dip angles may be determined at distances of 5 feet (1.5 meters), 10 feet (3 meters), 20 feet (6 meters), 50 feet (15 meters), 100 feet (305 meters), or even further from the wellbore. The maximum distance imaged from the well may depend on a number of factors that will vary from case to case. Without limitation, these factors may include formation complexity, strength of sonic transmitter, sensitivity of sonic receivers, formation factors such as formation attenuation and velocity, and/or combinations thereof. With the relative dip angle of the bedding away from the wellbore, a more accurate velocity model may be obtained and used in generation of reflection images. The reflection images generated using the velocity model guided by the estimated relative dip angle may be more accurate.
Systems and methods of the present disclosure may be implemented, at least in part, with information handling system 114. Information handling system 114 may include any instrumentality or aggregate of instrumentalities operable to compute, estimate, classify, process, transmit, receive, retrieve, originate, switch, store, display, manifest, detect, record, reproduce, handle, or utilize any form of information, intelligence, or data for business, scientific, control, or other purposes. For example, an information handling system 114 may be a processing unit 116, a network storage device, or any other suitable device and may vary in size, shape, performance, functionality, and price. Information handling system 114 may include random access memory (RAM), one or more processing resources such as a central processing unit (CPU) or hardware or software control logic, ROM, and/or other types of nonvolatile memory. Additional components of the information handling system 114 may include one or more disk drives, one or more network ports for communication with external devices as well as various input and output (I/O) devices, such as a input device 118 (e.g., keyboard, mouse, etc.) and a video display 120. Information handling system 114 may also include one or more buses operable to transmit communications between the various hardware components.
Alternatively, systems and methods of the present disclosure may be implemented, at least in part, with non-transitory computer-readable media 122. Non-transitory computer-readable media 122 may include any instrumentality or aggregation of instrumentalities that may retain data and/or instructions for a period of time. Non-transitory computer-readable media 122 may include, for example, storage media such as a direct access storage device (e.g., a hard disk drive or floppy disk drive), a sequential access storage device (e.g., a tape disk drive), compact disk, CD-ROM, DVD, RAM, ROM, electrically erasable programmable read-only memory (EEPROM), and/or flash memory; as well as communications media such wires, optical fibers, microwaves, radio waves, and other electromagnetic and/or optical carriers; and/or any combination of the foregoing.
As illustrated, borehole sonic logging tool 102 may be disposed in wellbore 124 by way of conveyance 110. Wellbore 124 may extend from a wellhead 134 into a formation 132 from surface 108. Generally, wellbore 124 may include horizontal, vertical, slanted, curved, and other types of wellbore geometries and orientations. Wellbore 124 may be cased or uncased. In examples, wellbore 124 may comprise a metallic material, such as tubular 136. By way of example, the tubular 136 may be a casing, liner, tubing, or other elongated steel tubular disposed in wellbore 124. As illustrated, wellbore 124 may extend through formation 132. Wellbore 124 may extend generally vertically into the formation 132. However, wellbore 124 may extend at an angle through formation 132, such as horizontal and slanted wellbores. For example, although wellbore 124 is illustrated as a vertical or low inclination angle well, high inclination angle or horizontal placement of the well and equipment may be possible. It should further be noted that while wellbore 124 is generally depicted as a land-based operation, those skilled in the art may recognize that the principles described herein are equally applicable to subsea operations that employ floating or sea-based platforms and rigs, without departing from the scope of the disclosure.
In examples, rig 106 includes a load cell (not shown) which may determine the amount of pull on conveyance 110 at surface 108 of wellbore 124. While not shown, a safety valve may control the hydraulic pressure that drives drum 126 on vehicle 104 which may reel up and/or release conveyance 110 which may move borehole sonic logging tool 102 up and/or down wellbore 124. The safety valve may be adjusted to a pressure such that drum 126 may only impart a small amount of tension to conveyance 110 over and above the tension necessary to retrieve conveyance 110 and/or borehole sonic logging tool 102 from wellbore 124. The safety valve is typically set a few hundred pounds above the amount of desired safe pull on conveyance 110 such that once that limit is exceeded; further pull on conveyance 110 may be prevented.
In examples, borehole sonic logging tool 102 may operate with additional equipment (not illustrated) on surface 108 and/or disposed in a separate borehole sonic logging system (not illustrated) to record measurements and/or values from formation 132. Borehole sonic logging tool 102 may comprise a transmitter 128. Transmitter 128 may be connected to information handling system 114, which may further control the operation of transmitter 128. Transmitter 128 may include any suitable transmitter for generating sound waves that travel into formation 132, including, but not limited to, piezoelectric transmitters. Transmitter 128 may be a monopole source or a multi-pole source (e.g., a dipole source). Combinations of different types of transmitters may also be used. During operations, transmitter 128 may broadcast sound waves from borehole sonic logging tool 102 that travel into formation 132. The sound waves may be emitted at any suitable frequency range. For example, a broad band response could be from about 0.2 KHz to about 20 KHz, and a narrow band response could be from about 1 KHz to about 6 KHz. It should be understood that the present technique should not be limited to these frequency ranges. Rather, the sounds waves may be emitted at any suitable frequency for a particular application.
Borehole sonic logging tool 102 may also include a receiver 130. As illustrated, there may be a plurality of receivers 130 disposed on borehole sonic logging tool 102. Receiver 130 may include any suitable receiver for receiving sound waves, including, but not limited to, piezoelectric receivers. For example, the receiver 130 may be a monopole receiver or multi-pole receiver (e.g., a dipole receiver). In examples, a monopole receiver 130 may be used to record compressional-wave (P-wave) signals, while the multi-pole receiver 130 may be used to record shear-wave (S-wave) signals. Receiver 130 may measure and/or record sound waves broadcast from transmitter 128 as received signals. The sound waves received at receiver 130 may include both direct waves that traveled along the wellbore 124 and refract through formation 132 as well as waves that traveled through formation 132 and reflect off of near-borehole bedding and propagate back to the borehole. The reflected waves may include, but are not limited to, compressional (P) waves and shear (S) waves. By way of example, the received signal may be recorded as an acoustic amplitude as a function of time. Information handling system 114 may control the operation of receiver 130. The measured sound waves may be transferred to information handling system 114 for further processing. In examples, there may be any suitable number of transmitters 128 and/or receivers 130, which may be controlled by information handling system 114. Information and/or measurements may be processed further by information handling system 114 to determine properties of wellbore 124, fluids, and/or formation 132. By way of example, the sound waves may be processed to generate a reflection image of formation structures, which may be used for dip analysis as discussed in more detail below.
With continued reference to
Without limitation, bottom hole assembly 228, transmitter 128, and/or receiver 130 may be connected to and/or controlled by information handling system 114, which may be disposed on surface 108. Without limitation, information handling system 114 may be disposed down hole in bottom hole assembly 228. Processing of information recorded may occur down hole and/or on surface 108. Processing occurring downhole may be transmitted to surface 108 to be recorded, observed, and/or further analyzed. Additionally, information recorded on information handling system 114 that may be disposed down hole may be stored until bottom hole assembly 228 may be brought to surface 108. In examples, information handling system 114 may communicate with bottom hole assembly 228 through a communication line (not illustrated) disposed in (or on) drill string 212. In examples, wireless communication may be used to transmit information back and forth between information handling system 114 and bottom hole assembly 228. Information handling system 114 may transmit information to bottom hole assembly 228 and may receive, as well as process, information recorded by bottom hole assembly 228. In examples, a downhole information handling system (not illustrated) may include, without limitation, a microprocessor or other suitable circuitry, for estimating, receiving and processing signals from bottom hole assembly 228. Downhole information handling system (not illustrated) may further include additional components, such as memory, input/output devices, interfaces, and the like. In examples, while not illustrated, bottom hole assembly 228 may include one or more additional components, such as analog-to-digital converter, filter and amplifier, among others, that may be used to process the measurements of bottom hole assembly 228 before they may be transmitted to surface 108. Alternatively, raw measurements from bottom hole assembly 228 may be transmitted to surface 108.
Any suitable technique may be used for transmitting signals from bottom hole assembly 228 to surface 108, including, but not limited to, wired pipe telemetry, mud-pulse telemetry, acoustic telemetry, and electromagnetic telemetry. While not illustrated, bottom hole assembly 228 may include a telemetry subassembly that may transmit telemetry data to surface 108. Without limitation, an electromagnetic source in the telemetry subassembly may be operable to generate pressure pulses in the drilling fluid that propagate along the fluid stream to surface 108. At surface 108, pressure transducers (not shown) may convert the pressure signal into electrical signals for a digitizer (not illustrated). The digitizer may supply a digital form of the telemetry signals to information handling system 114 via a communication link 230, which may be a wired or wireless link. The telemetry data may be analyzed and processed by information handling system 114.
As illustrated, communication link 230 (which may be wired or wireless, for example) may be provided which may transmit data from bottom hole assembly 228 to an information handling system 114 at surface 108. Information handling system 114 may include a processing unit 116, a video display 120, an input device 118 (e.g., keyboard, mouse, etc.), and/or non-transitory computer-readable media 122 (e.g., optical disks, magnetic disks) that may store code representative of the methods described herein. In addition to, or in place of processing at surface 108, processing may occur downhole.
As illustrated in
In this manner, sound waves, such as compressional (P) and/or shear (S) wave data may be gathered along wellbore 124. Typically, an operator who provides borehole sonic imaging services may use the average recorded velocity, for either P-wave or S-wave data depending on the mode of interest, along wellbore 124 as the background velocity model. In examples, an operator may be defined as an individual, group of individuals, or an organization. It may be desirable for reflection sonic imaging to separately image the crossing of dipping formation bed 304 with wellbore 124 and to combine the resultant image to create a 2-dimensional visualization. Pre-separation, which may use any suitable algorithm, of up going reflection waves 310 and down going reflection waves 318 received at receivers 130 may be utilized.
The borehole sonic data may include any suitable sonic data for generating a formation image for dip analysis. Suitable data may include full-waveform data and the corresponding velocity logs. The term “full-waveform” data may be defined as data recorded at each receiver of the signal response of the waves impacting the receiver, as a function of time. The data may include P-wave data, S-wave data, or both P-wave data and S-wave data.
After obtaining the borehole sonic data, step 404 may then be implemented. Step 404 may comprise generating an initial 1-dimensional (1-D) velocity model that follows the path of wellbore 124 as a function of depth. The initial 1-D velocity model may be generated using any suitable technique, including using a smoothed velocity log of the measured sounds (as either P-wave or S-wave data), for example, recorded by the borehole sonic logging tool 102 (e.g., referring to
Step 406 may be implemented before and/or after creating the 1-D velocity model. In step 406, a filter may be applied to the borehole sonic data to attenuate direct arrivals. The direct arrivals typically may include the measured sound waves that traveled directly along wellbore 124 from transmitter 128 to receiver 130 (e.g., referring to
After the attenuation of the direct arrivals, step 408 may comprise of separating up- and down-going arrivals in the borehole sonic data. As previously described, the up- and down-going arrivals may have been received along the borehole sonic logging tool 102 (e.g., referring to
After the separation of the up-going arrivals from the down-going arrivals, step 410 may occur. Step 410 may comprise generation of a first reflection image based on the borehole sonic data. The first reflection image may be a two-dimensional (2-D) image of subsurface structures in a subterranean formation (e.g., formation 132 on
The up-going and down-going reflection image may be generated from the up-and down-going arrivals and the 1-D background velocity model through a pre-stack depth imaging code, such as Reverse-Time Migration (RTM) imaging, to produce the reflection images of formation structures away from wellbore 124 (e.g., referring to
Flowchart 400 may then proceed to step 412, which may comprise of estimating the relative dip angle from the first reflection image. For example, the relative dip angle of bed 302 (e.g., referring to
An example of estimating relative dip angle from a reflection image, such as first reflection image is provided on
After the relative dip angle is estimated, step 414 may occur. Step 414 may comprise generating an updated velocity model. The updated velocity model may be a 2-D velocity model. In the 2-D velocity model, one of the dimensions may be radial distance away from wellbore (e.g., from borehole wall or borehole axis) and the other dimension may be logging depth along wellbore 124 (e.g.,
The velocity log may be prepared in a similar fashion as was done for the 1-D velocity model (e.g. smoothing the log response). Then the 2-D velocity model grids may be created. A first model may be created for imaging up-dip structures, and a second model may be created for imaging down-dip structures. To create the first and second models, a matrix representing a series of cells may be created that extends along the wellbore and laterally away from the wellbore to the extent of the desired distance to be imaged. For example, to see events about 100 feet (30.5 meters) from the well and from test data gathered in a 1000 feet (305 meters) section in the well, the grid may be created over the well depth interval and laterally to 100 feet (30.5 meters) from the well. Spacing between grid points may need to be close to achieve an image that is useful. In examples, too fine of a spacing may cause excessive computing time for the imaging process. The spacing parameter may be subjective. For example, the spacing parameter may be decided by trial and error. Without limitation, a spacing of about 0.25 feet (7.6 centimeters) may produce a good result for borehole sonic frequency imaging.
Next, the prepared velocity log may be placed on the same depth locations as the 2-D velocity model matrix. In examples, as the 2-D velocity model matrix may be at a finer depth sampling spacing than the prepared velocity log (e.g., 0.5 feet (16.5 centimeters) as opposed to 0.25 ft (7.6 centimeters), the prepared velocity log may be interpolated to get the velocity at the corresponding 2-D velocity matrix depth. Then, the velocity model grids may be populated. At the borehole wall, the velocity at each depth may be the prepared velocity model positioned at the 2-D velocity model depth locations. Without limitation, trigonometric methods may be used with the relative dip angle to populate the velocity model away from the wellbore. For example, the cell at a lateral distance “dx” from the borehole, for each borehole depth position “y” and lateral distance “x”, may be extracted by Equation (1):
dy=tan(α)*x (1)
where “dy” is the depth above the current borehole depth “y”. Once “dy” has been determined, the velocity for that matrix point may be calculated using Equations (2) and (3):
V_matrix(x,y)=V(y+dy) (2)
V_matrix(x,y)=V(y−dy) (3)
wherein “V” is the 1-D prepared velocity model and “V_matrix” is the 2-D velocity model matrix. Equation (2) may be used for a down-dip matrix, and Equation (3) may be used for an up-dip matrix.
An example of an updated 2-D velocity model 800 that may be generated using the relative dip angle is illustrated in
Alternatively, another example may be enhancement of processing to allow the imaging of a formation 132 that may be more complex located away from wellbore 124 by taking into more complex structural changes in formation 132 when generating updated velocity model. The methods previously described may be initially implemented using an assumption that the relative dip angle of formation 132 is constant (linear) for the imaged region away from wellbore 124. That may not always be the case as geological structures can change within relatively short distances. In this example, the iterative solution to update the 2-D velocity model along the relative dip angle as a function of depth in flowchart 400 may take into account complex structural changes in formation 132. Without limitation, the complex structural changes may include, but is not limited to, discrete relative dip angle changes away from wellbore 124, such as the presence of a fault, fold structure such as anticlines and synclines, and/or the like.
After the creation of the 2-D velocity model, step 416 may occur. Step 416 may comprise generating an updated reflection image, wherein the updated reflection image may be 2-D. In the updated reflection image, one of the dimensions may be radial distance away from wellbore (e.g., from borehole wall or borehole axis) and the other dimension may be logging depth along wellbore 124 (e.g.,
A subsequent step may be a decision step 418 to determine whether a stop criterion has been met. In decision step 418, a determination may be made whether change between the updated reflection image and the first reflection image is acceptable. In examples, this may occur manually and/or automatically based on a suitable tolerance based on the actual changes in the 2D image matrix from one iteration to the next. The suitable tolerance may be between 0% and 10%. Without limitation, a suitable tolerance may be from about 0% to about 2.5%, from about 2.5% to about 5%, from about 5% to about 7.5%, or from about 7.5% to about 10%. In examples, bedding may not be expected to change a given distance away from the borehole, but an up-dip structure near 12910 feet to 12890 feet (3935 meters to 3929 meters) observed on
In examples, a true dip angle of a formation bed (e.g., bed boundary 300 on
Next, the strike of the formation bed may be determined. The strike may refer to a line that represents the intersection of the formation bed with a horizontal plane. The strike may be determined using any suitable technique, including, but not limited to, by use of Horizontal Transverse Isotropy (HTI) analysis of the 4-component dipole data. In examples, for the case of borehole sonic logging tool 102 in a wellbore penetrating a dipping bed, as shown on
Without limitation, an example structural detail may comprise that formation 132 is drilled down-dip so that the direction close to wellbore 124 direction is the expected direction. Additional structural details may include a wellbore 124, that may be vertical, intersecting a formation 132 that is dipping, a deviated well intersecting a formation 132 that is flat, a deviated well intersecting a formation 132 that is dipping, and/or the like. In alternate examples, the ambiguity may be resolved by integrating with a dipmeter or a wellbore wall image analysis.
Once the relative dip angle, bedding strike direction, and wellbore deviation and direction are acquired, the true dip angle and direction of formation beds may be calculated. In examples, calculations may be done using standard methods with a suitable logging tool. With the dip angle, an improved reflection image may be obtained. As will be appreciated, the reflection image is typically used for a number of functions, including, but not limited to, providing information for making drilling, completion, and production decisions.
This method and system may include any of the various features of the compositions, methods, and system disclosed herein, including one or more of the following statements.
Statement 1. A method for borehole sonic reflection imaging, comprising: disposing a borehole sonic logging tool in a wellbore, wherein the borehole sonic logging tool comprises one or more transmitters and one or more receivers; emitting sound waves from the one or more transmitters; receiving sound waves at the one or more receivers to obtain borehole sonic data; separating up-going arrivals in the borehole sonic data from down-going arrivals in the borehole sonic data; generating a first reflection image based at least on the borehole sonic data; estimating a relative dip angle of a formation bed from the first reflection image; generating an updated velocity model based at least on the relative dip angle; and generating an updated reflection image based at least on the updated velocity model.
Statement 2. The method of statement 1, wherein the generating a first reflection image comprises separately imaging the up-going arrivals and the down-going arrivals to generate images from measurements on either side of a bed boundary and then combining the images to produce the first reflection image.
Statement 3. The method of statement 2, wherein the separately imaging the up-going arrivals and the down-going arrivals occurs through a pre-stack depth imaging code.
Statement 4. The method of statement 3, wherein the pre-stack depth imaging code is Reverse-Time Migration imaging.
Statement 5. The method of any of the previous statements, wherein the estimating the relative dip angle of the formation bed occurs manually from interpretation of the first reflection image or automatically through an information handling system.
Statement 6. The method of any of the previous statements, wherein the estimating the relative dip angle is performed on an information handling system applying a semblance algorithm.
Statement 7. The method of any of the previous statements, further comprising generating an initial one-dimensional velocity model from at least a smoothed velocity log, wherein the smooth velocity log is obtained by application of a filter to a velocity log in the borehole sonic data.
Statement 8. The method of any of the previous statements, further comprising attenuating direct arrival signals in the borehole sonic data.
Statement 9. The method of statement 8, wherein the direct arrival signals are attenuated with at least one filter selected from the group consisting of a frequency domain filter, an F-K filter, a median filter, and combinations thereof.
Statement 10. The method of any of the previous statements, wherein the updated velocity model comprises a two-dimensional velocity model that was generated by translating an initial one-dimensional velocity model along the relative dip angle as a function of depth.
Statement 11. The method of any of the previous statements, wherein the step of generating the updated reflection image based at least on the updated velocity model comprises separately imaging the up-going arrivals and the down-going arrivals using the updated velocity model to generate images from measurements on either side of a bed boundary and then combining the images to produce the updated reflection image.
Statement 12. The method of any of the previous statements, further comprising comparing the first reflection image to the updated reflection image to determine whether the updated velocity model should be further updated.
Statement 13. The method of any of the previous statements, further comprising determining a true dip angle of the formation bed.
Statement 14. The method of statement 13, wherein the step of determining the true dip angle comprises determining dip and direction of the wellbore, determining strike of the formation bed, and then determining the true dip angle from at least the dip and the direction of the wellbore, the strike, and the relative dip angle.
Statement 15. The method of statement 14, wherein the strike is determined by using Horizontal Transverse Isotropy analysis.
Statement 16. An apparatus for borehole sonic imaging, comprising: a borehole sonic logging tool comprising one or more transmitters configured to emit sound waves and one or more receivers configured to receive sound waves to obtain borehole sonic data; and an information handling system operate configured to obtain the borehole sonic data from the receivers, separate up-going arrivals in the borehole sonic data from down-going arrivals in the borehole sonic data; generate a first reflection image based at least on the borehole sonic data; estimate a relative dip angle of a formation bed from the first reflection image; generate an updated velocity model based at least on the relative dip angle; and generate an updated reflection image based at least on the updated velocity model.
Statement 17. The apparatus of statement 16, wherein the one or more receivers comprises a plurality of receivers spaced along a longitudinal axis of the borehole sonic logging tool.
Statement 18. The apparatus of statement 17, wherein the one or more transmitters comprises one or more piezoelectric transmitters, and wherein the plurality of receivers comprises a plurality of piezoelectric receivers.
Statement 19. The apparatus of any of statements 16 to 18, wherein the information handling system is further configurable to separately image the up-going arrivals and the down-going arrivals to generate images from measurements on either side of a bed boundary and then combine the images to generate the first reflection image.
Statement 20. The apparatus of statement 17, wherein the information handling system is further configurable to generate an initial one-dimensional velocity model from at least a smoothed velocity log, wherein the smooth velocity log is obtained by application of a filter to a velocity log in the borehole sonic data, and also further configured to attenuate direct arrival signals in the borehole sonic data.
The preceding description provides various examples of the systems and methods of use disclosed herein which may contain different method steps and alternative combinations of components. It should be understood that, although individual examples may be discussed herein, the present disclosure covers all combinations of the disclosed examples, including, without limitation, the different component combinations, method step combinations, and properties of the system. It should be understood that the compositions and methods are described in terms of “comprising,” “containing,” or “including” various components or steps, the compositions and methods can also “consist essentially of” or “consist of” the various components and steps. Moreover, the indefinite articles “a” or “an,” as used in the claims, are defined herein to mean one or more than one of the element that it introduces.
For the sake of brevity, only certain ranges are explicitly disclosed herein. However, ranges from any lower limit may be combined with any upper limit to recite a range not explicitly recited, as well as, ranges from any lower limit may be combined with any other lower limit to recite a range not explicitly recited, in the same way, ranges from any upper limit may be combined with any other upper limit to recite a range not explicitly recited. Additionally, whenever a numerical range with a lower limit and an upper limit is disclosed, any number and any included range falling within the range are specifically disclosed. In particular, every range of values (of the form, “from about a to about b,” or, equivalently, “from approximately a to b,” or, equivalently, “from approximately a-b”) disclosed herein is to be understood to set forth every number and range encompassed within the broader range of values even if not explicitly recited. Thus, every point or individual value may serve as its own lower or upper limit combined with any other point or individual value or any other lower or upper limit, to recite a range not explicitly recited.
Therefore, the present examples are well adapted to attain the ends and advantages mentioned as well as those that are inherent therein. The particular examples disclosed above are illustrative only, and may be modified and practiced in different but equivalent manners apparent to those skilled in the art having the benefit of the teachings herein. Although individual examples are discussed, the disclosure covers all combinations of all of the examples. Furthermore, no limitations are intended to the details of construction or design herein shown, other than as described in the claims below. Also, the terms in the claims have their plain, ordinary meaning unless otherwise explicitly and clearly defined by the patentee. It is therefore evident that the particular illustrative examples disclosed above may be altered or modified and all such variations are considered within the scope and spirit of those examples. If there is any conflict in the usages of a word or term in this specification and one or more patent(s) or other documents that may be incorporated herein by reference, the definitions that are consistent with this specification should be adopted.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/US2018/060709 | 11/13/2018 | WO | 00 |
