Abstract:
A system for determining the position of a piston in a subsea accumulator, comprising: a sensor module comprising: a housing; an ultrasonic transducer facing the piston and configured to transmit an ultrasonic pulse through a fluid medium toward a surface of the piston; a pressure sensor configured to; and a temperature sensor; a control connector coupled to the sensor module capable of providing hardware and software functions to measure transit time of the ultrasonic signal from the ultrasonic transducer to the surface of the piston, comprising electronics for controlling the ultrasonic transducer, pressure sensor and temperature sensor; wherein the transit times of the ultrasonic signals across the fluid medium are measured and combined with a computed velocity of sound as a function of temperature/pressure to determine the distance between the ultrasonic transducer and the surface of the piston.

Description:
This application is a continuation-in-part of U.S. application Ser. No. 13/457,871, filed Apr. 27, 2012. 
    
    
     BACKGROUND 
     This section is intended to introduce the reader to various aspects of art that may be related to various aspects of the presently described embodiments. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present embodiments. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art. 
     In most offshore drilling operations, a wellhead at the sea floor is positioned at the upper end of the subterranean wellbore lined with casing, a blowout preventer (“BOP”) stack is mounted to the wellhead and a lower marine riser package (“LMRP”) is mounted to the BOP stack. The upper end of the LMRP typically includes a flex joint coupled to the lower end of a drilling riser that extends upward to a drilling vessel at the sea surface. A drill string is hung from the drilling vessel through the drilling riser, the LMRP, the BOP stack and the wellhead into the wellbore. 
     During drilling operations, drilling fluid, or mud, is pumped from the sea surface down the drill string, and returns up the annulus around the drill string. In the event of a rapid invasion of formation fluid into the annulus, commonly known as a “kick,” the BOP stack and/or LMRP may actuate to help seal the annulus and control the fluid pressure in the wellbore. In particular, the BOP stack and the LMRP include closure members, or cavities, designed to help seal the wellbore and prevent the release of high-pressure formation fluids from the wellbore. Thus, the BOP stack and LMRP function as pressure control devices. 
     For most subsea drilling operations, hydraulic fluid for operating the BOP stack and the LMRP is provided using a common control system physically located on the surface drilling vessel. However, the common control system may become inoperable, resulting in a loss of the ability to operate the BOP stack. As a backup, or even possibly a primary means of operation, hydraulic fluid accumulators are filled with hydraulic fluid under pressure. The amount and size of the accumulators depends on the anticipated operation specifications for the well equipment. 
     An example of an accumulator includes a piston accumulator, which includes a hydraulic fluid section and a gas section separated by a piston movable within the accumulator. The hydraulic fluid is placed into the fluid section of the accumulator and pressurized by injecting gas (typically inert gas, e.g., nitrogen) into the gas section. The fluid section is connected to a hydraulic circuit so that the hydraulic fluid may be used to operate the well equipment. As the fluid is discharged, the piston moves within the accumulator under pressure from the gas to maintain pressure on the remaining hydraulic fluid until full discharge. 
     The ability or capacity of the accumulator to operate a piece of equipment depends on the amount of hydraulic fluid in the accumulator and the pressure of the gas. Thus, there is a need to know the volume of the hydraulic fluid remaining in an accumulator so that the capacity of the accumulator to operate well equipment may be determined and control of the well equipment may be managed. Measuring the volume of hydraulic fluid in the accumulator over time can also help identify if there is a leak in the accumulator or hydraulic circuit or on the gas side of the piston. 
     Currently, the capacity of an accumulator to power equipment is determined by measuring the pressure in the hydraulic circuit downstream of the accumulator. However, pressure is not an indicator of the overall capacity of an accumulator to operate equipment because the volume of hydraulic fluid remaining in the accumulator is not known. Also, accumulators are typically arranged in banks of multiple accumulators all connected to a common hydraulic circuit, therefore, the downstream pressure measurement is only an indication of the overall pressure in the bank, not per individual accumulator. 
     A possible way of determining the volume of hydraulic fluid remaining in the accumulator is to use a linear position sensor such as a cable-extension transducer or linear potentiometer that attaches inside the accumulator to measure the movement of the internal piston. However, these electrical components may fail and because the discharge of hydraulic fluid may be abrupt, the sensors may not be able to sample fast enough to obtain an accurate measurement. 
     Another method of determining the volume of hydraulic fluid is through the use of physical position indicators that extend from the accumulator. These indicators only offer visual feedback though and are insufficient for remote monitoring and pose a significant challenge to maintaining the integrity of the necessary mechanical seals under full operating pressures. 
     Through-the-wall sensors (e.g., Hall effect sensors) have also been considered. However, the thickness and specifications of an accumulator wall is such that these types of sensors are not always able to penetrate the material. 
     SUMMARY 
     Certain aspects of some embodiments disclosed herein are set forth below. It should be understood that these aspects are presented merely to provide the reader with a brief summary of certain forms the invention might take and that these aspects are not intended to limit the scope of the invention. Indeed, the invention may encompass a variety of aspects that may not be set forth below. 
     In accordance with the invention, a system for determining the location of a movable element within a container is provided in which an ultrasonic position sensing system is used to monitor the position of the movable element. In one embodiment, the position sensing system includes an ultrasonic sensor and control connector that measures and computes the position of the movable element relative to the position of the sensor. To determine the movable element position, an ultrasonic transducer in the accumulator directs an ultrasonic pulse toward a surface of the movable element. When the pulse is reflected off the surface, a corresponding echo is received by sensor module, and converted back into an electronic signal by the control connector. The control connector determines several parameters to compute the position of the movable element, including the velocity of the pulse as a function of temperature and pressure and a fluid transit time of the ultrasonic pulse. Thus, once travel time and velocity are known, the system is able to determine the distance traveled by the ultrasonic pulse, which corresponds to the position of the movable element within the accumulator and, accordingly, the level of hydraulic fluid remaining in the accumulator. 
     This summary is provided to introduce a selection of concepts that are further described below in the detailed description. This summary is not intended to identify key or essential features of the claimed subject matter, nor is it intended to be used as an aid in limiting the scope of the claimed subject matter. 
    
    
     
       DRAWINGS 
       For a detailed description of the preferred embodiments of the invention, reference will now be made to the accompanying drawings in which: 
         FIG. 1  shows a schematic view of an offshore system for drilling and/or producing a subterranean wellbore; 
         FIG. 2  shows a perspective view of a subsea BOP stack assembly and measurement system; 
         FIG. 3  shows a cross section view of an embodiment of a system for measuring the position of a movable element in a container; 
         FIG. 4  shows a detail view of a measurement system for measuring the position of a movable element in a container; 
         FIG. 5  shows an exploded view of an embodiment of a transducer; 
         FIG. 6  shows another exploded view of an embodiment of a transducer; and 
         FIG. 7  shows a cross section view of an embodiment of a system for measuring the position of a movable element in a container including ultrasonic transducers on the fluid and gas sides of the accumulator. 
     
    
    
     DETAILED DESCRIPTION 
     The following discussion is directed to various embodiments of the invention. The drawing figures are not necessarily to scale. Certain features of the embodiments may be shown exaggerated in scale or in somewhat schematic form and some details of conventional elements may not be shown in the interest of clarity and conciseness. Although one or more of these embodiments may be preferred, the embodiments disclosed should not be interpreted, or otherwise used, as limiting the scope of the disclosure, including the claims. It is to be fully recognized that the different teachings of the embodiments discussed below may be employed separately or in any suitable combination to produce the desired results. In addition, one skilled in the art will understand that the following description has broad application, and the discussion of any embodiment is meant only to be exemplary of that embodiment, and not intended to intimate that the scope of the disclosure, including the claims, is limited to that embodiment. 
     Certain terms are used throughout the following description and claims to refer to particular features or components. As one skilled in the art will appreciate, different persons may refer to the same feature or component by different names. This document does not intend to distinguish between components or features that differ in name but not function. The drawing figures are not necessarily to scale. Certain features and components herein may be shown exaggerated in scale or in somewhat schematic form and some details of conventional elements may not be shown in interest of clarity and conciseness. 
     In the following discussion and in the claims, the terms “including” and “comprising” are used in an open-ended fashion, and thus should be interpreted to mean “including, but not limited to . . . .” Also, the term “couple” or “couples” is intended to mean either an indirect or direct connection. Thus, if a first device couples to a second device, that connection may be through a direct connection, or through an indirect connection via other devices, components, and connections. In addition, as used herein, the terms “axial” and “axially” generally mean along or parallel to a central axis (e.g., central axis of a body or a port), while the terms “radial” and “radially” generally mean perpendicular to the central axis. For instance, an axial distance refers to a distance measured along or parallel to the central axis, and a radial distance means a distance measured perpendicular to the central axis. 
     Referring now to  FIG. 1 , an embodiment of an offshore system  10  for drilling and/or producing a wellbore  11  is shown. In this embodiment, the system  10  includes an offshore vessel or platform  20  at the sea surface  12  and a subsea BOP stack assembly  100  mounted to a wellhead  30  at the sea floor  13 . The platform  20  is equipped with a derrick  21  that supports a hoist (not shown). A tubular drilling riser  14  extends from the platform  20  to the BOP stack assembly  100 . The riser  14  returns drilling fluid or mud to the platform  20  during drilling operations. One or more hydraulic conduits  15  extend along the outside of the riser  14  from the platform  20  to the BOP stack assembly  100 . The one or more hydraulic conduits  15  supply pressurized hydraulic fluid to the assembly  100 . Casing  31  extends from the wellhead  30  into the subterranean wellbore  11 . 
     Downhole operations are carried out by a tubular string  16  (e.g., drill string, tubing string, coiled tubing, etc.) that is supported by the derrick  21  and extends from the platform  20  through the riser  14 , through the BOP stack assembly  100  and into the wellbore  11 . A downhole tool  17  is connected to the lower end of the tubular string  16 . In general, the downhole tool  17  may comprise any suitable downhole tools for drilling, completing, evaluating and/or producing the wellbore  11  including, without limitation, drill bits, packers, cementing tools, casing or tubing running tools, testing equipment, perforating guns, and the like. During downhole operations, the string  16 , and hence the tool  17  coupled thereto, may move axially, radially and/or rotationally relative to the riser  14  and the BOP stack assembly  100 . 
     Referring now to  FIGS. 1-2 , the BOP stack assembly  100  is mounted to the wellhead  30  and is designed and configured to control and seal the wellbore  11 , thereby containing the hydrocarbon fluids (i.e., liquids and gases) therein. In this embodiment, the BOP stack assembly  100  comprises a lower marine riser package (LMRP)  110  and a BOP or BOP stack  120 . 
     The BOP stack  120  is releasably secured to the wellhead  30  as well as the LMRP  110  and the LMRP  110  is releasably secured to the BOP stack  403  and the riser  14 . In this embodiment, the connections between the wellhead  30 , the BOP stack  120  and the LMRP  110  include hydraulically actuated, mechanical wellhead-type connections  50 . In general, the connections  50  may comprise any suitable releasable wellhead-type mechanical connection such as the DWHC or HC profile subsea wellhead system available from Cameron® International Corporation of Houston, Tex., or any other such wellhead profile available from several subsea wellhead manufacturers. Typically, such hydraulically actuated, mechanical wellhead-type connections (e.g., the connections  50 ) include an upward-facing male connector or “hub” that is received by and releasably engages a downward-facing mating female connector or receptacle  50   b . In this embodiment, the connection between LMRP  110  and the riser  14  is a flange connection that is not remotely controlled, whereas the connections  50  may be remotely, hydraulically controlled. 
     Referring still to  FIGS. 1-2 , the LMRP  110  includes a riser flex joint  111 , a riser adapter  112 , an annular BOP  113  and a pair of redundant control units or pods  114 . A flow bore  115  extends through the LMRP  110  from the riser  14  at the upper end of the LMRP  110  to the connection  50  at the lower end of the LMRP  110 . The riser adapter  112  extends upward from the flex joint  111  and is coupled to the lower end of the riser  14 . The flex joint  111  allows the riser adapter  112  and the riser  14  connected thereto to deflect angularly relative to the LMRP  110  while wellbore fluids flow from the wellbore  11  through the BOP stack assembly  100  into the riser  14 . The annular BOP  113  comprises an annular elastomeric sealing element that is mechanically squeezed radially inward to seal on a tubular extending through the LMRP  110  (e.g., the string  16 , casing, drillpipe, drill collar, etc.) or seal off the flow bore  115 . Thus, the annular BOP  113  has the ability to seal on a variety of pipe sizes and/or profiles, as well as perform a complete shut-off (“CSO”) to seal the flow bore  115  when no tubular is extending therethrough. 
     In this embodiment, the BOP stack  120  comprises an annular BOP  113  as previously described, choke/kill valves  131  and choke/kill lines  132 . The choke/kill line connections  130  connect the female choke/kill connectors of the LMRP  110  with the male choke/kill adapters of the BOP stack  120 , thereby placing the choke/kill connectors of the LMRP  110  in fluid communication with the choke lines  132  of the BOP stack  120 . A main bore  125  extends through the BOP stack  120 . In addition, the BOP stack  120  includes a plurality of axially stacked ram BOPs  121 . Each ram BOP  121  includes a pair of opposed rams and a pair of actuators  126  that actuate and drive the matching rams. In the illustrated embodiment, the BOP stack  120  includes four ram BOPs  121 —an upper ram BOP  121  including opposed blind shear rams or blades  121   a  for severing the tubular string  16  and sealing off the wellbore  11  from the riser  14 , and the three lower ram BOPs  121  including the opposed pipe rams  121   c  for engaging the string  16  and sealing the annulus around the tubular string  16 . In other embodiments, the BOP stack  120  may include a different number of rams, different types of rams, one or more annular BOPs or combinations thereof. As will be described in more detail below, the control pods  114  operate the valves  131 , the ram BOPs  121  and the annular BOPs  113  of the LMRP  110  and the BOP stack  120 . 
     The opposed rams  121   a, c  are located in cavities that intersect the main bore  125  and support the rams  121   a, c  as they move into and out of the main bore  125 . Each set of rams  121   a, c  is actuated and transitioned between an open position and a closed position by matching actuators  126 . In particular, each actuator  126  hydraulically moves a piston within a cylinder to move a connecting rod coupled to one ram  121   a, c . In the open positions, the rams  121   a, c  are radially withdrawn from the main bore  125 . However, in the closed positions, the rams  121   a, c  are radially advanced into the main bore  125  to close off and seal the main bore  125  and/or the annulus around the tubular string  16 . The main bore  125  is substantially coaxially aligned with the flow bore  115  of the LMRP  110 , and is in fluid communication with the flow bore  115  when the rams  121   a, c  are open. 
     As shown in  FIG. 2 , the BOP stack  120  also includes a set or bank  127  of hydraulic accumulators  127   a  mounted on the BOP stack  120 . While the primary hydraulic pressure supply is provided by the hydraulic conduits  15  extending along the riser  14 , the accumulator bank  127  may be used to support operation of the rams  121   a, c  (i.e., supply hydraulic pressure to the actuators  126  that drive the rams  121   a, c  of the stack  120 ), the choke/kill valves  131 , the connector  50   b  of the BOP stack  120  and the choke/kill connectors  130  of the BOP stack  120 . As will be explained in more detail below, the accumulator bank  127  may serve as a backup means to provide hydraulic power to operate the rams  121   a, c , the valves  131 , the connector  50   b , and the connectors  130  of the BOP stack  120 . 
     Although the control pods  114  may be used to operate the BOPs  121  and the choke/kill valves  131  of the BOP stack  120  in this embodiment, in other embodiments, the BOPs  121  and the choke/kill valves  131  may also be operated by one or more subsea remotely operated vehicles (“ROVs”). 
     As previously described, in this embodiment, the BOP stack  120  includes one annular BOP  113  and four sets of rams (one set of shear rams  121   a , and three sets of pipe rams  121   b, c ). However, in other embodiments, the BOP stack  120  may include different numbers of rams, different types of rams, different numbers of annular BOPs (e.g., annular BOP  113 ) or combinations thereof. Further, although the LMRP  110  is shown and described as including one annular BOP  113 , in other embodiments, the LMRP (e.g., LMRP  110 ) may include a different number of annular BOPs (e.g., two sets of annular BOPs  113 ). Further, although the BOP stack  120  may be referred to as a “stack” because it contains a plurality of ram BOPs  121  in this embodiment, in other embodiments, BOP  120  may include only one ram BOP  121 . 
     Referring now to  FIG. 3 , a more detailed cross-sectional view is provided that illustrates a hydraulic accumulator with a measurement system. The hydraulic accumulator  127   a  includes an element  401  movable within the internal volume, or cavity,  402 . The hydraulic accumulator  127   a  body is composed of an outer layer and an inner layer. The outer layer  409  of the accumulator  127   a  may include a metal, metal alloy and/or composite material (e.g., carbon fiber reinforced plastic). Composite materials are lighter than steel counterparts and possess high strength and stiffness, providing high performance in deep water, high pressure applications. The inner layer  410  of the accumulators  127   a  may include a metal and/or metal alloy. 
     In the embodiment in  FIG. 3 , the movable element  401  is a piston separating a hydraulic fluid  403  from a gas  404  stored in the internal volumes of the accumulators  127   a . It should be appreciated by those of ordinary skill in the art that the movable element could be any device movable in an internal volume of a container that is capable of separating fluids. The piston  401  may include a metal, metal alloy, plastic, or rubber. 
     In the embodiment in  FIG. 3 , the accumulator includes a measurement system which includes a sensor module  411  and a control connector  416  recessed in a housing  417 . The sensor module  411  and control connector  416  are installed in the fluid end of the accumulator  127   a  and configured to control the ultrasonic transducer  412  to emit ultrasonic pulses toward the piston  401 . In the illustrated embodiment, the fluid end of the accumulator  127   a  includes a recess configured to receive the sensor module  411  and control connector  416 . The sensor module  411  includes an ultrasonic transducer  412 , a temperature sensing device  414  a pressure sensing device  413  and a transducer window  415 . In certain embodiments, the temperature sensing device  414  may be a 4-wire resistance temperature detector. In certain embodiments, the transducer  412  may be of a model of an ultrasound transducer module manufactured by Cameron International Corporation. 
     In the illustrated embodiment, the temperature sensing device  414  and the pressure sensing device  413  are integrated within the ultrasonic transducer housing  417 , with the pressure sensing device being in contact with the hydraulic fluid in order to measure the pressure of the fluid in the cavity  402 . In alternative embodiments, the temperature sensing device  414  and the pressure sensing device  413  can be embedded on the ultrasonic transducer  412  or located outside of the sensor housing  417 . 
     In the present embodiment, an opening  418  is also provided and may extend through the head of the accumulator  127   a  to allow for the passage of wiring between the sensor module  411  and control connector  416 . 
     The sensor module  411  and control connector  416  may be secured within the recess  419  using any suitable mechanism. For instance, in one embodiment, both the recess  409  and the housing  417  may be threaded and generally cylindrical in shape. Accordingly, the sensor module  411  and control connector  416  may be installed in the recess  417  by simply rotating the housing  417  into the recess  419 , thus allowing the respective threads to engage one another. In other embodiments, the sensor module  411  and control connector  416  may be secured in the recess  419  using an adhesive, connectors, or any other suitable technique. Overall, this provides for straightforward installation of the sensor module  411  and control connector  416  without requiring significant and/or complex redesign of existing subsea equipment. 
     To monitor the linear position of the piston  401  during operation, the ultrasonic position sensor module  411  may intermittently transmit an ultrasonic pulse  420 . The pulse  420  may originate from the ultrasonic transducer  412  located in the sensor module  411 , and propagate through the window  415  and into the cavity  402 , which may be filled with pressurized hydraulic fluid  403 . The window  415  may include a high compressive strength plastic material having acoustic impedance properties that are similar to liquid. This allows for the transmitted pulse  420  to leave the sensor housing  417  while experiencing relatively little acoustic impedance. By way of example only, the window  415  may formed using a polyetherimide material, such as Vespel™, available from E.I. du Pont de Nemours and Company of Wilmington, Del., such as ULTEM™, available from SABIC of Saudi Arabia, organic polymer thermoplastic materials, such as polyether ether ketone (PEEK), or a polyimide-based plastic. The housing  417  may be manufactured using a metal material, such as steel or titanium, or may be formed using one of the aforementioned plastic materials, or using a combination of metal and plastic materials. In one embodiment, the housing  417  may be made of Inconel superalloy, such as Inconel 625. 
     After propagating through the window  415 , the pulse  420  then travels the distance  422  between the head of the accumulator  127   a  and the piston  401  through the hydraulic fluid  403 . Upon impacting the piston  401 , the pulse  420  is reflected in the form of a corresponding echo  421 . The transducer  412  receives the echo  421  as it propagates back toward the sensor module  411  through the hydraulic fluid  403  and the window  415 . 
     The transducer  412  may operate at any suitable frequency, such as between approximately 200 kilohertz and 5.0 megahertz. In one embodiment, the transducer  412  is configured to operate at a frequency of approximately 3.5 megahertz. Further, though not expressly shown in  FIG. 3 , the sensor module  411  and control connector  416  may include wiring that may be routed through the opening  418 . This wiring may represent the wiring that provides for communication between the sensor module  411  and control connector  416 . 
     While the recess  419  is shown in  FIG. 3  as having a width (e.g., a diameter in the case of a circular recess) that is greater than that of the opening  418 , in one embodiment, the recess  419  may be an opening that extends all the way through the end cap  423 . That is, the opening  418  and the recess  419  may have the same width. In such an embodiment, the sensor housing  417  may be configured to extend through the end cap  423 . Also, in such an embodiment, wiring from the sensor module  411  and control connector  416 , including the ultrasonic transducer  412 , pressure sensing device  417  and/or the temperature sensing device  414  may form a connector coupled to the housing  417 , wherein the connector is configured to electronically connect wiring within the sensor module  411  and the control connector  416 . For instance, such a connector may be accessible from outside the accumulator and may be coupled to control connector  416  using one or more suitable cables. This embodiment also allows for the sensor and control connectors to be installed from the outside of the accumulator, which obviates the need for any disassembly of the end cap  423  from the body of the accumulator during installation. For instance, where the recess  419  extends all the way through the end cap  423  and includes threads that engage corresponding threads on the sensor module  411  and control connector  416 , the sensor module  411  and control connector  416  may be installed from the outside by rotating the sensor module  411  and control connector  416  into the recess  419  from the outside of the end cap  423  until the threads securely engage one another. 
     The control connector  416  may obtain or otherwise determine several parameters which are used to compute the path length along which the ultrasonic pulse  420  traveled prior to being reflected. This path length may correspond to the distance  422 , which may enable an operator to determine the linear position of a particular device, such as the piston  401 . The parameters obtained and/or determined by the control connector  416  include a computed velocity of sound (VOS) through a fluid as a function of temperature and pressure, a delay time, and a signal path transit time. For example, the temperature parameter (e.g., the temperature within the cavity  402 ) may be measured using the temperature sensing device  414 . The pressure parameter (e.g., the pressure within the cavity  402 ) may be provided to the control connector  416  as an expected pressure value or, in other embodiments, may be measured pressure information provided to the control connector  416  by one or more pressure sensing devices. The VOS in the fluid can be determined by the control connector  416  based on the temperature and pressure measurements made in the sensor module  411 . The VOS of the fluid medium in the accumulator can be calculated according to the following formula:
 
VOS( P,T )=Water % ×Water VOS ( P,T )+MEG % ×MEG VOS ( P,T )
 
wherein VOS (P,T) represents velocity of sound in the fluid medium located in the accumulator  127   a  as a function of pressure and temperature. Water %  represents the percentage of water in the fluid medium. Water VOS (P,T) represents velocity of sound in water, which is a known quantity at known pressures and temperatures. MEG %  represents percentage of monoethylene glycol in the fluid medium. MEG VOS (P,T) represents the velocity of sound in monoethylene glycol, which is a known quantity at known pressures and temperatures. The example formula above considered a fluid medium comprising water and monoethylene glycol. Other fluid combinations commonly known in the art for use in an accumulator are also disclosed.
 
     The delay time may represent non-fluid delays present in the signal path which, as discussed above, includes the entire path (both electrical and acoustic portions) between the control connector  416  and the monitored device. For instance, the presence of the window  415  and the wiring may introduce non-fluid delays. By subtracting out the delay time from the total transit time and dividing the result by two, the fluid transit time of the pulse  420  (or of its corresponding echo  421 ) may be determined. Once the velocity of the ultrasonic pulse  420  or echo  421  through the hydraulic fluid  403  and the fluid transit time are known, the path length between the head of the accumulator  127   a  and the piston  401  may be calculated by the control connector  416  according to the following formula, thus providing the linear position of the piston  401 : 
             D   =       [       VOS   ⁡     (     P   ,   T     )       ×   t     ]     2           
wherein D represents the distance from the head of the accumulator  127   a  and the piston  401 . VOS (P,T) represents velocity of sound in the fluid medium located in the accumulator  127   a  as a function of pressure and temperature. t represents transmit time of the pulse through the fluid medium.
 
     By knowing the linear position of the piston  401 , the system can determine how much hydraulic fluid remains in the accumulator. In some embodiments, the fluid  403  need not necessarily be a liquid. For instance, the fluid  403  may include a gas or a gas mixture, such as air. 
     In the present example, the ultrasonic position sensor module  411  and control connector  416  are used to monitor the linear position of a piston in an accumulator of a subsea resource extraction system. Accordingly, the sensor module  411  and control connector  416  may be designed to be durable enough to withstand harsh environmental conditions often associated with subsea operation. In one embodiment, the housing  417 , in which the sensor module  411  and control connector  416  are disposed, may be manufactured using titanium, stainless steel, or any other suitable type of metal, alloy, or super-alloy, and may be capable of operating at pressures of between approximately 14 pounds per square inch (PSI) to 14,000 PSI. For example, the window  415  of the sensor housing  417  may withstand loads of up to 14,000 PSI. The sensor module  411  and control connector  416  may also be capable of withstanding operating temperatures of between 0 to 100 degrees Celsius. 
     As shown in  FIG. 4 , the sensor module  411  and control connector  416  may be recessed within the recess  419  by a distance shown by reference number  501 . This distance  501  may be selected based at least partially upon certain properties of the window  415 , such as thickness and sound velocity characteristics, to compensate for signal reverberation within the medium of the window  415 . This reverberation is due to resonating properties of the window  415 . For example, when the ultrasonic pulse  420  is transmitted from the sensor module  411 , a portion of the signal  420  may reverberate within the window  415  before dissipating. The amount of time that it takes for this reverberation to dissipate may constitute what is sometimes referred to as a signal dead band. If an echo (e.g.,  421 ) arrives at the sensor module  411  within this signal dead band, the sensor module  411  may be unable to acquire an accurate measurement due to interference from the ongoing signal reverberation within the window  415 . This is generally most problematic when the target device, here the piston  401 , is very close to the accumulator  127   a  head, such that the elapsed time for the echo  421  to return to the sensor module  411  and control connector  416  falls within the dead band. Accordingly, recessing the sensor module  411  by a distance  501  within the recess  419  may compensate for the dead band effects, thus allowing the sensor module  411  to accurately acquire measurements for generally any position of the piston  401  within the accumulator. 
     The distance  501  may be selected as a function of the thickness of the window and its resonance properties. For instance, a plastic material, such as VESPEL®, ULTEM™ or PEEK may have resonating properties in which an ultrasonic signal reverberates within the window  415  for approximately two round trips before dissipating. Thus, in this example, the goal in selecting the distance  501  is that the earliest time at which an echo  421  reflected from the piston  401  returns to the sensor is outside of the signal dead band time, with the most extreme case being when the piston  401  is in the open position. Additionally, it should be noted that the plastic materials discussed above generally have lower resonating properties when compared to that of certain other materials, particularly metals such as steel. By comparison, in a sensor where the ultrasonic pulse  420  is transmitted through a metal material, like steel, the ultrasonic signal  420  may reverberate for approximately ten or more round trips within the steel before dissipating. 
     As discussed above with reference to  FIG. 3 , the ultrasonic position sensor module  411  includes a transducer  412 . One embodiment of the transducer  412  is shown in more detail in  FIGS. 5-6 , which show assembled and exploded perspective views, respectively, of the transducer  412 . 
     The transducer  412  includes the above-described window  415 , as well as a casing  601 , piezoelectric material  602 , positive lead  603 , negative lead  604 . The transducer  412  also includes the above-described temperature sensing device  414 . As best shown in  FIG. 5 , the positive lead  603 , negative lead  604 , and temperature sensing device  414  extend outward from the rear end (e.g., the end opposite the window  415 ) of the transducer  412 . When assembled within a device, such as the head of an accumulator, such as accumulator  127   a , portions of the positive lead  603 , negative lead  604 , and temperature sensing device  414  may extend through the opening  418  ( FIG. 4 ). The casing  601  generally encloses the components of the transducer  412  and may be designed to fit within the sensor housing  417 , as shown in  FIG. 4 . In one embodiment, the casing  601  may be formed using the same high compressive strength plastic material as the window  415 , such as ULTEM™, PEEK, or VESPEL®. In other embodiments, the casing  601  may be formed using a metal material, such as steel, titanium, or alloys thereof. The piezoelectric material  602  may be formed using a crystal or ceramic material. For example, in one embodiment, the piezoelectric material  602  may include lead zirconate titanate (PZT). In another embodiment, the piezoelectric material  602  may include lead metaniobate. 
       FIG. 7  shows another illustrative embodiment of the accumulator measurement system, with another ultrasonic transducer  701  installed in the gas side  404  of the accumulator  127   a . In this embodiment, the ultrasonic transducer in the gas end is a lower frequency transducer than the ultrasonic transducer of the fluid end (e.g., 200 kilohertz). Such an embodiment provides for redundancy in the event the fluid-side ultrasonic transducer malfunctions. In addition, providing a gas-side ultrasonic transducer allows for accurate piston position determination from the gas side in the event of foaming in the liquid side, which can present noise in the liquid-side measurements reducing the accuracy of the measurements. 
     The ultrasonic position sensing system and techniques described herein may provide position information that is substantially as accurate as position information obtained using other existing solutions, such as position monitoring using LVDTs or other electromechanical position sensors. However, as discussed above, the ultrasonic position sensing system integrates much more easily with existing subsea components and does not require substantial and complex redesign of existing equipment. Further, as the ultrasonic position sensors described herein are generally not subject to common-mode failure mechanisms, as is the case with some electromechanical position sensors, the position information obtained by the ultrasonic position sensing system may better maintain its accuracy over time. 
     While the examples described above have focused on the use of an ultrasonic position sensor for monitoring the position of a ram of a blowout preventer, it should be appreciated the above-described techniques may be applicable to generally any device or component of a system that moves, such as in response to actuation. For example, in the context of the oilfield industry, other types of components having linearly actuated devices that may be monitored using the ultrasonic ranging techniques described herein include blowout preventer gate valves, wellhead connectors, a lower marine riser package connector, blowout preventer choke and kill valves and connectors, subsea tree valves, manifold valves, process separation valves, process compression valves, and pressure control valves, to name but a few. Additionally, as discussed above, components that move non-linearly may also be monitored using the position sensing techniques described above. 
     Although the present invention has been described with respect to specific details, it is not intended that such details should be regarded as limitations on the scope of the invention, except to the extent that they are included in the accompanying claims.