Champagne effect mitigation in hydrostatically compensated compressed gas energy storage systems

Abstract

A hydrostatically compensated compressed gas energy storage system includes an accumulator positioned below ground at an accumulator depth and a compensation shaft having a lower end in fluid communication with the accumulator and an upper portion in fluid communication with a reservoir of compensation liquid. A downcomer shaft extends between a downcomer inlet positioned in the reservoir and a downcomer outlet in fluid communication with the compensation shaft at a downcomer depth. The downcomer shaft is configured to direct a flow of compensation liquid having a relatively low gas saturation from the reservoir to the compensation shaft to mix with compensation liquid at the downcomer depth having a relatively high gas saturation, thereby diluting the compensation liquid and lowering the gas saturation of compensation liquid at the downcomer depth.

Description

CHAMPAGNE EFFECT MITIGATION IN HYDROSTATICALLY COMPENSATED COMPRESSED GAS ENERGY STORAGE SYSTEMSCROSS REFERENCE TO RELATED APPLICATIONS

[0001] This patent application claims priority to United States Provisional Patent Application No. 63 / 721,262, filed on November 15, 2024 and entitled “CHAMPAGNE EFFECT MITIGATION IN HYDROSTATICALLY COMPENSATED COMPRESSED GAS ENERGY STORAGE SYSTEMS”, and to United States Provisional Patent Application No.63 / 721,286, filed on November 15, 2024 and entitled “CHAMPAGNE EFFECT MITIGATION IN HYDROSTATICALLY COMPENSATED COMPRESSED GAS ENERGY STORAGE SYSTEMS”, the entire contents of which are incorporated herein by reference.FIELD OF THE DISCLOSURE

[0002] The present disclosure relates generally to compressed gas energy storage and power generation systems, and more particularly to a compressed gas energy storage system such as, for example, those including a hydrostatically compensated compressed air energy storage accumulator located underground.BACKGROUND

[0003] Electricity storage is highly sought after, in view of the cost disparities incurred when consuming electrical energy from a power grid during peak usage periods, as compared to low usage periods. The addition of renewable energy sources to the power grid, being inherently of a discontinuous or intermittent supply nature, increases the demand for affordable electrical energy storage worldwide.

[0004] Thus, there exists a need for effectively storing the electrical energy produced at a power grid or a renewable source during a non-peak period and returning it to the grid upon demand. Furthermore, to the extent that the infrastructural preparation costs and the environmental impact from implementing such infrastructure are minimized, the utility and desirability of a given solution is enhanced.

[0005] Furthermore, as grids transform and operators look to storage in addition to renewables to provide power and remove traditional forms of generation that also provide gridstability, such as voltage support, a storage method that offers inertia based synchronous storage is highly desirable.

[0006] As described herein, compressing and storing a gas (such as air), using a suitable compressed gas energy storage system, is one way of storing energy for later use. For example, during non-peak times, energy (i.e. electricity) can be used to drive compressors and compress a volume of gas to a desired, relatively high pressure for storage. The gas can then be stored at the relatively high pressure inside any suitable container or vessel, such as a suitable accumulator. To extract the stored energy, the pressurized gas can be released from the accumulator and used to drive any suitable expander apparatus or the like, and ultimately to be used to drive a generator or the like to produce electricity. The amount of energy that can be stored in a given compressed gas energy storage system may be related to the pressure at which the gas is compressed / stored, with higher pressure storage generally facilitating a higher energy storage for a given accumulator / system volume.

[0007] In some hydrostatically compensated compressed air energy storage systems, compensation liquid (such as water) within a compensation column can flow out of and into the accumulator as the system is charged and discharged, respectively, thereby helping to maintain the interior of the accumulator at a desired or target system pressure during the charging and discharging processes even as the quantity of air in the accumulator changes.

[0008] In some examples of hydrostatically compensated compressed air energy storage systems, the compressed gas can be soluble in the compensation liquid (e.g., air is soluble in water). Typically, there is a relatively large surface area / interface between the layer of gas and the layer of compensation liquid in the accumulator. Accordingly, where the compressed gas is air and the compensation liquid is water, some of the compressed air will dissolve into the water within the accumulator. The amount of air that can dissolve in the water is a function of the pressure within the accumulator (i.e. the pressure of the gas and the compensation liquid at the interface) and the length of time the gas is in contact with the water.

[0009] When the system is in a storage / standby mode (e.g. when compressed air is being stored at the system pressure instead of flowing in or out of the accumulator) the compensation water may also be generally static (i.e., there may be minimal water flow between the accumulator and the compensation column). This can lead to more air being dissolved in water that is resident within the accumulator than water in the compensation shaft and / or a source / sink reservoir (i.e., water that is not in contact with the compressed air). When thesystem is operated in a charging mode, additional compressed air is conveyed into the accumulator, leading to some of the compensation water that contains relatively higher amounts of dissolved gas being displaced from the accumulator towards the compensation source / sink reservoir via the compensation column, bringing with it a relatively large amount of dissolved gas. In some circumstances this may lead to what is known as the champagne effect, in which dissolved gas comes out of solution as the compensation water pressure decreases as it travels up the compensation column.SUMMARY

[0010] This summary is intended to introduce the reader to the more detailed description that follows and not to limit or define any claimed or as yet unclaimed invention. One or more inventions may reside in any combination or sub-combination of the elements or process steps disclosed in any part of this.

[0011] In accordance with one broad aspect, there is provided a hydrostatically compensated compressed gas energy storage system comprising: an accumulator positioned below ground at an accumulator depth, the accumulator being configured to selectively receive compressed gas for storage and to selectively release stored compressed gas for power generation; a compensation shaft having a lower end in fluid communication with the accumulator, an upper end, and an upper portion in fluid communication with a reservoir of compensation liquid, the reservoir being positioned at a reservoir elevation; and a downcomer shaft that extends between a downcomer inlet positioned in the reservoir and a downcomer outlet in fluid communication with the compensation shaft at a downcomer depth; wherein the downcomer shaft is configured to direct a flow of compensation liquid having a relatively low gas saturation from the reservoir to the compensation shaft to mix with compensation liquid at the downcomer depth having a relatively high gas saturation, thereby diluting the compensation liquid and lowering the gas saturation of compensation liquid at the downcomer depth.

[0012] In some embodiments, the accumulator depth is between about 400 m and 900 m, and the downcomer depth is between about 50 m and 200 m.

[0013] In some embodiments, the accumulator depth is about 600 m and the downcomer depth is about 85 m.

[0014] In some embodiments, the downcomer depth is determined based on an expected gas saturation of compensation liquid exiting the accumulator, an associated saturation pressure,and a depth at which compensation liquid in the compensation shaft reaches the saturation pressure.

[0015] In some embodiments, the downcomer shaft is configured to induce the flow of compensation liquid from the reservoir through the downcomer shaft based on a difference between a density of compensation liquid at the downcomer depth and a density of compensation liquid at the downcomer inlet.

[0016] In some embodiments, the hydrostatically compensated compressed gas energy storage system further comprises a pump configured to selectively direct the flow of compensation liquid from the reservoir through the downcomer shaft.

[0017] In some embodiments, the compensation liquid is water and the compressed gas is compressed ambient air.

[0018] In accordance with another broad aspect, there is provided a method of mitigating the champagne effect in a hydrostatically compensated compressed gas energy storage system, the method comprising: directing a flow of compensation liquid having a relatively low gas saturation from a reservoir to a hydrostatic compensation shaft in fluid communication with an accumulator positioned below ground at an accumulator depth, wherein the flow of compensation liquid is introduced to the compensation shaft at a dilution depth that is less than half of the accumulator depth.

[0019] In some embodiments, the dilution depth is less than a third of the accumulator depth.

[0020] In some embodiments, the accumulator depth is between about 400 m and 900 m, and the downcomer depth is between about 50 m and 200 m.

[0021] In some embodiments, the accumulator depth is about 600 m and the downcomer depth is about 85 m.

[0022] In some embodiments, the flow of compensation liquid is directed from the reservoir to the compensation shaft via a downcomer shaft that extends between a downcomer inlet positioned in the reservoir and a downcomer outlet in fluid communication with the compensation shaft at the dilution depth.

[0023] In some embodiments, directing the flow of compensation liquid comprises activating a pump configured to advance compensation liquid through the downcomer shaft.

[0024] In some embodiments, the directing is performed during or immediately following injection of compressed gas into the reservoir.

[0025] In some embodiments, the compensation liquid is water and the gas is ambient air.

[0026] In accordance with another broad aspect, there is provided a hydrostatically compensated compressed gas energy storage system comprising: an accumulator positioned below ground at an accumulator depth, the accumulator being configured to selectively receive compressed gas for storage and to selectively release stored compressed gas for power generation, the accumulator having an accumulator length, an accumulator width, an accumulator height measured from an accumulator ceiling to an accumulator floor, and an accumulator volume, the accumulator having a sump extending below the accumulator floor, the sump having a sump length, a sump width, a sump depth measured from the accumulator floor, wherein at least one end of the sump has a sump grade; and a hydrostatic compensation shaft having a lower end in fluid communication with the accumulator sump.

[0027] In some embodiments, the sump depth is less than 20 m.

[0028] In some embodiments, the sump length is at least 100 m, the sump width is at least 7 m, the sump depth is about 12 m, and the sump grade is about 12%.

[0029] In some embodiments, the sump grade is between about 10% and about 15%.

[0030] In some embodiments, sump volume is between about 0.5% and about 5% of the accumulator volume.

[0031] In some embodiments, the sump volume is sufficient to accommodate an expected maximum volume of water that may leave the accumulator after the end of a charge cycle due to end of charge dynamics and champagne effect momentum.

[0032] Other aspects and embodiments are described in further detail below.BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Example embodiments of the invention will now be described with reference to the appended drawings in which:

[0034] FIG. 1 is a schematic example of a waterway design for a hydrostatic CAES;

[0035] FIG. 2 is a schematic example of another waterway design for a hydrostatic CAES;

[0036] FIG. 3A is a schematic example of water compensation conditions at a first time;

[0037] FIG. 3B is a schematic example of water compensation conditions at a second time;

[0038] FIG. 3C is a schematic example of water compensation conditions at a third time;

[0039] FIG. 3D is a schematic example of water compensation conditions at a fourth time;

[0040] FIG. 4 is a plot illustrating cavern pressure and liquid velocity within an compensation shaft during a charge cycle;

[0041] FIG. 5 is a plot illustrating a modeled dynamic response of the column velocity as the champagne effect develops;

[0042] FIG. 6 is a plot illustrating a modeled cavern pressure variation relative to a situation where no champagne effect develops;

[0043] FIG. 7 is a plot illustrating a modeled impact on cavern water level / sump requirements;

[0044] FIG. 8 is a plot illustrating modeled values for mass transfer coefficients relative to bubble size from various literature sources / correlations;

[0045] FIG. 9 is a schematic example of a hydrostatically compensated CAES system with a downcomer shaft extending between a reservoir and a compensation column;

[0046] FIG. 10 is a plot illustrating modeled density mitigation with a downcomer outlet positioned at different depths;

[0047] FIG. 11 is a plot illustrating modeled velocity mitigation with a downcomer outlet positioned at different depths;

[0048] FIG. 12 is an enlarged view of a portion of FIG. 11 ;

[0049] FIG. 13 is a plot illustrating modeled void fraction mitigation with a downcomer outlet positioned at different depths;

[0050] FIG. 14 is a plot illustrating a modeled change in downcomer efficacy for downcomer shafts of various diameters;

[0051] FIG. 15 is schematic vertical and horizontal cross sections of hydrostatic compensation shaft and downcomer shaft interface configurations;

[0052] FIG. 16 is a schematic example of a hydrostatically compensated CAES system with an accumulator that includes a sump;

[0053] FIG. 17 plot illustrating a comparison of modelled cavem / sump water levels for different sump geometries;

[0054] FIG. 18 is a representative plot illustrating sump sizing, showing available trade-offs between sump depth and sump cross-sectional area; and

[0055] FIG. 19 is a representative plot illustrating the depth to which the air-water interface drops in a sump of various sizes, at two different flow rates.DETAILED DESCRIPTION

[0056] Various apparatuses or processes will be described below to provide an example of an embodiment of each claimed invention. No embodiment described below limits any claimed invention and any claimed invention may cover processes or apparatuses that differ from those described below. The claimed inventions are not limited to apparatuses or processes having all of the features of any one apparatus or process described below or to features common to multiple or all of the apparatuses described below. It is possible that an apparatus or process described below is not an embodiment of any claimed invention. Any invention disclosed in an apparatus or process described below that is not claimed in this document may be the subject matter of another protective instrument, for example, a continuing patent application, and the applicants, inventors or owners do not intend to abandon, disclaim or dedicate to the public any such invention by its disclosure in this document.

[0057] Energy produced by some types of energy sources, such as windmills, solar panels, and the like may tend to be produced during certain periods (for example when it is windy, or sunny, respectively), and not produced during other periods (for example when it is not windy, or at night, etc.). However, the demand for energy may not always match the production periods for these types of energy sources, and it may be useful to store produced energy for use at a later time. Similarly, it may be helpful to store energy generated using conventional power generators (for example, coal, gas, and / or nuclear power plants) to help facilitate storage of energy generated during non-peak demand periods (e.g. periods when electricity supply could be greater than demand and / or when the cost of electricity is relatively low) and allow that energy to be utilized during peak demand periods (e.g. when the demand for electricity may be equal to or greater than the supply, and / or when the cost of electricity is relatively high).

[0058] Compressing and storing a gas (such as air), using a suitable compressed gas energy storage system, is one way of storing energy for later use. For example, during non-peak times, energy (i.e., electricity) can be used to drive compressors and compress a volume of gas to a relatively high pressure for storage. The gas can then be stored at the relatively high pressure inside any suitable container or vessel, which may be referred to herein as an accumulator. Toextract the stored energy, the pressurized gas can be released from the accumulator and used to drive any suitable expander apparatus or the like, and ultimately to be used to drive a generator or the like to produce electricity. The amount of energy that can be stored in a given compressed gas energy storage system may be related to the pressure at which the gas is stored, with higher pressure storage generally facilitating a higher energy storage. However, storing gases at relatively high pressures (such as between about 45-150 atm) in conventional systems can require relatively strong, specialized, and often relatively costly pressure vessels or other storage containers.

[0059] As described herein, an accumulator may be an underground cavern that also holds a liquid to hydrostatically compensate the stored compressed gas. The gas pressure in such a cavern can be controlled by adjusting the hydrostatic pressure within the accumulator.

[0060] Figure 1 schematically illustrates an example of a waterway design for a hydrostatic compressed gas energy storage system. In the illustrated example, compressed gas (e.g. ambient air) can be injected into an underground accumulator 200 via conduit 15. A water compensation column 300 is in fluid communication with the interior of accumulator 200. In use, the hydrostatic pressure due to the weight of the water in the compensation column 300 is used to balance the pressure of the compressed air within the accumulator 200. Compensation water can freely flow into or out of the accumulator 200 as the system is charged (e.g. as additional compressed gas is added to the accumulator via conduit 15) and discharged (e.g. as compressed gas is removed from the accumulator via conduit 15), which assists in maintaining the interior of the accumulator at a desired or target system pressure during the charging and discharging processes, even as the quantity of air in the accumulator changes. In the illustrated example, the compensation column 300 is also in fluid communication (via a penstock 35) with a reservoir 30 that contains additional compensation liquid (e.g. compensation water).

[0061] Figure 2 schematically illustrates another example of a waterway design for a hydrostatic compressed gas energy storage system. In the illustrated example, the compensation column 300 is in fluid communication with reservoir 30 via a plurality of intake structures 37.Champagne Effect

[0062] One challenge in hydraulically compensated compressed gas energy storage systems and compressed air energy storage (CAES) systems is the Champagne Effect (CE). The Champagne Effect is a two-phase (air / water) flow instability whereby dissolved gas (e.g. oneor more components of ambient air) escapes from the compensation water as it ascends the vertical compensation column during a system or facility charging mode and the local pressure falls below the saturation pressure of the air in water solution. The Champagne Effect is a consequence of the solubility of high-pressure air in water within the underground air storage cavern and the variable saturation of this water as its pressure falls when travelling between the accumulator and the compensation reservoir. The Champagne Effect disrupts system dynamics, causing pressure and velocity fluctuations and potentially resulting in a change in the flow regime. In an un-mitigated worst-case scenario, the Champagne Effect could lead to the loss of the hydrostatic containment in the cavern and a mass loss event of stored compressed air through the compensation column.

[0063] The Champagne Effect is a well documented phenomenon associated with hard-rock compensated CAES systems, with relevant work dating back to the early 1980’s during the first wave of CAES development. However, results from that era suffer from the relative lack of computing resources then available and are substantially incomplete with regards to the design needs of current CAES systems and potential solutions to reduce impacts on CAES system operations.

[0064] At a high level of generality, and without intending to be bound by theory, the Champagne Effect develops as follows:• High-pressure air and water are in contact in the accumulator. As air is added to or removed from the accumulator (e.g., during a charge or discharge cycle), the contact between air and water may be characterized as a highly turbulent environment.• Air dissolves into water fairly readily in this environment. Computational fluid dynamics (CFD) simulations suggest that it is likely that the cavern water (i.e., compensation water present in the accumulator) becomes fully saturated with air within the span of a single charge / discharge cycle.• As pressurized air is added to the accumulator during a charge cycle, air-rich water is displaced into and up the compensation column. This air-rich water loses pressure as it rises. At some point - i.e. once the pressure of the air-rich falls below saturation pressure - air begins to come out of solution and forms bubbles. These bubbles continue to rise and expand, pulling more air out of solution.• This bubble formation causes an initial instability that accelerates the flow of water up the column. More air-rich water continues to enter the column from the bottom (i.e. from the accumulator).• Eventually, this process reaches a steady state where the column density is no longer changing. This can be characterized as a ‘fully developed’ Champagne Effect.

[0065] The severity of the Champagne Effect is determined by several factors:- Availability of bubble nucleation sites,- The fundamental mass transfer rate of dissolved air into gaseous air,- The surface area of air-water contact in the two phase flow, a product of various bubblephysics effects (specifically turbulent bubble break-up and coalescence).

[0066] This continues until the end of charge, with the effects including :- Increased flow velocity,- Increased void fraction in the column (and thus decreased density),- Possible flow regime change, and- Decreased cavern pressure.

[0067] Once charging is complete (i.e. once compressed air is no longer being added to the accumulator), the existing bubbles in the column continue to flow upward under their buoyancy. This creates an air-lift pump, which continues some upward flow in the column after the charge cycle has ended, perpetuating the Champagne Effect to some extent.

[0068] Eventually, all bubbles leave the column, the upward motion stops, and there is a short downward flow of compensation water from the reservoir into the column which equalizes the pressure to a new equilibrium state.

[0069] The expected behaviour of the water compensation system in a charging cycle with respect to the Champagne Effect is illustrated in Figures 3A to 3D and Figure 4.

[0070] With reference to Figure 3A, a charging cycle starts at rest with the compensation water volume primarily contained in the cavern / accumulator 200. The air pressure in the cavern is equal to the hydrostatic pressure of the water compensation column 300.

[0071] With reference to Figure 4, in a first phase (A), compressed air moves downwards through an air shaft or an air conduit (not shown) and displaces the water in the cavern, which is forced upwards into the compensation reservoir via the compensation column. The springlike dynamic interaction of cavern air pressure and fluid inertia causes extended oscillations with large variations in velocity and cavern pressure. With reference to Figure 5 and Figure 3B, the Champagne Effect generates additional velocity spikes (2), that are slightly smaller than the first spike from the start-up oscillation, which drive and prolong the start-uposcillations. These oscillations continue for a period of time, before being damped by frictional effects in the water column.

[0072] With reference to Figure 4 and Figure 3C, in a second phase (B), a steady state (3) is reached in the charging mode and can be maintained until the minimum water level in the cavern is reached. Due to the Champagne Effect, the cavern pressure is lower than the pressure at rest, despite the velocity head and hydraulic losses in the waterway.

[0073] Once the minimum water level in the cavern is reached, the air supply to the cavern is switched off and a third phase (C) begins. With reference to Figure 4 and Figure 3D, although there is no longer a driving force from the cavern to push the water up the column, the upward flow is sustained by the bubbles that keep rising (4). The lower velocity allows the bubbles more time to grow, increasing the void ratio and providing a higher buoyancy driving force to maintain the upward flow. During this time, the cavern pressure drops significantly as it tries to balance the weight of the water column, which is lower due to the higher void ratio.

[0074] With reference to Figure 4, in a final phase (D) before all flows finally come to a standstill, the bubbles rise out of the column and the weight of the water column begins to increase. Compared with the increasing water column head the cavern air pressure is now low, leading to a rush back of water down the column towards the cavern (5). This occurs very quickly with large velocity. Eventually, a cavern air pressure equal to the hydrostatic pressure of the water column is passed through. A spring-like dynamic interaction between the cavern air pressure and the inertia of the fluid begins, causing long-lasting oscillations before being damped by frictional effects.Simulations

[0075] Simulations of the Champagne effect - including CFD simulations - led to the determination of several details relevant to the design of a CAES water column. For example, even under conservative assumptions for the pressure differential required for bubble nucleation (i.e., differential pressure (DP) of zero - experimentation showed this value to be non-zero), and an assumption of abundant nucleation sites (as many as could be reasonably simulated, corresponding to water with significant visible turbidity), the mass transfer coefficient of air coming out of solution and the total bubble surface area across which this transfer occurs, limit the growth of bubbles such that the residence time in the column is insufficient for all air to come out of solution. A conclusion that may be drawn form this is that a large amount of the air dissolved in the cavern water passes up the column while in solutionand bubbles out in the reservoir, where it has no significant impact on the shaft and cavern behaviour. This does however mean that column diameter is correlated with Champagne Effect severity. Simulations were done with shafts in the 6-8 ft. (~2m) range, and also with shafts at 4m and 6m diameters. The effect becomes particularly pronounced above the 4m diameter.

[0076] Also, the assumption of the mass transfer coefficient is shown to be very important. Fortunately, this coefficient is a physical constant that has been the subject of a non-trivial amount of research. In simulating the phenomenon, the mass transfer coefficients used were conservative for the flow regime expected in the column (e.g. 1.3e-4 m / s).

[0077] Another significant ramification of this understanding of the phenomenon is that the Champagne Effect is potentially at its most severe after a charge cycle has concluded, since this is when all of the air left in solution in the column is able to bubble-out. Once all of the air has bubbled out, the density of the column returns to full-value, which has the effect of driving some volume of compensation water back into the cavern (e.g. out of a sump). This results in a small amount of cavern space being wasted.

[0078] The simulation results were principally focused on the resulting velocity and void fraction in the column, as these determine the resulting flow regime (bubble vs. chum vs. slug) and forces exerted on the column infrastructure.

[0079] Figure 5 is a plot illustrating the dynamic response of the column velocity as the champagne effect develops, reaches steady state, and then reacts to a sudden end of charge operations (black dashed line). It can be seen that the response to shutdown is similar to the one that occurs without a champagne effect (blue line), except that it is delayed timewise as the champagne effect runs on, and features a negative spike as the champagne effect ends and fresh water floods back into the column.

[0080] Figure 6 is a plot illustrating cavern pressure variation between an ‘end of charge’ scenario in which the champagne effect has developed relative to a scenario in which no champagne effect develops.

[0081] Figure 7 is a plot illustrating variations in level of the compressed air / compensation water interface within the accumulator between an ‘end of charge’ scenario in which the champagne effect has developed relative to a scenario in which no champagne effect develops. This plot illustrates a need for sump requirements to manage champagne effect impacts at the end of a charge cycle.

[0082] Figure 8 is a plot illustrating values for mass transfer coefficients relative to bubble size from various literature sources / correlations.

[0083] The column height at which transition from bubbly to chum flow occurs (and the resulting void fraction at the top of the column) as a function of time was also modelled for two different mass transfer coefficients (a limiting fundamental physical constant in Champagne Effect development). One conclusion drawn from the modelling is that the column remains in bubbly flow for all but the very upper section, even under very conservative assumptions.Champagne Effect Mitigation: Downcomer Shaft

[0084] As disclosed herein, one approach for mitigating the champagne effect is via midcolumn dilution of the air-saturated water in the compensation column. More specifically, airsaturated water in the compensation column is diluted by introducing fresh, unsaturated water (e.g. from the surface reservoir) at a location between the cavern and the compensation reservoir. To facilitate this dilution, a secondary conduit may be installed inside or adjacent to the main compensation column. Such a secondary conduit provides a flow path between the main compensation column at a specified depth and the compensation water reservoir, or to another source of fresh water (i.e. water with little-to-no dissolved air). Such a system can be used to dilute the air-rich water within the compensation column (e.g., during a system charging operation) and thereby mitigate the champagne effect. Such a secondary conduit, referred to herein as a ‘downcomer shaft’, may be used to passively supply dilution water (e.g., with atop-side check valve, using the density difference created by the Champagne Effect to drive flow into the compensation column), or to actively supply dilution water (e.g. using a pump to drive flow into the compensation column).

[0085] Figure 9 illustrates a schematic example of a hydrostatically compensated CAES system, referred to generally as 100. System 100 includes compression / expansion equipment 10 to compress gas (e.g. ambient air) and inject compressed gas into an underground accumulator 200 via conduit 15. In the illustrated example, the accumulator 200 is a cavern. The depth at which the accumulator 200 is positioned in the ground is preferably established according to gas pressures at which the compression / expansion equipment to be used is efficiently operated. In the illustrated example, the accumulator 200 is at an accumulator depth of ZComp. The accumulator depth Zcomp can vary in different embodiments of system 100, and in some embodiments can be between about 400 m and 900 m, and optionally may be about 600 m in some embodiments.

[0086] The gas that is compressed and stored in the accumulator 200 may be any suitable gas, including, but not limited to, air, nitrogen, noble gases, or combinations thereof. Using air may be preferable as a desired quantity of air may be drawn into the compression / expansion equipment 10 from the surrounding, ambient environment. Also, air released from within the accumulator 200 (e.g. via compression / expansion equipment 10) can be vented to the ambient environment without requiring further treatment.

[0087] System 100 also includes a water compensation column 300 that is in fluid communication with the interior of accumulator 200. In use, the hydrostatic pressure due to the weight of the water in the compensation column 300 is used to balance the pressure of the compressed air within the accumulator 200. The value of the accumulator depth Zcomp may affect the hydrostatic pressure due to the weight of the water in the compensation column 300 in a given embodiment. Compensation water can flow into or out of the accumulator 200 as the system is charged (e.g. as additional compressed gas is added to the accumulator via conduit 15) and discharged (e.g. as compressed gas is removed from the accumulator via conduit 15), which assists in maintaining the interior of the accumulator at a desired or target system pressure during the charging and discharging processes, even as the quantity of air in the accumulator changes. In the illustrated example, the compensation column (also referred to as a compensation shaft) 300 is also in fluid communication with a source / sink reservoir 30 that contains additional compensation water and is located at reservoir elevation that is schematically indicated as Zresin Figure 9. In the illustrated embodiment, the compensation shaft 300 has a lower end 302, an upper end 304 spaced from the lower end 302, and an upper portion 306 located between the lower end 302 and the upper end 304 that is in fluid communication with the reservoir 30 of compensation liquid.

[0088] System 100 is preferably configured so that a quantity of compensation liquid within the accumulator 200 isolates the compressed gas in the accumulator from the compensation liquid shaft 300, and functions as a liquid / water seal. Maintaining a sufficient quantity of water within the accumulator can prevent compressed gas from escaping into the compensation column 300 (rather than being extracted via the conduit 15 and directed through compression / expansion equipment 10), as such a gas escape represents a loss of stored energy that cannot be recovered.

[0089] In the illustrated example, the compensation shaft 300 penetrates through the cavern as a hanging string and terminates in a sump 220 in the cavern floor. Optionally, the lower end 302 of the compensation shaft 300 may be supported from below and / or above, but preferablyany supporting structure(s) should be designed to limit or preferably minimize any impairment of fluid flow into and out of the compensation shaft 300.

[0090] System 100 also includes a ‘downcomer’ shaft 350 that extends between a downcomer inlet 352 positioned in reservoir 30, and a downcomer outlet 354 positioned in the compensation column 300. Downcomer shaft 350 is in fluid communication with the compensation shaft 300 and can be used to direct a flow of water from the reservoir to the compensation column 300, where it is introduced into the column at a downcomer depth Za. The downcomer depth Za can, in a given embodiment, be selected based on at least one of the applicable reservoir elevation Zres, accumulator depth Zcomp, an expected gas saturation of compensation liquid exiting the accumulator, an associated saturation pressure, and a depth at which compensation liquid in the compensation shaft reaches the saturation pressure and / or other system parameters, and can optionally be between about 50 m and 200 m. In some embodiments, such as, for example, when the accumulator depth Zcomp is about 600 m, the downcomer depth Za may be about 85 m. The water at the downcomer shaft inlet 352 can be expected to have relatively low air saturation as compared to the compensation water within the accumulator 200. Accordingly, water introduced into the compensation column 300 via downcomer shaft 350 can be referred to as dilution water and the downcomer depth Za, at which water is introduced into the compensation shaft via downcomer shaft 350 can be referred to as a dilution depth. Optionally, in some preferred embodiments the dilution depth / downcomer depth Za at which water is introduced into the compensation shaft can be selected so that it is less than about half (e.g. !4) of the accumulator depth Zcomp, and optionally may be less than about one third (e.g. 1 / 3) of the accumulator depth Zcomp.

[0091] In the illustrated example, shaft 350 has an overall length La, and the position of shaft 320 that extends through the penstock 35 has a penstock length Lp.

[0092] Figure 15 illustrates schematic vertical and horizontal cross sections of five hydrostatic compensation shaft and downcomer shaft interface configurations.

[0093] In the example illustrated in Figure 9, a flow of water through downcomer shaft 350 is driven by relative water density differences at the inlet 352 and outlet 354. That is, in the illustrated embodiment the downcomer shaft 350 is configured to induce the flow of compensation liquid from the reservoir 30 through the downcomer shaft 350 at least substantially based on a difference between a density of compensation liquid at the downcomer depth Za and a density of compensation liquid at the downcomer inlet 352. Accordingly, theillustrated example may be characterized as a ‘passive’ and / or ‘density driven’ downcomer. Alternatively, one or more pumps (e.g. as shown schematically in one optional location using dashed lines as pump 356 in Figure 9 - but can be located in any suitable location relative to the downcomer shaft 350) may be used to selectively direct a flow of water through downcomer shaft 350. Providing a pump may have one or more advantages. For example, it may allow greater control of the water flow rate through the downcomer shaft 350.

[0094] Simulations of system 100 were conducted to explore the effect of different depths Za and flowrates of dilution water through downcomer 350 on the champagne effect in a compensation column 300.

[0095] Figure 10 is a plot illustrating density mitigation with a downcomer outlet 354 positioned at different depths. It can be seen that the addition of a downcomer significantly limits the density swing in the column, and thus the cavern pressure swing. For example, the density change is reduced by at least about 1 / 3, depending on the depth of dilution water injection. It can also be seen that dilution water injection at lower depths results in a smaller density difference developing within the column, due to the champagne effect being concentrated at the top of the column.

[0096] Figure 11 is a plot illustrating velocity mitigation with a downcomer outlet 354 positioned at different depths. Figure 12 is an enlarged view of a portion of Figure 11. Figures 11 and 12 illustrate that it is possible to eliminate a large negative spike and to dampen the post-charge oscillations much more quickly through use of a downcomer.

[0097] Figure 13 is a plot illustrating void fraction mitigation with a downcomer outlet 354 positioned at different depths. This plot illustrates a significant reduction in void fraction, thus demonstrating control of the flow regime via the presence of a downcomer shaft 350.

[0098] The plots of Figures 10 to 13 reflect the effect of a relatively large downcomer shaft 350 (~1 m in diameter). However, it is possible to effect a similar change in behaviour with a relatively narrower downcomer shaft 350.

[0099] Figure 14 is a plot illustrating the change in downcomer efficacy for downcomer shafts of various diameters. This plot illustrates that narrower pipes are less effective, however these plots were based on the use of a ‘passive’ downcomer. If the flow of water through downcomer shaft 350 is driven by a pump, it is expected that the flow rate through the downcomer can be increased, which is expected to increase the efficacy of a downcomer at a given diameter.

[0100] The simulation / modelling undertaken to produce the plots of Figures 10 to 14 was based on a number of what are thought to be conservative assumptions. For example, the water entering the compensation column 300 from the accumulator / cavem was assumed to be fully saturated with air. CFD simulations have shown that full saturation of the cavern water is at possible in timescales that approximately match the duration of a charge / discharge cycle, but the simulations did not assure full saturation. Also, the operation of system 100 may not always include full-duration cycles.

[0101] As another example, a pressure differential was assumed for bubble nucleation. Experimentation has shown this value to be non-zero. Nevertheless, simulation results were stress-tested under an assumption of zero differential pressure (DP) nucleation.

[0102] As yet another example, conservative values were used for the mass transfer coefficient. A study of existing literature indicates fairly tight agreement on what this value is, both for many-bubble turbulent regimes and for single-bubble quiescent regimes, with the former being significantly less than the latter. The simulation / modelling examined the champagne effect using mass transfer coefficients for either situation, despite the lower value being the one that likely applies.

[0103] As further examples, many experimental correlations exist for predicting flow regime (bubble vs. chum vs. slug, etc.), but the authors are not aware of any that have been done at comparable scales to a CAES project. As a result, when comparing results to these flow regime maps, the most conservative assumptions for predicting what flow regime will result were used. For example, if different flow regime maps predict bubble vs. chum flow, chum flow was assumed.Champagne Effect Mitigation: Accumulator Sump

[0104] As disclosed herein, another approach for mitigating the champagne effect is via an accumulator sump that provides an additional buffer volume of compensation liquid and pressure differential that can prevent a loss of water seal after charging due to the ongoing momentum of the champagne effect. As used herein, the term sump refers to a void volume below the main cavem / accumulator floor in which the lower end of the compensation shaft is submerged. This sump volume acts as a buffer for the air / water interface to ensure that overcharging does not occur.

[0105] The use of a U-bend or sump has been well documented as a design measure for preventing a loss of water seal and cavern blowout when charging a hydrostatically compensated CAES system.

[0106] Simulations (including CFD) suggest that a ‘swimming pool’ sump design is effective at mitigating the champagne effect and is in some ways preferred over a deeper U-bend sump design. At a high-level, there are two ways that a sump can reduce the chance of a cavern blowout: 1) the increased depth of the sump requires an increased drive pressure to push the air-water interface below the bottom of the compensation shaft; and 2) the increased water volume in the sump provides a ‘buffer’ of compensation water to provide the compensation shaft with additional compensation liquid to manage ongoing champagne effect momentum. A deeper U-bend design relies more on effect 1, while a shallower swimming pool design relies more on effect 2.

[0107] Figure 16 illustrates a schematic example of a hydrostatically compensated CAES system, referred to generally as 1000. System 1000 includes compression / expansion equipment 1010 to compress gas (e.g. ambient air) and inject compressed gas into an underground accumulator 1200 via conduit 1015. Accumulator 1200 has an associated accumulator volume. In the illustrated example, the accumulator 1200 is a cavern. The depth at which the accumulator 1200 is positioned in the ground is preferably established according to gas pressures at which the compression / expansion equipment to be used is efficiently operated. In the illustrated example, the accumulator 1200 is at a depth of Zcomp.

[0108] The gas that is compressed and stored in the accumulator 1200 may be any suitable gas, including, but not limited to, air, nitrogen, noble gases, or combinations thereof. Using air may be preferable as a desired quantity of air may be drawn into the compression / expansion equipment 1010 from the surrounding, ambient environment. Also, air released from within the accumulator 1200 (e.g. via compression / expansion equipment 1010) can be vented to the ambient environment without requiring further treatment.

[0109] System 1100 also includes a water compensation column 1300 (having a lower end 1302 and an upper end 1304) that is in fluid communication with the interior of accumulator 1200. In use, the hydrostatic pressure due to the weight of the water in the compensation column 1300 is used to balance the pressure of the compressed air within the accumulator 1200. Compensation water can flow into or out of the accumulator 1200 as the system is charged (e.g. as additional compressed gas is added to the accumulator via conduit 1015) anddischarged (e.g. as compressed gas is removed from the accumulator via conduit 1015), which assists in maintaining the interior of the accumulator at a desired or target system pressure during the charging and discharging processes, even as the quantity of air in the accumulator changes. In the illustrated example, the compensation column 1300 is also in fluid communication with a source / sink reservoir 1030 that contains additional compensation water.

[0110] System 1000 is preferably configured so that a quantity of compensation liquid within the accumulator 1200 isolates the compressed gas in the accumulator from the compensation liquid shaft 1300, and functions as a liquid / water seal. Maintaining a sufficient quantity of water within the accumulator can prevent compressed gas from escaping into the compensation column 1300 (rather than being extracted via the conduit 1015 and directed through compression / expansion equipment 1010), as such a gas escape represents a loss of stored energy that cannot be recovered.

[0111] In the illustrated example, the compensation shaft 1300 penetrates through the cavern as a hanging string and terminates in a sump 1220 in the cavern floor. The sump 1220 defines a respective sump volume (which is based on the sump dimensions described herein). A lower portion 1310, that includes the lower end 1302, of compensation shaft 1300 extends below the cavem / accumulator floor and into the sump 1220 by a submergence depth Z submergence- Optionally, the lower end 1302 of the compensation shaft 1300 may be supported from below and / or above, but preferably any supporting structure(s) should be designed to limit or preferably minimize ay impairment of fluid flow into and out of the compensation shaft 1300.

[0112] The basic reason for and function of the sump 1220 is to maintain a water seal at the lower end of the compensation column within the cavem / accumulator and prevent cavern air from entering the compensation shaft / compensation column. Accordingly, the sump must be appropriately located and sized for this purpose. Deriving this sizing requires consideration of at least two scenarios.

[0113] First, when the cavem / accumulator reaches its minimum water level (e.g., as determined by downhole manometers of other sensors) and the flow of compressed air into the accumulator stops, there will be some dynamics which play out, driven by the momentum in the compensation water as well as the sudden lack of drive pressure and resulting changes in dynamic friction. This results in a damped oscillation of the water-air interface within the accumulator. The depth of such oscillations depend on the cross-sectional area of the sump, and should be less than the depth of the sump to maintain the cavern seal. The accumulator willalso lose some pressure relative to the condition immediately before the charging stops, due to the loss of friction in the column. This will cause air in the accumulator to expand slightly. For example, if a charge (i.e., a flow of compressed air) was stopped when the compensation liquid level was aligned with the top of the sump, compressed air may enter the upper end of the sump as the compressed air expands slightly.

[0114] Second, at the end of a charge cycle, it is expected that there will be a fully developed champagne effect in the column. Depending on other mitigation measures, the champagne effect will reach its peak after the charge is stopped. The champagne effect results in, among other things, a drop in cavern water level as the column density falls to a minimum, followed by a rebound in cavern water level as bubbles rise out of the compensation shaft and the compensation liquid in the compensation column returns to full density.

[0115] Simulations (including CFD) were conducted to generate a sizing curve to address the trade-off between sump volume and sump depth, in consideration of the above dynamics. Figure 17 is a plot that includes a comparison of modelled cavem / sump water levels for i) a sump (“old geometry”) having a sump length LSUmp of 100 m, a sump with of 5 m, a sump depth Zsump of 10 m, and a sump grade 0SumPof 10%; and ii) a sump (“new geometry”) having a sump length Lsump of 100 m, a sump with of 7 m, a sump depth ZSUmp of 12 m, and a sump grade 0SumPof 12%.

[0116] Figure 18 is a representative plot illustrating sump sizing, showing available tradeoffs between minimum sump depth ZSUmp and sump cross sectional area (e.g. as defined by the sump length LSUmp and the sump width Wsump in the lateral direction as illustrated in Figure 16). This plot includes results for different sump geometries and for different flow rates of compressed air into the accumulator / cavem during a system charge cycle. The dashed lines represent best fit curves for the different modelled flow rates.

[0117] While consideration of the charge-stop dynamics may be useful to set a target depth and / or target volume for a sump 1220, when determining the shape of sump 1220 the constructability and / or stability of the sump should be considered. For example, a sump 1220 may be shaped as a long, low excavation of an entire cavern gallery, with slopes suitable for machine access. For example, with reference to Figure 16, the sump grade 0SUmp may be about 10% to 15% from horizontal e.g., to allow for accessibility by earth moving and other machinery used during cavern construction. As another example, the sump length Lsump may be within 25%, within 10%, or substantially the same as the length of the cavern LaccUmuiator(e.g. -180 m). In some embodiments, the sump length LSUmp may be less than the length of the cavern LaccUmuiator, but can be at least about 100 m.

[0118] In the example illustrated in Figure 16, only one end of the sump is depicted as having a sump grade Osump, which may configured based on the requirements of a given system and optionally may be between about 10% and about 15%, and may be approximately 12% in some embodiments. It will be appreciated that both ends of sump 1220 could be graded.

[0119] As another example, sump 1220 may be relatively shallow in absolute terms. For example, the sump 1220 may have a depth ZSUmp of less than 20 m. Additionally, or alternatively, sump 1220 may be relatively shallow in relative terms. For example, the sump 1220 may have a depth ZSUmp that is less than a height HaccUmuiator of cavem / accumulator 1200, where Haccumuiator is measured from an accumulator ceiling 1210 to an accumulator floor 1205. Similarly, the sump 1220 may have a sump length LSUmp that is less than an accumulator length Laccumuiator (which may be about 180 m in some embodiments), and a sump width WSUmp that is optionally about equal to or less than an accumulator width WaccUmuiator (both widths measured in a direction that is ‘into the page’ in the schematic illustration of Figure 16).

[0120] A relatively shallow sump - that is nevertheless sized to accommodate an expected maximum volume of water that may leave the cavem / accumulator after the end of a charge cycle due to end of charge dynamics and champagne effect momentum - may have one or more advantages. For example, a sump with a lower depth of excavation may result in easier and / or safer constructability, and / or reduced construction costs. For example, the size and / or type of construction machinery needed to construct a relatively shallow sump may be different than the size and / or type of construction machinery needed to construct a deeper (e.g. 30 m or more) U-bend sump.

[0121] As another example, sump 1220 may have a relatively small volume compared to the volume of the cavem / accumulator 1200. For example, sump 1220 may have a sump volume that is between about 0.5% and about 5% of the accumulator volume of cavem / accumulator 1200.

[0122] A relatively small sump - that is nevertheless sized to accommodate an expected maximum volume of water that may leave the cavem / accumulator after the end of a charge cycle due to end of charge dynamics and champagne effect momentum - may have one or more advantages. For example, a sump with a lower overall volume may result in easier and / or safer constructability, and / or reduced construction costs.

[0123] Simulations (including CFD) were conducted to assess the effect of a relatively small, narrow sump. As an example, a cylindrical sump, concentric to the column string, with a diameter of 6 m was considered. Simulations concluded that such a sump caused much more rapid oscillations around charge shut down, but otherwise had minimal effect. Preventing cavern blow-out with such a sump would require significant sump depth (e.g. about 12 m or more).

[0124] Subsequent simulations were conducted to understand the effect of sumps of many, generally much larger sizes. In general, such larger sumps were found to be more effective in damping oscillations, and were also able to be effective at more reasonable sump depths.

[0125] Figure 19 is a representative plot illustrating the depth to which the air-water interface drops in a sump of various sizes, at two different flow rates of compressed air into the accumulator / cavem during a system charge cycle. A first modelled sump was 180 m long, 9 m wide, with a 10% sump grade. A second modelled sump was 100 m long, 5 m wide, with a 10% sump grade. A third modelled sump was 80 m long, 5 m wide, with a 12.5% sump grade. The largest cavern water level drops (at each flow rate) correspond to the narrower, shorter sump, and the smallest cavern water level drops (at each flow rate) correspond to the wider, longer sump.

[0126] As illustrated, similar results independent of the compressed air flow rates, with different minimum fill levels but similar times until the minimum fill level was reached. Also, there was a difference in the final height in the cavern at the end of shut off behaviour, with full flow rate yielding -0.01 m, and a half flow rate yielding -0.06 m.

[0127] Overall, it can be observed from Figure 19 that that constructing a sump with a relatively large cross-sectional area (and e.g. with a sump depth ZSUmp as disclosed herein) results in relatively small incursions of the air-water interface into such a sump.

[0128] For simplicity and clarity of illustration, reference numerals may be repeated among the figures to indicate corresponding or analogous elements. In addition, numerous specific details are set forth to provide a thorough understanding of the subject matter described herein. However, it will be understood by those of ordinary skill in the art that the subject matter described herein may be practiced without these specific details. In other instances, well-known methods, procedures, and components have not been described in detail so as not to obscure the subject matter described herein.

[0129] It will be appreciated that the particular example embodiments shown in the figures and described above are for illustrative purposes only and many other variations can be used according to the example embodiments described herein. For example, various features described herein from different example embodiments can be combined together, although such combinations have not been explicitly described.

[0130] Although the above has been described with reference to specific example embodiments, various modifications thereof will be apparent to those skilled in the art as outlined in the appended claims.

Claims

We claim:

1. A hydrostatically compensated compressed gas energy storage system comprising:an accumulator positioned below ground at an accumulator depth, the accumulator being configured to selectively receive compressed gas for storage and to selectively release stored compressed gas for power generation;a compensation shaft having a lower end in fluid communication with the accumulator, an upper end, and an upper portion in fluid communication with a reservoir of compensation liquid, the reservoir being positioned at a reservoir elevation; anda downcomer shaft that extends between a downcomer inlet positioned in the reservoir and a downcomer outlet in fluid communication with the compensation shaft at a downcomer depth;wherein the downcomer shaft is configured to direct a flow of compensation liquid having a relatively low gas saturation from the reservoir to the compensation shaft to mix with compensation liquid at the downcomer depth having a relatively high gas saturation, thereby diluting the compensation liquid and lowering the gas saturation of compensation liquid at the downcomer depth.

2. The hydrostatically compensated compressed gas energy storage system of claim 1, wherein the accumulator depth is between about 400 m and 900 m, and the downcomer depth is between about 50 m and 200 m.

3. The hydrostatically compensated compressed gas energy storage system of claim 2, wherein the accumulator depth is about 600 m and the downcomer depth is about 85 m.

4. The hydrostatically compensated compressed gas energy storage system of any one of claims 1 to 3, wherein the downcomer depth is determined based on an expected gas saturation of compensation liquid exiting the accumulator, an associated saturation pressure, and a depth at which compensation liquid in the compensation shaft reaches the saturation pressure.

5. The hydrostatically compensated compressed gas energy storage system of any one of claims 1 to 4, wherein the downcomer shaft is configured to induce the flow of compensation liquid from the reservoir through the downcomer shaft based on a difference between adensity of compensation liquid at the downcomer depth and a density of compensation liquid at the downcomer inlet.

6. The hydrostatically compensated compressed gas energy storage system of any one of claims 1 to 4, further comprising a pump configured to selectively direct the flow of compensation liquid from the reservoir through the downcomer shaft.

7. The hydrostatically compensated compressed gas energy storage system of any one of claims 1 to 6, wherein the compensation liquid is water and the compressed gas is compressed ambient air.

8. A method of mitigating the champagne effect in a hydrostatically compensated compressed gas energy storage system, the method comprising:directing a flow of compensation liquid having a relatively low gas saturation from a reservoir to a hydrostatic compensation shaft in fluid communication with an accumulator positioned below ground at an accumulator depth, wherein the flow of compensation liquid is introduced to the hydrostatic compensation shaft at a dilution depth that is less than half of the accumulator depth.

9. The method of claim 8, wherein the dilution depth is less than a third of the accumulator depth.

10. The method of claim 8, wherein the accumulator depth is between about 400 m and 900 m, and the dilution depth is between about 50 m and 200 m.

11. The method of claim 10, wherein the accumulator depth is about 600 m and the dilution depth is about 85 m.

12. The method of any one of claims 8 to 11, wherein the flow of compensation liquid is directed from the reservoir to the compensation shaft via a downcomer shaft that extends between a downcomer inlet positioned in the reservoir and a downcomer outlet in fluid communication with the compensation shaft at the dilution depth.

13. The method of claim 12, wherein directing the flow of compensation liquid comprises activating a pump configured to advance compensation liquid through the downcomer shaft.

14. The method of any one of claims 8 to 13, wherein the directing is performed during or immediately following injection of compressed gas into the accumulator.

15. The method of claim 14, wherein the compensation liquid is water and the compressed gas is ambient air.

16. A hydrostatically compensated compressed gas energy storage system comprising:an accumulator positioned below ground at an accumulator depth, the accumulator being configured to selectively receive compressed gas for storage and to selectively release stored compressed gas for power generation,the accumulator having an accumulator length, an accumulator width, an accumulator height measured from an accumulator ceiling to an accumulator floor, and an accumulator volume,the accumulator having a sump extending below the accumulator floor, the sump having a sump length, a sump width, a sump depth measured from the accumulator floor, and a sump volume, wherein at least one end of the sump has a sump grade; anda hydrostatic compensation shaft having a lower end in fluid communication with the sump,wherein the sump depth is less than 20 m.

17. The system of claim 16, wherein the sump length is at least 100 m, the sump width is at least 7 m, the sump depth is about 12 m, and the sump grade is about 12%.

18. The system of claim 16, wherein the sump grade is between about 10% and about 15%.

19. The system of any one of claims 16 to 18, wherein the sump volume is between about 0.5% and about 5% of the accumulator volume.

20. The system of any one of claims 16 to 19, wherein the sump volume is sufficient to accommodate an expected maximum volume of water that may leave the accumulator after the end of a charge cycle due to end of charge dynamics and champagne effect momentum.

Images