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CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a Continuation claiming priority benefit from U.S. patent application Ser. No. 12/586,254, filed Sep. 18, 2009 now U.S. Pat. No. 8,146,732 which claims priority to U.S. Provisional Application No. 61/192,432 filed on Sep. 18, 2008. 
    
    
     FIELD OF THE INVENTION 
     The present invention relates to an improved method and apparatus for moving fluid. In particular, the invention relates to a synchronized drive head assembly containing a set of counter rotating sheaves with an endless conveyor and used to move fluids. 
     BACKGROUND OF THE INVENTION 
     Using a continuous rope or belt as a conveyor looped between a sheave at a particular destination and a sheave at a particular origin to move fluid is known in the prior art. Often the fluid conveyor is used to lift water or oil from beneath the surface of the ground to a storage receptacle on the surface. In this specific use of lifting fluid up to the surface, a well bore of sufficient length to reach the fluid is drilled and a fluid entraining conveyor or belt is secured around a sheave submerged in the fluid. A sheave system rigged on the surface is designed to minimize the effort required to lift the fluid entraining conveyor to the surface. The system must have sufficient traction between the sheaves and the conveyor to lift the combined weight of the conveyor and the fluid. Typical fluid conveyors of the prior art use a mechanical device to turn one sheave which pulls a rope up out of a well and returns the rope back into the well as it unwinds off the sheave. The fluid in the well follows the rope up and is subsequently collected in a containment vessel on the surface. 
     The efficiency of a fluid conveyor is determined by the amount of product collected as compared to the amount of energy used to run the device. Efficiency is lost when the conveyor slips on the drive sheave due to low traction between the conveyor and the sheave. Slippage causes wear on the conveyor and therefore reduces its useful life. To generate sufficient traction to prevent slippage, tension in the rope is typically high. The tension in the conveyor being a combination of factors such as, the type of fluid being lifted, the speed of the conveyor, the diameter of the conveyor, and the friction of the conveyor against the sheaves. A common problem with the fluid conveyors of the prior art is the failure of the conveyor due to slippage or high tension. The typical lifespan of the conveyor used in the prior art is approximately ninety (90) days. The relatively short lifespan of the conveyor increases the cost of the system which is a distinct disadvantage of the prior art. 
     Typical of the prior art is U.S. Pat. No. 4,652,372 to Threadgill. Threadgill discloses a liquid separator utilizing an endless belt for skimming extraction of oil from a liquid body and doctoring rollers for gathering the oil from both sides of the belt. The endless belt is fabricated from a material which is preferentially wettable by the liquid to be extracted. One drive roller winds the belt up out of the well and around a pair of doctoring rollers. Both sides of the belt engage a doctoring roller to skim the liquid off the belt. An additional roller positioned in the liquid maintains tension in the belt. The tension in the belt and the skimming process needed to remove the liquid from both sides of the belt tend to shorten the lifespan of the belt. 
     U.S. Pat. No. 6,158,515 to Greer, et al. discloses an artificial lifting device for well fluids using a continuous loop of fibrous material, such as a rope. The rope loop is formed around a drive sheave on the surface with a return sheave down inside of the well. The drive sheave has ridges along the side surfaces of a groove. The rope lays in the groove in contact with the ridges. A motor rotates the drive sheave, as guides and wipers direct the rope into the drive sheave and to the wipers. The wipers are slotted cards that scrape a quantity of fluid from the outside surface of the rope. The useful life of the rope is diminished by the contact with the ridges in the groove and the scraping of the wipers. 
     U.S. Pat. No. 5,080,781 to Evins, IV discloses a down-hole hydrocarbon collector that incorporates an endless absorption belt for collecting low-viscosity hydrocarbon liquids from a well and pumping those liquids to the surface. The collector of the invention has a means for driving the belt through a body of liquid to absorb low-viscosity hydrocarbons, which includes rollers engaging the endless belt in a manner that squeezes the hydrocarbons from the belt. The use of springs enables the squeezing of the belt between rollers. The squeezing of the belt exposes the belt to additional abrasion and hence limits its lifespan. 
     U.S. Pat. No. 5,423,415 to Williams discloses a rope pump for conveying fluid-like material from a reservoir to a select location. The surface assembly for the rope pump includes an endless rope, sheaves for forming the endless rope into a loop extending between the reservoir and the select location and a drive for driving the rope about the sheaves. The drive includes a first and second sheave each having a plurality of circumferential grooves. The endless rope is wrapped between the first and second sheaves in the grooves in a block and tackle fashion. A tensioning wheel biases the rope to maintain the rope in constant engagement with the final grooves of the first and second sheave. The tensioning wheel provides constant tension on the rope on the drive sheaves to continuously eliminate rope slack. The constant tension in the rope, especially on the downward side of the loop puts undue strain on the rope and reduces its lifespan. 
     SUMMARY OF INVENTION 
     The preferred embodiment of the present invention provides an efficient and dependable device for driving a conveyor through the length of a well bore to collect fluids. The present invention incorporates two synchronized sheaves. A “figure-8” conveyor path between the synchronized sheaves maximizes the contact of the conveyor with the sheaves and not only improves traction between the sheaves and the conveyor but also allows for zero tension on the conveyor as it reenters the tubing in the well bore. The sheaves include coaxial grooves, each having a unique and novel cross-section that further improves traction without unnecessary abrasion on the conveyor. Under normal working load conditions, as measured by conveyor tension, the invention significantly increases conveyor lifespan. 
     Accordingly, an embodiment of the present invention provides a drive head assembly for a fluid conveyor which includes a double sided drive mechanism, such as gears or a double sided drive belt, engaged with a drive wheel and three follower wheels. A first follower wheel shares a rotational axis with a first sheave. A second follower wheel shares a rotational axis with a second sheave. The drive mechanism engages the first and second follower wheels in such a way as to impart a synchronous but opposite rotation to them. The first and second sheaves are connected to the first and second follower wheels respectively via shared rotational axes. The first and second follower wheels impart a synchronous but opposite rotation to the first and second sheaves. The first and second sheave each has a set of coaxial grooves. The preferred embodiment has four coaxial grooves on each sheave. Each groove on the first sheave matched to a groove on the second sheave to form a set of grooves. An endless conveyor follows a “figure-8” conveyor path, through each groove between the sheaves. The “figure-8” conveyor path maximizes the contact surface between the sheaves and the conveyor providing improved traction on the conveyor. The cross-sectional area of the conveyor expands as tension in the conveyor is reduced following each loop around the pair of sheaves. Similarly, the width of each consecutive groove increases to accommodate the conveyor. The depth of each groove, between the lowest portion of each groove and the center of the sheave, is also related to the cross-sectional area of the conveyor. The first groove of each sheave is slightly shallower than that of the adjacent groove which is slightly shallower than the next adjacent groove and so forth. As a result of the progressive increase in depth of each groove, the distance between the cross-sectional center of the conveyor and the rotational axis is slightly reduced in each consecutive groove of the sheave. The conveyor travels down a two-channeled tubing to a remote sheave and returns up the tubing to the sheaves entraining fluid from a reservoir. The drive head assembly of the present invention is surrounded by a sealed cover. The cover, which acts as a containment vessel, protects the environment from the fluids lifted. Additionally, the cover allows a pressurized interior, if necessary, and collects the fluid entrained on the returning conveyor. An outlet port in the cover directs the collected fluid to a holding tank. 
     A single pair of sheaves is described for simplicity. However, the drive head may contain more than two sheaves. 
     Those skilled in the art will further appreciate the above-mentioned features and advantages of the invention together with other important aspects upon reading the detailed description that follows in conjunction with the drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the detailed description of the preferred embodiments presented below, reference is made to the accompanying drawings. 
         FIG. 1  is an elevation view of the drive head of a preferred embodiment with the cover removed. 
         FIG. 2  is an elevation view of the drive head of a preferred embodiment showing the conveyor path. 
         FIG. 3  is a partial elevation view of the sheaves of a preferred embodiment showing the conveyor path. 
         FIG. 4  is a partial elevation view of a sheave of a preferred embodiment showing the cross-section areas of the conveyor. 
         FIG. 5  is a close up elevation view of a groove of a preferred embodiment. 
         FIG. 6  is an isometric view of the drive head of a preferred embodiment. 
         FIG. 7  is a cross-section view of a well bore in operation with the drive head of a preferred embodiment. 
         FIG. 8  is an isometric view of an alternate embodiment. 
         FIG. 9  is a cutaway view of sheaves of  FIG. 3 , showing the variables necessary to formulate the equations for the radii of each groove in a given sheave. 
         FIG. 10  is a cutaway view of a sheave, showing the deformation of the conveyor inside a sheave. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     In the descriptions that follow, like parts are marked throughout the specification and drawings with the same numerals, respectively. The drawing figures are not necessarily drawn to scale and certain figures may be shown in exaggerated or generalized form in the interest of clarity and conciseness. 
       FIGS. 1 ,  2  and  6  show a preferred embodiment of drive head  100 . Base  102  provides a connecting platform for motor  116 , transmission  118 , and frames  104  and  106 . In the preferred embodiment, base  102  is mounted to ground surface  108  via a concrete slab. Brace  220  stabilizes frame  104  to frame  106 . Frames  104  and  106  are parallel to each other and extend from base  102  at angle A. Angle A may be any angle, including perpendicular. In the preferred embodiment, angle A ranges from 80° to 85°. 
     In the preferred embodiment, motor  116  generates up to 10 horsepower and is powered by fuel or electricity. However, motor  116  may be of any size or type. The size of motor  116  may be altered to account for the weight of the conveyor  142 , density of the fluid, speed of operation, the size of the sheaves  110  and  112 , and the size of follower wheels  124 ,  126 , and  128 . Motor  116  is removably secured to base  102  and is additionally connected to transmission  118  to provide rotational motion to drive shaft  122 . Drive shaft  122  extends from transmission  118 . Drive wheel  120  is notched along its perimeter and is concentrically mounted on drive shaft  122 . Drive shaft  122  provides a rotational axis for drive wheel  120 . 
     Follower wheels  124 ,  126 , and  128  are concentrically mounted on one end of shafts  134 ,  136 , and  138  respectively. In the preferred embodiment, follower wheels  124 ,  126 , and  128  are all generally equal in shape and size and their midpoints are linearly aligned on the longitudinal midline  140  of frame  104 . In the preferred embodiment, the diameter of follower wheels ranges from 8 to 10 inches. However, the follower wheels  124 ,  126 , and  128  may be of any size. Additionally, geometry could be selected such that follower wheels  124 ,  126 , and  128  were not the same size as each other. The size of the follower wheels  124 ,  126 , and  128  are generally selected based on the weight of the conveyor  142 , the diameter of sheaves  110  and  112 , density of the fluid and power of the motor  116 . Additionally, in a different prepared embodiment follower wheels  124  and  134  are not used. 
     Shafts  134 ,  136 , and  138  are mounted in and perpendicularly extend between frames  104  and  106 . Rotating shaft support  230  mounted in frame  104  and rotating shaft support  232  mounted in frame  106  provide for rotation of shaft  138 . Rotating shaft support  234  mounted in frame  104  and rotating shaft support  236  mounted in frame  106  for rotation of shaft  136 . Rotating shaft support  238  mounted in frame  104  and rotating shaft support  240  mounted in frame  106  for rotation of shaft  134 . Additionally, in a different preferred embodiment, Follower wheels  124  and  134  are not used. 
     In a preferred embodiment, the perimeter of follower wheels  124 ,  126 , and  128  have equally spaced cogs for engagement with double-sided toothed belt  114 . Belt  114  has teeth on opposite surfaces for engagement with the notches of drive wheel  120  and the cogs of the follower wheels. Belt  114  is propelled by drive wheel  120 . 
     As shown in  FIG. 1 , belt  114  winds from drive wheel  120 , around follower wheel  124 , crosses midline  140 , around follower wheel  126 , crosses midline  140  again, around follower wheel  128 , and back down to drive wheel  120 . The arrows shown on drive wheel  120  and the follower wheels indicate the rotational direction of the follower wheels with respect to the drive wheel. Belt  114  is wound as such to ensure that follower wheels  126  and  128  rotate in opposite directions. Although follower wheels  126  and  128  rotate in opposite directions, belt  114  synchronizes them to rotate at the same speed. 
     Sheave  110  is generally cylindrical in shape and is rigidly mounted to shaft  138 . Shaft  138  is a rotational axis for sheave  110 . Sheave  112  is generally cylindrical in shape and is rigidly mounted to shaft  136 . Shaft  136  is a rotational axis for sheave  112 . Follower wheel  128 , shaft  138 , and sheave  110  all rotate in unison and in an opposite direction of follower wheel  126 , shaft  136 , and sheave  112  which also rotate in unison. Because follower wheel  126  and  128  are synchronized to rotate at the same speed in opposite directions, it follows that sheaves  110  and  112  are also synchronized and rotate at the same speed in opposite directions. In the preferred embodiment, sheave  110  and follower wheel  128  rotate at the same RPM as sheave  112  and follower wheel  126 . 
     As shown in  FIGS. 2 ,  4 , and  6 , sheave  110  in a preferred embodiment of the present invention is made up of four integrally formed coaxial grooves  202 ,  204 ,  206 , and  208 . In alternate embodiments, the total number of grooves on each sheave varies depending on the depth of the well bore and the traction required. The total number of grooves on each sheave is determined by the amount of tractive force required to propel the conveyor. The curvature of the groove walls has a cross sectional profile determined by a function described in  FIG. 9 . The grooves are adjacent each other and increase in width as the diameter of the conveyor  142  increases. Thus, the cross sectional profile of groove  202  (and conveyer segment  402 ) is the most narrow and groove  208  (and conveyor segment  408 ) is the widest. Generally, the ratio of the profile of groove  202  to the profile of groove  204  and the ratio of the profile of groove  204  to the profile of groove  206  and so forth should be in the range of 1.01 to 1.1. The width of the groove profile depends on the elasticity of the conveyor (which is assumed to be constant) and the amount of tensile force applied to it. The tensile force applied to the conveyor is a function of the diameter of the conveyor, the speed at which the conveyor is being propelled, the viscosity of the fluids being moved, and overall weight of the conveyor. The functions are more fully explained with the descriptions of  FIGS. 9 and 10  that follow. 
     In the preferred embodiment, sheave  112  is generally the same size as sheave  110 . Sheave  112  is also made up of four integrally formed coaxial grooves  212 ,  214 ,  216 , and  218 . The grooves are adjacent each other and linearly step down in radius where groove  212  has the largest radius and groove  218  the smallest, as described for sheave  110  above. 
       FIG. 4  shows a partial view of sheave  110 . It is understood that sheave  112  is structurally similar. The step down in radius of the grooves is necessary to counteract the expanding diameter of conveyor  142 . Accordingly, radius  422  of groove  202  is greater than radius  424  of groove  204 . Radius  424  of groove  204  is greater than radius  426  of groove  206 . Radius  426  of groove  206  is greater than radius  428  of groove  208 . As conveyor  142  loops around the grooves of the sheaves (the preferred path to be described below), tension is lessened and the cross-sectional area of conveyor  142  increases. In the preferred embodiment, distance  422  ranges from approximately 5.5 to 6 inches to as small as 2 inches. However, distance  422  may be of any size. Distance  422  may be selected based on the diameter of follower wheels  124 ,  126 , and  128 , weight of conveyor  142 , density of fluid  630  and size of motor  116 . Because of the elasticity of the conveyor, as tension in a segment of conveyor  142  is reduced the length of the segment is also reduced. Therefore the shorter radius of each sequential groove is necessary to keep slack out of the windings and prevent slippage. Slippage produces unwanted wear on the conveyor. 
       FIG. 5  shows the shape of the conveyor receiving grooves. The cross-section of each groove has two sides, each side having a different profile and slope, as described by equations 11 and 13, due to point  508  not being located along centerline  522  of groove  202 . For clarity, only grooves  202  and  204  are shown. It is understood that all additional grooves will be similarly shaped. The unique shape of the grooves eliminates the need for tension on down portion  304  of conveyor  142  and grips the conveyor without cinching the conveyor thereby prolonging conveyor life. Groove  202  includes profile  502  and groove  204  includes profile  504 . Profile  502  is formed by the two curves  506  and  510  which are defined by a specific equation. The equation is a function of the groove radius and the pitch between alternate grooves on different sheaves. As previously mentioned and shown later with the descriptions of  FIGS. 9 and 10 , the groove radius depends on the elasticity of the conveyor and the amount of tensile force applied to the conveyor. The tensile force applied to the conveyor is a function of the diameter of the conveyor, the speed at which the conveyor is being propelled, the viscosity of the fluids being moved, and the overall weight of the conveyor. Curve  506  and  510  intersect at point  508 . Intersection point  508  is located off centerline  522 . Because the intersection point of curves  506  and  510  is off centerline  522 , curve  510  has a more gradual slope than curve  506  and the conveyor naturally rests in profile  502  off-center as well. Curve  506  provides a less obstructive angle of departure as conveyor  142  proceeds from one groove on a sheave to another groove on a different sheave. Profile  504  is formed by the two curves  512  and  516  which intersect at point  514  and are defined by a different equation. The equation is not the same as the equation for curves  506  and  510  defining profile  502  because the equations are a function of groove radius and the radius of groove  204  is less than that of groove  202 . 
     As best shown in  FIG. 3 , sheave  110  is located distance  310  from sheave  112 . As conveyor  142  passes from sheave  110 , crosses midline  140  and loops back around on sheave  112 , conveyor  142  generally makes contact with a majority of the perimeter of each sheave. As the conveyor first enters sheave  110  from the well bore and finally exits sheave  112  to enter the well bore, the contact with sheaves  110  and  112  is reduced as the conveyor  142  enters and leaves vertically. This is further described in equation 1. Conveyor  142  continues this “figure-8” conveyor path, alternating between the sheaves for as many grooves as there are in each sheave. As distance  310  decreases, the more contact conveyor  142  makes with each sheave and thus more tractive force. The optimal distance between the sheaves maximizes the contact conveyor  142  has with the perimeters of each sheave while still allowing enough space for conveyor  142  to cross grooves without obstruction. Conveyor  142  contacts both sheaves through angle B. In the preferred embodiment, angle B ranges from 320° to 340° except for the first and last groove as described above. The more surface contact conveyor  142  has with the sheaves, the more tractive force will be produced. 
     Referring to  FIG. 6 , cover  602  is generally rectangular and hollow. Cover  602  encases frames  104  and  106  and sheaves  110  and  112 . Follower wheels  124 ,  126 , and  128  are adjacent cover  602  and located on the exterior of cover  602 . Cover  602  further defines entrance hole  610  and exit hole  612 . Drain hole  606  allows the fluid moved from the reservoir to be removed from collection area  618  and transported to an additional storage receptacle. Standpipe  604  is fitted to the underside of cover  602  below collection area  618 . Standpipe  604  extends from the upper portion of the well bore. 
     The preferred path of conveyor  142  can be seen in  FIGS. 2 ,  3 , and  6 . Up portion  302  of conveyor  142  enters drive head  100  through entrance hole  610  in cover  602 . It is not necessary for conveyor  142  to be perpendicular to base  102  while it is in the enclosed area of cover  602 . Up portion  302  must have an unobstructed path from entrance hole  610  to groove  202  and down portion  304  must have an equally unobstructed path from groove  218  to exit hole  612 . After entering cover  602 , conveyor  142  passes over and around sheave  110  in groove  202 . Conveyor  142  leaves groove  202 , crosses midline  140  between the sheaves and rounds sheave  112  in groove  212  in an opposite rotational direction than around sheave  110 . Arrows  306  and  308  indicate the rotational directions of each sheave are opposite each other. Conveyor  142  then leaves groove  212 , crosses midline  140  and rounds sheave  110  in groove  204 . This “figure-8” conveyor path continues for the remaining grooves until conveyor  142  leaves groove  218  and down portion  304  exits covers  602  through exit hole  612 . 
     Referring to  FIGS. 6 and 7 , once conveyor  142  passes through exit hole  612  it travels through down chamber  616  of flexible tubing  608 . Flexible tubing  608  has two separate passageways that extend throughout the length of flexible tubing  608 , down chamber  616  and up chamber  614 . Drop housing  620  is affixed to the end of flexible tubing  608  that is furthest from drive head  100 . Drop housing  620  is lowered to a sufficient depth in well bore  704  in order to come into contact with fluid  630 . Conveyor  142  enters drop housing  620  and travels around distal sheave  624 . Distal sheave  624  is secured to a cone shaped section of drop housing  620  shown as nose  622 . Drop housing  620  further includes a plurality of inlets  626 . Inlets  626  are openings in drop housing  620  which allow fluid  630  to enter into the interior of drop housing  620  and become adjacent to conveyor  142 . After looping around distal sheave  624 , the conveyor returns through up chamber  614  and begins the path again starting in groove  202  of sheave  110 . 
     In operation, drive head assembly  100  is mounted to standpipe  604  extending from well bore  704 . Up portion  302  of conveyor  142  is looped between sheave  110  and sheave  112  in a “figure-8” conveyor path. Down portion  304  is looped around distal sheave  624  secured to drop housing  620 . Drop housing  620  is lowered into well bore  704  until it reaches the fluid to be pumped. A power delivery system turns drive shaft  122  which in turn rotates drive wheel  120 . Belt  114  is strung around drive wheel  120  and follower wheels  124 ,  126 , and  128 . Belt  114  causes follower wheels  124  and  128  to rotate in the same direction as drive wheel  120  and follower wheel  126  to rotate in the opposite direction of drive wheel  120 . Belt  114  synchronizes follower wheels  126  and  128  to rotate at the same speed. Follower wheel  128  causes sheave  110  to rotate and follower wheel  126  causes sheave  112  to rotate. As a result, belt  114  synchronizes sheaves  110  and  112  to rotate at the same speed. In the preferred embodiment, follower wheels rotate in the range of approximately 250 RPM to 600 RPM resulting in a conveyor speed ranging between approximately 700 feet per minute (fpm) and 1,700 fpm. However, other speeds are envisioned based on the diameter of the follower wheels, the diameter of the sheave and the overall weight of the conveyor. 
     In alternate embodiments, follower wheels  124 ,  126  and  128  may be smooth and driven by a smooth belt. Alternately, they may consist of meshed gears. Finally, they may be sprockets utilizing a chain drive from the drive wheel  120 . 
     Sheaves  110  and  112  pull conveyor  142  up through up chamber  614  of flexible tubing  608 , up through entrance hole  610 , and around each other. Sheave  112  guides conveyor  142  down through exit hole  612  and through down chamber  616 . Down portion  304  of conveyor  142  moves as a result of the force applied by sheaves  110  and  112  to up portion  302 . As conveyor  142  travels through the length of well bore  704 , conveyor  142  uses the principals of Couette flow theory to entrain a quantity of fluid  630 . In fluid dynamics, Couette flow refers to the laminar flow of a viscous liquid in the space between two surfaces, one of which is moving relative to the other. The flow is driven by virtue of viscous drag force acting on the fluid and the applied pressure gradient between the surfaces. Here, the two surfaces are conveyor  142  moving relative to flexible tubing  608 . Fluid  630  travels with conveyor  142  up flexible tubing  608  and acts to support, displace, or offset the conveyor from the sides of the tubing. For a more detailed description of a fluid entraining conveyor and flexible tubing advantageously used with the invention, reference is made to U.S. Pat. No. RE 35,266 to Crafton, et al., this is fully incorporated by reference herein. 
     Fluid  630  enters cover  602  through entrance hole  610  and pools in collection area  618 . Fluid  630  is pumped or otherwise transported from collection area  618  through drain hole  606  to a storage receptacle until processed or transported further. 
       FIG. 8  shows an alternate embodiment of the present invention. Drive head  800 , including hydraulic motor  820  and follower wheels  826  and  828  are all encased in sealed cover  823 . Cover  823  (shown in cutaway) is generally cylindrical in shape and encloses the working components of drive head  800 . Cover  823  is mounted to lip  802  via a plurality of bolts through attachment holes  806 . Seal  824  resides in annular grooves  826  and  827 . Seal  824 , in cooperation with annular grooves  826  and  827 , seals the working components of drive head  800  with respect to the outside pressure. Lip  802  is integrally formed with the open end of standpipe  804 . Standpipe  804  extends from the upper portion of the well bore. Base  814  is mounted to standpipe  804 . Base  814  is a disc shape having rectangular opening  818 . Rectangular opening  818  provides access for the conveyor (not shown) down into the well bore. Frame  808  is supported on base  814  by buttresses  824  and  826 . In the preferred embodiment, frame  808  extends from base  814  at an angle that ranges from 80° to 85°. However other angles including perpendicular to the base are envisioned. 
     Frame  808  is generally a rectangular shape and provides mounting points for sheaves  810  and  812  and also follower wheels  826  and  828 . Frame  808  includes frame extension  816 . Frame extension  816  provides a mounting point for hydraulic motor  820 . Hydraulic motor includes valves  822  for input and output of the hydraulic fluid that powers hydraulic motor  820 . Sheaves  810  and  812  are mounted on axles which axially rotate in frame  808 . Follower wheels  828  and  826  are linearly aligned and mounted on the same axles extending through frame  808 . 
     In the preferred embodiment, follower wheels  828  and  826  have equally spaced cogs for engagement with a double-sided toothed belt. A double-sided toothed belt driven by a drive wheel connected to hydraulic motor  820  rotates follower wheels  826  and  828 . Follower wheels  826  and  828  are synchronized to rotate at the same velocity and in opposite directions. By virtue of follower wheels  826  and  828  being mounted on the same rotational axes as sheaves  812  and  810  respectively, sheaves  810  and  812  also rotate at the same speed and in opposite directions. 
     In alternate embodiments, follower wheels  826  and  828  may be smooth and driven by a smooth belt. Alternately, they may consist of meshed gears. Finally, they may be sprockets utilizing a chain drive from the drive wheel. 
     Sheaves  810  and  812  are each shown with two coaxial grooves. The total number of coaxial grooves on each sheave can vary depending on the depth of the well bore and the traction required to propel the conveyor. The grooves have a cross-sectional shape of a V with concave sides as previously described. The conveyor is wrapped around the sheaves and down into the well bore via a double chambered flexible tubing in the same manner as described in previous embodiments. 
     The embodiment in  FIG. 8  is used in situations where the fluid to be moved is under pressure. The outer casing includes the cover and standpipe  804 , as well as seals and gaskets between them to maintain the pressure. In the preferred embodiment, container vessel can maintain pressure up to several thousand psi. However, greater pressures may be achieved as such casings, seals and fittings are well known in the art. 
     The present invention is useful for any fluid production system by which fluid is to be transported a long distance using a conveyor. Additionally, the drive head assembly of the present invention incorporating the synchronized sheaves, the “figure-8” conveyor path between the sheaves, and the uniquely shaped grooves of the sheaves can be used in any conveyor configuration wherein high tractive forces are required of the conveyor and prolonged conveyor life is desired. 
     Referring now to  FIGS. 9 and 10  determination of the radii and shape of those grooves will be described assuming an elastic conveyor, driven under tension by friction between the groove walls and the conveyor. 
     The size of gap, w 1 , between the sheaves and the grooves controls the departure and entry points for the conveyor in each of the respective sheave grooves. The entry and departure points are the points on the centerline of contact between the groove walls and the conveyor arrives at or leaves from its resting point in the groove. A line is drawn in  FIG. 9  between the center point of the first sheave  110  and the departure point of the conveyor and annotated at “r 1 ”. A similar line from the center point of the second sheave  112  to the conveyor entry point in its first groove is shown as “r 2 ”. A midline  140  is shown between the center points of the two sheaves, which are a distance “D” apart. Notice that the midline  140  is canted from vertical by an angle of δ. 
     Referring to  FIG. 10 , the centerline of contact with the conveyor is shown. That centerline is also the location of a point load on the walls and conveyor, which is equivalent to the distributed load over the contact area.  FIG. 10  also portrays the cross-section of the sheave grooves and an approximate shape of the loaded conveyor, when in the groove. A V-shaped sheave groove is utilized for ease of calculating angle γ. As previously described, the walls of the groove may be concave to allow for deformation of the conveyor and the pitch between grooves on alternate sheaves. The position of the entry and departure points depends on the conveyor velocity, mechanical properties of the conveyor and geometry of the groove. 
     The angle between the line denoted as “r 1 ” and the line between the sheave center points is referred to as “β 1 ”. The angle between “r 2 ” and the midline  140  on the second sheave is identified as “β 2 ”. Assuming that the conveyor entry and departure points are tangent to the circular centerline of contact, then fundamental principles of analytic geometry require that the angles “β 2 ” and “β 1 ” are equal. By the same geometric principles that triangles with similar angles must have proportional sides, then: 
                       r   1       r   2       =         h   1       h   2       =         r   1     +     fw   1           r   2     +       w   1     ⁡     (     1   -   f     )                     eq   .           ⁢     (   1                 
where “h 1 ” represents the distance from the center point of the first sheave  110  and the point where the conveyor crosses the line between the center points and “h2” that relative to the center point of the second sheave. The variable “w 1 ” represents the distance between the grooves of sheave  110  and sheave  112 . The distance between the sheave grooves is measured at the centerline of contact with the conveyor, as depicted in  FIG. 10 .
 
     The value of “f” is related to “w 1 ” such that the product, “f×w 1 ”, is that fraction of the gap from the center of contact on the first sheave  110  to the crossing point of the conveyor. Solving Eqn. 1 for “f” yields: 
                   f   =       r   1         r   1     +     r   2                 eq   .           ⁢     (   2                 
so,
 
                       h   1     =       r   1     ⁡     (     1   +       w   1         r   1     +     r   2           )         ⁢     
     ⁢   and           eq   .           ⁢     (   3                   h   2     =       r   2     ⁡     (     1   +       w   1         r   1     +     r   2           )               eq   .           ⁢     (   4                 
By those definitions, them
 
     
       
         
           
             
               
                 
                   
                     β 
                     1 
                   
                   = 
                   
                     
                       
                         cos 
                         
                           - 
                           1 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           
                             r 
                             1 
                           
                           
                             h 
                             1 
                           
                         
                         ) 
                       
                     
                     = 
                     
                       
                         cos 
                         
                           - 
                           1 
                         
                       
                       ⁡ 
                       
                         ( 
                         
                           1 
                           + 
                           
                             
                               
                                 r 
                                 1 
                               
                               + 
                               
                                 r 
                                 2 
                               
                             
                             
                               
                                 r 
                                 1 
                               
                               + 
                               
                                 r 
                                 2 
                               
                               + 
                               
                                 w 
                                 1 
                               
                             
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     5 
                   
                 
               
             
           
         
       
     
     So for the first groove on the first sheave  110 , the conveyor  302  enters the first sheave  110  at 90 degrees yielding a total conveyor contact angle of: 
                     θ   1     =       (       3   2     -   δ   -     β   1       )     ⁢   π             eq   .           ⁢     (   6                 
Notice that the total contact angle is a function of the radius of the groove on the second sheave  112 , because “β 1 ” depends on the value of “r 2 ”. By similar logic, the total contact angle for the second groove, where the conveyor is more fully in contact with the sheave than the first groove, is:
 
θ 2 =(2−β 1 −β 2 )π  eq. (7
 
     The same relationships applies to all of the other grooves, except for the first and last grooves where the conveyor enters or departs from the sheaves, so
 
θ i =(2−β i−1 −β i )π  eq. (8
 
     The relationship for the last groove is similar to that of the first groove: 
                     θ   n     =       (       1   2     -   δ   -     β     n   -   1         )     ⁢   π             eq   .           ⁢     (   9                 
Where “n” is even and the number of the last groove in the train. The total contact angle still depends on the radii of both the last and preceding sheave grooves.
 
The combined total contact angle of all the grooves is:
 
                     θ   total     =       (     n   -   1   -     2   ⁢     (     δ   +       ∑     i   =   1       i   =     n   -   1         ⁢     β   i         )         )     ⁢   π             eq   .           ⁢     (   10                 
So, clearly, the solution for each of the groove total contact angles is iterative, since it depends on the radius of both the groove in question and the following groove. The iterative solution converges to a suitable tolerance in two to five iterations.
 
     If the conveyor were inelastic, the design of the conveyor drive mechanism would simply depend on the coefficient of friction between the conveyor and the sheave groove walls and the combined total contact angle. In fact, the conveyor is quite elastic and for this analysis assumed to exhibit proportional Hookean behavior. That is, the stretch of the bulk conveyor is proportional to the load placed on it. Elastic materials also exhibit a change of shape when loaded. Thus, elastic materials have a functional relationship between the change in length as loading occurs and change in diameter, in this case. The relationship is the Poisson&#39;s Ratio. The groove train radii and cross-sections must be corrected for these phenomena. 
     The change in size of the conveyor depends on these mechanical properties and the change in tension as the conveyor passes through each groove in the train. In order to determine tractive effort exerted by one groove, assuming the parabolic profile shown in  FIG. 10 , it is necessary to first determine the slope of the side of the grooves where the conveyor contacts the groove wall. The equation describing the parabolic profile is:
 
 x   2 =4 p ( y−k )  eq. (11
 
Differentiating this equation with respect to “x” gives the slope of the side:
 
                       ⅆ   y       ⅆ   x       =       2   ⁢   x       4   ⁢   p               eq   .           ⁢     (   12                 
Thus the angle of the side is:
 
                   γ   =       π   2     -       tan     -   1       ⁡     (       ⅆ   y       ⅆ   x       )                 eq   .           ⁢     (   13                 
It appears that the angle is dependent on the distance between the sides of the groove (2×). That distance is dependent on the loaded tension, hence diameter, of the conveyor.
 
     If in the unloaded condition, the conveyor has a characteristic length “L 0 ” and diameter “d r0 ”, then when fully loaded for entry into the first groove on the first sheave  110 , its length will be: 
                     L   1     =         L   0     +     Δ   ⁢           ⁢   L       =       L   0     ⁡     (     1   +     E   ⁢           ⁢       T   1       A   1           )                 eq   .           ⁢     (   14                 
where “T 1 ” is the maximum tension load (force) on the conveyor,
 
“ΔL” represents the change in length
 
“E” is the elasticity of the material and
 
“A 1 ” is the cross-sectional area of the loaded conveyor.
 
The loaded diameter is:
 
 d   r1   =d   r0 (1 −Δd   r )= d   r0 (1 −μΔL )  eq. (15
 
where “μ” is Poisson&#39;s Ratio for the bulk conveyor.
 
The loaded area is then:
 
                     A   1     =       π   ⁢           ⁢     d     r   ⁢           ⁢   1     2       4             eq   .           ⁢     (   16                 
This computation is also iterative, since the amount of stretch depends on the degree of shrinkage of cross-sectional area. The computation begins by assuming the cross-sectional area of the unloaded conveyor, then correcting the computations as the corrected area in Eqn. 16 is recalculated. The iteration between Eqns. 14-16 is finished when sufficient accuracy is achieved, typically in two to five iterations depending on the elasticity and deformability of the materials.
 
     Based on the diameter determined in Eqn. 15, the aperture of the parabola at the contact centerline is now known. From that dimension, given the desired depth of the groove, typically, but not necessarily, two conveyor diameters, the value of “p” in Eqn. 11 can be determined. Taking the contact centerline to have a relative value of “y” equal to zero, then the value of “p” is: 
                   p   =       d     r   ⁢           ⁢   1       40             eq   .           ⁢     (   17                 
and since “x” in Eqn. 12 is also equal to “d r1 ”, then the slope is not a function of the conveyor properties or diameter. Thus, the angle of the slope is only a function of the chosen depth of the groove.
 
     Since the radius of the first groove would be specified and the width and geometry of the groove are now known, it is possible to determine the amount of tension exerted in the traverse of the groove by the conveyor. The theoretical solution is shown below: 
                     T   2     =       T   1     ⁢     exp   ⁡     (       -     σθ   1         sin   ⁢           ⁢   δ       )                 eq   .           ⁢     (   18                 
Recall that “θ 1 ” depends on the size of the groove in the second sheave  112 . The conveyor is now shorter and fatter, because of the reduced tension on it as it leaves the first groove. To minimize wear, it is necessary to require that the conveyor not slip in any of the grooves. Therefore, since it is difficult to change their rotational speed, it is best to select a radius that accommodates the reduced length and increased diameter. The second groove will thus have a slightly smaller radius than the first to compensate for the increased diameter and resulting upward movement of the center of contact of the conveyor. The characteristic length under the new loading conditions is:
 
                     L   2     =       L   0     ⁡     (     1   +     E   ⁢       T   2       A   2           )               eq   .           ⁢     (   19                 
where the area and diameter are iterated just as with Eqns. 14-16. So the radius of the second groove (first groove on the second sheave  112 ) will be:
 
     
       
         
           
             
               
                 
                   
                     r 
                     2 
                   
                   = 
                   
                     
                       r 
                       1 
                     
                     ⁢ 
                     
                       
                         L 
                         2 
                       
                       
                         L 
                         1 
                       
                     
                   
                 
               
               
                 
                   eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     20 
                   
                 
               
             
           
         
       
     
     The estimate of “r 2 ” based on the conveyor properties now permits a recalculation of “β 1 ” and “θ 1 ”. This external iteration then proceeds until a suitable tolerance for “r 2 ” has been achieved, typically two to five iterations. Notice, also, that the gap, “w 1 ”, is also a function of the values of “r 1 ” and “r 2 ”. The original value was based on the assumption that the radii were equal, however, now:
 
 w   i   =D −( r   i   +r   i+1 )  eq. (21
 
for the i th  gap, where D is the distance between the sheave center points.
 
     The identical calculation is performed for each subsequent groove/sheave pair, including the last one. The only fundamental difference is the use of the appropriate total contacted angle relationship for each groove (Eqns. 6-10). As previously noted, the computations are iterative, but quickly converge. 
     A critical test exists for the sizing of the sheaves  110  and  112 . The radius of the sheaves must be large enough that the radial force pulling the conveyor into the groove is substantially larger than the centrifugal force attempting to fling the conveyor out of the groove. For the sake of computation, assume a unit length “μ” of the conveyor, perhaps one inch or one centimeter. The angle subtended by the length “μ” is: 
     
       
         
           
             
               
                 
                   
                     η 
                     i 
                   
                   = 
                   
                     u 
                     
                       r 
                       i 
                     
                   
                 
               
               
                 
                   eq 
                   . 
                   
                       
                   
                   ⁢ 
                   
                     ( 
                     22 
                   
                 
               
             
           
         
       
     
     The radial force pulling the conveyor into the groove over that angle “η” is:
 
 T   ri   =T   i  sin η i   eq. (23
 
The centrifugal force is:
 
                     T   C     =       Wv   2       gr   1               eq   .           ⁢     (   24                 
where W is the conveyor weight per unit length “μ”
 
g is the gravitational constant, 32.2 ft/sec2
 
v is the velocity of the conveyor and
 
r i  is the radius of the i th  groove
 
     As a design criterion of sheave systems, a factor of safety of 10 between the radial force and the centrifugal force is common, yielding:
 
 T   ri ≧10 T   C   eq. (25
 
thus defining either a maximum conveyor velocity or a minimum groove and sheave diameter. The maximum velocity imposes a maximum flowrate for a given conveyor/tubing size combination.
 
     While the preferred embodiments shown use a vertical orientation, it is understood and contemplated that the invention may be utilized in a horizontal orientation without departing from the spirit of the invention. 
     It will be appreciated by those skilled in the art that changes could be made to the embodiments described above without departing from the broad inventive concept thereof. It is understood, therefore, that this invention is not limited to the particular embodiments disclosed, but it is intended to cover modifications within the spirit and scope of the present invention as defined by the appended claims.

Summary:
The invention disclosed provides a drive head assembly for a fluid conveyor system that propels a fluid entraining conveyor through a well bore to carry fluids to the surface. The invention is comprised of a pair of synchronized follower wheels connected to a set of counter rotating sheaves. A fluid entraining conveyor is wrapped in a “figure-8” conveyor path around the sheaves in a plurality of coaxial grooves and around a distal sheave located in the fluid in the well bore. The coaxial grooves incorporate a unique shape which in conjunction with the wrap pattern provide improved tractive qualities and thus reduce tension in the conveyor and increase the durability of the conveyor. The conveyor can run at increased speeds and with no tension on the downward portion of the conveyor resulting in higher efficiency and less down time due to breakage.