Waste Heat Sources Research Articles

(Invited) The SOFC Program at the DOE’s Office of Fossil Energy and Carbon Management (FECM) and National Energy Technology Laboratory (NETL)

The Solid Oxide Fuel Cell (SOFC) Program, managed by the U.S. Department of Energy (DOE) Office of Fossil Energy (FE) and administered by the FE’s National Energy Technology Laboratory (NETL) is currently developing low-cost SOFC power generation systems. SOFC power systems have the potential to achieve greater than 60 percent efficiency. The SOFC’s operating temperature is lower than combustion-based processes and precludes NOx formation. In addition, there are near-zero emissions of CO2, criteria pollutants, and particulates. Furthermore, SOFC power systems require approximately one-third the amount of water relative to conventional combustion-based power systems. The Program includes the testing of SOFC with natural gas in distributed applications, including data centers. In addition to SOFC, there are several projects on various aspects of high temperature solid oxide electrolysis cell (SOEC) for electrolysis of water. The development of efficient systems for hydrogen production is very interesting, especially when supplementary heat is provided from solar or other waste heat sources such as nuclear or coal power plants.

MIMO state feedback control for redundantly-actuated LiBr/H[formula omitted]O absorption heat pumping devices and experimental validation

Absorption heat pumping devices (AHPDs, comprising absorption heat pumps and chillers) use mainly thermal energy instead of electricity as the driving energy to provide resource-efficient heating and cooling when using waste heat or renewable heat sources. Despite this benefit, AHPDs are still not a very common technology due to their complexity. However, better modulation and part-load capability, which can be achieved through advanced control strategies, can simplify the use of AHPDs and help to better integrate them into complex energy systems. Therefore, this paper presents a new, dynamic model-based control approach for single-stage AHPDs that can extend an AHPD’s operating range by employing multi-input-multi-output (MIMO) control methods. The control approach can be used for different AHPD applications and thus control configurations, i.e., different combinations of manipulated and controlled variables, and can also be used for redundantly-actuated configurations with more manipulated than controlled variables. It consists of an observer for the state variables and unknown disturbances, a state feedback controller and, in case of redundantly-actuated configurations, a dynamic control allocation algorithm. The proposed control approach is experimentally validated with a representative AHPD for two different control configurations and compared to two benchmark control approaches – single-input-single-output (SISO) PI control representing the state-of-the-art, and model-predictive control (MPC) as an alternative advanced control concept. The experimental validation shows that the two MIMO control approaches (the proposed state feedback and the MPC approach) allow for a wider operating range and hence better part load capability compared to the SISO PI control approach. While MPC generally results in a comparably high computational effort due to the necessity of continuously solving an optimization problem, the proposed state feedback control approach is mathematically simple enough to be implemented on a conventional programmable logic controller. It is therefore considered a promising new control approach for AHPDs with the ability to extend their operating range and improve their part load capability, which in turn facilitates their implementation and thus the use of sustainable heat sources in heating and cooling systems.

Evaluation of low temperature waste heat as a low carbon heat resource in the UK

The capture and transport of waste heat represents a great opportunity for the decarbonisation of heat supply in buildings. To date, mostly high temperature waste heat has been reused and reported. However, with the recent advent of low and ambient temperature (4th and 5th generation) district energy networks, there is scope for the recovery and utilisation of heat from a range of novel, low temperature sources. The current study represents one of the first attempts to quantify the size of this opportunity, with particular focus in the UK, and complements the few previous attempts at estimating low temperature waste heat by focussing on a range of novel sources. The approach used was to evaluate a number of low temperature waste heat sources to determine: (a) the annual quantity of waste heat generated; and (b) the temperature(s) of the waste heat, for each heat source. In many cases, this was achieved using methodology and assumptions derived from the authors’ earlier investigations. The relative merits and potential of each heat source are also discussed, with respect to location, proximity to end users, need for upgrade using a heat pump, continuity of supply and distribution options for reuse, for example by using district energy networks with different operating temperatures. The total quantity of waste heat energy identified from the heat sources considered in this study, for England, Wales and Northern Ireland, was estimated to be 572 TWh.a−1, which would represent 132% of the total energy consumption for heat in these countries (432 TWh.a−1). Although this study focused on the UK potential for low temperature waste heat, the estimation methods developed and resulting analysis are generic and could also be applied in the context of other countries.

Achieving reasonable waste heat utilization in all truck operating conditions via a dual-pressure organic rankine cycle and its operating strategy

The engine of truck contains multiple waste heat sources. Waste heat recovery (WHR) in truck is a necessary approach to achieve energy saving and cleaner production. These heat sources vary transiently and have thermal management requirements. Therefore, effective waste heat utilization should fulfill both waste heat recovery and thermal management requirements. The dual-pressure organic Rankine cycle (DPORC) is suitable for complex and fluctuating heat sources. Furthermore, a suitable operation strategy is essential for the reasonable waste heat utilization under all engine working conditions and complex road conditions. Therefore, this study designs a DPORC-WHR system and its operation strategy. The essence of this operating strategy is that the evaporation pressure of system can be regulated at different engine loads, thus regulating the heat exchange of each waste heat source. The goal of this operating strategy is to control the waste heat utilization of exhaust gas, coolant and charge air to near 100% at all operating conditions. The dynamic model is established to validate the effectiveness of the proposed DPORC-WHR system and its operation strategy. The results show that the utilization rate of coolant, charge air and exhaust gas is greater than 87.47%, 88.34% and 95.45% respectively for all engine operating conditions. Under the road conditions tested, the DPORC-WHR system can improve engine BTE by 5.98%. The temperature of the coolant and charge air after heat exchange, superheat degree and pressure can be maintained within the target range. This study provides a basis for the operation and control of ORC-WHR system after coupling with the vehicle in the future.

Structural optimization of resonance tubes for a looped thermoacoustic engine with multiple heat sources

The advantage of coupling different heat sources with each thermoacoustic core unit in a three-stage looped traveling-wave thermoacoustic system is used to solve the application problem of multiple waste heat sources. The effects of the heat-side heat exchanger temperature, the resonance tube radius and length, and their interaction terms on the thermoacoustic thermodynamic properties are analyzed using response surface methodology on the premise that thermoacoustic core structures remain unchanged. The results indicate that prediction deviations for acoustic power, thermoacoustic conversion efficiency, and relative Carnot efficiency are within ±9%, ±3%, and ±3%, respectively. The acoustic power can be improved by increasing the hot-side heat exchanger temperature and the resonance tube radius. Under the same heat source conditions, the acoustic power, thermoacoustic conversion efficiency, and relative Carnot efficiency of the optimized thermoacoustic system show the highest increases of 49.63%, 4.82%, and 3.20%, respectively, compared to the non-optimized thermoacoustic system. The optimized variable-temperature system not only has higher thermodynamic efficiency compared with the optimized constant-temperature system but also can realize the complementary regulation among the thermoacoustic engine units by matching decreasing-gradient variable temperature and increasing-gradient variable radii and effectively broaden the working temperature range of the looped thermoacoustic system.

Identification of waste heat energy sources of a conventional steam propulsion plant of an LNG carrier

Identification of waste heat energy sources of a conventional steam propulsion plant of an LNG carrier

Utilization of mine waste heat in phase change rechargeable battery

Mine geothermal energy has been recognized as “heat hazard”, which is harmful to the health of miners and causes disasters. In order to realize the transformation of mine geothermal energy and waste heat from “hazard/waste” into “treasure”, this paper analyzes the distribution characteristics and genesis of mine geothermal energy with the field geothermal temperature monitoring data, evaluates geothermal reserves, and reveals the mutual influencing mechanism of stratified exploitation of two-layer geothermal reservoir and the law of thermal energy conduction and evolution in the stope of geothermal-coal synergetic mining (GE-COSM), using numerical models verified by experiments. In the end, the improvement effect of mine waste heat on the development potential of geothermal-coal mine (G-CM) was analyzed. The result shows that: The present geothermal field distribution characteristics of Anju Mine are high in the north and low in the south, high in the east and low in the west. There are two layers of zoned reservoir, with the temperatures of 43 °C and 54 °C respectively, the average heat flow value 70.1 mW/m2 and 80.9 mW/m2 respectively, and the geothermal water type SO42--Na+·Ca2+. The simultaneous exploitation of the two geothermal reservoirs will form a Coal-Austria geothermal reservoir joint influence area(C-Area) with lower temperature, which reduces the harm of “heat hazard” to miners. But the phase change heat storage function of functional cemented paste backfill material for phase change heat storage (F-CBM) is not fully utilized in the late stage of geothermal exploitation. The mine generates 4.6 × 1011 J of waste heat per day, and according to the type of heat source of mine waste heat can be continuously “heat charging” for a conventional backfill working face. Moreover, under the action of high temperature surrounding rock, the thermal energy recovery rate is greater than 1, and under the action of “heat charging”, the average maximum value of solid phase ratio is greater than 70 %. Therefore, the phase change rechargeable battery mode creatively proposed by this paper is significantly better than the traditional rock layer heat storage mode and is worth vigorously popularizing.

Driving success towards zero carbon energy targets for UK’s Local Authorities

This paper draws on three recent case studies which have shown encouraging economic results in meeting net zero carbon emissions targets through Smart Local Energy Systems (SLES) in different localities across England, based on the GreenSCIES model. The blueprint for the GreenSCIES SLES was developed in Islington, London, and consists of a 5th generation ambient loop district heat network using wasteheat from a large data centre, and includes electric vehicle charging, storage and solar PV. This allows for heat sharing between buildings and applications for heat recovery from local sources. In Sandwell, Birmingham, where the heating demand is nearly ten times higher than the cooling demand the design is based on a 4th generation heat network with wasteheat from a local metal foundry and some cooling supply and heat storage in the aquifer. A study in Barnsley, Sheffield, explored wasteheat from a local glass factory and considered mine workings for providing seasonal storage of heat for resilience to a single source industry. This scheme could be further expanded, increasing the available carbon emissions savings. These examples provide feasible and economic SLES projects demonstrating the importance of collaboration between researchers, local government and industry. They also illustrate adaptations of the original GreenSCIES concept providing pathways towards net zero carbon for a diverse range of urban locations with different housing density and waste heat sources.

Sustainable Energy Planning and Management Vol 38

This 38th volume of the International Journal of Sustainable Energy Planning and Management presents some of the newest work within in the energy planning, energy systems analyses and district heating area. Articles focus on multi objective optimisarion for a community in the Alps, carbon neutrality in Estonia, the prospects of heat pumps combined with thermal energy storage in maximising self-consumpotion from a photovoltaic field and methods for assessing district heating options. Other work focus on gamification tools for assessing energy efficiency measures, country analyses of economic and environmental indicators, the adaption of alternative fuel vehicles, and the use of waste heat sources for district heating.

Design approach to extend and decarbonise existing district heating systems - case study for German cities

This paper aims to present an approach for the planning of carbon low heat supply in a future district heating system based on open data for German cities with existing district heating networks. One focus is on the integration of industrial waste heat and the uncertainty of future waste heat sources as well as restrictions on the use of biomass. For that purpose, knowledge about the energy demand is necessary. In a first step it is shown how the demand around a heating network is estimated with spatial data and a load profile is generated. Local available heat sources are examined according to their suitability and their kind of integration in the heating network. As heat production from different units are optimised, the development of a simulation model will be presented. The simulation is based on the optimisation of the operational costs of the used technologies for heating supply. Different scenarios covering various technologies and economic assumptions are applied. The results show the levelized costs of heating as well as the ecological performance. A sensitivity analysis shows the importance of uncertainties for the economic assumptions. The results showing levelized costs of heating as well as the ecological performance underlining the advantage of excess heat integration.

Experimental assessment of the first industrial implementation of ejector refrigeration system operating with R1233zd(E) driven by ultra-low temperature heat source

Among the available technologies of heat driven refrigeration systems, ejector systems allow for utilisation of heat at the lowest potential for generation of refrigeration capacity, i.e. temperature of heat source lower than 80 °C. The paper provides with the results of experimental investigations of the ejector refrigeration system applied in industrial company for recovering waste heat from reciprocating compressors units. For the first time the ejector system has been tested for operation with extremely low GWP and non-flammable R1233zd(E) refrigerant receiving heat at a temperature lower than 70 °C. The performance of the tested refrigeration system in term of mass entrainment ratio, COP, and refrigeration capacity for three levels of motive temperature are presented. The available thermal capacity of the waste heat source for tested system has been 200 kW. The system has achieved the entrainment ratio of up to 0.24 which allowed for obtaining up to 45 kW of refrigeration capacity. The overall efficiency coefficients in the range of 0.63–0.78 have been determined. It has been shown that the overall efficiency of the tested system is lower than that achieved with use of R1234zd(E) refrigerant and isobutane (R600a) under similar range of operation conditions.

Control-oriented modeling of a LiBr/H[formula omitted]O absorption heat pumping device and experimental validation

Absorption heat pumping devices (AHPDs, comprising absorption heat pumps and chillers) are devices that use thermal energy instead of electricity to generate heating and cooling, thereby facilitating the use of waste heat and renewable energy sources such as solar or geothermal energy. Despite this benefit, widespread use of AHPDs is still limited. One reason for this is partly unsatisfactory control performance under varying operating conditions, which can result in poor modulation and part load capability. A promising approach to tackle this issue is using dynamic, model-based control strategies, whose effectiveness, however, strongly depend on the model being used. This paper therefore focuses on the derivation of a viable dynamic model to be used for such model-based control strategies for AHPDs such as state feedback or model-predictive control. The derived model is experimentally validated, showing good modeling accuracy. Its modeling accuracy is also compared to alternative model versions, that contain other heat transfer correlations, as a benchmark. Although the derived model is mathematically simple, it does have the structure of a nonlinear differential–algebraic system of equations. To obtain an even simpler model structure, linearization at an operating point is discussed to derive a model in linear state space representation. The experimental validation shows that the linear model does have slightly worse steady-state accuracy, but that the dynamic accuracy seems to be almost unaffected by the linearization. The presented new modeling approach is considered suitable to be used as a basis for the design of advanced, model-based control strategies, ultimately aiming to improve the modulation and part load capability of AHPDs.

Estimating the Potential for Waste Heat Recovery in Italian Dairy Sector Using a Bottom-Up Approach and Data from Energy Audits

As a result of the expected increase in food demand, improving the sustainability of the food industry has become a priority worldwide. The recovery of industrial waste heat is widely regarded as a key strategy to reduce the energy consumption and greenhouse gas emissions of food manufacturing processes. Estimating the available recoverable waste heat can contribute to driving actions that promote the effective exploitation of such an untapped energy source. This study aimed to evaluate the waste heat potential of large and energy-intensive Italian dairy companies. To this end, a methodology that combined key transfer figures adapted to the Italian industrial context and data on fossil fuels consumption from energy audits was adopted to assess the technical waste heat potential. A comparison with the overall waste heat recovered from the projects proposed by large and energy-intensive dairy companies was carried out to estimate the residual waste heat available. Finally, the economic waste heat potential was assessed by varying the heat transfer operating conditions between the waste heat sources and sinks, and assuming that waste heat recovery was operated through heat exchanger technology. The technical waste heat potential of large and energy-intensive dairy industries was valued at roughly 75.6 GWht/year. Simulation results also showed that more than 90% of the studied companies exhibited payback periods below three years for all waste heat recovery projects, except for those involving gas-to-gas or gas-to-liquid heat transfers.

Design of the Organic Rankine Cycle for High-Efficiency Diesel Engines in Marine Applications

Over the past few years, fuel prices have increased dramatically, and emissions regulations have become stricter in maritime applications. In order to take these factors into consideration, improvements in fuel consumption have become a mandatory factor and a main task of research and development departments in this area. Internal combustion engines (ICEs) can exploit only about 15–40% of chemical energy to produce work effectively, while most of the fuel energy is wasted through exhaust gases and coolant. Although there is a significant amount of wasted energy in thermal processes, the quality of that energy is low owing to its low temperature and provides limited potential for power generation consequently. Waste heat recovery (WHR) systems take advantage of the available waste heat for producing power by utilizing heat energy lost to the surroundings at no additional fuel costs. Among all available waste heat sources in the engine, exhaust gas is the most potent candidate for WHR due to its high level of exergy. Regarding WHR technologies, the well-known Rankine cycles are considered the most promising candidate for improving ICE thermal efficiency. This study is carried out for a six-cylinder marine diesel engine model operating with a WHR organic Rankine cycle (ORC) model that utilizes engine exhaust energy as input. Using expander inlet conditions in the ORC model, preliminary turbine design characteristics are calculated. For this mean-line model, a MATLAB code has been developed. In off-design expander analysis, performance maps are created for different speed and pressure ratios. Results are produced by integrating the polynomial correlations between all of these parameters into the ORC model. ORC efficiency varies in design and off-design conditions which are due to changes in expander input conditions and, consequently, net power output. In this study, ORC efficiency varies from a minimum of 6% to a maximum of 12.7%. ORC efficiency performance is also affected by certain variables such as the coolant flow rate, heat exchanger’s performance etc. It is calculated that with the increase of coolant flow rate, ORC efficiency increases due to the higher turbine work output that is made possible, and the condensing pressure decreases. It is calculated that ORC can improve engine Brake Specific Fuel Consumption (BSFC) from a minimum of 2.9% to a maximum of 5.1%, corresponding to different engine operating points. Thus, decreasing overall fuel consumption shows a positive effect on engine performance. It can also increase engine power output by up to 5.42% if so required for applications where this may be deemed necessary and where an appropriate mechanical connection is made between the engine shaft and the expander shaft. The ORC analysis uses a bespoke expander design methodology and couples it to an ORC design architecture method to provide an important methodology for high-efficiency marine diesel engine systems that can extend well beyond the marine sector and into the broader ORC WHR field and are applicable to many industries (as detailed in the Introduction section of this paper).

Impact of external electric resistance on the power generation in the thermoelectric energy harvesting blocks

Energy can be harvested from various energy sources within a building. In this study, a thermoelectric generator-assisted energy harvesting block was proposed, aiming to utilize the waste heat source of the exterior wall of the building. The energy harvesting block comprises a thermoelectric generator and phase change material for converting waste heat from the building envelope and heat flux from the outside into electricity. Multiple energy harvesting blocks are required to construct an energy harvesting block wall. Thus, the electrical arrangements of multiple energy harvesting blocks and their effects on external resistance were analyzed. The arrangements consisted of a series array, parallel array, and combination array. Experiments were performed with a total of nine cases by connecting 1.6 Ω, 15 Ω, and 60 Ω with the same external resistance as the internal resistance of each array. The temperature and closed-circuit voltage were measured based on the sol-air temperature profile in December. The voltage and current were more affected by the connected external resistance than by the type of array. The maximum generated energy was 0.837 Wh/day when 60 Ω was connected to the series arrangement. In terms of the generated energy, the series arrangement was the most advantageous.

(Invited) The SOFC Program at the DOE’s Office of Fossil Energy and Carbon Management (FECM) and National Energy Technology Laboratory (NETL)

The Solid Oxide Fuel Cell (SOFC) Program, managed by the U.S. Department of Energy (DOE) Office of Fossil Energy and Carbon Management (FECM) and administered by the FECM’s National Energy Technology Laboratory (NETL) is currently developing low-cost SOFC’s and reversible SOFC systems (rSOCFs). SOFC power systems have the potential to achieve greater than 60 percent efficiency. The SOFC’s operating temperature is lower than combustion-based processes and precludes NOx formation. In addition, there are near-zero emissions of CO2, criteria pollutants, and particulates. Furthermore, SOFC power systems require approximately one-third the amount of water relative to conventional combustion-based power systems. The Program includes the testing of SOFC with natural gas in distributed applications, including data centers. In addition to SOFC, there are several projects on various aspects of high-temperature solid oxide electrolysis cell (SOEC) for electrolysis of water. Development of reversible SOFC systems, rSOCFs, is the new central focus of FECM. The development of efficient systems for hydrogen production is very interesting, especially when supplementary heat is provided from solar or other waste heat sources such as nuclear power plants.

Recent progress in membrane distillation configurations powered by renewable energy sources and waste heat

Membrane distillation (MD) is a promising process for high-quality water reclamation mainly due to its high capacity to retain non-volatile components and operate without the need for hydraulic pressure. However, its low energy efficiency limits its widespread use. With that in mind, this paper critically summarizes the different engineered configurations of membrane distillation coupled with renewable energy sources and waste heat, namely: solar, geothermal, and waste heat, to overcome the limitations associated with low energy efficiency commonly reported. From all sources, solar-driven processes are preferred due to the greater technological maturity related to flat plate collectors (FPCs), evacuated tube collectors (ETCs), compound parabolic concentrators (CPCs), salt-gradient solar ponds (SGSPs), and solar stills. The integration with renewable energy sources represents one of the leading solutions for energy consumption, proving to be a decisive choice for the system's economic viability. The summarized studies suggest membrane distillation's potential to be economically competitive with the classical membrane separation process (ultrafiltration, nanofiltration, and reverse osmosis) when waste heat is considered for wastewater treatment. Even under these conditions, alternative energy sources have a few shortcomings to be investigated in future studies, such as short periods of solar radiation and the intermittence of waste heat sources. These factors still represent obstacles to an uninterrupted and large-scale operation of membrane distillation and must be overcome in a near future. Even so, successful case studies on full-scale systems that integrate membrane distillation and solar energy sources suggest the process's potential for widespread use in the near term.

Novel multi-helical coil heat exchanger-based small-scale organic Rankine cycle: A detailed heat transfer analysis

This paper discusses a prototype of the ORC, which is developed utilizing a novel multi-coil evaporator and condenser for the waste heat source with a temperature below 100 °C. R123 acts as a working fluid for the ORC. The thermal performance of a multi-helical coil is evaluated experimentally and compared to the single-helical coil heat exchanger available in the literature.The performance of a novel multi-coil heat exchanger depicts that when the Reynolds Number varies from 60000 to 120000, the heat transfer coefficient varies from 1560 W/(m2K) to 2900 W/(m2K) for a single coil heat exchanger and 3014 W/(m2K) to 4531 W/(m2K) for multi helical coil evaporator. The Nusselt Number varies from 300 to 570 for single-coil heat exchangers and 715 to 1076 for multi-helical coil heat exchangers. The results show that the expander's power output is around 2.14 kW and proportional to the evaporator temperature and pressure increase. The high condensing temperature decreases the expander power output. The main contribution of the present work is developing a small ORC system with novel multi-helical coil heat exchangers and testing them on a lab scale for the most probable application to fulfill the electricity requirement in remote areas in the future.

Influence of engine heat source conditions on a small-scale CO2 power generation system

Employing a CO2 power generation system to recover waste heat from engines can reduce fuel consumption and CO2 emissions by producing additional electric power. Nevertheless, the fluctuation in engine operating conditions would cause variations in waste heat sources and affect system performances largely. Hence, an experimental performance test at various engine conditions was implemented by the construction of a small-scale (10 kW) CO2 power generation system. Key components, including the turbine expander and printed circuit heat exchanger, were specifically designed and constructed. The steady-state and transient performances of critical components and the integrated system were carried out. Experimental results of the turbine expander at varying engine conditions revealed the potential for long-term and stable operation under dynamic mass flow rate, inlet temperature, and pressure ratio. The maximum total generation power and efficiency reached 11.55 kW and 58.92%. The printed circuit heat exchanger used to exploit engine exhaust gas showed satisfactory performances in balancing the trade-off between heat transfer and pressure drop. The total pressure drop of engine exhaust gas was lower than 4 kPa determined by both exhaust mass flow and temperature, considering all the variable engine conditions. Despite that a performance penalty was observed at the off-design operation of the integrated system because of the decrease in the waste heat input, the maximum net power and thermal efficiency reached 10.57 kW and 6.59%, respectively, at the engine condition of 1100 rpm, 1200 N m, with a relative improvement of 6.3% in engine brake thermal efficiency.

Modelling of waste heat integration into an existing district heating network operating at different supply temperatures

A promising way to make use of waste heat sources is to distribute the heat to nearby buildings via district heating systems to cover the heat demands of the buildings. The integration of a waste heat source into an existing district heating system must be studied in advance to avoid difficulties in network operation and to ensure the required heat supply to all connected buildings. Simultaneously, supply temperature reduction can improve the overall system efficiency and should also be considered for a sustainable transformation of existing district heating systems.In this paper, we develop a district heating model with multiple supplying heat sources to study the influence of an additional integrated heat source and the effects of reduced supply temperatures on the network conditions. With the developed model, we investigate the waste heat integration into an existing district heating system at a German research facility campus. Therefore, we test different integrated waste heat shares to identify arising bottlenecks and to check for the sufficient heat supply to the connected consumers. Furthermore, we test the opportunity to additionally lowering the supply temperatures in the district heating network. The simulation results show that waste heat integration is possible at the investigated district heating system up to 40%. However, simultaneously lowering the supply temperature leads to greater challenges as more bottlenecks arise and additional buildings are affected by insufficient supply.