CROSS-REFERENCE TO RELATED APPLICATION- The present document is based on and claims priority to U.S. Provisional Application Ser. No. 61/175,266, filed May 4, 2009 incorporated herein. 
BACKGROUND- A variety of subsea control systems are employed for use in controlling subsea wells during, for example, emergency shutdowns. Depending on the environment and location of a given subsea well, various standards or protocols govern operation of the well. In some applications, gas and oil wells are required to meet specific safety integrity levels. Instrumented systems have been integrated into subsea wells to ensure against unwanted discharge of fluids into the surrounding subsea environment. 
SUMMARY- In general, the present invention provides a technique for enabling protection of subsea wells. The technique employs a subsea test tree and associated control system to ensure control over the well in a variety of situations. The subsea test tree may be formed with an upper portion releasably coupled to a lower portion. The upper portion employs at least one upper shut-off valve, and the lower portion employs at least one lower shut-off valve to protect against unwanted release of fluids from either above or below the subsea test tree. The subsea test tree also is coupled with the control system in a manner which allows control to be exercised over the at least one upper and at least one lower shut-off valves. 
BRIEF DESCRIPTION OF THE DRAWINGS- Certain embodiments of the invention will hereafter be described with reference to the accompanying drawings, wherein like reference numerals denote like elements, and: 
- FIG. 1 is an illustration of one example of a subsea installation and an associated control system, according to an embodiment of the present invention; 
- FIG. 2 is an illustration of a portion of one example of a subsea test tree that can be used at the subsea installation, according to an embodiment of the present invention; 
- FIG. 3 is a schematic illustration of a portion of the associated control system, according to an embodiment of the present invention; 
- FIG. 4 is a schematic illustration of another portion of the associated control system, according to an embodiment of the present invention; 
- FIG. 5 is a schematic illustration of another portion of the associated control system, according to an embodiment of the present invention; 
- FIG. 6 is a schematic illustration of safety relevant parameters topside and subsea, according to an embodiment of the present invention; 
- FIG. 7 is a schematic illustration of one example of the subsea control system incorporating a pressure balanced accumulator, according to an embodiment of the present invention; 
- FIG. 8 is a cross-sectional view of one example of the pressure balanced accumulator illustrated inFIG. 7, according to an embodiment of the present invention; 
- FIG. 9 is a cross-sectional view of an enlarged portion of the pressure balanced accumulator illustrated inFIG. 8, according to an embodiment of the present invention; and 
- FIG. 10 is a graph illustrating fluid volume expelled from the pressure balanced accumulator at different hydrostatic pressure levels, according to an embodiment of the present invention. 
DETAILED DESCRIPTION- In the following description, numerous details are set forth to provide an understanding of the present invention. However, it will be understood by those of ordinary skill in the art that the present invention may be practiced without these details and that numerous variations or modifications from the described embodiments may be possible. 
- The present invention generally relates to an overall subsea control system comprising a subsea test tree, such as a subsea test tree located within a riser, and an associated control. According to one embodiment, the subsea control system is a subsea wellhead control system comprising a subsea installation with an independently controlled subsea test tree. The subsea test tree comprises an upper portion separable from a lower portion and a plurality of shut-off valves. At least one shut-off valve is located in each of the upper portion and the lower portion. 
- The present technique and components, as described in greater detail below, may be used in cooperation with existing components and control systems. In one specific embodiment, for example, the present technique may be employed with the SenTURIAN Deep Water Control System manufactured by Schlumberger Corporation. The system may be employed as a safety instrumented system as defined by one or more applicable standards, such as IEC61508. In this example, the IEC61508 standard is selected and covers safety-related systems when such systems incorporate electrical, electronic, or programmable electronic (E/E/PE) devices. Such devices may include a variety of devices from electrical relays and switches through programmable logic controllers (PLCs). The standard is designed to cover possible hazards created when failures of the safety functions performed by E/E/PE safety-related systems occur. The international standard IEC61508, although generic, is an example of a standard which is becoming more widely accepted as a basis for the specification, design and operation of programmable electronic systems in the petroleum production industry. 
- Various control systems, e.g. deep water control systems, are designed according to predetermined safety integrity levels (SILs). In the description herein, SIL level determination is not addressed, but instead SIL levels are discussed as outlined by the Norwegian Petroleum Directorate for the safety functions carried out by the system, e.g. SIL2. By definition, SIL2 ensures that the safe failure fraction is between 90% and 99% assuming a hardware fault tolerance of zero. SIL2 also implies that the probability of failure on demand for dangerous undetected failures is between 0.01 and 0.001, thus resulting in a risk reduction factor of between 100 and 1000. 
- Referring generally toFIG. 1, a well system20 is illustrated, according to one embodiment of the present invention. In the example illustrated, well system20 is a subsea control system comprising asubsea installation22 which includes a production control system24 cooperating with a subsea test tree26. Thesubsea installation22 is positioned at asubsea location28 generally over a well30 such as an oil and/or gas production well. Additionally, acontrol system32 is employed to control operation of the production control system24 and subsea test tree26. Thecontrol system32 may comprise an integrated system or independent systems for controlling the various components of the production control system and the subsea test tree. 
- Although the production control system24 and subsea test tree26 may comprise a variety of components depending on the specific application and well environment in which a production operation is to be conducted, specific examples are discussed to facilitate an understanding of the present system and technique. The present invention, however, is not limited to the specific embodiments described. In one embodiment, production control system24 comprises a horizontal tree section34 having, for example, a production line36 and anannulus line38. A blowout preventer40, e.g. a blowout preventer stack, may be positioned in cooperation with the horizontal tree section34 to protect against blowouts. These components also comprise an internal passageway42 to accommodate passage of tubing string components44 and related components, such as a tubing hanger/running tool46. 
- The production control system24 also may comprise a variety of additional components incorporated into or positioned above blowout preventer40. For example, at least onepipe ram46 may be mounted insubsea installation22 at a suitable location. In embodiment illustrated, twopipe rams46 are employed. The system also may comprise at least one shear ram48, such as the two shear rams illustrated. Additionally, one or more, e.g. two, annular rams50 may be employed in the system. The various production control systems24 accommodate a riser52 designed to receive subsea test tree26. 
- In the embodiment illustrated, the subsea test tree26 comprises an upper portion54 releasably coupled with a lower portion56 via a connector58, such as a latch connector. The upper portion54 and the lower portion56 each contain at least one shut-off valve which may be selectively actuated to block flow of production fluid through thesubsea installation22. The various components ofsubsea installation22 are designed to allow an emergency shutdown. For example, subsea test tree26 enables provision of a safety system installed within riser52 during completion operations to facilitate safe, temporary closure of the subsea well30. Thecontrol system32 provides hydraulic power to the subsea test tree26 to enable control over the shut-off valves. Control over the subsea test tree26 may be independent of the safety functions of the production control system24, such as actuation of blowout preventer40. 
- The shut-off valves in subsea test tree26 may range in number and design. In one embodiment, however, the upper portion54 comprises aretainer valve60, as further illustrated inFIG. 2. In the specific embodiment illustrated, lower portion56 comprises a pair of valves in the form of aflapper valve62 and a ball valve64. As desired for a given application, other components may be incorporated into subsea test tree26. For example, the upper portion54 may comprise additional components in the form of a space out sub66, a bleed off valve68, and a shear sub70. Similarly, the lower portion56 may comprise additional components, such as a ported joint72 extending down totubing hanger46. 
- The shut-off valves may be controlled electrically, hydraulically, or by other suitable techniques. In the embodiment illustrated, however,valves60,62,64 are controlled hydraulically via hydraulic lines74. For example, the position of thevalves60,62,64 may be controlled via a combination of opened or closed directional control valves76 located in, for example, a subsea control module78. The directional control valve76 control whether hydraulic pressure is present or vented on its assigned output port in the subsea test tree. The directional control valves76 within subsea control module78 may be controlled via solenoid valves or other actuators which may be energized via electrical signals sent from the surface. Accordingly, theoverall control system32 for controlling subsea test tree26 may have a variety of topside and subsea components which work in cooperation. 
- During a specific valve operation, an operations engineer may issue a command via a human machine interface80 of amaster control station82, such as a computer-based master control station. In some applications, themaster control station82 comprises or works in cooperation with one or more programmable logic controllers. Electric current is sent down through an umbilical84 to the solenoid valves and subsea control module78 to actuate directional control valves76. The umbilical84 also may comprise one or more hydraulic control lines extending down to the subsea control module from ahydraulic power unit86. In the embodiment illustrated inFIGS. 1 and 2, the hydraulic lines74 also are routed to an accumulator88, such as a subsea accumulator module. 
- When a desired directional control valve76 is opened, hydraulic pressure supplied byhydraulic power unit86 is passed through its assigned output port to the subsea test tree26. Conversely, when a directional control valve76 is closed, any hydraulic pressure present at its output port is vented. Hydraulic power is transferred from the subsea accumulator module88 to aparticular valve60,62,64 located in the subsea test tree26. The designated valve transitions and fulfills the intended safety instrumented function for a given situation. 
- An emergency shutdown sequence may be achieved through a series of commands sent to one or more of thevalves60,62 and64. The emergency shutdown sequence may be designed to bring the overall system to a safe state upon a given command. Depending on the specific application, the emergency shutdown sequence also may control transition of additional valves, e.g. a topside production control valve, to a desired safety state. 
- If a complete loss of communication between the topside and subsea equipment occurs, i.e. loss or severing of the umbilical84, the directional control valves76 are designed to return to a natural or default state via, for example, spring actuation. This action automatically brings the well to a fail safe position with the topside riser and the well sealed and isolated. If the topside equipment is unable to bring the well into a safe state, then the operator can institute a block-and-bleed on thehydraulic power unit86 to cause the subsea test tree to transition into its failsafe configuration. Additionally, visual and/or audible alerts may be used to alert an operator to a variety of fault or potential fault situations. 
- In the specific example illustrated inFIG. 2, the subsea test tree26 has four basic functions utilizingretainer valve60, connector58,flapper valve62, and ball valve64. Theretainer valve60 functions to contain riser fluids in riser52 after upper portion54 is disconnected from lower portion56. The connector58, e.g. latch mechanism, enables the riser52 and upper portion54 to be disconnected from the remainingsubsea installation22. Theflapper valve62 provides a second or supplemental barrier used to isolate and contain the subsea well. Similarly, the ball valve64 is used to isolate and contain the subsea well as a first barrier against release of production fluid. 
- The subsea test tree26 may be used in a variety of operational modes. For example, the subsea test tree26 may be transition to a “normal mode”. In this mode, a standard emergency shutdown sequence may be used in which a ball valve close function is performed to close ball valve64. By way of example, the ball valve64 may be closed by supplying hydraulic fluid at a desired pressure, e.g. 5 kpsi. Another mode is employed as the subsea test tree system is run in hole or pulled out of hole (RIH/POOH mode). In this mode, the valve functions are disabled to prevent a spurious unlatch at connector58 while the assembly is suspended in riser52. In another example, the system is placed in a “coil tubing” mode when coil tubing is present in riser52 while a disconnect is to be initiated. In this mode, the ball valve is actuated under a higher pressure, e.g. 10 kpsi, to enable severing of the tubing via, for example, shear rams48. 
- Thecontrol system32 also may be designed to operate in a diagnostic mode. The diagnostic mode is useful in determining the integrity of the signal path as well as the basic functionality of the subsea control module, including the solenoid valves and directional control valves. In this mode, a selected current, e.g. a 30 mA current, is delivered down each of the electric lines, e.g. seven lines, within umbilical84. Then, by verifying the voltage required to drive this current, the impedance of the system can be inferred. This current is insufficient to trigger a solenoid into actuation, but the current may be used to verify various operational parameters. Examples of verifying operational parameters include: verifying delivery of power to the system from an uninterruptible power supply; verifying the solenoid driver power supply is functional; verifying performance of a programmable logic controller; verifying that all connectors are intact; and verifying solenoids have not failed in an open or shorted manner. The diagnostic testing can be performed on command from a SCADA, or as a self-diagnostic function at pre-determined time intervals depending on results of a hazard and operability application. 
- Referring generally toFIGS. 3-5, a variety of subsea control system functions/implementations are illustrated via schematic block diagrams. In the embodiment illustrated inFIG. 3, for example,control system32 utilizes a surface basedmaster control system82 comprising a programmablelogic control system90 to isolate topside flow output via a production wing valve92. The wing valve92 may comprise a master valve, a downhole safety valve, or another wing valve operated by the production control system. By way of example, the overall system may be designed at an SIL3 level while the subsea test tree employed in thesubsea installation22 is at an SIL2 level. 
- In the embodiment illustrated inFIG. 3, the topside wing valve92 is operated by a high pressure system through a solenoid actuated valve94 controlled viaprogrammable logic controller90 inmaster control system82. The valve94 is considered to be in a safe state when it is in its closed position. To avoid problems ifprogrammable logic controller90 fails to actuate the valve when desired, the system may be designed to enable manual triggering of the valve. Verification that wing valve92 has been actuated can be based on select parameters. For example, the verification may be based on detection of actuation current delivered by the master control system; detection of the actuation voltage required to achieve the desired current (implied impedance); and/or operator verification of the position of the wing valve via an appropriate gauge or sensor. 
- In the specific example illustrated,programmable logic controller90 is coupled to an emergency shutdown panel96. Additionally, theprogrammable logic controller90 comprises an input module98, alogic module100, and anoutput module102. Theprogrammable logic controller90 may be powered by an uninterruptible power supply104, and theoutput module102 may be independently coupled to a power supply unit106. Theoutput module102 controls actuation of solenoid valve94 which, in turn, controls delivery of hydraulic actuation fluid to wing valve92. Additional components may be positioned between solenoid valve94 and wing valve92 to provide an added level of control and safety. Examples of such components comprise a supplemental valve108 and an air block110. 
- A similar control technique may be used to control actuation ofretainer valve60 in upper portion54, as illustrated inFIG. 4. In this example, the emergency shutdown sub-function begins at themaster control system82 where the demand is initiated, however the function does not include other initiating factors. The function concludes with theretainer valve60 closing with respect to riser52. An appropriate SIL level for this sub-function may be SIL2. Verification thatretainer valve60 has been actuated to a closed position can be based on select parameters. For example, the verification may be based on detection of actuation current delivered by the master control system; detection of the actuation voltage required to achieve the desired current (implied impedance); detection of flow as measured by flow meters on thehydraulic power unit86; and/or measuring a pressure response with transducers on the subsea accumulator module88. 
- Another control technique/sub-function is used to isolate subsea well30 via the shut-off valves,e.g. valves62,64, in the lower portion56 of subsea test tree26, as illustrated inFIG. 5. In this specific example, two shut-off valves are utilized for the sake of redundancy in the form offlapper valve62 and ball valve64, however one valve is sufficient to leave the subsea well30 in a safe state. In this example, the emergency shutdown sub-function begins at themaster control system82 where the demand is initiated, however the function does not include other initiating factors. The function concludes with theflapper valve62 and/or ball valve64 closing with respect to subsea well30. An appropriate SIL level for this sub-function may be SIL2. Verification that at least one of theflapper valve62 and ball valve64 has been actuated to a closed position can be based on select parameters. For example, the verification may be based on detection of actuation current delivered by the master control system; detection of the actuation voltage required to achieve the desired current (implied impedance); detection of flow as measured by flow meters on thehydraulic power unit86; and/or measuring a pressure response with transducers on the subsea accumulator module88. 
- The safety integrity levels (SILs) described herein are not necessarily derived from a risk-based approach for determining SIL levels as described in standard IEC61508. Instead, the SIL levels sometimes are based on industry recognized standards for production system safety functions. Based on the minimum SIL requirements for each function as applies to the existing layers of protection, the minimum SIL level for the various safety integrity functions, e.g. the sub-functions outlined inFIGS. 3-5, may be selected as SIL2. 
- Additionally, the subsea test tree26 and its corresponding shut-offvalves60,62,64 may be operated completely independently with respect to operation of the production control system24 which is used during normal operations. In this case, theoverall control system32 may comprise completely independent control systems for the subsea test tree26 and the production control system24. The subsea test tree26 may be installed within the production control system24, e.g. inside a Christmas tree, during operation inside the blowout preventer stack40. In the event that the blowout preventer40 is required to close, the subsea test tree26 is sealed and disconnected from the string (separated at connector58). This allows the upper portion54 of the subsea test tree26 to be retracted so the blowout preventer rams can be closed without interference. 
- If the upper portion54 cannot be unlatched and retracted during a subsea test tree failure mode, the shear rams48 may be operated to sever the tool and safely close the well. The blowout preventer control system has no influence on the safety functions of the subsea test tree system. One example of a closing pattern comprises closing theupper retainer valve60, followed by closure of the lower ball valve64 and subsequent closure of theflapper valve62. Once the upper production string is sealed viaretainer valve60 and access to the wellbore is sealed via ball valve64 andflapper valve62, the subsea test tree is disconnected and separated at connector58. 
- Specific safety relevant parameters may be selected according to the system design, environment, and applicable requirements in a given geographical location. However, one example of a typical approach is illustrated inFIG. 6 as having a safe failure fraction exceeding 90% on the topside for a Type B safety system (complex) and a hardware fault tolerance of zero, per standard IEC61508-2. At the subsea location, the system comprises a Type A subsystem having a safe failure fraction greater than 60% and a hardware fault tolerance of zero. Final elements on the topside may be evaluated to the DC fault model per IEC61508-2 (fault stuck at Vcc and stuck at Gnd, as well as stuck open and stuck shorted). Final elements in the subsea portion of the system are evaluated as a Type A system because only discrete passive components are used. All failure modes of these components are well defined and sufficient field data exists to be able to assume all fault conditions. 
- The accumulator module88 may be incorporated into the overall system in a variety of configurations and at a variety of locations. In one example, accumulator module88 is a pressure balanced accumulator to provide hydraulic power to the system in case of emergency closure and disconnect and/or loss of hydraulic power from the surface. 
- Accumulators are devices that provide a reserve of hydraulic fluid under pressure and are used in conventional hydraulically-driven systems where hydraulic fluid under pressure operates a piece of equipment or a device. The hydraulic fluid is pressurized by a pump that maintains the high pressure required. 
- If the piece of equipment or the device is located a considerable distance from the pump, a significant pressure drop can occur in the hydraulic conduit or pipe which is conveying the fluid from the pump to operate the device. Therefore, the flow may be such that the pressure level at the device is below the pressure required to operate the device. Consequently, operation may be delayed until such a time as the pressure can build up with the fluid being pumped through the hydraulic line. This result occurs, for example, with deep water applications, such as with subsea test tree and blowout preventer equipment used to shut off a wellbore to secure an oil or gas well from accidental discharges to the environment. Thus, accumulators may be used to provide a reserve source of pressurized hydraulic fluid for this type of equipment. In addition, if the pump is not operating, accumulators can be used to provide a reserve source of pressurized hydraulic fluid to enable the operation of a piece of equipment or device. 
- Accumulators may include a compressible fluid, e.g., gas, nitrogen, helium, air, etc., on one side of a separating mechanism, and a non-compressible fluid (hydraulic fluid) on the other side. When the hydraulic system pressure drops below the precharged pressure of the gas side, the separating mechanism will move in the direction of the hydraulic side displacing stored hydraulic fluid into the piece of equipment or the device as required. 
- When some types of accumulators are exposed to certain hydrostatic pressure, such as the hydrostatic pressure encountered in subsea operations, the available hydraulic fluid is decreased since the hydrostatic pressure must first be overcome in order to displace the hydraulic fluid from the accumulator. However, pressure balanced accumulators may be employed to overcome the above-described shortcomings. Examples of pressure-balanced accumulators are disclosed in U.S. Pat. No. 6,202,753 to Benton and U.S. Patent Publication No. 2005/0155658-A1 to White. 
- Referring generally toFIG. 7, an example of one implementation of accumulator module88 is illustrated. In this example, accumulator module88 is a pressure balanced accumulator system. The accumulator system88 is connected with the one or more hydraulic lines74 routed betweenhydraulic power unit86 and subsea test tree26.Hydraulic power unit86 may comprise one or more suitable pumps110 for pumping hydraulic fluid. Thehydraulic power unit86 is located above a sea surface111 and provides control fluid for the operation of, for example, blowout preventer40 and thevalves60,62,64 of subsea test tree26. The pressurized hydraulic fluid fromhydraulic power unit86 also is used to charge the pressure balanced accumulator system88. By way of example, the hydrostatic pressure PHSsupplied by pump110 is approximately 7500 psi, although other pressure levels may be used. 
- Referring generally toFIGS. 8 and 9, one embodiment of a pressure balanced accumulator88 is illustrated. The illustrated embodiment is readily utilized in conjunction with subsea test tree26, production control system24, andcontrol system32. As illustrated, the pressure balanced accumulator88 comprises a housing112, which is a generally tubular-shaped member having two ends114 and116. An accumulator mechanism118 is located within the housing112 proximate the first end114. The accumulator mechanism118 comprises a first chamber120 (seeFIG. 9) for receiving a pressurized gas at a first pressure. The pressurized gas may, for example, be injected intochamber120 through gas precharge port122. In one embodiment of the present invention, the gas in thefirst chamber120 is helium, and it is pressurized to approximately 3500 psi, although other pressures may be used depending on the specific application. 
- With further reference toFIGS. 8 and 9, accumulator mechanism118 also comprises a second chamber124 for receiving a first pressurized fluid at a second pressure. The pressure of the fluid in chamber124 is sometimes referred to as the “gauge pressure.” In one embodiment, liquid may be injected into chamber124 via a seal stab port126. The liquid injected into chamber124 may be in the form of a water glycol mixture according to one embodiment of the present invention. By way of example, the mixture may be injected into chamber124 at a pressure of approximately 5000 psi, although other pressures may be utilized in other applications.Chambers120 and124 are hermetically sealed from one another atregions128 and130. 
- The pressure balanced accumulator system88 may further comprise a third chamber132 which abuts accumulator mechanism118 in housing112. Third chamber132 contains a fluid, which may be injected into chamber132 via fluid fill port134. In one embodiment, the fluid injected into third chamber132 is silicon oil, which is selected for use because of its lubricity and because it will not adversely affect seals136 deployed to seal along one end of chamber132. Initially, the silicon fluid is not injected into third chamber132 under pressure. In operation, however, the pressure of the fluid in chamber132 tracks the pressure of the fluid in second chamber124, as described below. 
- Pressure balanced accumulator88 also comprises a piston138 which is located within the housing proximate the second end116 of housing112. The piston138 has a first end140 and a second end142 which have first and second cross-sectional areas, respectively. In one embodiment, the cross-sectional areas of piston ends140 and142 are circular in shape. Piston138 is movable between a first position, as shown inFIG. 8, and a second position in which piston end140 is stopped by a shoulder144. 
- Housing end116 also may comprise an ambient pressure port146. When pressure balanced accumulator88 is used in a subsea environment, ambient pressure port146 permits the ambient subsea pressure to impinge on end140 of piston138. 
- In the illustrated embodiment, pressure balanced accumulator system88 also comprises an atmospheric chamber148 which includes anannular recess150 formed between piston138 and the wall of housing112; an axial cavity152 which is formed by hollowing out a portion of piston138; and a passage154 connectingannular recess150 and axial cavity152. This atmospheric chamber allows differential pressure to exist across piston138 which enables the piston to start to move when an equilibrium pressure exists across piston138 as discussed below. In one embodiment, the pressure in the atmospheric chamber is 14.7 psi, the volume ofannular recess150 is approximately 10 in.sup.3, and the volume of axial cavity152 is approximately 200 in.sup.3. 
- In subsea applications, such as the subsea applications described above, accumulator module88 may be located in a subsea environment to control the operation of an in-riser or open water intervention system, such as subsea test tree26 and associatedvalves60,62,64. The first andsecond chambers120 and124 in accumulator mechanism118 of pressure balanced accumulator system88 are precharged prior to placement of pressure balanced accumulator system88 in the subsea environment. Pump110, which is located above the sea surface111, provides the control fluid for the operation of blowout preventer40 and shut-offvalves60,62,64. The pump110 also provides a charging input to second chamber124 of accumulator mechanism118 in pressure balanced accumulator system88. 
- For purposes of illustration, it can be assumed that the hydrostatic pressure, PHS, in which pressure balanced accumulator88 is operating is 7500 psi, although other pressures may be employed. This ambient pressure is communicated through ambient pressure port146 of accumulator system88 and impinges on end140 of piston138. The force acting on piston138 at its end140 is given by the formula: 
 F1=PHS×(the area of piston end140).  (1)
 
- The force on end142 of piston138 is given by the formula: 
 F2=(PHS+5000)×(the area of piston end142).  (2)
 
- In one specific example of the present invention, piston ends140 and142 are circular in cross-section and have cross-sectional areas established by diameters of 3.375 inches and 2.688 inches, respectively, although the sizes are for purposes of explanation only. At the hydrostatic pressure of 7500 psi, the equilibrium pressure, PE, at which the piston138 starts to move is: 
 
- The gauge pressure PGat which the piston begins to move is given by the formula: 
 PG=PE−PHS=11,824−7,500PG=4,324 psi  (4)
 
- In accordance with the present invention, the diameter of piston ends140 (D1) and142 (D2) may be sized for optimal efficiency at a predetermined hydrostatic pressure, using the following formula: 
 
- where PCis the pressure to which the second chamber of accumulator mechanism118 is charged, e.g., 5000 psi, and S is a hydraulic safety factor which is an allowance given to prevent instability in maximum hydrostatic conditions. For a hydrostatic pressure of 7500 psi, S is approximately 500 psi. If D2=2.688 inches as in the above calculation with respect to equations (3) and (4) then D4according to equation (5) is 3.40 inches. 
- InFIG. 10, a graph is presented with a graph line156 provided to illustrate the fluid volume of fluid expelled from the accumulator mechanism118 at a hydrostatic pressure of 7500 psi and with D1and D2being 3.375 inches and 2.688 inches, respectively. Graph lines158,160 and162 illustrate fluid volume expelled at hydrostatic pressures of 6500, 5500 and 4500 psi, respectively. 
- The overall subsea control system20 may be designed for use in a variety of well applications and well environments. Accordingly, the number, type and configuration of components and systems within the overall system may be adjusted to accommodate different applications. For example, the subsea test tree may include different numbers and types of shut-off valves as well as a variety of connectors, e.g. latch mechanisms, for releasably connecting the upper and lower parts of the subsea test tree. The production control system also may comprise various types and configurations of subsea installation components. Similarly, thecontrol system32 may rely on various topside and subsea components which enable independent control over the subsea test tree and the blowout preventer. In some applications, the control system utilizes surface components which are computer-based to enable easy input of commands and monitoring of subsea functions. As described above, programmable logic controllers also may be employed and used to carry out various sub-functions implemented in emergency shutdown procedures. Various adaptations may be made to accommodate specific environments, types of well equipment, applicable standards, and other parameters which affect a given subsea well application. 
- Although only a few embodiments of the present invention have been described in detail above, those of ordinary skill in the art will readily appreciate that many modifications are possible without materially departing from the teachings of this invention. Accordingly, such modifications are intended to be included within the scope of this invention as defined in the claims.