[0014]Storing energy in the form of compressed gas has a long history and components tend to be well tested, reliable, and have long lifetimes. The general principles for compressed gas energy storage are the storage of original generated energy in terms of pressure 
potential energy by compression of gas and subsequent recovery of energy in useful form through expansion of the gas. Advantages to compressed gas energy storage include low specific-energy costs, long lifetime, low maintenance, reasonable 
energy density, and good reliability.
[0015]If the 
gas expansion occurs slowly relative to the rate at which heat flows into the gas, then the gas remains at a relatively constant temperature as it expands (isothermal 
gas expansion). Gas stored at ambient temperature and expanded isothermally recovers approximately three times the energy of ambient-temperature gas expanded adiabatically. Therefore, there is a significant energy 
advantage to expanding gas isothermally.
[0017]The 
power output of the 
system described in the '057 application is governed by how fast the gas expands isothermally. Therefore, the ability to expand / compress the gas isothermally at a faster rate will result in a greater 
power output of the system. By adding a heat-transfer circuit to the system described in the '057 application, the 
power density of said system can be increased substantially. Novel heat-transfer circuits are shown and described in U.S. 
patent application Ser. No. 12 / 639,703 (the '703 application), entitled SYSTEMS AND METHODS FOR 
ENERGY STORAGE AND 
RECOVERY USING RAPID ISOTHERMAL 
GAS EXPANSION AND COMPRESSION, the disclosure of which is hereby incorporated by reference herein in its entirety. By incorporating a 
variable displacement hydraulic-pneumatic pump / motor, the efficiency of the compressed gas energy storage and recovery system may be further improved, as described in U.S. 
patent application Ser. No. 12 / 723,084 (the '084 application), entitled SYSTEMS AND METHODS FOR IMPROVING 
DRIVETRAIN EFFICIENCY FOR COMPRESSED GAS 
ENERGY STORAGE USING STAGED HYDRAULIC CONVERSION, the disclosure of which is hereby incorporated by reference herein in its entirety.
[0018]The novel 
compressed air energy storage and recovery systems using staged hydraulic conversion described in the '057 application include a 
hydraulic pump / motor which is driven by or used to pump 
hydraulic fluid over a range of pressures, i.e., from a mid-pressure to a 
high pressure (e.g., 300 psi to 3000 psi). For a typical such expansion or compression over a 
pressure range, using a fixed displacement 
hydraulic motor, as pressure drops, torque and power drop. In many instances, it would be advantageous to minimize these changes in 
power level over the 
pressure range. For example, efficiency for an 
electric motor / generator can vary substantially based on torque and RPM; when the 
hydraulic pump / motor in the staged hydraulic conversion described in the '057 application is attached to an 
electric motor / generator, it would be advantageous to operate at a 
narrow range or fixed value for RPM (e.g., ˜1800 RPM) and torque to operate at peak efficiency, increasing electric-
motor efficiency and thus system efficiency. Likewise, operating at a fixed RPM and power (and thus 
constant voltage, frequency, and current for an 
electric generator) during system 
discharge could allow an 
electric generator to be synchronized with the grid and potentially eliminate additional power 
conditioning equipment that would be required for a variable frequency, variable 
voltage, and / or variable 
power output. One method for maintaining a constant or nearly 
constant power output over the range of pressures is to use a 
variable displacement hydraulic pump / motor in lieu of a constant displacement pump / motor. By using a 
variable displacement hydraulic pump / motor, the displacement per revolution can be controlled in such a way as to maintain a nearly 
constant torque and proportionally increasing flow rate such that the RPM and power output are kept nearly constant. For the novel 
compressed air energy storage and recovery system using staged hydraulic conversion described in the '057 application, this constant RPM and power allows for a reduction in electric system costs by potentially eliminating power 
conditioning equipment necessary for a variable frequency, 
voltage, or power output, while at the same time improving overall system efficiency by operating at the peak efficiency region of the 
electric generator; likewise, increasing flow rate maintains a nearly 
constant power throughout a decreasing 
pressure range, also adding value to the energy storage and recovery system.
[0044]The invention is also directed toward efficiently utilizing high-pressure compressed air in combination with hydraulic-pneumatic cylinders and a 
hydraulic motor to provide the primary means of propulsion for a vehicle, such as an automobile, 
truck, boat, or 
train. Specifically, high-pressure compressed air, stored in pressure vessels, is expanded in batches in hydraulic-pneumatic cylinders, driving high-pressure 
hydraulic fluid through a hydraulic motor to provide propulsive force. The compressed air undergoes quasi-isothermal controlled expansion in the hydraulic-pneumatic cylinders, which are integrated with heat exchangers. The hydraulic-pneumatic cylinders may include intensifiers to maintain a high 
hydraulic pressure even as the air pressure decreases within each batch expansion. Additional hydraulic boosters may be used to intensify and / or add pressures from multiple expanding cylinders. During braking and coasting, the hydraulic motor may be run in reverse, recompressing the air in the pneumatic-hydraulic cylinders and storing energy from the motion of the vehicle as compressed-air 
potential energy. In an alternative embodiment of this application, when the compressed air reaches a lower pressure (e.g., 120 psi), it is expanded in an air-
turbine-based motor attached to the same shaft as the hydraulic motor, thus greatly increasing the 
power density of the hydraulic-pneumatic conversion system. In an additional embodiment, the lower-pressure compressed air is used in combination with 
compressed natural gas to drive a 
turbine-based motor attached to the same shaft as the hydraulic motor, further increasing 
power density and 
energy density.
[0047]Near-isothermal expansion permits increased round-trip thermodynamic efficiency in the compressed-air energy storage component, e.g., ˜95% versus <40% for an adiabatic system. For the same reason, the 
energy density of a near-isothermal system is more than double the energy density of an adiabatic compressed-air storage system. Moreover, with near-isothermal compression and expansion, there is a 
nonlinear gain in energy density and power density with increasing maximum storage pressure—e.g., storage at 10,000 psi more than triples (increases ˜3.7 times) energy density over storage at 3,333 psi. In addition, increasing 
maximum pressure reduces the amount of energy in each expansion at low pressures, thus reducing any losses that would be associated with the inclusion of a low-pressure air 
turbine motor to increase power density, as described in FIG. 33 herein.