Abstract:
A regulating valve assembly for regulating fluid flow through a passage, the assembly having: a back-flow valve comprising a seat and a closure element, wherein the closure element engages with the seat in a closed configuration and disengages from the seat in an open configuration; a lock in mechanical communication with the back-flow valve to lock the backflow valve in the open configuration; and a forward-flow valve in mechanical communication with the lock and comprising a seat and a closure element, wherein the closure element engages with the seat in a closed configuration and disengages from the seat in an open configuration.

Description:
BACKGROUND  
       [0001]     This invention relates to reverse cementing operations. In particular, this invention relates to methods and apparatuses for floating the casing and controlling fluid flow through the casing shoe.  
         [0002]     After a well for the production of oil and/or gas has been drilled, casing may be run into the wellbore and cemented. In conventional cementing operations, a cement composition is displaced down the inner diameter of the casing. The cement composition is displaced downward into the casing until it exits the bottom of the casing into the annular space between the outer diameter of the casing and the wellbore apparatus. It is then pumped up the annulus until a desired portion of the annulus if filled.  
         [0003]     The casing may also be cemented into a wellbore by utilizing what is known as a reverse-cementing method. The reverse-cementing method comprises displacing a cement composition into the annulus at the surface. As the cement composition is pumped down the annulus, well fluids ahead of the cement composition are displaced down and around the lower end of the casing string and up the inner diameter of the casing string and out to surface. The fluids ahead of the cement composition may also be displaced upwardly through a work string that has been run into the inner diameter of the casing string and sealed off at its lower end. Because the work string by definition has a smaller inner diameter, fluid velocities in a work string configuration may be higher and may more efficiently transport the cuttings washed out of the annulus during cementing operations.  
         [0004]     The reverse circulation cementing process, as opposed to the conventional method, may provide a number of advantages. For example, cementing pressures may be much lower than those experienced with conventional methods. Cement composition introduced in the annulus falls down the annulus so as to produce little or no pressure on the formation. Fluids in the wellbore ahead of the cement composition may be bled off through the casing at surface. When the reverse-circulating method is used, less fluid may be handled at surface and cement retarders may be utilized more efficiently or eliminated altogether.  
         [0005]     In many applications, float devices are used as the casing is run into the wellbore. Float shoes and float collars typically contain a back pressure check valve to prevent the flow of fluid into the bottom of the casing string as the casing is run into the wellbore or once the casing has reached its target depth. Float apparatuses may be used to prevent back flow of cement composition into the casing inner diameter after the cementing operations have been completed. Float apparatuses may also prevent oil and/or gas under high pressure from entering the inner diameter of the casing as the casing string is being run into the wellbore. If gas or oil under high pressure does enter the wellbore, it can result in a well blowout. Additionally, the weight of the casing, particularly with deep wells, often creates a tremendous amount of stress and strain on the derrick surface equipment and on the casing. Float apparatuses may minimize that stress as the casing is lowered into the wellbore because they make the casing string more buoyant in the wellbore.  
       SUMMARY  
       [0006]     This invention relates to reverse cementing operations. In particular, this invention relates to methods and apparatuses for floating the casing and controlling fluid flow through the casing shoe.  
         [0007]     According to one aspect of the invention, there is provided a regulating valve assembly for regulating fluid flow through a passage, the assembly having: a back-flow valve comprising a seat and a closure element, wherein the closure element engages with the seat in a closed configuration and disengages from the seat in an open configuration; a lock in mechanical communication with the back-flow valve to lock the back-flow valve in the open configuration; and a forward-flow valve in mechanical communication with the lock and comprising a seat and a closure element, wherein the closure element engages with the seat in a closed configuration and disengages from the seat in an open configuration.  
         [0008]     A further aspect of the invention provides a regulating valve assembly for regulating fluid flow through a passage, the assembly having: a back-flow valve comprising a seat and a closure element, wherein the closure element engages with the seat in a closed configuration and disengages from the seat in an open configuration; a sleeve, wherein the sleeve stings into the seat of the back-flow valve when the back-flow valve is in the open configuration and unstings from the seat of the back-flow valve when the back-flow valve is in the closed  
         [0009]     configuration; and a forward-flow valve positioned with the sleeve and comprising a seat and a closure element, wherein the closure element engages with the seat in a closed configuration and disengages from the seat in an open configuration.  
         [0010]     According to still another aspect of the invention, there is provided a method for reverse-cementing casing in a wellbore, the method having steps as follows: locking a back-flow valve in an open configuration and making the back-flow valve up to the casing; running the casing equipped with the back-flow valve into the wellbore to a target depth; reverse-circulating a cement composition into an annulus defined in the wellbore by the casing; taking fluid returns through the back-flow valve as the cement composition is reverse-circulated into the annulus; unlocking the back-flow valve; and closing the back-flow valve, whereby the cement composition is retained in the annulus by the back-flow valve.  
         [0011]     The objects, features, and advantages of the present invention will be readily apparent to those skilled in the art upon a reading of the description of the exemplary embodiments which follows.  
     
    
     BRIEF DESCRIPTION OF THE FIGURES  
       [0012]     The present invention may be better understood by reading the following description of non-limitative embodiments with reference to the attached drawings wherein like parts of each of the several figures are identified by the same referenced characters, and which are briefly described as follows.  
         [0013]      FIG. 1A  is a cross-sectional, side view of a reverse cementing float apparatus having back-flow and forward-flow flappers, wherein both flappers are open.  
         [0014]      FIG. 1B  is a cross-sectional, side view of the reverse cementing float apparatus of  FIG. 1A , wherein the forward-flow flapper is closed.  
         [0015]      FIG. 1C  is a cross-sectional, side view of the reverse cementing float apparatus of  FIGS. 1A and 1B , wherein the back-flow flapper is closed.  
         [0016]      FIG. 2A  is a cross-sectional, side view of a reverse cementing float apparatus having a back-flow flapper and a poppet valve, wherein both the back-flow flapper and poppet valve are open.  
         [0017]      FIG. 2B  is a cross-sectional, side view of the reverse cementing float apparatus of  FIG. 2A , wherein the poppet valve is closed.  
         [0018]      FIG. 2C  is a cross-sectional, side view of the reverse cementing float apparatus of  FIGS. 2A and 2B , wherein the back-flow flapper is closed.  
         [0019]      FIG. 3A  is a cross-sectional, side view of a reverse cementing float apparatus having back-flow and forward-flow flappers, and also having a float plug locked in a stinger sleeve.  
         [0020]      FIG. 3B  is a cross-sectional, side view of the reverse cementing float apparatus of  FIG. 3A , wherein the float plug is unlocked from the stinger sleeve.  
         [0021]      FIG. 3C  is a cross-sectional, side view of the reverse cementing float apparatus of  FIGS. 3A and 3B , wherein the float plug is removed from the stinger sleeve. 
     
    
       [0022]     It is to be noted, however, that the appended drawings illustrate only typical embodiments of this invention and are therefore not to be considered limiting of its scope, as the invention may admit to other equally effective embodiments.  
       DETAILED DESCRIPTION  
       [0023]     This invention relates to reverse cementing operations. In particular, this invention relates to methods and apparatuses for floating the casing and controlling fluid flow through the casing shoe.  
         [0024]     Referring to  FIG. 1A , a cross sectional side view of a dual flapper apparatus of the present invention is illustrated. This figure shows the float apparatus in the run-in-hole position. An upper flapper is retained in the open position by a pinned stinger sleeve that is attached to a lower assembly which contains a lower flapper valve. With this assembly installed in the casing, reverse circulation may be performed through the lower flapper as shown. The lower flapper also allows the casing to self-fill as it is run-in-hole. Not shown in this figure is a fill-up assembly that holds the lower flapper open to allow conventional circulation through the apparatus.  
         [0025]     The float apparatus  1  has a pipe section  2  having a female box end  3  for mating with an upper casing string (not shown). The pipe section  2  also has a male pin end  4  at its lower end for mating with a casing shoe or other tool (not shown). A back-flow flapper seat  5  is positioned within the pipe section  2  and is mechanically shouldered inside pipe section  2  on the bottom side of the seat  5  to prevent downward movement of the seat  5  with the application of forces exerted in that direction. Cement  41  or other drillable material fills an annular space above the seat  5  to further secure the seat  5  in the casing  2 . A back-flow flapper  6  pivotally connected to the back-flow flapper seat  5 . At the hinge point  7  between the back-flow flapper  6  and the back-flow flapper seat  5 , a spring is employed to bias the back-flow flapper  6  to a closed position ( FIG. 1A  illustrates the back-flow flapper  6  in an open position). A stinger sleeve  8  is positioned within the pipe section  2  and is stung into the back-flow flapper seat  5 . The stinger sleeve  8  has a stinger section  9 , a valve section  10 , and a seal section  11 .  
         [0026]     The stinger section  9  is a tubular structure having an outside diameter at its upper end that is slightly smaller than the inside diameter of a hole  12  through the back-flow flapper seat  5 . At its distal end, the stinger section  9  has a notch  13  for receiving a shear pin (or pins)  14  that extends from the back-flow flapper seat  5 . A beveled shoulder  15  extends radially from the stinger section  9  and rests on a conical rim  16  of the back-flow flapper seat  5 , when the stinger section  9  is stung into the back-flow flapper seat  5 . Thus, the upper (back) end of the stinger sleeve  8  is shouldered off solidly in the back flow flapper seat  5  so as to prevent backward movement of the stinger sleeve  8 .  
         [0027]     The valve section  10  of the stinger sleeve  8  has a forward-flow flapper seat  17  and a forward-flow flapper  18 . The forward-flow flapper  18  is connected to the forward-flow flapper seat  17  at hinge point  19 . The forward-flow flapper seat  17  has a conical rim  20  for receiving the forward-flow flapper  18  when the flapper is in a closed configuration. The forward-flow flapper seat  17  also has a hole  21  through its center for transmitting fluids through the flapper seat when the flapper is in an open configuration. A series of one-way pressure equalizer valves  40  are positioned in the side walls of the valve section  10  between the stinger section  9  and the forward flow flapper seat  17 .  
         [0028]     The seal section  11  of the stinger sleeve  8  is positioned below (forward) the valve section  10 . The seal section  11  has a cylindrical structure with a bore for passing fluids through its center. It also has three annular seal ribs  22  which extend outwardly to engage the interior surface of the pipe section  2 . In alternative embodiments of the invention, any number of annular seal ribs may be used. Because the seal ribs  22  extend in an upward (backward) direction relative to the interior surface of the pipe section  2 , the seal section  11  permits the stinger sleeve  8  to be moved in a downward (forward) direction.  
         [0029]     The float apparatus  1  is run into the wellbore in the configuration illustrated in  FIG. 1A . In particular, the stinger sleeve  8  is stung into the back-flow flapper seat  5  so that the back-flow flapper  6  is locked in an open configuration. Further, while the forward-flow flapper  18  is biased to a closed position by a spring at the hinge point  19 , the forward-flow flapper  18  remains in an unlocked configuration so that fluid may freely flow back through the flow apparatus  1  as it is run into the wellbore. Back flow through the forward flow flapper seat  17  is intermittent as the casing and float apparatus  1  are lowered into the wellbore one casing joint at a time. The forward flow flapper  18  opens as positive differential pressure acting from the bottom (forward) side of the flapper becomes sufficient to overcome the spring bias at hinge point  19 , with the forward flow flapper  18  re-closing as the differential pressure becomes insufficient to keep the flapper open (as casing movement is stopped to connect the next joint). As the float apparatus  1  is run into the wellbore, the equalizer valves  40  relieve an annular dead air space otherwise trapped around the outside of the stinger sleeve  8  between the seal section  11  and the back flow flapper seat  5 . The equalizer valves  40  allow trapped air and or fluids to evacuate into the inner diameter of the stinger sleeve  8  and thus to surface as the casing is being run into the wellbore.  
         [0030]      FIG. 1B  is a cross-sectional side view of the float apparatus  1  shown in  FIG. 1A . This figure shows the apparatus at target depth and after slurry has entered the casing inner diameter either confirmed by calculation or by returns through the work string at the surface. Once adequate slurry has been pumped, fluid flow is reversed and pumped down the casing inner diameter. This process closes the forward-flow flapper  18  and applies a hydraulic load to the shear pins  14  which hold the stinger sleeve  8  in place. When downward flow is initiated down the casing string to pump the stinger sleeve  8  out of the back flow flapper seat  5 , the equalizer valves  40  seal to permit application of fluid pressure against the closed forward flow flapper  18 , as described more fully below.  
         [0031]     With the bottom of the casing (not shown) at the target depth, a reverse circulation cementing operation may be conducted in the wellbore. Circulation fluid is reverse circulated down the annulus between the casing and the wellbore and up through the stinger sleeve  8  and pipe section  2  of the float apparatus  1 . Because the forward-flow flapper  18  is merely biased toward a closed configuration, it opens freely as the circulation fluid is pumped up through the stinger sleeve  8 . A cement composition slurry is pumped down the annulus behind the circulation fluid to fill the annulus between the casing and the wellbore. When the cement composition slurry reaches the bottom of the wellbore and enters the inner diameter of the casing, either confirmed by calculation or by returns at the surface, the reverse circulation flow is stopped. Fluid flow in the wellbore is then reversed and pumped down the inner diameter of the casing to apply a hydraulic load to the interior of the pipe section  2  and stinger sleeve  8 . With the forward-flow flapper  18  bias toward a closed position, the forward-flow flapper  18  readily positions itself in the conical rim  20  of the forward-flow flapper seat  17  to completely seal the interior of the stinger sleeve  8  against the hydraulic load. The hydraulic pressure within the stinger sleeve  8  is increased until a downward force applied to the stinger sleeve  8  is sufficient to overcome the shear strength of the shear pins  14 .  
         [0032]      FIG. 1C  illustrates a cross-sectional side view of the float apparatus shown in  FIG. 1A and 1B . This figure shows the back-flow flapper  6  in the closed position after the stinger sleeve  8  has sheared loose from the upper flapper. This design allows for both over balanced and under balanced cementing operations to be performed in the reverse direction. In certain embodiments of the invention, the flow area through the forward flow flapper seat  17  and/or through the minimum bore of the stinger section  9  (whichever has the lesser flow area) may be less than the flow area of the annulus defined by the wellbore and the casing. Those embodiments may create a pressure drop or choke to assist in keeping the hydrostatic overbalance in the annulus (generally the cement will be heavier than the well fluid it is displacing) from completely running away with itself as the fluid flows in the reverse direction.  
         [0033]     In  FIG. 1C  the shear pins  14  have released the stinger section  9  of the stinger sleeve  8 . Further, the hydraulic load applied to the inside of the pipe section  2  and the stinger sleeve  8  has pumped the stinger sleeve  8  downwardly relative to the pipe section  2 . Once the stinger section  9  has cleared the back-flow flapper seat  5 , the seal section  11  of the stinger sleeve  8  shares the hydraulic load with the forward-flow flapper  18  so that the stinger sleeve  8  is pumped even further downwardly (forwardly) relative to the pipe section  2 . If desired, the stinger sleeve  8  may be pumped completely out of the bottom of the pipe section  2  and allowed to free fall to the bottom of the rat hole in the wellbore. The stinger sleeve  8  may be displaced to a guide shoe or other landing seat at what would be the lower end of the shoe track. After the stinger section  9  clears the back-flow flapper seat  5 , the back-flow flapper  6  pivots about the hinge point  7  to a closed configuration. When displacement stops, the back-flow flapper  6  closes and retains the differential pressure from the weighted slurry in the annulus. With the back-flow flapper  6  closed, the hydrostatic load on the inner diameter of the casing and pipe section  2  may be released. The closed back-flow flapper  6  prevents the cement composition slurry in the annulus from U-tubing back up through the float apparatus  1  into the inner diameter of the casing.  
         [0034]     Referring to  FIG. 2A , a cross-sectional side view of a float apparatus of the present invention is illustrated. The float apparatus  1  has a pipe section  2  having a female box end  3  for mating with an upper casing string (not shown). The pipe section  2  also has a male pin end  4  at its lower end for mating with a lower casing shoe or other tool (not shown). The float apparatus  1  has a back-flow flapper seat  5  that is mechanically shouldered inside pipe section  2  on the bottom side of the seat  5  to prevent downward movement of the seat  5  with the application of forces exerted in that direction. Cement  41  fills an annular space above the seat  5  to further secure the seat  5  in the casing  2 . A back-flow flapper  6  is pivotally connected to the back-flow flapper seat  5  at a hinge point  7  between the back-flow flapper  6  and the back-flow flapper seat  5 . At the hinge point  7 , a hinge spring biases the back-flow flapper  6  to a closed position (see  FIG. 2B ). A stinger sleeve  8  is positioned within the pipe section  2  and is stung into the back-flow flapper seat  5 . The stinger sleeve has a stinger section  9 , a valve section  10 , and a seal section  11 .  
         [0035]     The stinger section  9  and the seal section  11  are similar to those described above with reference to  FIGS. 1A through 1C . The valve section  10  of the stinger sleeve  8  has a float collar  23 . The float collar  23  is equipped with a poppet valve  24  that is biased to a closed position by a coil spring  25 . A poppet valve mount  26  is held by cement  27  within the stinger sleeve  8 . The poppet valve  24  and the poppet valve mount  26  may be constructed of a phenolic plastic or other suitable material. The coil spring  25  may be constructed of a drillable metal or composite material or other suitable resilient or elastomeric material. In the closed position, the poppet valve  24  mates with a poppet seat  28 . The coil spring  25  pulls the poppet valve  24  down (forward) through the poppet valve mount  26  so as so bias the poppet valve  24  towards the closed position. Further, a series of one-way pressure equalizer valves, similar to those illustrated in  FIGS. 1A through 1C  may be positioned in the side walls of the valve section  10  between the stinger section  9  and the poppet valve seat  28 . The equalizer valves  40  may be positioned in the tubular cross section of the stinger section  9  immediately below the back-flow flapper seat  5  where the stinger section  9  stings into the back-flow flapper seat  5 , or in the heavy-walled, tapered portion of the stinger section  9 .  
         [0036]     The operation of the float apparatus illustrated in  FIG. 2A  is described with reference to  FIGS. 2A through 2C .  FIGS. 2B and 2C  are cross-sectional side views of the float apparatus illustrated in  FIG. 2A , wherein the poppet valve  24  is closed in  FIG. 2B , and the back-flow flapper  6  is closed in  FIG. 2C . The float apparatus  1  is run into a wellbore on a casing string in the configuration illustrated in  FIG. 2A . In particular, the stinger sleeve  8  is stung into the hole  12  in the back-flow flapper seat  5  so as to lock the back-flow flapper  6  in an open position. The stinger sleeve  8  is retained in the back-flow flapper seat  5  by a shear pin  14  or a plurality of shear pins or other suitable frangible device(s). As the float apparatus  1  is inserted into the well, static hydraulic fluid pressure in the wellbore increases relative to the static fluid pressure within the pipe section  2 . This pressure differential induces a force on the poppet valve  24  and eventually overcomes the biased force of the coil spring  25 . When the biased force is overcome, the poppet valve  24  becomes disengaged from the poppet valve seat  28  so as to allow fluid to flow from the wellbore into the pipe section  2  through the valve section  10  of the stinger sleeve  8 . This configuration is illustrated on  FIG. 2A .  
         [0037]     After the float apparatus  1  has been run into the wellbore to its target depth and the cement composition has been reverse circulated into the annulus, the inner diameter of the casing is pressurized to stop or reverse fluid flow through the poppet valve seat  28 . The bias force of the coil spring  25  drives the poppet valve  24  downwardly so as to rest firmly in the poppet valve seat  28 . This configuration is illustrated in  FIG. 2B . With the poppet valve  26  closed, the fluid pressure within the casing string is further increased to induce a force on the top of the poppet valve  26 . As the internal pressure continues to increase, it eventually becomes great enough to overcome the restraining force of the shear pin  14 . When the shear pin  14  structurally fails, the stinger sleeve  8  is released from the back-flow flapper seat  5 . The stinger sleeve  8  is then pumped downwardly in the pipe section  2  as illustrated in  FIG. 2C . When the stinger section  9  of the stinger sleeve  8  clears the back-flow flapper  6 , the spring at the hinge point  7  rotates the back-flow flapper  6  about the hinge point  7  to a closed position resting in the back-flow flapper seat  5 . With the back-flow flapper  6  in the closed position, the internal pressure in the casing string may be released, wherein the closed back-flow flapper  6  prevents fluid in the wellbore annulus from U-tubing into the casing inner diameter.  
         [0038]     Referring to  FIG. 3A , a cross-sectional side view of a float apparatus of the present invention is illustrated. The float apparatus  1  is similar to that described previously with reference to  FIG. 1A . However, this apparatus further comprises a float plug  30 . The float plug  30  has a float stopper  31  that fits into the neck of the stinger section  9  of the stinger sleeve  8 . A stopper seal  32  seals the float stopper  31  to the stinger section  9  to prevent fluid from flowing through the stinger sleeve  8 . A plurality of dogs  33  are positioned in slots in the midsection of the float stopper  31 . The float stopper  31  has a hollow bore into which a dog lock  34  is inserted. When the float stopper  31  is locked in the stinger sleeve  8 , the dog lock  34  is positioned in the middle of the dogs  33  so as to push the dogs  33  radially outward into a retainer groove  35 . The retainer groove  35  is in the inner bore of the stinger section  9  of the stinger sleeve  8 . At the top of the float stopper  31 , hooks  36  extend radially into the center of the float stopper  31 .  
         [0039]     The float plug  31  also has a stinger catcher  37  that is positioned in a relatively wider bore above the back-flow flapper seat  5 . The stinger catch  37  is connected to the dog lock  34  by a tie rod  38 . The stinger catcher  37  also has stinger hooks  39  that extend radially inward toward the middle of the stinger catcher  37  for engagement with a stinger (not shown). In alternative embodiments, the stinger catcher  37  need not be housed in the wider bore above the back-flow flapper seat  5  as illustrated, but rather, it may extend above the top of the concrete  41  and may be an extension of tie rod  38  that is retrievable with any number of OD or ID grapples commonly known to persons of skill in the fishing tool industry. The basic function of the catcher  37  remains the same regardless of the type fishing neck (or catcher) used.  
         [0040]     Referring to  FIG. 3B , a cross-sectional side view of the float apparatus of  FIG. 3A  is illustrated. While a stinger is not shown for simplicity,  FIG. 3B  illustrates a configuration of the float plug  30  after a stinger has been inserted into the stinger catcher  37  and the dogs  33  have been unlocked. To unlock the dogs  33 , the stinger catcher  37  is pulled upwardly in the apparatus to draw the dog lock  34  upwardly within the float stopper  31  via the tie rod  38 . When the dog lock  34  is no longer positioned behind the dogs  33 , the dogs  33  are free to move radially inward toward the middle of the float stopper  31 . As the dogs  33  move radially inward, they disengage from the retainer groove  35 . This disengagement unlocks the float stopper  31  from the stinger sleeve  8  so that the float stopper  31  is free to be withdrawn therefrom. As the dog lock  31  is pulled from behind the dogs  33 , it engages hooks  36  at the top of the float stopper  31 . When the stinger catcher pulls the dog lock  34  upwardly by the tie rod  38 , the dog lock  34  engages the hooks  36  to drag the float stopper  31  out of the stinger sleeve  8 .  
         [0041]      FIG. 3C  illustrates a cross-sectional side view of the float apparatus of  FIGS. 3A and 3B . In this illustration, the float stopper  31  is completely withdrawn from the float apparatus  1 , so as to allow fluid to freely flow up through the float apparatus  1 . In particular, the fluid flows up through the forward-flow flapper seat  17  by working against the biasing spring of the forward-flow flapper  18 . The back-flow flapper  6  is held in the open position by the stinger sleeve  8 .  
         [0042]     The float stopper  31  illustrated in  FIGS. 3A through 3C , may be used to close the float apparatus  1 , as the apparatus is run into the wellbore. Because the float stopper  31  prevents fluid from flowing into the casing from the wellbore, the casing may become buoyant in the wellbore so that not all of the weight of the casing is born by the derrick surface equipment. When the casing reaches the target depth, a stinger may be run into the inner diameter of the casing on a wire line, coil tubing or any other mechanism known to persons of skill so as to engage the stinger catcher  37 . Once the casing and float apparatus  1  are positioned in the wellbore at the target depth, the stinger catcher  37  may be used to pull the float stopper  31  from the float apparatus to allow fluid to flow into the casing inner diameter. With the float apparatus now open, reverse circulation cementing operations may be conducted in the wellbore. A cement composition slurry is pumped down the annulus while returns are taken up through the float apparatus  1  until the cement composition reaches the float apparatus or any other desired depth. When a desired amount of cement composition has been pumped into the annulus, the inner diameter of the casing is pressurized such that the fluid in the wellbore begins to flow in a conventional direction. The bias spring at hinge point  19  then rotates the forward-flow flapper  18  to a closed position in the forward-flow flapper seat  17 . As previously described, the stinger sleeve  8  is then pumped downwardly relatively to the back-flow flapper seat  5  so as to release the back-flow flapper  6 . When the back-flow flapper  6  becomes closed, the pressure within the inner diameter of the casing may be released and the cement composition is held in the annulus by the back-flow flapper  6 .  
         [0043]     While the float plug  30  is described with reference to a dual-flapper embodiment of the invention as illustrated in  FIGS. 3A through 3C , in other embodiments of the invention, the float plug may be employed in float apparatuses such as that illustrated in  FIGS. 2A through 2C .  
         [0044]     In alternative embodiments, a float plug may be a one-way valve that allows fluid to escape the inner diameter of the casing through the float plug, but prevents fluid from flowing from the annulus into the casing inner diameter. In these embodiments, the float plug may be pumped out of the bottom of the float apparatus  1  by dropping a ball on the float plug and pressuring the inner diameter of the casing string. Also, a service string may be inserted down the casing inner diameter to push the float plug out of the float apparatus. Float plugs suitable for use with this invention are illustrated in U.S. Pat. No. 6,244,342, the disclosure of which is incorporated herein by reference in its entirety.  
         [0045]     The inventive float apparatuses disclosed herein may be useful in reverse circulation cementing operations. These float apparatuses may be run into wellbores at the lower end of a casing string to be cemented into the wellbore. Once the casing and float apparatus have reached the target depth, a cement composition may be pumped down the annulus between the casing and the wellbore while returns are taken up through the float apparatus and the inner diameter of the casing. As these returns reverse circulate up through the float apparatus, the valve sections of the stinger sleeves remain open so as to allow the returns to flow through the float apparatus. When the cement composition reaches the bottom of the annulus at the float apparatus, reverse circulation is stopped and fluid pressure on the inner diameter of the casing is increased. The pressure increase on the inner diameter of the casing acts on the closed valve section of the float apparatus as previously described. Further increased pressure on the inner diameter of the casing pumps the stinger sleeve out of the back-flow flapper seat so as to allow the back-flow flapper to close. The fluid pressure in the inner diameter of the casing string may then be released, and the back-flow flapper seals the float apparatus to hold the cement composition in the annulus. U-tubing up through the float apparatus into the casing inner diameter is thereby prevented.  
         [0046]     Therefore, the present invention is well adapted to carry out the objects and attain the ends and advantages mentioned as well as those that are inherent therein. While the invention has been depicted and described with reference to embodiments of the invention, such a reference does not imply a limitation on the invention, and no such limitation is to be inferred. The invention is capable of considerable modification, alternation, and equivalents in form and function, as will occur to those ordinarily skilled in the pertinent arts and having the benefit of this disclosure. The depicted and described embodiments of the invention are exemplary only, and are not exhaustive of the scope of the invention. Consequently, the invention is intended to be limited only by the spirit and scope of the appended claims, giving full cognizance to equivalents in all respects.