Patent Publication Number: US-9428992-B2

Title: Method and apparatus for restricting fluid flow in a downhole tool

Description:
BACKGROUND 
     This disclosure relates generally to ball-operated valves, and more specifically to such valves having a ball-receiving baffle, and to configurations for such baffles. 
     Subterranean well operations commonly employ valves at different locations along a wellbore for a variety of purposes. In some applications, downhole valves are employed to isolate sections of conduit within a wellbore. Such valves can be individually actuated opened/closed to isolate different portions of a string of conduits along the length of the wellbore. One type of valve employed in subterranean wells is a ball seat valve. 
     A typical ball seat valve has a bore or passageway that is restricted by a baffle forming a seat to receive a ball (which may literally be a spherical “ball” or in some examples may be another configuration of a plug or other mechanism that will engage the seat. The term “ball” as used herein, unless expressly indicated otherwise, refers to any sphere or other configuration of a plug intended to engage a baffle to close or substantially restrict a flow path through a tool. A ball can be dropped down the conduit within a wellbore to be disposed on the seat. Once the ball is seated, the fluid passage through the valve is closed and thereby prevents fluid from flowing through the bore of the ball seat valve, which, in turn, isolates the conduit section in which the valve is disposed. As the fluid pressure above the ball builds up, the conduit can be pressurized for any of a number of potential purposes, including for example, tubing testing, actuating a tool connected to the ball seat such as setting a packer, or fracturing particular layers of a formation through which the wellbore passes. 
     SUMMARY 
     Examples according to this disclosure include a split-ring baffle that can be employed in a ball seat valve in a conduit string of a wellbore. One example includes an apparatus for restricting fluid flow through a downhole tubular member. The apparatus, e.g., a ball seat valve, includes an annular sleeve and a resilient split-ring baffle. The annular sleeve is configured to be received within an annular housing and has an inner surface defining a first section of a first diameter and a second section of a second, smaller, diameter. The split-ring baffle is at least partially received within the sleeve. The baffle includes a longitudinal seam forming two separate circumferential ends in the baffle. The baffle is also longitudinally moveable between a first position in the first section and a second position in the second section of the sleeve. An outer surface of the baffle is configured to engage the inner surface of the sleeve to cause the baffle, when in the first position to be relatively radially expanded, and, when moved to the second position in the sleeve, to radially contract. 
     The details of one or more examples of the disclosure are set forth in the accompanying drawings and the description below. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  schematically depicts an example fracturing system including a tool string arranged within a wellbore that passes through a number of layers of a formation of a well. 
         FIG. 2  depicts a section view of a portion of a tool string including an example ball seat valve in accordance with this disclosure. 
         FIGS. 3A-3C  depict section views of an example split-ring baffle and annular sleeve arranged within the tool string of  FIG. 2 . 
         FIGS. 4A and 4B  depict perspective views of an example split-ring baffle. 
         FIG. 5  depicts a section view of a portion of a tool string, which illustrates an example ball seat valve in a closed state with a split-ring baffle expanded within a sleeve. 
         FIG. 6  depicts a section view of a portion of a tool string, which illustrates an example ball seat valve in an open state with a split-ring baffle contracted within a sleeve with a dropped ball seated in the baffle. 
         FIG. 7  is a flowchart illustrating an example method of actuating an apparatus for restricting fluid flow through a downhole tubular member. 
     
    
    
     DETAILED DESCRIPTION 
     As noted above, ball seats can be employed to isolate different layers of a formation for fracturing. A fracturing system commonly includes pumps that pressurize fracturing fluid, which may be communicated downhole via the central passageway of a string of conduits disposed within a wellbore. The string can include sections with ball seat valves that are aligned with different layers of the formation. Opening and closing the ball seat valves at different locations along the string is used to control fluid flow between the central passageway of the string and different layers of the formation. For example, a ball seat can be actuated to isolate a particular section of conduit aligned with a target layer of the formation. In combination with actuating the ball seat, one or more apertures in the conduit above the ball seat can be opened or exposed to allow fracturing fluid to pass through the conduit into the target layer of the formation. 
     In practice, a ball seat valve can be activated by dropping a ball into the string from the surface of the well. The dropped ball descends through the conduit within the wellbore until it lodges in the seat of the valve. After the ball lodges in the ball seat, fluid flow through the central passageway of the string becomes restricted, a condition that allows fluid pressure to be applied from the surface of the well for purposes of exerting a downward force on the ball. The ball seat typically is attached to a sleeve of the valve to transfer the force to the sleeve to cause the valve to open. However, in other examples, the seating of the ball in the ball seat and the fluidic isolation of the associated zone of the tool string is separate from opening of the valve to allow fluid to pass through the tool string housing into the surrounding formation. For example, a separate sleeve within the tool string conduit can be actuated, e.g., moved axially to expose apertures in the tool string conduit. Once the valve has been opened, fracturing fluid can be transmitted through the string of conduit to one or more apertures opened/exposed by the value to carry out fracturing operations on a portion of the formation aligned with the ball seat valve. Thus, seating the ball in the ball seat fluidically isolates a particular zone of the wellbore and the valve is then opened to allow fracturing fluid to pass through the tool string conduit into a particular region of the formation. 
     A fracturing system can employ multiple ball seat valves to form multiple zones along the length of the wellbore. The zones of the wellbore can be used to target different layers of a formation for fracturing operations. In some fracturing systems, the valves may contain many different size ball seats to enable remote operation of the ball seat valves from the surface of the well. For example, to target and actuate the valves, differently sized balls may be dropped into the string from the surface of the well. Each ball size may be uniquely associated with a different valve, so that a particular ball size is used to actuate a specific valve. The smallest ball commonly opens the deepest valve. The ball seats of the string have different diameters, which are respectively associated with the different sized balls. 
     In systems employing multiple ball seat valves of varying size, the annular area that is consumed by each ball seat along the string restricts the cross-sectional flow area through the string (even in the absence of a ball), and the addition of each valve (and ball seat) to the string further restricts the cross-sectional flow area through the central passageway of the string, as the flow through each ball seat becomes progressively more narrow as the number of ball seats increase. Thus, a large number of valves may significantly restrict the cross-sectional flow area through the string. 
     To address the issue of progressively more restriction to the conduit of the string, multiple ball seat valves of the same size can be employed, in which the seat of each valve is configured to expand and contract such that the seat can selectively catch a dropped ball or allow the ball to pass down the string to the next valve. In other words, adjustable ball seat valves can be employed that are capable of being expanded to larger diameters and contracted to smaller diameters. The seat of a ball seat valve is, more generally, a baffle, configured to receive a ball (or other plug, as noted earlier herein) to substantially block movement of fluids through the conduit of the wellbore. 
     Examples according to this disclosure include a split-ring baffle that can be employed in a ball seat valve in a conduit string within a wellbore. One example includes an apparatus for restricting fluid flow through a downhole annular member. The apparatus, e.g., a ball seat valve, includes an annular sleeve and a resilient split-ring baffle. The annular sleeve is configured to be received within an annular housing and has an inner surface defining a first section of a first diameter and a second section of a second, smaller, diameter. The split-ring baffle is at least partially received within the sleeve. The baffle includes a longitudinal seam forming two separate circumferential ends in the baffle. The baffle is also longitudinally moveable between a first position in the first section and a second position in the second section of the sleeve. An outer surface of the baffle is configured to engage the inner surface of the sleeve to cause the baffle, when in the first position to be relatively radially expanded, and, when moved to the second position in the sleeve, to radially contract. 
     Example split-ring baffles in accordance with this disclosure may provide a number of advantages. For example, split-ring baffles in accordance with this disclosure provide a simple and low cost (e.g. both material and manufacturing) component that can include a relatively short length to reduce the overall size of a tool including the baffle. Additionally, the baffle only includes one junction to seal and which reduces interaction between the baffle and materials transmitted through the tool string conduit. The baffle can include support structures for reducing the likelihood of deflection and to lock the baffle into at least one position relative to the sleeve of the valve. The baffle can be re-expanded to the full internal diameter of the sleeve and is capable of being contracted and re-expanded multiple times without significant impacts on function. 
     Split-ring baffles in accordance with this disclosure are described as employed as part of a ball seat valve used to isolate and target layers of a formation during fracturing operations. However, split-ring baffles and ball seat valves in accordance with this disclosure can be employed in other applications. For example, a ball seat valve including a split-ring baffle in accordance with this disclosure can be employed to catch a dart employed for positive displacement in cementing applications, to set mechanical packers, as part of a shut-off collar at the toe of the tool in cementing applications, and in conjunction with liner hangers. 
       FIG. 1  is a schematic illustration of fracturing system  10  including tool string  12  arranged within wellbore  14 , which passes through a number of layers of formation  18  of the well. Tool string  12  includes a number of ball seat valves  20  in accordance with this disclosure. Tool string  12  also includes a number of packers  22 . Packers  22  seal off an annulus formed radially between tool string  12  and wellbore  14 . Packers in this example are designed for sealing engagement with an uncased or open hole wellbore  14 , but if the wellbore is cased or lined, then cased hole-type packers may be used instead. Swellable, inflatable, expandable, and other types of packers can be used, as appropriate for the well conditions, or no packers may be used. 
     In the  FIG. 1  example, ball seat valves  20  permit selective fluid communication between the central passageway of tool string  12  and each section of the annulus isolated between two of the packers  22 , which are located above and below each of the valves in wellbore  14 . Each such section of the annulus surrounding tool string  12  is in fluid communication with a corresponding earth formation zone or layer of formation  18 . Of course, if packers  22  are not used, then ball seat valves  20  can be placed in communication with the individual zones by other mechanisms, for example, with perforations, etc. 
     The zones of formation  18  can be, for example, sections of the same formation, or they may be sections of different formations. Each zone may be associated with one or more of ball seat valves  20 . In order to carry out a fracturing operation on a particular one of the zones of formation  18 , the associated ball seat valve  20  can be opened to allow communication between the central passageway of tool string  12  and the associated zone. 
     For example, one of ball seat valves  20  can be activated by dropping a ball into tool string  12  from the surface of the well. The dropped ball descends through the conduit forming string  12  within wellbore  14  until it lodges in a seat of valve  20 . In one example, ball seat valve  20  includes an annular sleeve and a resilient split-ring baffle that functions as the ball seat of valve  20 . The split-ring baffle of ball seat valve  20  is at least partially received within the sleeve. An outer surface of the baffle is configured to engage the inner surface of the sleeve to cause the baffle, when in a first position to be relatively radially expanded, and, when moved to a second position in the sleeve, to radially contract. 
     After the ball lodges in the ball seat, fluid flow through the central passageway of tool string  12  becomes restricted, a condition that allows fluid pressure to be applied from the surface of the well for purposes of exerting a downward force on the ball. Additionally, after the ball lodges in the ball seat, ball seat valve  20  can be opened to allow communication between the central passageway of tool string  12  and the associated zone of formation  18 . In one example, a sleeve is located within tool string  12  above the split-ring baffle in which the ball is seated. The sleeve can be configured to be actuated to move axially within the outer conduit of tool string  12  to expose one or more apertures in the conduit. In another example, the ball seat is attached to a sleeve of ball seat valve  20  to transfer the force generated by fluid pressure in the central passageway of tools string  12  to the sleeve to cause the sleeve to move within the housing, thereby opening the valve. 
     Once ball seat valve  20  has been opened, fracturing fluid can be transmitted through conduit of tool string  12  to one or more apertures opened/exposed by valve  20  to carry out fracturing operations on a particular zone of formation  18  aligned with ball seat valve  20 . Thus, seating the ball in the ball seat of ball seat valve  20  fluidically isolates a particular zone of wellbore  14  and thereafter valve  20  is opened to allow fracturing fluid to pass through the sleeve into a particular portion of formation  18 . 
     In some cases, when tool string  12  is run downhole, all of ball seat valves  20  are initially closed. In one example, thereafter, ball seat valves  20  are successively opened one at a time in a predetermined sequence for purposes of fracturing layers of formation  18 . For example, ball seat valves  20  are opened in a sequence that begins at the bottom of tool string  12 , proceeds uphole to the next immediately adjacent valve  20 , then to the next immediately adjacent valve  20 , etcetera. 
     For purposes of opening a particular valve  20 , a free-falling or forced plug is deployed from the surface of the well into the central passageway of tool string  12 . In the following examples, the dropped plug is described and illustrated as a spherical ball. However, other plug types, e.g., differently-shaped plugs may be used. 
     In one example, the balls deployed for different ball seat valves  20  within tool string  12  can have the same diameter. In another example, some or all of the balls can have different diameters. As noted, initially, all of ball seat valves  20  can be closed, and none of split-ring baffles of valves  20  are in a contracted, ball catching state. When in the ball catching state, the split-ring baffle of valve  20  forms a seat that presents a restricted cross-sectional flow passageway to catch a ball that is dropped into the central passageway of tool string  12 . Unopened ball seat valves  20  that are located above the opened or unopened valve  14  with the split-ring baffle in the contracted, ball-catching state allow the ball to pass through the conduit of tool string  12 . 
       FIG. 2  is a section view of a portion of tool string  100  including example ball seat valve  102 . In the example of  FIG. 2 , ball seat valve  102  includes sleeve  106  and split-ring baffle  108 . Sleeve  106  of ball seat valve  102  is received within housing  110 , which forms a portion of the central conduit of the tool string  100 . 
     Tool string  100  includes a number of sections defined by different cylindrical housings connected to one another. The example of  FIG. 2  shows only a portion of tool string  100  and it is noted that tool string  100  can include a number of additional portions, one or more of which can include additional ball seat valves in accordance with this disclosure, similar to example tool string  12  and ball seat valves  20  illustrated in  FIG. 1 . 
     In  FIG. 2 , tool string  100  includes housing  110 , within which sleeve  106  of ball seat valve  102  is arranged. Housing  110  is coupled above to upper housing  112  and below to lower housing  114 . Housings of tool string  100 , including housings  110 ,  112 , and  114 , can be coupled to one another in a variety of ways, including, e.g., threaded or spline connections, interference fits, and other mechanisms for connecting such components. Housings  110 ,  112 , and  114  form a hollow generally cylindrical casing of tool string  100  that defines central conduit  116 , by which fluids can be communicated from the surface, down a wellbore within which tool string  100  is deployed. 
     Housings  110 ,  112 , and  114 , as well as other components of tool string  100  like sleeve  106  can be sealed to one another employing various types of sealing mechanisms configured to inhibit ingress and egress of fluids and other materials into and out of central conduit  116  of tool string  100 . For example, junctions between housing  110  and  112  and housing  110  and  114  include one or more O-ring seals  118 . 
     As noted, ball seat valve  102  includes sleeve  106  and split-ring baffle  108 . Sleeve  106  is received within housing  110  such that the outer surface of sleeve  106  abuts the inner surface of housing  110 . Sleeve  106  is configured to move longitudinally within housing  110 . The central passageway of sleeve  106  forms part of central conduit  116  of tool string  100 . 
     Ball seat valve  102  can be actuated within tool string  100  using a variety of mechanisms. In the example of  FIG. 2 , tool string  100  includes piston  120 , which can be configured to actuate ball seat valve  102 . Piston  120  is arranged and configured to move within upper housing  112 . In the example of tool string  100 , upper housing  112  includes a number of apertures  122 , which expose central conduit  116  of string  100  to the surrounding formation. 
     As described further below, when piston  120  moves in a downward direction within upper housing  112 , apertures  122  in upper housing  112  are exposed to place ball seat valve  102  in an open state, a state in which fluid communication occurs between the central conduit  116  and the region that surrounds tool string  100 . Additionally, movement of piston  120  downward within upper housing  112  can cause piston  120  to engage split-ring baffle  108  and move baffle  108  from the first position within sleeve  106  to the second position, in which baffle  108  assumes a contracted, ball-catching state. In the example of  FIG. 2 , multiple O-rings  124  circumscribe the outer surface of piston  120  and form corresponding annular seals between the outer surface of piston  120  and the inner surface of upper housing  112 , e.g., for purposes of sealing off radial apertures  122  in upper housing  112  when ball seat valve  102  is in the closed state. 
       FIGS. 3A-3C  depict section views and  FIGS. 4A and 4B  depict perspective views illustrating the structure of example split-ring baffle  108  of ball seat valve  102  and example sleeve  106  of valve  102  in greater detail. With reference to  FIGS. 2-4C , multiple O-rings  126  circumscribe the outer surface of sleeve  106  and form corresponding annular seals between the outer surface of sleeve  106  and the inner surface of upper housing  112 . Sleeve  106  includes first section  130  and second section  132 . The inner diameter of first section  130  of sleeve  106  is greater than second section  132 . The transition between the larger inner diameter of first section  130  of sleeve  106  and the smaller inner diameter of second section  132  is characterized by a generally tapered inner surface of second section  130 . 
     Ball seat valve  102  also includes split-ring baffle  108 , which is at least partially received within sleeve  106 . Split-ring baffle  108  includes longitudinal seam  140  forming two separate circumferential ends  142 ,  144  of baffle  108 . As will be described in greater detail with reference to  FIGS. 5 and 6  and as shown in  FIGS. 3A and 3B , split-ring baffle  108  is longitudinally moveable between a first position in first section  130  and a second position in second section  132  of sleeve  106 . The outer surface of split-ring baffle  108  is configured to engage the inner surface of sleeve  106  to allow baffle  108  to be expanded in the first position ( FIG. 3A ), and cause it to be contracted in the second position in the sleeve ( FIG. 3B ). 
     The outer surface of split-ring baffle  108  is tapered to engage the tapered portion of the inner surface of first section  130 . As split-ring baffle  108  is urged downward within tool string  100 , the tapered outer surface of baffle  108  engages the tapered portion of the inner surface of first section  130 , which causes split-ring baffle  108  to radially contract. Radially contracting split-ring baffle  108  in this manner by moving baffle  108  from the first position to the second position, places split-ring baffle  108  in the closed, or “ball-catching,” state. Thus, in the radially contracted state, split-ring baffle  108  is configured to receive a dropped ball or other plug to restrict fluid flow through central conduit  116  of tool string  100 . Once the ball is lodged in split-ring baffle  108 , fluid pressure can be applied from the surface of the well for purposes of exerting a downward force on the ball. 
       FIGS. 4A and 4B  depict split-ring baffle  108  in the radially expanded and contracted states, respectively. As illustrated in  FIGS. 4A and 4B , as split-ring baffle  108  contracts from the expanded state, circumferential ends  142 ,  144  formed by longitudinal seam  140  are progressively moved closer to one another. In the contracted state illustrated in  FIG. 4B , circumferential ends  142 ,  144  of baffle  108  abut one another at seam  140 . In some examples, however, circumferential ends  142 ,  144  may be offset from one another by a small distance even when baffle  108  is in the contracted state. 
     The tapered portion of the outer surface of split-ring baffle  108  is defined by tapered surface  150  and tapered tabs  152 . Tapered tabs  152  protrude outward from and are distributed around the circumference of one end of split-ring baffle  108 . Example split-ring baffle  108  includes four tabs  152  distributed evenly around the circumference of split-ring baffle  108 . In other examples, a split-ring baffle in accordance with this disclosure can include more or fewer tabs that are evenly or unevenly distributed around the circumference of the baffle. 
     Tapered tabs  152  of split-ring baffle  108  can serve a number of functions. Tabs  152  provide a mechanical stop that can inhibit or prevent baffle  108  from moving axially upward and out of sleeve  106 . As illustrated in  FIGS. 3A and 3B , tapered tabs  152  are configured to be received by and engage tapered groove  154  in the tapered portion of second section  132  of sleeve  106 . As split-ring baffle  108  moves from the second position within sleeve  106  to the first position within sleeve  106 , tabs  152  of baffle  108  are configured to engage groove  154  in sleeve  106 , as baffle  108  expands. When split-ring baffle  108  is in the second position and expanded, tapered grooves  152  are received in and mate with tapered groove  154 . 
     Tapered tabs  152  can provide another function for split-ring baffle  108  in addition to stopping baffle  108  from axial translation beyond sleeve  106 . As will be described in more detail below, when split ring baffle  108  is radially contracted and seated with a ball or other plug and ball seat valve  102  is opened during fracking operations, the pressure within central conduit  116  of tool string  100  can reach high levels, e.g., between approximately 3000 to approximately 5000 pounds per square inch (psi). In such situations, when split-ring baffle  108  is in the second position within sleeve  106  and radially contracted, the pressure within conduit  116  of string  100  can cause the lower end of baffle  108  to deflect radially outward. In the event the deflection of the baffle  108  persists and increases past a threshold, the ball seated within split-ring baffle  108  can become dislodged and flow through baffle  108  and sleeve  106 , thereby opening the fluid restriction achieved by the baffle and preventing further fracking operations. 
     Tapered tabs  152  protrude radially outward and structurally support the lower end of split-ring baffle  108  when baffle  108  is in the contracted, ball-catching state. Tabs  152  provide a structure interposed between the lower end of split-ring baffle  108  and the inner surface of sleeve  106 , which can act to inhibit or prevent the lower end of baffle  108  from deflecting radially outward. Split-ring baffle  108  can be configured to withstand the pressure within central conduit  116  of tool string  100 , which can reach high levels, including, e.g., between approximately 1000 to approximately 5000 psi. In some examples, an estimated maximum pressure within central conduit  116  of tool string  100  is between approximately 3000 and 5000 psi. However, more commonly, split-ring baffle  108  can be configured to withstand pressures between approximately 1000 and 2500 psi. 
     In ball seat valves employed in subterranean fracking operations and other such applications, there is a need for collapsible and re-expandable baffles for use in, e.g., sliding sleeve fracking tools, such as split-ring baffle  108  and other split-ring baffles in accordance with this disclosure. Wells made with, for example, 4.5 inch casing, balls dropped at the surface preferably have a diameter less than 3.5 inches, so the ball can travel through the conduit of the tool string. In such applications, tool string inner diameters, e.g., the diameter of central conduit  116  of tool string  100 , may have a need for a diameter equal to or greater than 3.75 inches. Due to these two factors, a baffle employed as the ball seat in a ball seat valve ideally is capable of collapsing from a large diameter of approximately 3.75 inches to a smaller diameter equal to or less than approximately 3.443 inches. The relatively large amount of baffle diameter travel, which is equal to 0.45 inches (3.75−3.3) in the foregoing example, can significantly complicate the baffle design. 
     A number of environmental and operational complications are also present in such applications, which can also impact the effectiveness of baffles employed as ball seats in ball seat valves. For example, the environments in which such baffles are employed are often laden with sand. During baffle contraction, segments of the baffle that enable such contraction can accumulate sand, potentially preventing full collapse. Additionally, in cemented wellbore environments, segmented designs will tend to collect cement between the segments of the baffle. Moreover, because multiple fracking stages may be pumped through the baffles before they are contracted, erosion of the baffle components can be a significant concern. Collapsible and re-expandable baffles employed in ball seat valves need to be of sufficient strength and flexibility to support the pressure load during fracking and to allow for contraction and expansion through the relatively large range of diameters. Also, sealing segments of the baffle that enable contraction/re-expansion can be important, because segments in the baffle design are potential points for leakage and any leak points can have a jetting effect, which can quickly erode the ball and baffle. 
     With the foregoing challenges and operational requirements in mind, split-ring baffle  108  is designed to achieve relatively large changes in diameter between the expanded and contracted states, and is also designed to withstand significant loading during fracking operations. Additionally, split-ring baffle  108  includes a single seam  140 , thus reducing or minimizing the number of segments the baffle includes. To achieve large diametrical changes and support high load conditions, in some examples, split-ring baffle  108  is fabricated from a material that allows baffle  108  to compress from a large diameter to a small diameter and support the loads from the ball impact and the load generated from pressure once the ball is on seat and sealing conduit  116  below ball seat valve  102 . In general, split-ring baffle  108  can be fabricated from materials with high toughness, or, put another way, materials with high yield strength and low Young&#39;s Modulus. The low Young&#39;s Modulus enables a larger change in diameter and higher yield strength enables the baffle to support greater loads. Additionally, high yield strength can also assist in allowing larger changes in diameter for split-ring baffle  108 . 
     In one example, split-ring baffle  108  is fabricated from high yield strength and low Young&#39;s Modulus steel. Example steels from which split-ring baffle  108  can be fabricated include Society of Automotive Engineers (SAE) steel grades  4140  or  4130 , an austenitic nickel-chromium alloy (e.g. an Inconel® alloy from Special Metals Corp. of New Hartford, N.Y.), titanium, and a martensitic stainless steel. In other examples, split-ring baffle  108  can be fabricated from other metals. In one example, to achieve the desired contractibility and load support, split-ring baffle  108  is fabricated from a material with yield strength in a range from approximately 100 ksi to approximately 150 ksi and with Young&#39;s Modulus in a range from approximately 16,000 ksi to approximately 30,000 ksi. A split-ring baffle in accordance with this disclosure, including example baffle  108  can thus achieve diametrical changes on the order of approximately 0.25 to approximately 0.50 inches and can withstand stresses due to compression on the order of approximately 120,000 psi or 120 kilo pounds per square inch (ksi). In one example, a split-ring baffle in accordance with this disclosure can withstand stresses due to compression in a range from approximately 70% to approximately 110% of the yield strength of the material from which the baffle is fabricated. 
     It is desirable to have the section thickness of split-ring baffle  108  as great as possible. Split-ring baffle  108  can, in certain applications, be exposed to the effects of erosion where various fluids are pumped at high rates through central conduit  116  of tool string  100 , causing erosion (material losses). Thus, in order to counter or account for such erosion effects, it is beneficial to maximize the section thickness of split-ring baffle  108  to ensure baffle  108  will allow for the maximum erosion possible in a given application. Additionally, a thicker cross section can also enable split-ring baffle  108  to support greater loads, such as loads from the ball, pressure, sealing, etc. 
     Limiting factors for the cross-sectional thickness of split-ring baffle  108  may be the stress introduced into the part when it is fully compressed coupled with the properties of the material from which baffle  108  is fabricated. A thinner cross-section baffle will be stressed less than a thicker cross-section baffle, assuming both are compressed to and from the same mid-point diameter. Additionally, it is desirable to maintain a stress on the baffle that is less than the yield strength of the material so the baffle is not plastically deformed. Plastic deformation of the baffle may cause the baffle to have a reduced diameter when it is re-expanded. Further, if it is necessary to exceed the yield strength, the second target could be to limit the stress on the baffle below the ultimate tensile strength of the material from which the baffle is fabricated. If the ultimate tensile strength is exceeded, the baffle can crack or break. Cracks and breakage can also occur even at the yield strength of the material. Thus, in order to reduce the possibility of cracks, breakage, and plastic deformation, it may be best to minimize the stress as much as possible. Thus, in some examples, it may be desirable to design the baffle cross-section thickness such that the stress on the baffle during operation is less than the yield strength of the material from which the baffle is made. In some examples, split-ring baffle  108  is designed such that the stress on baffle  108  during operation is equal to or less than approximately 80% of the yield strength of the material from which baffle  108  is fabricated. 
     In some examples, the configuration of split-ring baffle  108  can be analytically determined or informed using a mathematical relationship between properties of baffle  108  and the stresses that baffle  108  will encounter during use. For example, assuming a split-ring baffle in accordance with this disclosure is fabricated from a material with a Young&#39;s Modulus, E, of 29,000 ksi and a cross-section thickness, t, an expanded outer diameter, ODE, and a contracted outer diameter, ODC, then the compression stress, σ, on the baffle when in a compressed state can be calculated according to the following formula.
 
σ=[ E×t ×(ODE−ODC)]/[(ODE− t )×(ODC− t )]
 
     In the foregoing formula, the section thickness, t, is equal to the wall thickness of the baffle (e.g., [outer diameter−inner diameter]/2). The formula can be employed to calculate stress at one section of the baffle. Therefore, in cases where the baffle includes a varying cross section, the stress can be estimated by calculating stress at a number of axial sections along the baffle. 
     The foregoing calculated compression stress, a, on the baffle can be compared to the yield and ultimate strengths of the baffle to determine the risk of the baffle cracking and/or fracturing. For example, the foregoing calculated compression stress, a, on the baffle can be compared to the yield strength of the baffle to determine if the compression stress is equal to or less than approximately 80% of the yield strength. 
     One feature of split-ring baffle  108  that affects the cross-section thickness is tapered tabs  152 . As illustrated in  FIG. 4A  and as noted above, split-ring baffle  108  includes intermittent tapered tabs  152  protruding from the circumference of baffle  108 . Intermittent tabs  152  are employed with split-ring baffle  108 , instead of, e.g., a continuous tapered or other shaped lip that extends around the entire circumference of the baffle. Intermittent tabs can be provided in examples according to this disclosure to provide structural support and mechanical interlock functions, while preventing or reducing the risk of baffle  108  cracking and/or fracturing when moving between the radially expanded and contracted states. The presence of a continuous lip around the entire circumference of the baffle may cause stresses in the baffle that exceed design specifications, e.g., exceed 80% of yield strength, which, in turn, can cause cracking and/or fracturing when moving the baffle between the radially expanded and contracted states. 
     As noted above, during fracturing operations enabled by actuation of ball seat valve  102 , fracturing fluid communicated down central conduit  116  of tool string  100  can act to erode split-ring baffle  108  when there are any potential fluid pathways in baffle  108  other than the central conduit through the baffle. As such, portions of split-ring baffle  108  that are susceptible to leaking can be coated to assist in sealing baffle  108  when in the radially contracted, ball-catching state. For example, inner ball seat surfaces  146  and  148  of split-ring baffle  108  can be coated with rubber to assist in sealing the interface between baffle  108  and a dropped ball from leaking. Additionally, the surfaces of circumferential ends  142 ,  144  of split-ring baffle  108  can be coated with rubber to provide an improved sealed interface between ends  142 ,  144  when the ends abut one another at seam  140  in the radially contracted state of baffle  108 . A rubber coating on portions of split-ring baffle  144  can also protect the baffle from erosion. 
     In some examples, a combination of coatings can be employed on portions of split-ring baffle  144 . For example, circumferential ends  142  can be coated with a carbide coating or nikel coating, which can then be coated with rubber. The rubber coating applied to baffle  144  can include a Durometer in a range from approximately 40 to approximately 100. In one example, the rubber coating includes a Viton (FKM), Nitrile (NBR), or Hydrogenated Nitrile Butadiene Rubber (HNBR) coating. 
     Operation of ball seat valve  102  is described with reference to and illustrated in  FIGS. 5 and 6 , which are both section views of a portion of tool string  100 . In  FIG. 5 , ball seat valve  102  is in a closed state with split-ring baffle  108  expanded in the second position within sleeve  106 . In  FIG. 6 , ball seat valve  102  is open with split-ring baffle  108  contracted in the ball-catching state and with dropped ball  160  seated in baffle  108 . 
     In practice, split-ring baffle  108  is initially deployed in the first position, interlocked with sleeve  106  via tapered tabs  152  and groove  154 . Baffle  108  is configured to move within sleeve  106  from the first position to the second position to cause baffle  108  to assume the contracted, ball-catching state. For example, split-ring baffle  108  of ball seat valve  102  is at least partially received within sleeve  106  in the first position. Baffle  108  includes longitudinal seam  140  forming two separate circumferential ends  142 ,  144  in the baffle. The outer tapered surface of baffle  108  is configured to engage the inner tapered surface of sleeve  106  to cause split-ring baffle  108 , when in the first position to be relatively radially expanded, and, when moved to the second position in sleeve  106 , to radially contract. Split-ring baffle  108  ball seat of ball seat valve  102  can be engaged to move into the second position in the radially contracted state such that baffle  108  catches dropped ball  160 . 
     Piston  120  arranged and moveable within upper housing  112  of tool string  100  is configured to actuate split-ring baffle  108  to move the baffle from the open, expanded position to the closed, contracted ball-catching state. For example, movement of piston  120  downward within upper housing  112  can cause piston  120  to engage split-ring baffle  108  and move baffle  108  from the first position within sleeve  106  ( FIG. 5 ) to the second position ( FIG. 6 ). In the second position, split-ring baffle  108  assumes a contracted, ball-catching state and is configured to catch dropped ball  160 . 
     Movement of piston  120  within tool string  100  can be achieved with a variety of mechanical or electromechanical mechanisms. In one example, piston  120  is dropped within upper housing  112  to engage split-ring baffle  108  using a hydraulic mechanism. In  FIG. 5 , a small chamber  162  is defined between a portion of the outer surface of piston  120  and the inner surface of upper housing  112 . Chamber  162  can be filled with a hydraulic fluid such that the presence of the incompressible fluid prevents piston  120  from being pushed downward within upper housing  112 . During fracturing operations using tool string  100 , the pressure within central conduit  116  remains relatively high, e.g., approximately 2000 psi or more when fracking fluid is not being actively transmitted under pressure through the conduit. Thus, in the absence of the hydraulic fluid in chamber  162 , piston  120  would be pushed by the pressure in central conduit  116  from the position in  FIG. 5  down to the position in  FIG. 6 . 
     In one example, therefore, piston  120  is dropped within upper housing  112  to engage split-ring baffle  108  by evacuating the hydraulic fluid from chamber  162 . When the hydraulic fluid in chamber  162  is removed or substantially removed, the pressure within chamber  162  holding piston  120  in position is reduced, creating a pressure imbalance between the pressure within central conduit  116  of tool string  100  and chamber  162  that causes piston  120  to move down within upper housing  112 . Eventually piston  120  engages split-ring baffle  108  to move baffle  108  into the contracted, ball-catching state illustrated in  FIG. 6 . 
     The hydraulic fluid can be removed from chamber  162  to actuate piston  120  in a variety of ways. In one example, the hydraulic fluid is evacuated from chamber  162  by piercing a membrane that covers an outlet port of chamber  162 . However, in another example, a small mechanical door or valve can be actuated to open a fluid outlet to remove the hydraulic fluid from chamber  162 . For example, an electromagnetic mechanism can be employed to pierce the membrane to evacuate the hydraulic fluid from chamber  162  and, thereby, actuate piston  120 . 
     In one example, to actuate piston  120 , a magnetic device is deployed within a chamber or other passage in tool string  100  that is adjacent to an actuator that is employed to evacuate the hydraulic fluid from chamber  162 . The magnetic device can be a ferromagnetic cylinder or other shaped ferromagnetic material like a ball, dart, plug, fluid, gel, etc. In one example, a ferrofluid, magnetorheological fluid, or any other fluid having magnetic properties could be pumped to or past a magnetic sensor in order to transmit a magnetic signal to the actuator. Once deployed, the signal(s) generated by the magnetic device can be detected by a magnetic sensor in tool string  100 . 
     In the event the magnetic sensor detects a signature signal that corresponds to deployment of the magnetic device, electronics incorporated into tool string  100  can be configured to engage the actuator to open the valve, which functions to evacuate the hydraulic fluid from chamber  162  to actuate piston  120  to move within housing  112 . For example, if the electronic circuitry determines that the sensor has detected a predetermined magnetic signal(s), the electronic circuitry causes a valve device to open. In one example, the valve device includes a piercing member which pierces the membrane that covers an outlet port of chamber  162 . The piercing member that is engaged to pierce the membrane sealing chamber  162  can be driven by any means, such as, by an electrical, hydraulic, mechanical, explosive, chemical or other type of actuator. Additional details about and examples of such electro-hydraulic valves are described in U.S. Publication No. 2013/0048290, entitled “INJECTION OF FLUID INTO SELECTED ONES OF MULTIPLE ZONES WITH WELL TOOLS SELECTIVELY RESPONSIVE TO MAGNETIC PATTERNS,” which was filed on Aug. 29, 2011. 
     In the example of ball seat valve  102 , piston  120  also forms a component of valve  102  in that movement of piston  120  within upper housing  112  functions to open valve  102 . For example, prior to being actuated, piston  120  covers and seals central conduit  116  of tool string  100  from apertures  122 , which is illustrated in  FIG. 5 . When piston  120  is actuated by evacuating chamber  162 , or by some other mechanism, to move down, apertures  122  in housing  112  are exposed to place ball seat valve  102  in an open state, as illustrated in  FIG. 6 . In the state illustrated in  FIG. 6 , ball seat valve  102  is fully actuated with dropped ball  160  seated in contracted baffle  108  and piston  120  actuated to expose apertures  122 . In this state, fluid communication can occur between central conduit  116  of tool string  100  and the region that surrounds the tool string, e.g., the formation surrounding the tool within the wellbore. Fracking fluid can then be communicated downhole, through central conduit  116  and can exit apertures  122  to strike the layer of the formation surrounding tool string  100 . 
     In the foregoing example, movement of piston  120  down within upper housing  112  exposes apertures  122  and, thereby, functions to open ball seat valve  120 . In another example, however, movement of the sleeve within which the ball seat is arranged may function to open a ball seat valve in accordance with this disclosure. For example, movement of sleeve  106  can cause apertures in housing  110  to be exposed, which can function to open the ball seat valve. In such an example, sleeve  106  can be caused to move within housing  110  either as a result of force exerted by piston  120  or as a result of fluid pressure on sleeve  106  after ball  160  has been dropped and lodged in baffle  108 . 
       FIG. 7  depicts a flowchart illustrating an example method of actuating an apparatus for restricting fluid flow through a downhole tubular member. The example method of  FIG. 7  includes moving a split-ring baffle from a first position within a first section of an annular sleeve to a second position within a second section of the sleeve to cause the baffle to radially contract ( 400 ) and dropping a plug into the baffle when the baffle is in the second position and relatively radially contracted ( 402 ). The sleeve includes an inner surface defining the first section of a first diameter and the second section of a second, smaller, diameter. The baffle includes a longitudinal seam forming two separate circumferential ends in the baffle. An outer surface of the baffle is configured to engage the inner surface of the sleeve to cause the baffle, when in the first position to be relatively radially expanded, and, when moved to the second position in the sleeve, to radially contract. The plug is configured to lodge in the baffle to restrict fluid flow through the baffle when the baffle is contracted. 
     The method of  FIG. 7  may form part of a process by which a ball seat valve in a tool string is closed to restrict fluid flow within a portion of the tool string and to communicate a fracturing fluid out of the tool string to engage a zone of formation surrounding the string. An example of the method of  FIG. 7  is described above with reference to  FIGS. 5 and 6 , which illustrate actuation of ball seat valve  102  including split-ring baffle  108 , annular sleeve  106 , and ball  160  arranged within housing  110  of tool string  100 . 
     Various examples have been described. These and other examples are within the scope of the following claims.