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Hydrogen refueling station compression and storage optimization with tube-trailer deliveries
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Hydrogen refueling station compression and storage optimization with tube-trailer deliveries Krishna Reddi a,*, Amgad Elgowainy a, Erika Sutherland b a
Argonne National Laboratory, 9700 South Cass Avenue, Argonne IL 60439, United States U.S. Department of Energy, Fuel Cell Technologies Office, 1000 Independence Avenue SW, Washington, DC 20585, United States
b
article info
abstract
Article history:
Hydrogen refueling stations require high capital investment, with compression and storage
Received 8 May 2014
comprising more than half of the installed cost of refueling equipment. Refueling station
Received in revised form
configurations and operation strategies can reduce capital investment while improving
18 September 2014
equipment utilization. Argonne National Laboratory developed a refueling model to eval-
Accepted 19 September 2014
uate the impact of various refueling compression and storage configurations and tube
Available online 11 October 2014
trailer operating strategies on the cost of hydrogen refueling. The modeling results revealed that a number of strategies can be employed to reduce fueling costs. Proper sizing
Keywords:
of the high-pressure buffer storage reduces the compression requirement considerably,
Hydrogen refueling station
thus reducing refueling costs. Employing a tube trailer to initially fill the vehicle's tank also
Tube-trailer
reduces the compression and storage requirements, further reducing refueling costs.
Simulation model
Reducing the cut-off pressure of the tube trailer for initial vehicle fills can also significantly
Compression
reduce the refueling costs. Finally, increasing the trailer's return pressure can cut refueling
Storage
costs, especially for delivery distances less than 100 km, and in early markets, when
Fuel cell electric vehicles
refueling stations will be grossly underutilized. Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Background In the United States, the transportation sector is the secondlargest consumer of energy, after the electric power sector, accounting for about 28% of the total energy expended [18]. The transportation sector is heavily dependent on petroleum, which accounts for 97% of its energy sources. Of this petroleum, 56% is imported to U.S. refineries [18]. This dependence on crude oil underscores three transportation sector needs
that must, ideally, be met by alternative energy sources [1]: energy security [2], environmental sustainability, and [3] economic vitality [14]. Federal and State governments in the United States have been addressing these needs by mandating higher fuel economy standards for automobiles and funding research on alternative fuels such as hydrogen, electricity, and biofuels [17]. The new corporate average fuel economy standards require U.S. manufactures of vehicles to (CAFE) improve the minimum fuel economy of their passenger vehicles from 36.7 miles per gallon (MPG) in 2017 to 54.5 MPG in 2025 [29]. Hydrogen fuel cell electric vehicles (FCEVs) with certification fuel economy of more than 80 miles per gallon of
* Corresponding author. Tel.: þ1 630 252 1479. E-mail address: [email protected] (K. Reddi). http://dx.doi.org/10.1016/j.ijhydene.2014.09.099 0360-3199/Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
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Fig. 1 e Schematic of hydrogen refueling station.
gasoline equivalent (MPGGE) can play an important role in achieving the 54.5 MPG fuel economy target in 2025. Further, state level initiatives such as the zero emissions vehicle (ZEV) mandate by State of California requires major automakers to ramp up their sales of ZEVs from 4.5% in 2018 to 22% by 2025 [4]. Other states that follow California emissions rules may choose to adopt the ZEV mandate as well. ZEVs are either hydrogen FCEVs or battery electric vehicles (BEVs). FCEVs have several advantages over BEVs, including longer driving range on a single tank fill, fast refueling, and better performance in cold weather. Hydrogen is a clean fuel with significant potential to reduce U.S. demand for petroleum fuels because it can be produced from a variety of domestically available non-fossil and renewable sources. Fuel cells efficiently convert hydrogen into electricity with a peak efficiency of about 60% [10]. The electricity produced is subsequently used to power electric motors for vehicle propulsion. This process is more efficient than thermal efficiency of heat engines and results in a fuel economy gain of 183% compared to gasoline internal combustion engine vehicles [25]. Hydrogen FCEVs are being developed by many automobile original equipment manufacturers (OEMs) for early market deployment in the 2015e2017 timeframe to meet California's ZEV mandate and to satisfy various FCEV deployment initiatives in Japan, Germany, and other European countries. Many governments have already completed projects to demonstrate and validate the technical feasibility of FCEVs [3,15,24]. The demand for hydrogen must be supported by provision of sufficient infrastructure. Construction of supporting infrastructure might not be profitable during the initial deployment of FCEVs because of the high capital investment required to build hydrogen refueling stations (HRS) and underutilization of the installed infrastructure in early FCEV markets. Thus, many governments have initiated public-private partnerships to demonstrate the economic viability of the hydrogen infrastructure needed for pre-commercial deployment of FCEVs. The H2 Mobility initiatives in Europe by Germany, the United Kingdom, and France; the H2 USA initiative co-launched by the United States Department of Energy (DOE); and the Japan Hydrogen & Fuel Cell (JHFC) (Phase 3) initiative are examples of international efforts that promote the coordinated deployment of HRS and FCEVs [13,21,34]. Germany and Japan plan to deploy 50 and 100 HRS by 2015, while California plans to deploy a network of 68 HRS by 2015 to support OEMs' plans to roll out hydrogen FCEVs [3,5,33]. Almost all OEMs agree that gaseous hydrogen stored onboard at a pressure of 70 MPa is the appropriate option to enable an FCEV driving range of over 300 miles (480 km) on a
single fill [17]. Fast refueling of 70-MPa tanks requires significant refrigeration, compression capacity, and high-pressure storage equipment at the refueling sites. The Society of Automotive Engineers (SAE) developed the SAE J2601 refueling protocol that defines safety limits and performance requirements for gaseous hydrogen refueling; the protocol covers a wide range of refueling pressures as well as ambient and precooling temperatures [31]. The fact that refueling costs are dominated by compression and storage requirements [16] motivated the current investigation of optimum hydrogen refueling station compression and storage configurations.
Objective The cost for HRS accounts for half or more of the total cost of hydrogen delivery [27]. Fig. 1 shows the main components of an HRS: a hydrogen storage system that stores hydrogen to meet daily demand, a high-pressure buffer storage system (also known as cascade storage) to deliver gaseous hydrogen to the vehicle tank, a compressor that pressurizes hydrogen from the storage source pressure to the buffer storage pressure (typically higher than vehicle's maximum service pressure), a refrigeration system that pre-cools the hydrogen gas being dispensed into the vehicle's tank, a dispenser that manages the flow of hydrogen to the vehicle's tank, as well as various controls and safety equipment. Fig. 2 provides estimates of HRS total installed cost, showing the contribution of each component to the total capital investment for various station capacities. The cost estimates in the figure are based on vendor quotes for large purchased quantities (~100 units) and incorporate a backup
Fig. 2 e Estimated hydrogen refueling station costs for various capacities [16].
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compressor to ensure continuity of refueling operations. The figure shows that the compressor and cascade storage together account for approximately half of the total capital investment for all station capacities. So this study focuses on configurations that reduce the station cost by optimizing the sizing of these two components. Typically the sizes of these two components are interdependent. Extensive high pressure buffer storage implies that sequential vehicle fill-up demand can be readily met without extensive use of the compressor system, thus rendering the use of a small sized compressor feasible. In such case, the compressor is engaged, mainly to compress hydrogen to 950 bar at the high pressure buffer storage, for a longer period of time. Even though the amount of hydrogen that must be compressed is constant, the expanded period of time over which compression can occur allows the use of a smaller compressor. Conversely, a larger compressor with a high flow rate will require a small highpressure buffer storage to satisfy the same refueling demand. The optimum configuration is decided primarily by the following factors [1]: the total daily station demand [2]; the hourly variation of demand in a given day, which determines the number of back-to-back vehicle fills during peak hour [3]; the installed cost [4]; the operation and maintenance cost, and [5] the lifetime of these two components. Given the interdependency between the high-pressure buffer storage and the compressor capacities, the best economic option would achieve a balance between the two components. In this paper, we describe a model developed by Argonne that simulates the operation of a refueling station. The model is used to optimize the combination of compressor and buffer storage with the objective of minimizing refueling cost [in $/kgH2] for a given set of parameters such as: station daily demand, hourly demand profile, vehicle tank configuration and capacity, vehicle tank thermal and mechanical characteristics, hydrogen dispensing temperature and fill rate, compressor cost, cascade vessel cost, and hydrogen source capacity and pressure. Section project description summarizes the present state of research and gaps that will be addressed by this study. Sections simulation model and simulation model verification and validation provide a description of the simulation model and the verification and validation of the simulations conducted. Results and conclusions are presented in Sections simulation results and conclusions.
Project description With support from DOE's Fuel Cell Technologies Office (under the Energy Efficiency and Renewable Energy Office), Argonne National Laboratory, along with the National Renewable Energy Laboratory and Pacific Northwest National Laboratory, developed the Hydrogen Delivery Scenario Analysis Model (HDSAM). The model uses an engineering and economics approach to estimate the costs of various hydrogen delivery and refueling options [1]. HDSAM is used by DOE to identify the components with the greatest impact on hydrogen delivery cost and to guide research directed at reducing delivery costs. Other stakeholders use HDSAM to evaluate the impact of various delivery and refueling options on the total dispensed cost of hydrogen under various market conditions.
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The refueling station module of HDSAM incorporates cost and sizing details for all refueling components, setback distance and land area requirements, maintenance and operation costs, as well as other costs factors (e.g., site preparation, engineering and design, permitting, and installation). However, a few refueling station configuration details that are critical to identifying the most economical combination of components are fixed in HDSAM. Gaps in the present model [1] are listed below; these have to be addressed to make the model more rigorous and robust and allow us to determine the optimal configurations for hydrogen refueling. The size of the cascade vessels is fixed, and the number of pressure levels is fixed at three. This configuration is not the most economical option to meet all station demands. The optimum pressure for switching between the cascade vessel banks during vehicle fill is not considered; the switch point plays an important role in controlling the vehicle fill duration, which is critical for customer satisfaction [6,19]. The pressure drop in the lines and fittings between the buffer storage vessels and the dispensers is not considered. The mass, temperature, and pressure inside the vehicle's tank during the filling operation are not monitored during simulations. Keeping track of these three parameters is important, as described in the SAE J2601 refueling protocol [31]. The effect of the overshooting pressure in the vehicle's tank at the end of the fill is not considered; this is an important factor for the proper specification of the compressor's discharge pressure and the maximum working pressure of the buffer storage vessels. To overcome these gaps and ensure that refueling demand and the requirements of the SAE J2601 fueling protocol are satisfied, we developed a comprehensive model that solves the physical laws of mass, momentum, and energy conservation, as well as the hydrogen equation of state and other thermodynamics properties relations subject to specified initial and boundary conditions. The physical model, known as the Hydrogen Station Cost Optimization & Performance Evaluation (H2SCOPE), tracks mass, pressure, and temperature over time throughout the refueling system d from the hydrogen source to the vehicle's tank. The employed equation of state for hydrogen is a modified ideal gas equation with a compressibility factor to simulate the behavior of real gas. The compressibility factor and all other thermodynamic variables are defined by a set of empirical constants, the values of which are based on the experimental data and provided by Ref. [35]. In building the H2SCOPE model, we benefited from a considerable body of research that examined the impacts of various refueling parameters on pressure and temperature changes within vehicle's tank during fills [7,11,12,20,23,26,28,35,36,]. The heat transfer through the vehicle tank wall during fills is ignored in some of the previous work [19,22,35] but when considered, it is assumed to be steady [35] or transient [11,23]. Most of the previous research is focused on the vehicle's tank, but in a few cases, the source d comprising the buffer storage system [6,30,36] and the pipeline at constant pressure
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[35] is also examined. However, in most cases, the drop in temperature [6,36] in the buffer storage vessels caused by withdrawal of hydrogen during the refueling process is ignored. Inclusion of the temperature drop in the buffer storage vessels is important, especially in the case of back-toback fills. Rothuizen et al. [30] showed that the pressure drop, and hence the temperature drop, in the hydrogen storage system (buffer storage vessels) has a significant effect on the mass flow rate and cooling demand at the dispenser nozzle. Rothuizen et al. [30] also showed that having multiple buffer storage tanks (e.g., three) reduces the cooling demand and compression energy compared with having a single, large, high-pressure storage tank. To our knowledge, a complete study of all of the factors impacting the cost of hydrogen refueling d station components, from the hydrogen supply to the vehicle's tank, and operating parameters such as the daily demand, the hourly demand profile, and the SAE J2601 refueling protocol [31] dhas not been conducted. For this study, we developed a model to simulate the operation of refueling stations to identify the optimum combination of compression and buffer storage capacities to meet a specific refueling demand and provide the lowest refueling cost.
Simulation model The major components of a gaseous hydrogen (H2) refueling station include the following: A tube trailer that supplies hydrogen at a pre-determined maximum and minimum pressure; A compressor that draws hydrogen from the tube trailer tubes and fills a buffer storage system; A buffer storage system that consists of multiple (cascade) vessels, each of which is maintained within a specific pressure range; A dispenser that regulates the flow of H2 from the buffer storage system to the onboard vehicle tank; and A refrigeration unit that cools the H2 to 233 K (40 C) before dispensing. Typically, when a vehicle comes in for refueling, the dispenser connects to the low-pressure vessel in the buffer storage system, regulating the flow to keep it between the maximum allowed flow of 3.33 kg/min and the switch point between the vessels for a cascade refueling (which varies with operating strategy, but is typically 0.1 kg/min). Once the flow between the connected bank of vessels and vehicle tank drops below the cascade switch point (i.e., as the pressures equalize), the dispenser connects to the next cascade bank, where H2 is stored at a higher pressure. This routine of sequentially connecting each cascade bank with higherpressure H2 to the vehicle tank is continued until the vehicle tank is filled with 5 kg of hydrogen or the flow from the highest-pressure bank is below a predetermined minimum value. Typically, the buffer storage vessels are maintained within a definite range to ensure that the vehicle tank receives 5 kg of H2 after connecting to the high-pressure bank. The compressor draws hydrogen from the tube
trailer and keeps filling the buffer storage vessels to the rated operating pressure following a predetermined priority order.
Model assumptions In this study, the complexity of modeling refueling station operations is limited by the following assumptions. The flow of hydrogen in the lines between the tube trailer, buffer storage, and the dispenser is adiabatic, quasi-steady, and compressible [32]. The fanning friction factor [32] is constant along the piping that connects the station components. Frictional loss within the piping causes a drop in pressure from the exit of the buffer storage vessels to the dispenser. For subsonic velocities of hydrogen flow (Mach number < 0.1), the dispenser outlet pressure is assumed to be equal to the back pressure from the vehicle tank. The kinetic energy is small compared to the enthalpy of the flow but is not insignificant. Thus, we account for the kinetic energy of hydrogen flow into the vehicle's tank when calculating the buildup of internal energy of hydrogen inside the tank. The hydrogen flow is regulated by controlling the upstream pressure at the dispenser inlet to restrict the flow rate and keep it below the SAE J2601 maximum allowable flow rate (60 g/s) [31]. The heat transfer through the walls of the vehicle's tank is transient and employs an internal heat transfer coefficient of 325 W/m2-K. We assumed 5 W/m2-K for the external heat transfer coefficient. The external heat transfer coefficient is less likely to impact the simulation results, especially for type IV tanks with short fill times. The refrigeration system is placed between the buffer storage vessels and the dispenser and cools the hydrogen to 40 C (233 K). We did not model the cooling system and assumed that a cooling system which can address the above cooling demand is installed. Current practices oversize the cooling equipment and/or heat exchangers to ensure that 40 C can be achieved within 30 s as called for by the SAE J2601 protocol. The compressor has a constant throughput and always replenishes the buffer storage banks in the order of decreasing cascade operating pressures (i.e., starts with the high-pressure bank and ends with low-pressure bank). Any buffer storage bank can be either filled or emptied at any given time (i.e., both operations cannot be conducted on the same buffer storage bank simultaneously). Each 250 kg of daily hydrogen demand requires a dispenser with a single hose.
Component specifications The H2SCOPE model receives the specifications of the vehicle's tank and the components of the refueling station (i.e., physical dimensions, thermal characteristics, and operating pressures of each component) as inputs. While any sizes and operating pressures can be simulated for components such as the vehicle tank, buffer storage vessels, hydrogen source and
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compressors, the following specifications were used for the simulation results presented in this paper: A 5-kg capacity, 129-L, type IV vehicle tank with a maximum working pressure of 87.5 MPa at 358 K or 70 MPa at 298 K. Vehicles are assumed to begin the fill with a pressure of 2 MPa at 298 K, reflecting an initial state of charge of 0.2 kg; A buffer storage system with multiple type IV cascade vessels, each with 12-kg capacity and 255-L volume, with a service pressure of 95 MPa at 298 K; and For the hydrogen source, a tube trailer storage unit comprising four type IV tubes at a maximum working pressure of 35 MPa at 298 K and a minimum pressure of 1.5 MPa at 298 K. Each of the four tubes has a capacity of about 200 kg stored in 8500 L volume, for a total usable capacity of about 800 kg.
Operating strategy The H2SCOPE model has the flexibility to simulate a variety of operating strategies, which are differentiated by the number of cascade pressure levels in the buffer storage system and the manner in which the tube trailer tubes are used. The number of banks or cascade pressure levels within the buffer storage system can vary. In our study, three to nine pressure levels (cascade banks) within the buffer storage system were modeled and simulated; of these, three to five pressure levels were considered for further analysis on the basis of the initial cost tradeoffs. The order in which hydrogen is drawn from the cascade banks while refueling the vehicle's tank is fixed. The refueling of vehicles starts from the low-pressure bank and ends with the highpressure bank, while the replenishing of the buffer storage vessels, the compressor follows the reverse order (i.e., starts with high-pressure bank and ends with low-pressure bank). The tube trailers can serve different functions during the day-to-day operations of the refueling station; they can be used to supply hydrogen to the buffer storage vessels through the compressor. The high-pressure tubes (25 MPa or higher) on the tube trailer can also be used to initially charge the vehicle's tank, with the buffer storage system completing the fill. The cut-off pressure and return pressure define the particular use of tube trailers at the refueling stations. The cut-off pressure is the pressure below which the tube trailer is not used to fill the vehicle tank. The return pressure is the pressure at which the tube trailer is considered empty and returned to the supplier for recharging. Many other parameters have been kept constant for the simulations presented in this study. Parameters such as the pre-cooling temperature, the length of the piping between the buffer storage system and dispenser, thermal properties of the buffer storage vessels and vehicle tank materials, ambient temperature, vehicle tank initial pressure and temperature, etc., can be varied to simulate their impacts on the operation of any refueling station. The hourly demand profile used for
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the simulations is similar to the gasoline vehicles refueling profiles provided by Chevron [8]. Fig. 3 shows the hourly demand profile for a daily demand of 250 kg/day. The horizontal axis in Fig. 3 represents the hour of the day, while the left vertical axis represents the demand for hydrogen (in kg) per hour and the right vertical axis represents the number of vehicle fills per hour.
Simulation model verification and validation The simulation model was developed in three steps (Fig. 4) and was verified and validated after each step. STEP 1: Initially, we modeled a buffer storage system filling a vehicle tank through a dispenser to identify the configuration of buffer storage vessels that permits the highest number of back-to-back vehicle fills. The energy equation [35], continuity equation, flow equation [32], equation of state [35], and heat transfer equations [23] were integrated to estimate the temperature, pressure, and mass of hydrogen in the vehicle tank and buffer storage vessels throughout the refueling process. The conservation equations, equation of state, and thermodynamic relations used in this study are included in the Appendix. We employed an explicit numerical scheme that solves the transient heat transfer equations through the tank wall, subject to the inner and outer heat transfer boundary conditions described in the Appendix. The employed algorithm ensured the numerical stability of the solution by implementing a time-step with a Fourier number less than 0.5. The modeled filling process follows the SAE J2601 fueling protocol [31]. We modeled and simulated a variety of buffer storage system configurations and determined the number of back-to-back vehicle fills that could be achieved by each configuration. The configuration of the buffer storage system is characterized by the number of pressure levels (banks) and vessels at each pressure level. The top two buffer storage system configurations, which resulted in the maximum hydrogen use at the lowest cost, were selected for further analysis, along with the conventional threecascade-vessel storage configuration currently used in most refueling stations [1].
Fig. 3 e Hourly demand profile for a 250-kg/day-capacity refueling station [8].
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Fig. 4 e Schematic representation of the refueling station components. STEP 2: The model from step 1 was expanded to include a compressor, which is assumed to refill the idle buffer storage vessels with hydrogen. In this context, a buffer storage vessel is assumed to be idle when the vehicle tank is not connected to the buffer storage vessels through the dispenser during the refueling process or when the dispenser is not occupied. The compressor refills the high-pressure buffer storage bank, followed by the medium- and low-pressure banks. In this step, we did not include the source of the hydrogen supplying the compressor, and we modeled only its output state, as represented by the hourly throughput, temperature, and pressure of hydrogen delivered to the buffer storage vessels. The formula for compressor work is provided in the Appendix. Conner and Manousiouthakis [9] developed a theorem for optimizing the total annualized cost of a series of compressor sequences. The compressor's adiabatic efficiency was assumed at 65%. The contribution of the energy consumption of the compressor to the dispensed cost of hydrogen is small compared to the contribution of the capital cost of the compressor and other refueling equipment. STEP 3: Finally, we expanded the model to include the hydrogen source: a high-pressure tube trailer. The heat transfer from the tube-trailer tubes was assumed to be quasi-steady because it is emptied over a span of hours or days depending upon the station's daily demand. We modeled and simulated two operation strategies for the tube-trailers at the refueling station.
The model accuracy was verified by incrementally adding capabilities (Steps 1 through 3) and verifying the results with respect to mass and energy balance at the component and system levels, for consistency, after each of the three steps described above. We validated the model using published experimental data from Ref. [23]. The boundary conditions and initial conditions provided by Ref. [23] were adopted for the simulation, and the temperature and pressure of the vehicle tank were estimated for the duration of the vehicle's fill. We incorporated the properties of the vehicle's tank, both thermal (e.g., thermal conductivity of the liner and composite materials) and physical (e.g., length and diameter and thickness of the liner and composite materials), from Ref. [23]. The boundary conditions include the inlet mass flow rate and temperature, the ambient temperature, and the internal and external heat transfer coefficients. The initial condition includes the initial mass, pressure, and temperature in the vehicle's tank, buffer storage vessels, and tube trailer. Fig. 5 shows the measurements from a controlled experiment by Ref. [23] as denoted by the solid lines, along with the replicated initial and boundary conditions for our simulations, and the calculated vehicle's tank temperature and pressure as denoted by the dotted lines. During the experiment, the flow
was set and controlled at 30 g/s, excluding the final part of the fill. Although the inlet temperature was desired at 40 C, it
Fig. 5 e Model estimates compared with experimental results [23] (Reprinted with permission from SAE paper 2011-01-1342©2011 SAE International).
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installation of the buffer storage system at the refueling station. The cost estimates for five diaphragm compressors with a rated discharge pressure of 97 MPa and throughputs of 2.5, 5, 15, 21, and 50 kg/h were provided by a vendor and plotted in Fig. 6. We developed an equation for the compressor cost using the cost data for these five compressors; this equation was later used to estimate the compressor cost for any specific throughput. Fig. 6 shows the equation for the compressor cost, along with the cost quotes obtained for the five compressors.
Fig. 6 e Plot showing compressor costing equation.
Simulation results Buffer storage system configurations
was never achieved during the experimental fill. Furthermore, the precooled hydrogen temperature was not sustained at any single value throughout the experiment. As the figure shows, we replicated the inlet mass flow rate and precooling temperature as closely to the measured values as possible. Additionally we have assumed the inlet pressure to equalize with the pressure in the vehicle tank throughout the fill. We solved the physical laws (see Appendix) to predict the pressure and temperature rise in the vehicle's tank during the fill operation. Fig. 5 shows that the calculated pressure and temperature from the model closely replicate the measured values, providing confidence in the simulation results. We note that the data in Fig. 5 was obtained from a controlled experiment with constant flow rate and do not represent a typical cascade fill that take place in refueling stations.
Compressor and buffer storage system costing The cost of a H2 storage vessel with maximum design pressure of 100 MPa (working pressure of 95 MPa) was quoted by a vendor at $1475 per kg of hydrogen stored with volume production. The vessel has a storage capacity of 12 kg of hydrogen. In addition, 1% of the total cost of buffer storage vessels is added for plumbing expenses, which include valves and piping of the vessel banks. Another 30% is added for
The buffer storage system consists of a cascade of vessel banks that are recharged by a dedicated compressor. When a vehicle activates a dispenser for refueling, the dispenser draws hydrogen from the lowest-pressure bank and then sequentially switches to the next higher-pressure bank until the fill is completed. Various buffer storage system configurations have been simulated to identify configurations that satisfies maximum possible back-to-back vehicle fills at low cost and high utilization. Each buffer storage bank operates within a high- and lowpressure window, which limits full utilization of the stored hydrogen. The high operating pressure is defined by the maximum working pressure of the vessels, while the low operating pressure is defined by the switching pressure between the cascade of banks to maintain the required vehicle fill rate. The number of pressure banks and the number of vessels in each bank play an important role in determining the utilization of the stored hydrogen. The optimum buffer storage vessel configuration would provide more utilization (U) at lower cost (C). We systematically tested 16 configurations of the buffer storage (cascade) banks to determine the configuration with the minimum cost-to-utilization (C/U) ratio. The description of each cascade configuration is provided on the right side of Fig. 7. For example, the 2-3-4 description of
Fig. 7 e Results of various cascade storage system configurations.
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Fig. 8 e Schematic of hydrogen refueling station operating scenario 1. configuration number 10 indicates three banks, with two vessels in the high-pressure bank, three vessels in the medium-pressure bank, and four vessels in the low-pressure bank. In Fig. 7, the right vertical axis represents the hydrogen utilization, defined as the ratio of the mass of hydrogen dispensed into the vehicle's tanks to the mass of hydrogen carried by the buffer storage system. The left vertical axis represents both the buffer storage system capital cost and the economic index (C/U). Fig. 7 shows that configuration number 11, with four banks and one vessel in each bank, is the optimum configuration for the chosen vessel capacity; configuration number 12 is the second best. Note that configuration number 1, the previous default in our modeling, does not represent the lowest-cost option. Going forward, we considered only these three configurations [1,11,12] to represent three-, four-, and five-cascade-vessel configurations, respectively, for more detailed modeling and analysis.
Simulation scenarios While the components of the refueling station remain the same, the operating strategy of the tube-trailer can be different, as described below. We examined two scenarios with different operating strategies, as shown in Figs. 8 and 9. In this refueling station operating scenario 1 (Fig. 8), the tube trailer is delivered to the refueling station at a predefined working pressure (35 MPa in this simulation) [2] and is returned at a specific return pressure (1.5 MPa in this simulation) [1]. The tube trailer is a dedicated hydrogen supply
source for the buffer storage system. The compressor refills the buffer storage (cascade) vessels in the order of priority (high-pressure to low-pressure) from the tube trailer tubes. In this scenario, the compressor draws hydrogen from the tubetrailer until all the tubes within the tube-trailer are at or below the return pressure. This scenario represents the traditional operation of hydrogen refueling stations that are served by tube trailer deliveries. In scenario 2 of refueling station operations (Fig. 9), the tube trailer is used to initially fill the vehicle tank, in addition to supplying hydrogen to the station. The tubes within the tube trailer are used to fill the vehicle tank only when their pressures are above a predefined value (i.e., the cut-off pressure), below which the tube trailer would no longer be used to fill the vehicle tank and would default to scenario 1 operation. In this scenario, the dispenser first connects the tube trailer tube with the highest pressure (greater than the cutoff pressure) to the vehicle tank for initial refueling. The vehicle's fill will be subsequently completed from the buffer storage system. This operating strategy reduces the amount of hydrogen drawn from the buffer storage system by supplementing it with hydrogen from the tube trailer, thus reducing the amount of compression and storage required at the refueling station.
Results: tradeoff between buffer storage and compression Fig. 10 shows the required compressor throughput, denoted by the solid markers (measured on the right vertical axis), and
Fig. 9 e Schematic of hydrogen refueling station operating scenario 2.
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Fig. 10 e Required compressor throughput for various buffer storage (cascade) system Configurations and tube-trailer operating strategies.
the corresponding storage/compression cost, denoted by the open markers (measured on the left vertical axis), for various refueling operating scenarios [1,2] and cascade configurations (three, four, and five cascade vessels) at several tube trailer cut-off pressures on the horizontal axis (the pressure below which the tube trailer is not used to fill the vehicle tank) for a station size of 250 kg/day. The figure shows that scenario 2 always requires lower compressor throughout, indicating that using the tube trailer to initially fill the vehicle's tank is always more advantageous than scenario 1. Regardless of the employed refueling operation scenario (1 or 2), the four- and five-cascade vessel configurations require much lower compression throughput (capacity) compared with the threecascade-vessel configuration. These results demonstrate that, for the assumed buffer storage vessel size, having additional pressure levels reduces the compressor throughput requirement, leading to lower compression cost.
Fig. 10 also shows that lower tube trailer cut-off pressure values require less compressor throughput and reduce the cost of storage/compression. This reduction in the storage/ compression cost is expected because lower tube trailer cutoff pressure means more hydrogen is dispensed directly from the tube trailer to the vehicle's tank, thus reducing the load on refueling equipment (i.e., storage and compression). However, the required compressor throughput does not decrease monotonically with the reduction in the cut-off pressure, because very low cut-off pressures (below 7 MPa) require significantly more connection time with the vehicle's tank, thus making the tube trailer frequently unavailable to connect with the compressor/cascade system when needed (primarily when only one tube trailer tube has pressure above return pressure). Because there is no decrease in the required compressor throughput for all the cascade storage system configurations for cut-off pressures below 7 MPa, the cut-off
Fig. 11 e Effect of tube-trailers returning at a higher pressure.
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Fig. 12 e Contribution of delivery and refueling costs for various tube trailer delivery scenarios.
pressure was fixed at 7 MPa for all further analyses of the scenario 2 operating strategy. Note that, although the fivecascade-vessel configuration has the lowest compressor throughput, the four-cascade-vessel configuration has the lowest storage/compression cost d but less than 1% lower than that of the five-cascade-vessel configuration.
figure shows, though, the refueling cost savings achieved by reducing the compressor throughput more than offsets the cost incurred for additional trips of tube trailers between the distribution center (delivery) and the stations. If the tube trailer delivery distance significantly exceeds 100 km, however, the increase in delivery cost may exceed the savings achieved by employing higher tube trailer return pressures.
Results: relationship between tube trailer return pressure and required compression throughput
Conclusions Fig. 11 shows the impact of the return pressure of the tube trailer on the required compressor throughput and the combined storage/compression cost for the two refueling operating scenarios [1,2]. The compressor throughout values are represented by the solid markers and measured on the vertical axis, while the storage/compression costs are indicated by the vertical stacked bars and measured on the left vertical axis. The horizontal axis represents the tube trailer operating strategy, with the return pressure denoted within the brackets. As Fig. 11 shows, returning the tube trailer at a higher pressure would reduce the required compressor throughput for all cascade configurations. Note that returning the tube trailer at a higher pressure (5 MPa) makes the fivecascade-vessel (rather than the four-cascade vessel) configuration the lowest-cost option (but by less than 1%). Fig. 11 also shows the tradeoff between compression cost and storage cost, with higher compression and lower storage cost for the four-cascade-vessel configuration compared with the fivecascade-vessel configuration. Fig. 12 shows the contribution of delivery and refueling costs (not including production cost) for delivering hydrogen from a central production/terminal facility to 80 refueling stations (250 kg/day each) located at an average distance of 100 km from the distributing terminal facility. Although the high return pressure decreases the required compressor throughput, thus reducing the refueling cost, it increases the number of tube trailer truck deliveries from the terminal facility to the refueling station, which increases the delivery cost of hydrogen. Fig. 12 shows that, while the refueling cost decreases with increasing tube trailer return pressure from 1.5 MPa to 5 MPa, the corresponding hydrogen delivery cost increases (for the examined delivery parameters). As the
We developed a rigorous model to evaluate various refueling configuration options and operating strategies to determine the lowest-cost option for hydrogen refueling. Our study reveals that there is a tradeoff between the compression and storage capacities for any given fueling demand. Finding the optimum configuration that offers the lowest cost of compression and storage can dramatically reduce the refueling cost. Furthermore, employing a tube trailer to initially fill the vehicle's tank can reduce the compression and storage requirement, thus reducing the refueling cost. Lowering the tube trailer cut-off pressure for initial vehicle refueling and increasing the trailer's return pressure can also reduce the refueling cost, especially in early markets, when the refueling stations will be significantly underutilized. The specific results obtained using the H2SCOPE model depend on many factors, such as vehicle tank size and characteristics, vehicle tank initial pressure, hourly refueling demand, size of buffer storage vessels, cost of components, etc. Although the results cannot be generalized to all hydrogen refueling station capacities and refueling demands, they provide a better understanding of the relationships and tradeoffs among various station components and operating strategies.
Acknowledgment This research effort was supported by the Fuel Cell Technologies Office of the U.S. Department of Energy's Office of Energy Efficiency and Renewable Energy under Contract Number DEAC02-06CH11357.
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Ainner is the inner surface area of the tank Aouter is the outer surface area of the tank THydrogen is the temperature of the Hydrogen gas inside the tank Tinner wall is the temperature of the inner tank wall Touter wall is the temperature of the outer tank wall Tambient is the temperature of the ambient
Appendix Mass Conservation Equation X dm X ¼ min mout dt where, dm/dt is the rate of change of mass inside the vehicle tank min is the mass flowing into the vehicle tank mout is the mass flowing out of the vehicle tank Energy Conservation Equation
Equation of State [35] (Please refer to [35] for the expressions of ao and ar and their partial derivatives) r va Pðt; dÞ ¼ rRT 1 þ vd t Tc r t ¼ ; and d ¼ rc T where,
dU dQ dm ¼ þ Einlet dt dt dt where, dU/dt is the rate of change of internal energy dQ/dt is the rate of heat transfer through the inner tank wall Einlet is the enthalpy entering the tank per unit mass of hydrogen The enthalpy (E) in the energy equation is the sum of the static enthalpy and the kinetic energy per unit mass. The transient heat transfer through the tank wall is modeled via the following partial differential equation: vTðr; tÞ 1 1 v vT ¼ $ rlðr; TÞ vt cðr; TÞrðr; TÞ r vr vr
P is the pressure inside the tank a is the dimensionless reduced Helmholtz free energy ar is the residual contribution rc is Critical molar density r is molar density Tc is critical temperature T is temperature R is Real gas constant Internal Energy [35] (Please refer to [35] for the expressions of ao and ar and their partial derivatives) uðt; dÞ ¼ RTc
where,
vao vt
þ d
o va vt d
where,
T(r,t) is the temperature of the tank wall at any radius r and time t c is the specific heat of the tank material l is the thermal conductivity of the tank material r is the density of the tank material r is the radius of the tank Subject to the following boundary conditions at the inner and outer tank walls: Heat transfer rate at the inner tank wall,
Qin ¼ hinside;avg Ainner THydrogen Tinner wall
u is the molar internal energy ao is the ideal gas contribution Enthalpy [35] (Please refer to [35] for the expressions of ao and ar and their partial derivatives) r r o va va va þ þ1 þd Eðt; dÞ ¼ RT t vt d vt d vd d where E is the molar internal energy
Heat transfer rate at the outer tank wall, QOut ¼ houtside;avg Aouter ðTouter wall Tambient Þ where, Qin is the rate of heat transfer from the hydrogen to the inner tank wall Qout is the rate heat transfer from the outer tank wall to the ambient hinside,avg is the average convective heat transfer coefficient at the inner tank wall houtside,avg is the average convective heat transfer coefficient at the outer tank wall
Compressor Power [8] # " ðk1Þ kJ 1 k Poutlet k _ ¼ ZmRTn 1 Power; sec h k1 Pinlet where, Z is the mean compressibility factor i. h ¼ ZðT; PÞdischarge ZðT; PÞsuction . i h LN ZðT; PÞdischarge ZðT; PÞsuction
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m_ is the mass flow rate; kg mole=sec R is the universal gas constant; kJ=kg mole K T is the inlet gas temperature, K n is the number of stages, h is the isentropic efficiency, k is the ratio of specific heats, Poutlet is the compressor discharge pressure, bar or psi Pinlet is the compressor inlet pressure, bar or psi
references
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[14] DOE Fuel Cell Technologies Office (FCTO). Technical plan: delivery, fuel cell technologies office multi-year research, development, and demonstration plan. 20133.2-1. [15] DOE Fuel Cell Technologies Office (FCTO). Technical plan: technology validation, the fuel cell technologies office multiyear research, development, and demonstration (MYRD&D) plan. 20123.6-1. [16] Elgowainy A, Reddi K, Mintz M, Brown D. 2013 DOE hydrogen program review: hydrogen delivery infrastructure analysis. 2012. May 5, available at: http://www.hydrogen. energy.gov/pdfs/review13/pd014_mintz_2013_o.pdf [accessed 21.01.14]. [17] Elgowainy A, Wang M. Well-to-wheel analysis of sustainable vehicle fuels. In: Meyers RA, editor. Encyclopedia of sustainability, science and technology. Springer; 2011. [18] Energy Information Administration (EIA). Annual energy outlook 2013 with projections to 2040. 2013 [Washington, DC]. [19] Farzaneh-Gord M, Deymi-Dashtebayaz M, Rahbari HR. Effects of storage types and conditions on compressed hydrogen fueling stations performance. Int J Hydrogen Energy 2012;37:3500. [20] Galassi MC, Baraldi D, Iborra BA, Moretto P. CFD analysis of fast filling scenarios for 70-MPa hydrogen type IV tanks. Int J Hydrogen Energy 2012;37:6886. [21] Hara K. Research and development of fuel cells vehicle and hydrogen in Japan. 2011. May 17, available at: http://www. hfc2011.com/wp-content/uploads/2011/07/HFC2011_Japan. pdf [accessed 21.013.14]. [22] Harty R, Mathison S, Gupta N. Improving hydrogen tank refueling performance through the use of an advanced fueling algorithm d the MC method. In: Proceedings of the national hydrogen association conference, May 4th 2010; 2010. [23] Immel R, Mark-Gardner A. Development and validation of a numerical Thermal simulation model for compressed hydrogen gas storage tanks. SAE Int J Engines 2011;4(1):1850. [24] Japan Hydrogen & Fuel Cell (JHFC), undated, “JHFC Demonstration Project,” available at: http://www.jari.or.jp/ Portals/0/jhfc/e/jhfc/index.html, [accessed 21.01.14]. [25] Joseck F, Ward J. Cradle to grave lifecycle analysis of vehicle and fuel pathways. 2014. DOE Hydrogen and Fuel Cells Program Record, Record # 14006, March 21, available at: http://www.hydrogen.energy.gov/pdfs/14006_cradle_to_ grave_analysis.pdf [accessed 06.08.14]. [26] Liu Y, Zhao Y, Zaho L, Chen H, Zhang L, Zhao H, et al. Experimental studies on temperature rise within a hydrogen cylinder during refueling. Int J Hydrogen Energy 2010;35:2627. [27] Mintz M, Elgowainy A, Gardiner M. Rethinking hydrogen fueling: insights from delivery modeling. J Transp Res Board 2009;2139:46. [28] Monde M, Woodfield P, Takano T, Kosaka M. Estimation of temperature change in practical hydrogen pressure tanks being filled at high pressures of 35 and 70 MPa. Int J Hydrogen Energy 2012;37:5723. [29] “2017-2025 CAFE GHG Supplemental rules”. NHTSA. Retrieved 28 August 2012. [30] Rothuizen E, Merida W, Rokni M, Wistoft-Ibsen M. Optimization of hydrogen vehicle refueling via dynamic simulation. Int J Hydrogen Energy 2013;38:4221. [31] Society of Automotive Engineers (SAE). SAE international surface vehicle technical information report: fueling protocols for light duty gaseous hydrogen surface vehicles. SAE International; 2010. SAE J2601. [32] Thomas P. Simulation of industrial processes for control engineers [chapter 6]. Steady-state compressible flow. 1st ed. Butterworth Heinemann; 1999.
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Available online at www.sciencedirect.com
ScienceDirect journal homepage: www.elsevier.com/locate/he
Hydrogen refueling station compression and storage optimization with tube-trailer deliveries Krishna Reddi a,*, Amgad Elgowainy a, Erika Sutherland b a
Argonne National Laboratory, 9700 South Cass Avenue, Argonne IL 60439, United States U.S. Department of Energy, Fuel Cell Technologies Office, 1000 Independence Avenue SW, Washington, DC 20585, United States
b
article info
abstract
Article history:
Hydrogen refueling stations require high capital investment, with compression and storage
Received 8 May 2014
comprising more than half of the installed cost of refueling equipment. Refueling station
Received in revised form
configurations and operation strategies can reduce capital investment while improving
18 September 2014
equipment utilization. Argonne National Laboratory developed a refueling model to eval-
Accepted 19 September 2014
uate the impact of various refueling compression and storage configurations and tube
Available online 11 October 2014
trailer operating strategies on the cost of hydrogen refueling. The modeling results revealed that a number of strategies can be employed to reduce fueling costs. Proper sizing
Keywords:
of the high-pressure buffer storage reduces the compression requirement considerably,
Hydrogen refueling station
thus reducing refueling costs. Employing a tube trailer to initially fill the vehicle's tank also
Tube-trailer
reduces the compression and storage requirements, further reducing refueling costs.
Simulation model
Reducing the cut-off pressure of the tube trailer for initial vehicle fills can also significantly
Compression
reduce the refueling costs. Finally, increasing the trailer's return pressure can cut refueling
Storage
costs, especially for delivery distances less than 100 km, and in early markets, when
Fuel cell electric vehicles
refueling stations will be grossly underutilized. Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
Introduction Background In the United States, the transportation sector is the secondlargest consumer of energy, after the electric power sector, accounting for about 28% of the total energy expended [18]. The transportation sector is heavily dependent on petroleum, which accounts for 97% of its energy sources. Of this petroleum, 56% is imported to U.S. refineries [18]. This dependence on crude oil underscores three transportation sector needs
that must, ideally, be met by alternative energy sources [1]: energy security [2], environmental sustainability, and [3] economic vitality [14]. Federal and State governments in the United States have been addressing these needs by mandating higher fuel economy standards for automobiles and funding research on alternative fuels such as hydrogen, electricity, and biofuels [17]. The new corporate average fuel economy standards require U.S. manufactures of vehicles to (CAFE) improve the minimum fuel economy of their passenger vehicles from 36.7 miles per gallon (MPG) in 2017 to 54.5 MPG in 2025 [29]. Hydrogen fuel cell electric vehicles (FCEVs) with certification fuel economy of more than 80 miles per gallon of
* Corresponding author. Tel.: þ1 630 252 1479. E-mail address: [email protected] (K. Reddi). http://dx.doi.org/10.1016/j.ijhydene.2014.09.099 0360-3199/Copyright © 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.
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Fig. 1 e Schematic of hydrogen refueling station.
gasoline equivalent (MPGGE) can play an important role in achieving the 54.5 MPG fuel economy target in 2025. Further, state level initiatives such as the zero emissions vehicle (ZEV) mandate by State of California requires major automakers to ramp up their sales of ZEVs from 4.5% in 2018 to 22% by 2025 [4]. Other states that follow California emissions rules may choose to adopt the ZEV mandate as well. ZEVs are either hydrogen FCEVs or battery electric vehicles (BEVs). FCEVs have several advantages over BEVs, including longer driving range on a single tank fill, fast refueling, and better performance in cold weather. Hydrogen is a clean fuel with significant potential to reduce U.S. demand for petroleum fuels because it can be produced from a variety of domestically available non-fossil and renewable sources. Fuel cells efficiently convert hydrogen into electricity with a peak efficiency of about 60% [10]. The electricity produced is subsequently used to power electric motors for vehicle propulsion. This process is more efficient than thermal efficiency of heat engines and results in a fuel economy gain of 183% compared to gasoline internal combustion engine vehicles [25]. Hydrogen FCEVs are being developed by many automobile original equipment manufacturers (OEMs) for early market deployment in the 2015e2017 timeframe to meet California's ZEV mandate and to satisfy various FCEV deployment initiatives in Japan, Germany, and other European countries. Many governments have already completed projects to demonstrate and validate the technical feasibility of FCEVs [3,15,24]. The demand for hydrogen must be supported by provision of sufficient infrastructure. Construction of supporting infrastructure might not be profitable during the initial deployment of FCEVs because of the high capital investment required to build hydrogen refueling stations (HRS) and underutilization of the installed infrastructure in early FCEV markets. Thus, many governments have initiated public-private partnerships to demonstrate the economic viability of the hydrogen infrastructure needed for pre-commercial deployment of FCEVs. The H2 Mobility initiatives in Europe by Germany, the United Kingdom, and France; the H2 USA initiative co-launched by the United States Department of Energy (DOE); and the Japan Hydrogen & Fuel Cell (JHFC) (Phase 3) initiative are examples of international efforts that promote the coordinated deployment of HRS and FCEVs [13,21,34]. Germany and Japan plan to deploy 50 and 100 HRS by 2015, while California plans to deploy a network of 68 HRS by 2015 to support OEMs' plans to roll out hydrogen FCEVs [3,5,33]. Almost all OEMs agree that gaseous hydrogen stored onboard at a pressure of 70 MPa is the appropriate option to enable an FCEV driving range of over 300 miles (480 km) on a
single fill [17]. Fast refueling of 70-MPa tanks requires significant refrigeration, compression capacity, and high-pressure storage equipment at the refueling sites. The Society of Automotive Engineers (SAE) developed the SAE J2601 refueling protocol that defines safety limits and performance requirements for gaseous hydrogen refueling; the protocol covers a wide range of refueling pressures as well as ambient and precooling temperatures [31]. The fact that refueling costs are dominated by compression and storage requirements [16] motivated the current investigation of optimum hydrogen refueling station compression and storage configurations.
Objective The cost for HRS accounts for half or more of the total cost of hydrogen delivery [27]. Fig. 1 shows the main components of an HRS: a hydrogen storage system that stores hydrogen to meet daily demand, a high-pressure buffer storage system (also known as cascade storage) to deliver gaseous hydrogen to the vehicle tank, a compressor that pressurizes hydrogen from the storage source pressure to the buffer storage pressure (typically higher than vehicle's maximum service pressure), a refrigeration system that pre-cools the hydrogen gas being dispensed into the vehicle's tank, a dispenser that manages the flow of hydrogen to the vehicle's tank, as well as various controls and safety equipment. Fig. 2 provides estimates of HRS total installed cost, showing the contribution of each component to the total capital investment for various station capacities. The cost estimates in the figure are based on vendor quotes for large purchased quantities (~100 units) and incorporate a backup
Fig. 2 e Estimated hydrogen refueling station costs for various capacities [16].
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compressor to ensure continuity of refueling operations. The figure shows that the compressor and cascade storage together account for approximately half of the total capital investment for all station capacities. So this study focuses on configurations that reduce the station cost by optimizing the sizing of these two components. Typically the sizes of these two components are interdependent. Extensive high pressure buffer storage implies that sequential vehicle fill-up demand can be readily met without extensive use of the compressor system, thus rendering the use of a small sized compressor feasible. In such case, the compressor is engaged, mainly to compress hydrogen to 950 bar at the high pressure buffer storage, for a longer period of time. Even though the amount of hydrogen that must be compressed is constant, the expanded period of time over which compression can occur allows the use of a smaller compressor. Conversely, a larger compressor with a high flow rate will require a small highpressure buffer storage to satisfy the same refueling demand. The optimum configuration is decided primarily by the following factors [1]: the total daily station demand [2]; the hourly variation of demand in a given day, which determines the number of back-to-back vehicle fills during peak hour [3]; the installed cost [4]; the operation and maintenance cost, and [5] the lifetime of these two components. Given the interdependency between the high-pressure buffer storage and the compressor capacities, the best economic option would achieve a balance between the two components. In this paper, we describe a model developed by Argonne that simulates the operation of a refueling station. The model is used to optimize the combination of compressor and buffer storage with the objective of minimizing refueling cost [in $/kgH2] for a given set of parameters such as: station daily demand, hourly demand profile, vehicle tank configuration and capacity, vehicle tank thermal and mechanical characteristics, hydrogen dispensing temperature and fill rate, compressor cost, cascade vessel cost, and hydrogen source capacity and pressure. Section project description summarizes the present state of research and gaps that will be addressed by this study. Sections simulation model and simulation model verification and validation provide a description of the simulation model and the verification and validation of the simulations conducted. Results and conclusions are presented in Sections simulation results and conclusions.
Project description With support from DOE's Fuel Cell Technologies Office (under the Energy Efficiency and Renewable Energy Office), Argonne National Laboratory, along with the National Renewable Energy Laboratory and Pacific Northwest National Laboratory, developed the Hydrogen Delivery Scenario Analysis Model (HDSAM). The model uses an engineering and economics approach to estimate the costs of various hydrogen delivery and refueling options [1]. HDSAM is used by DOE to identify the components with the greatest impact on hydrogen delivery cost and to guide research directed at reducing delivery costs. Other stakeholders use HDSAM to evaluate the impact of various delivery and refueling options on the total dispensed cost of hydrogen under various market conditions.
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The refueling station module of HDSAM incorporates cost and sizing details for all refueling components, setback distance and land area requirements, maintenance and operation costs, as well as other costs factors (e.g., site preparation, engineering and design, permitting, and installation). However, a few refueling station configuration details that are critical to identifying the most economical combination of components are fixed in HDSAM. Gaps in the present model [1] are listed below; these have to be addressed to make the model more rigorous and robust and allow us to determine the optimal configurations for hydrogen refueling. The size of the cascade vessels is fixed, and the number of pressure levels is fixed at three. This configuration is not the most economical option to meet all station demands. The optimum pressure for switching between the cascade vessel banks during vehicle fill is not considered; the switch point plays an important role in controlling the vehicle fill duration, which is critical for customer satisfaction [6,19]. The pressure drop in the lines and fittings between the buffer storage vessels and the dispensers is not considered. The mass, temperature, and pressure inside the vehicle's tank during the filling operation are not monitored during simulations. Keeping track of these three parameters is important, as described in the SAE J2601 refueling protocol [31]. The effect of the overshooting pressure in the vehicle's tank at the end of the fill is not considered; this is an important factor for the proper specification of the compressor's discharge pressure and the maximum working pressure of the buffer storage vessels. To overcome these gaps and ensure that refueling demand and the requirements of the SAE J2601 fueling protocol are satisfied, we developed a comprehensive model that solves the physical laws of mass, momentum, and energy conservation, as well as the hydrogen equation of state and other thermodynamics properties relations subject to specified initial and boundary conditions. The physical model, known as the Hydrogen Station Cost Optimization & Performance Evaluation (H2SCOPE), tracks mass, pressure, and temperature over time throughout the refueling system d from the hydrogen source to the vehicle's tank. The employed equation of state for hydrogen is a modified ideal gas equation with a compressibility factor to simulate the behavior of real gas. The compressibility factor and all other thermodynamic variables are defined by a set of empirical constants, the values of which are based on the experimental data and provided by Ref. [35]. In building the H2SCOPE model, we benefited from a considerable body of research that examined the impacts of various refueling parameters on pressure and temperature changes within vehicle's tank during fills [7,11,12,20,23,26,28,35,36,]. The heat transfer through the vehicle tank wall during fills is ignored in some of the previous work [19,22,35] but when considered, it is assumed to be steady [35] or transient [11,23]. Most of the previous research is focused on the vehicle's tank, but in a few cases, the source d comprising the buffer storage system [6,30,36] and the pipeline at constant pressure
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[35] is also examined. However, in most cases, the drop in temperature [6,36] in the buffer storage vessels caused by withdrawal of hydrogen during the refueling process is ignored. Inclusion of the temperature drop in the buffer storage vessels is important, especially in the case of back-toback fills. Rothuizen et al. [30] showed that the pressure drop, and hence the temperature drop, in the hydrogen storage system (buffer storage vessels) has a significant effect on the mass flow rate and cooling demand at the dispenser nozzle. Rothuizen et al. [30] also showed that having multiple buffer storage tanks (e.g., three) reduces the cooling demand and compression energy compared with having a single, large, high-pressure storage tank. To our knowledge, a complete study of all of the factors impacting the cost of hydrogen refueling d station components, from the hydrogen supply to the vehicle's tank, and operating parameters such as the daily demand, the hourly demand profile, and the SAE J2601 refueling protocol [31] dhas not been conducted. For this study, we developed a model to simulate the operation of refueling stations to identify the optimum combination of compression and buffer storage capacities to meet a specific refueling demand and provide the lowest refueling cost.
Simulation model The major components of a gaseous hydrogen (H2) refueling station include the following: A tube trailer that supplies hydrogen at a pre-determined maximum and minimum pressure; A compressor that draws hydrogen from the tube trailer tubes and fills a buffer storage system; A buffer storage system that consists of multiple (cascade) vessels, each of which is maintained within a specific pressure range; A dispenser that regulates the flow of H2 from the buffer storage system to the onboard vehicle tank; and A refrigeration unit that cools the H2 to 233 K (40 C) before dispensing. Typically, when a vehicle comes in for refueling, the dispenser connects to the low-pressure vessel in the buffer storage system, regulating the flow to keep it between the maximum allowed flow of 3.33 kg/min and the switch point between the vessels for a cascade refueling (which varies with operating strategy, but is typically 0.1 kg/min). Once the flow between the connected bank of vessels and vehicle tank drops below the cascade switch point (i.e., as the pressures equalize), the dispenser connects to the next cascade bank, where H2 is stored at a higher pressure. This routine of sequentially connecting each cascade bank with higherpressure H2 to the vehicle tank is continued until the vehicle tank is filled with 5 kg of hydrogen or the flow from the highest-pressure bank is below a predetermined minimum value. Typically, the buffer storage vessels are maintained within a definite range to ensure that the vehicle tank receives 5 kg of H2 after connecting to the high-pressure bank. The compressor draws hydrogen from the tube
trailer and keeps filling the buffer storage vessels to the rated operating pressure following a predetermined priority order.
Model assumptions In this study, the complexity of modeling refueling station operations is limited by the following assumptions. The flow of hydrogen in the lines between the tube trailer, buffer storage, and the dispenser is adiabatic, quasi-steady, and compressible [32]. The fanning friction factor [32] is constant along the piping that connects the station components. Frictional loss within the piping causes a drop in pressure from the exit of the buffer storage vessels to the dispenser. For subsonic velocities of hydrogen flow (Mach number < 0.1), the dispenser outlet pressure is assumed to be equal to the back pressure from the vehicle tank. The kinetic energy is small compared to the enthalpy of the flow but is not insignificant. Thus, we account for the kinetic energy of hydrogen flow into the vehicle's tank when calculating the buildup of internal energy of hydrogen inside the tank. The hydrogen flow is regulated by controlling the upstream pressure at the dispenser inlet to restrict the flow rate and keep it below the SAE J2601 maximum allowable flow rate (60 g/s) [31]. The heat transfer through the walls of the vehicle's tank is transient and employs an internal heat transfer coefficient of 325 W/m2-K. We assumed 5 W/m2-K for the external heat transfer coefficient. The external heat transfer coefficient is less likely to impact the simulation results, especially for type IV tanks with short fill times. The refrigeration system is placed between the buffer storage vessels and the dispenser and cools the hydrogen to 40 C (233 K). We did not model the cooling system and assumed that a cooling system which can address the above cooling demand is installed. Current practices oversize the cooling equipment and/or heat exchangers to ensure that 40 C can be achieved within 30 s as called for by the SAE J2601 protocol. The compressor has a constant throughput and always replenishes the buffer storage banks in the order of decreasing cascade operating pressures (i.e., starts with the high-pressure bank and ends with low-pressure bank). Any buffer storage bank can be either filled or emptied at any given time (i.e., both operations cannot be conducted on the same buffer storage bank simultaneously). Each 250 kg of daily hydrogen demand requires a dispenser with a single hose.
Component specifications The H2SCOPE model receives the specifications of the vehicle's tank and the components of the refueling station (i.e., physical dimensions, thermal characteristics, and operating pressures of each component) as inputs. While any sizes and operating pressures can be simulated for components such as the vehicle tank, buffer storage vessels, hydrogen source and
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compressors, the following specifications were used for the simulation results presented in this paper: A 5-kg capacity, 129-L, type IV vehicle tank with a maximum working pressure of 87.5 MPa at 358 K or 70 MPa at 298 K. Vehicles are assumed to begin the fill with a pressure of 2 MPa at 298 K, reflecting an initial state of charge of 0.2 kg; A buffer storage system with multiple type IV cascade vessels, each with 12-kg capacity and 255-L volume, with a service pressure of 95 MPa at 298 K; and For the hydrogen source, a tube trailer storage unit comprising four type IV tubes at a maximum working pressure of 35 MPa at 298 K and a minimum pressure of 1.5 MPa at 298 K. Each of the four tubes has a capacity of about 200 kg stored in 8500 L volume, for a total usable capacity of about 800 kg.
Operating strategy The H2SCOPE model has the flexibility to simulate a variety of operating strategies, which are differentiated by the number of cascade pressure levels in the buffer storage system and the manner in which the tube trailer tubes are used. The number of banks or cascade pressure levels within the buffer storage system can vary. In our study, three to nine pressure levels (cascade banks) within the buffer storage system were modeled and simulated; of these, three to five pressure levels were considered for further analysis on the basis of the initial cost tradeoffs. The order in which hydrogen is drawn from the cascade banks while refueling the vehicle's tank is fixed. The refueling of vehicles starts from the low-pressure bank and ends with the highpressure bank, while the replenishing of the buffer storage vessels, the compressor follows the reverse order (i.e., starts with high-pressure bank and ends with low-pressure bank). The tube trailers can serve different functions during the day-to-day operations of the refueling station; they can be used to supply hydrogen to the buffer storage vessels through the compressor. The high-pressure tubes (25 MPa or higher) on the tube trailer can also be used to initially charge the vehicle's tank, with the buffer storage system completing the fill. The cut-off pressure and return pressure define the particular use of tube trailers at the refueling stations. The cut-off pressure is the pressure below which the tube trailer is not used to fill the vehicle tank. The return pressure is the pressure at which the tube trailer is considered empty and returned to the supplier for recharging. Many other parameters have been kept constant for the simulations presented in this study. Parameters such as the pre-cooling temperature, the length of the piping between the buffer storage system and dispenser, thermal properties of the buffer storage vessels and vehicle tank materials, ambient temperature, vehicle tank initial pressure and temperature, etc., can be varied to simulate their impacts on the operation of any refueling station. The hourly demand profile used for
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the simulations is similar to the gasoline vehicles refueling profiles provided by Chevron [8]. Fig. 3 shows the hourly demand profile for a daily demand of 250 kg/day. The horizontal axis in Fig. 3 represents the hour of the day, while the left vertical axis represents the demand for hydrogen (in kg) per hour and the right vertical axis represents the number of vehicle fills per hour.
Simulation model verification and validation The simulation model was developed in three steps (Fig. 4) and was verified and validated after each step. STEP 1: Initially, we modeled a buffer storage system filling a vehicle tank through a dispenser to identify the configuration of buffer storage vessels that permits the highest number of back-to-back vehicle fills. The energy equation [35], continuity equation, flow equation [32], equation of state [35], and heat transfer equations [23] were integrated to estimate the temperature, pressure, and mass of hydrogen in the vehicle tank and buffer storage vessels throughout the refueling process. The conservation equations, equation of state, and thermodynamic relations used in this study are included in the Appendix. We employed an explicit numerical scheme that solves the transient heat transfer equations through the tank wall, subject to the inner and outer heat transfer boundary conditions described in the Appendix. The employed algorithm ensured the numerical stability of the solution by implementing a time-step with a Fourier number less than 0.5. The modeled filling process follows the SAE J2601 fueling protocol [31]. We modeled and simulated a variety of buffer storage system configurations and determined the number of back-to-back vehicle fills that could be achieved by each configuration. The configuration of the buffer storage system is characterized by the number of pressure levels (banks) and vessels at each pressure level. The top two buffer storage system configurations, which resulted in the maximum hydrogen use at the lowest cost, were selected for further analysis, along with the conventional threecascade-vessel storage configuration currently used in most refueling stations [1].
Fig. 3 e Hourly demand profile for a 250-kg/day-capacity refueling station [8].
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Fig. 4 e Schematic representation of the refueling station components. STEP 2: The model from step 1 was expanded to include a compressor, which is assumed to refill the idle buffer storage vessels with hydrogen. In this context, a buffer storage vessel is assumed to be idle when the vehicle tank is not connected to the buffer storage vessels through the dispenser during the refueling process or when the dispenser is not occupied. The compressor refills the high-pressure buffer storage bank, followed by the medium- and low-pressure banks. In this step, we did not include the source of the hydrogen supplying the compressor, and we modeled only its output state, as represented by the hourly throughput, temperature, and pressure of hydrogen delivered to the buffer storage vessels. The formula for compressor work is provided in the Appendix. Conner and Manousiouthakis [9] developed a theorem for optimizing the total annualized cost of a series of compressor sequences. The compressor's adiabatic efficiency was assumed at 65%. The contribution of the energy consumption of the compressor to the dispensed cost of hydrogen is small compared to the contribution of the capital cost of the compressor and other refueling equipment. STEP 3: Finally, we expanded the model to include the hydrogen source: a high-pressure tube trailer. The heat transfer from the tube-trailer tubes was assumed to be quasi-steady because it is emptied over a span of hours or days depending upon the station's daily demand. We modeled and simulated two operation strategies for the tube-trailers at the refueling station.
The model accuracy was verified by incrementally adding capabilities (Steps 1 through 3) and verifying the results with respect to mass and energy balance at the component and system levels, for consistency, after each of the three steps described above. We validated the model using published experimental data from Ref. [23]. The boundary conditions and initial conditions provided by Ref. [23] were adopted for the simulation, and the temperature and pressure of the vehicle tank were estimated for the duration of the vehicle's fill. We incorporated the properties of the vehicle's tank, both thermal (e.g., thermal conductivity of the liner and composite materials) and physical (e.g., length and diameter and thickness of the liner and composite materials), from Ref. [23]. The boundary conditions include the inlet mass flow rate and temperature, the ambient temperature, and the internal and external heat transfer coefficients. The initial condition includes the initial mass, pressure, and temperature in the vehicle's tank, buffer storage vessels, and tube trailer. Fig. 5 shows the measurements from a controlled experiment by Ref. [23] as denoted by the solid lines, along with the replicated initial and boundary conditions for our simulations, and the calculated vehicle's tank temperature and pressure as denoted by the dotted lines. During the experiment, the flow
was set and controlled at 30 g/s, excluding the final part of the fill. Although the inlet temperature was desired at 40 C, it
Fig. 5 e Model estimates compared with experimental results [23] (Reprinted with permission from SAE paper 2011-01-1342©2011 SAE International).
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installation of the buffer storage system at the refueling station. The cost estimates for five diaphragm compressors with a rated discharge pressure of 97 MPa and throughputs of 2.5, 5, 15, 21, and 50 kg/h were provided by a vendor and plotted in Fig. 6. We developed an equation for the compressor cost using the cost data for these five compressors; this equation was later used to estimate the compressor cost for any specific throughput. Fig. 6 shows the equation for the compressor cost, along with the cost quotes obtained for the five compressors.
Fig. 6 e Plot showing compressor costing equation.
Simulation results Buffer storage system configurations
was never achieved during the experimental fill. Furthermore, the precooled hydrogen temperature was not sustained at any single value throughout the experiment. As the figure shows, we replicated the inlet mass flow rate and precooling temperature as closely to the measured values as possible. Additionally we have assumed the inlet pressure to equalize with the pressure in the vehicle tank throughout the fill. We solved the physical laws (see Appendix) to predict the pressure and temperature rise in the vehicle's tank during the fill operation. Fig. 5 shows that the calculated pressure and temperature from the model closely replicate the measured values, providing confidence in the simulation results. We note that the data in Fig. 5 was obtained from a controlled experiment with constant flow rate and do not represent a typical cascade fill that take place in refueling stations.
Compressor and buffer storage system costing The cost of a H2 storage vessel with maximum design pressure of 100 MPa (working pressure of 95 MPa) was quoted by a vendor at $1475 per kg of hydrogen stored with volume production. The vessel has a storage capacity of 12 kg of hydrogen. In addition, 1% of the total cost of buffer storage vessels is added for plumbing expenses, which include valves and piping of the vessel banks. Another 30% is added for
The buffer storage system consists of a cascade of vessel banks that are recharged by a dedicated compressor. When a vehicle activates a dispenser for refueling, the dispenser draws hydrogen from the lowest-pressure bank and then sequentially switches to the next higher-pressure bank until the fill is completed. Various buffer storage system configurations have been simulated to identify configurations that satisfies maximum possible back-to-back vehicle fills at low cost and high utilization. Each buffer storage bank operates within a high- and lowpressure window, which limits full utilization of the stored hydrogen. The high operating pressure is defined by the maximum working pressure of the vessels, while the low operating pressure is defined by the switching pressure between the cascade of banks to maintain the required vehicle fill rate. The number of pressure banks and the number of vessels in each bank play an important role in determining the utilization of the stored hydrogen. The optimum buffer storage vessel configuration would provide more utilization (U) at lower cost (C). We systematically tested 16 configurations of the buffer storage (cascade) banks to determine the configuration with the minimum cost-to-utilization (C/U) ratio. The description of each cascade configuration is provided on the right side of Fig. 7. For example, the 2-3-4 description of
Fig. 7 e Results of various cascade storage system configurations.
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Fig. 8 e Schematic of hydrogen refueling station operating scenario 1. configuration number 10 indicates three banks, with two vessels in the high-pressure bank, three vessels in the medium-pressure bank, and four vessels in the low-pressure bank. In Fig. 7, the right vertical axis represents the hydrogen utilization, defined as the ratio of the mass of hydrogen dispensed into the vehicle's tanks to the mass of hydrogen carried by the buffer storage system. The left vertical axis represents both the buffer storage system capital cost and the economic index (C/U). Fig. 7 shows that configuration number 11, with four banks and one vessel in each bank, is the optimum configuration for the chosen vessel capacity; configuration number 12 is the second best. Note that configuration number 1, the previous default in our modeling, does not represent the lowest-cost option. Going forward, we considered only these three configurations [1,11,12] to represent three-, four-, and five-cascade-vessel configurations, respectively, for more detailed modeling and analysis.
Simulation scenarios While the components of the refueling station remain the same, the operating strategy of the tube-trailer can be different, as described below. We examined two scenarios with different operating strategies, as shown in Figs. 8 and 9. In this refueling station operating scenario 1 (Fig. 8), the tube trailer is delivered to the refueling station at a predefined working pressure (35 MPa in this simulation) [2] and is returned at a specific return pressure (1.5 MPa in this simulation) [1]. The tube trailer is a dedicated hydrogen supply
source for the buffer storage system. The compressor refills the buffer storage (cascade) vessels in the order of priority (high-pressure to low-pressure) from the tube trailer tubes. In this scenario, the compressor draws hydrogen from the tubetrailer until all the tubes within the tube-trailer are at or below the return pressure. This scenario represents the traditional operation of hydrogen refueling stations that are served by tube trailer deliveries. In scenario 2 of refueling station operations (Fig. 9), the tube trailer is used to initially fill the vehicle tank, in addition to supplying hydrogen to the station. The tubes within the tube trailer are used to fill the vehicle tank only when their pressures are above a predefined value (i.e., the cut-off pressure), below which the tube trailer would no longer be used to fill the vehicle tank and would default to scenario 1 operation. In this scenario, the dispenser first connects the tube trailer tube with the highest pressure (greater than the cutoff pressure) to the vehicle tank for initial refueling. The vehicle's fill will be subsequently completed from the buffer storage system. This operating strategy reduces the amount of hydrogen drawn from the buffer storage system by supplementing it with hydrogen from the tube trailer, thus reducing the amount of compression and storage required at the refueling station.
Results: tradeoff between buffer storage and compression Fig. 10 shows the required compressor throughput, denoted by the solid markers (measured on the right vertical axis), and
Fig. 9 e Schematic of hydrogen refueling station operating scenario 2.
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Fig. 10 e Required compressor throughput for various buffer storage (cascade) system Configurations and tube-trailer operating strategies.
the corresponding storage/compression cost, denoted by the open markers (measured on the left vertical axis), for various refueling operating scenarios [1,2] and cascade configurations (three, four, and five cascade vessels) at several tube trailer cut-off pressures on the horizontal axis (the pressure below which the tube trailer is not used to fill the vehicle tank) for a station size of 250 kg/day. The figure shows that scenario 2 always requires lower compressor throughout, indicating that using the tube trailer to initially fill the vehicle's tank is always more advantageous than scenario 1. Regardless of the employed refueling operation scenario (1 or 2), the four- and five-cascade vessel configurations require much lower compression throughput (capacity) compared with the threecascade-vessel configuration. These results demonstrate that, for the assumed buffer storage vessel size, having additional pressure levels reduces the compressor throughput requirement, leading to lower compression cost.
Fig. 10 also shows that lower tube trailer cut-off pressure values require less compressor throughput and reduce the cost of storage/compression. This reduction in the storage/ compression cost is expected because lower tube trailer cutoff pressure means more hydrogen is dispensed directly from the tube trailer to the vehicle's tank, thus reducing the load on refueling equipment (i.e., storage and compression). However, the required compressor throughput does not decrease monotonically with the reduction in the cut-off pressure, because very low cut-off pressures (below 7 MPa) require significantly more connection time with the vehicle's tank, thus making the tube trailer frequently unavailable to connect with the compressor/cascade system when needed (primarily when only one tube trailer tube has pressure above return pressure). Because there is no decrease in the required compressor throughput for all the cascade storage system configurations for cut-off pressures below 7 MPa, the cut-off
Fig. 11 e Effect of tube-trailers returning at a higher pressure.
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Fig. 12 e Contribution of delivery and refueling costs for various tube trailer delivery scenarios.
pressure was fixed at 7 MPa for all further analyses of the scenario 2 operating strategy. Note that, although the fivecascade-vessel configuration has the lowest compressor throughput, the four-cascade-vessel configuration has the lowest storage/compression cost d but less than 1% lower than that of the five-cascade-vessel configuration.
figure shows, though, the refueling cost savings achieved by reducing the compressor throughput more than offsets the cost incurred for additional trips of tube trailers between the distribution center (delivery) and the stations. If the tube trailer delivery distance significantly exceeds 100 km, however, the increase in delivery cost may exceed the savings achieved by employing higher tube trailer return pressures.
Results: relationship between tube trailer return pressure and required compression throughput
Conclusions Fig. 11 shows the impact of the return pressure of the tube trailer on the required compressor throughput and the combined storage/compression cost for the two refueling operating scenarios [1,2]. The compressor throughout values are represented by the solid markers and measured on the vertical axis, while the storage/compression costs are indicated by the vertical stacked bars and measured on the left vertical axis. The horizontal axis represents the tube trailer operating strategy, with the return pressure denoted within the brackets. As Fig. 11 shows, returning the tube trailer at a higher pressure would reduce the required compressor throughput for all cascade configurations. Note that returning the tube trailer at a higher pressure (5 MPa) makes the fivecascade-vessel (rather than the four-cascade vessel) configuration the lowest-cost option (but by less than 1%). Fig. 11 also shows the tradeoff between compression cost and storage cost, with higher compression and lower storage cost for the four-cascade-vessel configuration compared with the fivecascade-vessel configuration. Fig. 12 shows the contribution of delivery and refueling costs (not including production cost) for delivering hydrogen from a central production/terminal facility to 80 refueling stations (250 kg/day each) located at an average distance of 100 km from the distributing terminal facility. Although the high return pressure decreases the required compressor throughput, thus reducing the refueling cost, it increases the number of tube trailer truck deliveries from the terminal facility to the refueling station, which increases the delivery cost of hydrogen. Fig. 12 shows that, while the refueling cost decreases with increasing tube trailer return pressure from 1.5 MPa to 5 MPa, the corresponding hydrogen delivery cost increases (for the examined delivery parameters). As the
We developed a rigorous model to evaluate various refueling configuration options and operating strategies to determine the lowest-cost option for hydrogen refueling. Our study reveals that there is a tradeoff between the compression and storage capacities for any given fueling demand. Finding the optimum configuration that offers the lowest cost of compression and storage can dramatically reduce the refueling cost. Furthermore, employing a tube trailer to initially fill the vehicle's tank can reduce the compression and storage requirement, thus reducing the refueling cost. Lowering the tube trailer cut-off pressure for initial vehicle refueling and increasing the trailer's return pressure can also reduce the refueling cost, especially in early markets, when the refueling stations will be significantly underutilized. The specific results obtained using the H2SCOPE model depend on many factors, such as vehicle tank size and characteristics, vehicle tank initial pressure, hourly refueling demand, size of buffer storage vessels, cost of components, etc. Although the results cannot be generalized to all hydrogen refueling station capacities and refueling demands, they provide a better understanding of the relationships and tradeoffs among various station components and operating strategies.
Acknowledgment This research effort was supported by the Fuel Cell Technologies Office of the U.S. Department of Energy's Office of Energy Efficiency and Renewable Energy under Contract Number DEAC02-06CH11357.
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Ainner is the inner surface area of the tank Aouter is the outer surface area of the tank THydrogen is the temperature of the Hydrogen gas inside the tank Tinner wall is the temperature of the inner tank wall Touter wall is the temperature of the outer tank wall Tambient is the temperature of the ambient
Appendix Mass Conservation Equation X dm X ¼ min mout dt where, dm/dt is the rate of change of mass inside the vehicle tank min is the mass flowing into the vehicle tank mout is the mass flowing out of the vehicle tank Energy Conservation Equation
Equation of State [35] (Please refer to [35] for the expressions of ao and ar and their partial derivatives) r va Pðt; dÞ ¼ rRT 1 þ vd t Tc r t ¼ ; and d ¼ rc T where,
dU dQ dm ¼ þ Einlet dt dt dt where, dU/dt is the rate of change of internal energy dQ/dt is the rate of heat transfer through the inner tank wall Einlet is the enthalpy entering the tank per unit mass of hydrogen The enthalpy (E) in the energy equation is the sum of the static enthalpy and the kinetic energy per unit mass. The transient heat transfer through the tank wall is modeled via the following partial differential equation: vTðr; tÞ 1 1 v vT ¼ $ rlðr; TÞ vt cðr; TÞrðr; TÞ r vr vr
P is the pressure inside the tank a is the dimensionless reduced Helmholtz free energy ar is the residual contribution rc is Critical molar density r is molar density Tc is critical temperature T is temperature R is Real gas constant Internal Energy [35] (Please refer to [35] for the expressions of ao and ar and their partial derivatives) uðt; dÞ ¼ RTc
where,
vao vt
þ d
o va vt d
where,
T(r,t) is the temperature of the tank wall at any radius r and time t c is the specific heat of the tank material l is the thermal conductivity of the tank material r is the density of the tank material r is the radius of the tank Subject to the following boundary conditions at the inner and outer tank walls: Heat transfer rate at the inner tank wall,
Qin ¼ hinside;avg Ainner THydrogen Tinner wall
u is the molar internal energy ao is the ideal gas contribution Enthalpy [35] (Please refer to [35] for the expressions of ao and ar and their partial derivatives) r r o va va va þ þ1 þd Eðt; dÞ ¼ RT t vt d vt d vd d where E is the molar internal energy
Heat transfer rate at the outer tank wall, QOut ¼ houtside;avg Aouter ðTouter wall Tambient Þ where, Qin is the rate of heat transfer from the hydrogen to the inner tank wall Qout is the rate heat transfer from the outer tank wall to the ambient hinside,avg is the average convective heat transfer coefficient at the inner tank wall houtside,avg is the average convective heat transfer coefficient at the outer tank wall
Compressor Power [8] # " ðk1Þ kJ 1 k Poutlet k _ ¼ ZmRTn 1 Power; sec h k1 Pinlet where, Z is the mean compressibility factor i. h ¼ ZðT; PÞdischarge ZðT; PÞsuction . i h LN ZðT; PÞdischarge ZðT; PÞsuction
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m_ is the mass flow rate; kg mole=sec R is the universal gas constant; kJ=kg mole K T is the inlet gas temperature, K n is the number of stages, h is the isentropic efficiency, k is the ratio of specific heats, Poutlet is the compressor discharge pressure, bar or psi Pinlet is the compressor inlet pressure, bar or psi
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