Simulation Of Process Research Articles

Numerical Modeling of the Fluids Petroleum Flow Through the Supersonic Separator

In the context of increasing concerns regarding the amplification of the thermal effects of climate change, the Council of the European Union has proposed the reduction (up to the elimination) of the use of fossil fuels. For this purpose, the implementation of new ecological (renewable) fuels is being analyzed to reduce the carbon dioxide footprint, natural gas being the transition fuel. Also, in the next period, an increase in the demand for methane, the exploitation of condensate deposits, those with natural gas mixed with acid gases (containing hydrogen sulfide, carbon dioxide, and nitrogen), as well as oil deposits with associated natural gas, which will require their treatment (to eliminate saline or non-saline water, mechanical impurities, of condensate and acid gases). At the same time, the exploitation of offshore deposits in deep waters will be emphasized, which will lead to the location of treatment equipment on the seabed. The present work discusses the simulation of natural gas treatment processes, focusing on the separation from methane (in the supersonic field) of water, condensate, and acid gases.

Exploring the promotion effect of low MnCoOx doping for low-temperature NH3-SCR of 13X zeolite synthesized from coal fly ash

Using fly ash rich in SiO2 and Al2O3 to prepare heterogeneous zeolite catalysts is an efficacious pathway for the resource development of solid waste. Herein, 13X zeolite with a rich specific surface area was synthesized from fly ash, and low amount of active components (Mn and Co) was added during the preparation of the 13X zeolite. Finally, a series of low-load xMnyCo/13X denitration catalysts were successfully prepared. The results show that the low supported 1Mn2Co/13X zeolite catalyst exhibits excellent selective catalytic performance, with higher than 80 % NO conversion and more than 90 % N2 selectivity during 150–350 ℃. It also demonstrates excellent resistance to both water and sulfur. Physicochemical characterization analysis indicated that a little Mn and Co were doped on the surface of 13X zeolite did not have a detailed crystal structure. The element Co doping increased the proportion of Mn3+, Mn4+ and Ov on 13X zeolite. The results of in situ DRIFTs demonstrated that the NH3-SCR reaction on the surface of 1Mn2Co/13X zeolite followed both the E-R and L-H mechanisms. Additionally, process simulation results further show that using 1Mn2Co/13X zeolite as an industrial denitration agent can reduce material costs by 64.0 % and operating costs by nearly 20 %.

A GIS-based assessment of the carbon emission reduction potential of the solar-enhanced char-cycling biomass pyrolysis process in China

Bioenergy and solar energy are the two widely used renewable energies, which have great potential to satisfy the global energy demand. Solar enhanced char-cycling biomass pyrolysis (SCCP) was proposed to integrate bioenergy and solar energy, could be used to make bioenergy fully carbon-negative. A geographical information system (GIS) based method was used to assess the GHG reduction potential and biofuel production potential of SCCP in China. Existing datasets were used to obtain geographical potential and biomass resource amount. Process simulation was conducted to obtain the technical data. The geographical potential results showed that with a DNI (direct normal irradiance) threshold of 1400 kWh/m2, the national suitable area for SCCP plant construction was 3.25 % of the total national area, the total convertible biofuel potential ranges from 1.86E+06 to 1.94E+06 GWh with different concentrating solar technologies. When considering biochar sequestration, the GHG emission reduction potential increased further, the total GHG emission reduction potential increased from 13.97 Mt CO2 eq to 15.42 Mt CO2 eq. Notably, Yunnan has the highest GHG emission reduction potential per unit of energy when running the pyrolysis process with solar energy, which was −8.58 g CO2 eq/kWh. The results revealed that the SCCP process could further decarbonize biofuel production in China.

The transient dynamic wave process in unidirectional composites

The propagation of nonstationary waves in unidirectional composite material is simulated by finite-element analysis. The composite material is explicitly formulated, i.e., discrete, stiff, elastic inclusions uniformly distributed in a viscoelastic matrix are modeled. An original procedure rooted in the linear Boltzmann–Volterra equations accounts for the viscoelastic effects in the matrix behavior. The chosen approach involves finite-element simulations of the transient wave process in two indicative configurations to study the effects attributed to wave scattering by the inclusions. The transient wave propagation in the unidirectional composite material and a viscoelastic specimen without inclusions are compared. Peculiarities in the numerical results due to the finite-element algorithm employed are decoupled from the output that reveals purely mechanical phenomena. For this purpose, the transient wave propagation in a one-dimensional elastic continuum, for which the exact analytical solution is well known, is effectively obtained by finite-element analysis. Furthermore, based on the unidirectional composite a homogenized model is defined by applying the mixture rule. An additional comparison between the composite containing discrete inclusions and the analogous homogenized material provides a basis to assess the output of models obtained by implementing a self-consistent scheme in a broader context.

Optimizing emergency department efficiency: a comparative analysis of process mining and simulation models to mitigate overcrowding and waiting times

ObjectiveOvercrowding and extended waiting times in emergency departments are a pervasive issue, leading to patient dissatisfaction. This study aims to compare the efficacy of two process mining and simulation models in identifying bottlenecks and optimizing patient flow in the emergency department of Al-Zahra Hospital in Isfahan. The ultimate goal is to reduce patient waiting times and alleviate population density, ultimately enhancing the overall patient experience.MethodsThis study employed a descriptive, applied, cross-sectional, and retrospective design. The study population consisted of 39,264 individuals referred to Al-Zahra Hospital, with a sample size of at least 1,275 participants, selected using systematic random sampling at a confidence level of 99%. Data were collected through a questionnaire and the Hospital Information System (HIS). Statistical analysis was conducted using Excel software, with a focus on time-averaged data. Two methods of simulation and process mining were utilized to analyze the data. First, the model was run 1000 times using ARENA software, with simulation techniques. In the second step, the emergency process model was discovered using process mining techniques through Access software, and statistical analysis was performed on the event log. The relationships between the data were identified, and the discovered model was analyzed using the Fuzzy Miner algorithm and Disco tool. Finally, the results of the two models were compared, and proposed scenarios to reduce patient waiting times were examined using simulation techniques.ResultsThe analysis of the current emergency process at Al-Zahra Hospital revealed that the major bottlenecks in the process are related to waiting times, inefficient implementation of doctor’s orders, delays in recording patient test results, and congestion at the discharge station. Notably, the process mining exercise corroborated the findings from the simulation, providing a comprehensive understanding of the inefficiencies in the emergency process. Next, 34 potential solutions were proposed to reduce waiting times and alleviate these bottlenecks. These solutions were simulated using Arena software, allowing for a comprehensive evaluation of their effectiveness. The results were then compared to identify the most promising strategies for improving the emergency process.ConclusionIn conclusion, the results of this research demonstrate the effectiveness of using simulation techniques and process mining in making informed, data-driven decisions that align with available resources and conditions. By leveraging these tools, unnecessary waste and additional expenses can be significantly reduced. The comparative analysis of the 34 proposed scenarios revealed that two solutions stood out as the most effective in improving the emergency process. Scenario 19, which involves dedicating two personnel to jointly referring patients to the ward, and scenario 34, which creates a dedicated discharge hall, have the potential to create a more favorable situation.

Runtime integration of machine learning and simulation for business processes: Time and decision mining predictions

Recent research in Computer Science has investigated the use of Deep Learning (DL) techniques to complement outcomes or decisions within a Discrete Event Simulation (DES) model. The main idea of this combination is to maintain a white box simulation model complement it with information provided by DL models to overcome the unrealistic or oversimplified assumptions of traditional DESs. State-of-the-art techniques in BPM combine Deep Learning and Discrete Event Simulation in a post-integration fashion: first an entire simulation is performed, and then a DL model is used to add waiting times and processing times to the events produced by the simulation model.In this paper, we aim at taking a step further by introducing Rims (Runtime Integration of Machine Learning and Simulation). Instead of complementing the outcome of a complete simulation with the results of predictions a posteriori, Rims provides a tight integration of the predictions of the DL model at runtime during the simulation. This runtime-integration enables us to fully exploit the specific predictions while respecting simulation execution, thus enhancing the performance of the overall system both w.r.t. the single techniques (Business Process Simulation and DL) separately and the post-integration approach. In particular, the runtime integration ensures the accuracy of intercase features for time prediction, such as the number of ongoing traces at a given time, by calculating them during directly the simulation, where all traces are executed in parallel. Additionally, it allows for the incorporation of online queue information in the DL model and enables the integration of other predictive models into the simulator to enhance decision point management within the process model. These enhancements improve the performance of Rims in accurately simulating the real process in terms of control flow, as well as in terms of time and congestion dimensions. Especially in process scenarios with significant congestion – when a limited availability of resources leads to significant event queues for their allocation – the ability of Rims to use queue features to predict waiting times allows it to surpass the state-of-the-art. We evaluated our approach with real-world and synthetic event logs, using various metrics to assess the simulation model’s quality in terms of control-flow, time, and congestion dimensions.

Optimal iterative learning PI controller for SISO and MIMO processes with machine learning validation for performance prediction

The multivariable process plays a significant role in industrial applications, and designing a controller for the Multi-Input Multi-Output process is challenging due to dynamic process changes and interactions between system variables. Traditionally, the PI family of controllers has been used for its simple design, easy tuning, and quick deployment. However, these processes require complex control actions due to multiple loops in process plants. Thus, this paper proposes an Iterative Learning Controller Dead-time compensating PI, which utilizes the newly developed hybrid Simulated Annealing-Ant Lion Optimization algorithm for Single-Input Single-Output process simulation and real-time experimentation on the Quadruple Tank System. To validate the effectiveness of the developed controller, Machine Learning techniques such as regression and ensemble trees are used to accurately predict the actual system response using error values from respective processes. The simulation and experimental results demonstrate that the proposed controller achieved better performance. The regression and ensemble tree algorithm models effectively predicted the actual response. The obtained data shows that the proposed controller improved system stability and robustness by minimizing nearly half of the overshoot and improving settling time, with an average of 29.9596% faster than the other controller in the SISO process and 14.6116% in the MIMO process.

Business process simulation: Probabilistic modeling of intermittent resource availability and multitasking behavior

In business process simulation, resource availability is typically modeled by assigning a calendar to each resource, e.g., Monday–Friday, 9:00–18:00. Resources are assumed to be always available during each time slot in their availability calendar. This assumption often becomes invalid due to interruptions, breaks, or time-sharing across processes. In other words, existing approaches fail to capture intermittent availability. Another limitation of existing approaches is that they either do not consider multitasking behavior, or if they do, they assume that resources always multitask (up to a maximum capacity) whenever available. However, studies have shown that the multitasking patterns vary across days. This paper introduces a probabilistic approach to model resource availability and multitasking behavior for business process simulation. In this approach, each time slot in a resource calendar has an associated availability probability and a multitasking probability per multitasking level. For example, a resource may be available on Fridays between 14:00–15:00 with 90% probability, and given that they are performing one task during this slot, they may take on a second concurrent task with 60% probability. We propose algorithms to discover probabilistic calendars and probabilistic multitasking capacities from event logs. An evaluation shows that, with these enhancements, simulation models discovered from event logs better replicate the distribution of activities and cycle times, relative to approaches with crisp calendars and monotasking assumptions.

Understanding the Level of Integration in Existing Chemical Clusters: Case Study in the Port of Rotterdam

AbstractThe petrochemical industry is composed of several interconnected processes that use fossil-based feedstock for producing chemicals. These processes are typically geographically clustered and often belong to different parties. Reducing the environmental impacts of the petrochemical industry is not straightforward due to, on the one hand, their reliance on fossil fuels for energy and as a feedstock and, on the other hand, the significant level of interconnected energy and material flows among processes. Current methods for analyzing changes to existing processes cannot capture the multitude and level of interactions. The goal of this paper is to create a model of a petrochemical cluster and analyze its physical characteristics and performance. This paper addresses this goal by developing an assessment method that combines process simulations, multiplex graph analysis, and key performance indicators. The method is applied to a case study based on the petrochemical cluster in the Port of Rotterdam, resulting in a uniquely highly detailed model of a petrochemical cluster. The network analysis results show that only some of the processes are very interconnected. From the performance analysis, it can be observed that the olefins process is the most carbon-intense and has high CO2 emissions. Additionally, the results showed the importance of considering existing interconnections when assessing the current performance of existing petrochemical clusters or the performance due to future changes to chemical processes. For instance, some changes would occur to an industrial cluster by introducing alternative carbon sources, such as biomass or CO2.

Numerical Simulation and Critical Threshold Analysis of the Failure Process for Shield Tail Sealing System under High Water Pressure

Numerical Simulation and Critical Threshold Analysis of the Failure Process for Shield Tail Sealing System under High Water Pressure

Shooting Simulator «Inhibitor»: Mathematical Support of Shot Special Effects

The algorithms for preparing shooters to perform an exercise, conducting its course with real-time informing, as well as the implementation of mathematical support of shot special effects (sounds, tracers, explosions, hits, and misses) for the optical-electronic shooting simulator 'Inhibitor' developed at Institute of Mechanics UdmFRC UB RAS and at facilities of Computer Department of Kalashnikov ISTU jointly with JSC «Kalashnikov» Concern» are described. A tactical and technical task is given for the visual and sound effects of a shot, such as tracers, grenade ruptures, misses, return fire, and controlled flight of PTURS. In addition, the manager must monitor the weapon simulator sensors during the preparation of the exercise (magazine, fire switch, cartridge inside the barrel and sight readings) and conduct the course of the exercise with real-time viewing of both targets and shots and altering the ammunition number and type (all ammunition can be made tracer ones). The arrows are selected from the department database for convenience. Viewing shooting errors and aiming along with hit points allows correction of trainees’ actions by means of commands and quick display service information for trainee independent classes on the projection screen. The study the factors affecting ballistic dispersion was carried out and the recommendations for its modeling were formulated. The literature review confirms the potential of further research and development of electronic rifle simulators via improvement of computational tools and the development of software libraries in order to increase the accuracy of shot process simulation and flexible display adjustment of current training exercise results. It is necessary to expand realistic opportunities of shot special effects and reduce the cost constantly, which means to increase the competitiveness of electronic shooting simulators.

High-Accuracy Positivity-Preserving Finite Difference Approximations of the Chemotaxis Model for Tumor Invasion.

Numerical simulation of the complex evolution process for tumor invasion plays an extremely important role in-depth exploring the bio-taxis phenomena of tumor growth and metastasis. In view of the fact that low-accuracy numerical methods often have large errors and low resolution, very refined grids have to be used if we want to get high-resolution simulating results, which leads to a great deal of computational cost. In this paper, we are committed to developing a class of high-accuracy positivity-preserving finite difference methods to solve the chemotaxis model for tumor invasion. First, two unconditionally stable implicit compact difference schemes for solving the model are proposed; second, the local truncation errors of the new schemes are analyzed, which show that they have second-order accuracy in time and fourth-order accuracy in space; third, based on the proposed schemes, the high-accuracy numerical integration idea of binary functions is employed to structure a linear compact weighting formula that guarantees fourth-order accuracy and nonnegative, and then a positivity-preserving and time-marching algorithm is established; and finally, the accuracy, stability, and positivity-preserving of the proposed methods are verified by several numerical experiments, and the evolution phenomena of tumor invasion over time are numerically simulated and analyzed.

Software for CO2 Storage in Natural Gas Reservoirs

The paper presents a simulation-based approach for optimizing CO2 injection into depleted gas reservoirs, with the goal of enhancing underground CO2 storage. The research employs a two-dimensional dynamic reservoir model, developed using Darcy’s law, to describe gas flow in a pressure-homogeneous porous medium, along with real gas equations. The model integrates the Du Fort–Frenkel and finite-difference methods to accurately simulate the behavior of CO2 during injection and storage. Real data from an operational gas storage facility were used to calibrate the model. CO2sim v1 software, specifically developed for this purpose, simulates CO2 injection cycles and quiescence phases, enabling the optimization of storage capacity and energy efficiency. The reservoir model, based on the engineering of the geological structure, is discretized into approximately 16,000 cells and solved using the finite-difference method, allowing for rapid simulation of CO2 injection and quiescence processes. The average computation time for a 150-day cycle is approximately 5 min. Simulation results indicate that increasing the number of injection wells and carefully controlling the injection rates significantly improves the distribution of CO2 within the reservoir, thereby enhancing storage efficiency. Additionally, appropriate well placement and prolonged quiescence periods lead to better CO2 dispersion, increasing the storage potential while reducing energy costs. The study concludes that further development of the software, along with comprehensive technical and economic assessments, is required to fully optimize CO2 storage on a commercial scale.

From process to property: multi-physics modeling of dislocation dynamics and microscale damage in metal additive manufacturing

AbstractMetal additive manufacturing (AM) has the potential to tailor the mechanical performance of materials. Due to the complex thermal history and unique microstructure, AM materials are reported to contain distinct dislocation networks with a high dislocation density, which affect the plastic deformation behavior and fracture. However, it is challenging to experimentally observe the formation of such dislocation structures. In this work, a multi-scale multi-physics crystal plasticity modeling framework that integrates the process-structure-property relationship in metal AM is developed. The temperature field obtained from thermal-fluid flow simulations of the AM process and the microstructure from the phase field model of grain growth are combined into thermo-mechanical crystal plasticity simulations to obtain grain-scale thermal stresses. These stresses are used as input to simulate the evolution of dislocation structures within individual grains. Taking AM 316L stainless steel as the material of interest, the effect of initial dislocation configuration on the slip plane and cross-slip mechanism on the dislocation structure formation are investigated. Furthermore, a phase field damage model is implemented to study the initiation of microscale damage and their relationship with dislocation structures, which is a main novelty of this work. This modeling framework provides comprehensive simulations of all aspects of metal AM and offers insights into the dislocation mechanisms and damage formation at microscale in AM materials, which could be used to guide the manipulation of the mechanical properties of AM materials.

Simulation and optimization for flue gas CO2 capture by energy efficient water-lean ionic liquid solvent

Ionic liquids (IL) are treated as advanced materials for energy-saving carbon dioxide (CO2) capture from flue gas but suffer from serious challenges in energy and mass management. Herein, a water-lean IL-based deep eutectic solvent with 1,8-diazabicyclo [5.4.0] undec-7-ene imidazole ([DBU] [IM]) and ethylene glycol (EG) blends was prepared with a screened proportion of IL:EG=7:3. The CO2 loading and saturated solvent viscosity were 1.89 mol/L and 95 mPa·s, respectively. The foundational properties of the IL-EG solvent were determined by experimental measurements and thermodynamic modeling. The vacuum flashing desorption technology was innovatively adopted for energy-saving solvent regeneration. Industrial-scale process simulation of multistage flashing was used to explore the energy consumption during solvent regeneration. Meanwhile, the segmented cooling paved a route for water separation from water-lean solvent. A comprehensive analysis was performed out to optimize the operating parameters for CO2 absorption and desorption. For the recommended 3-stage flashing configuration, the specific process regeneration energy consumption amounted to only 1.54 GJ/tCO2. Consequently, the total capture cost reduced to 48.1 $/tCO2, marking a decrease of 31.28 %, 16.55 % and 10.25 %, compared with MEA solvent, water-lean solvent and biphasic solvent, respectively. This work offered insights for future endeavors in the development of IL-based CO2 capture process from industrial flue gas.

Simulation Research on the Control Method of Bow-Collapse in Gear Cold Roll-Beating

Bow-collapse is a type of geometric defect in the gear cold roll-beating process. In order to effectively control bow-collapse and improve material utilization, this paper calculates the cross-section radius of the blank according to the volume invariance principle of metal plastic deformation, and then performs FE simulation of the cold roll-beating process by using the cyclic beating of adjacent tooth spaces and intermittent blank feeding method. The flow state of metal particles is investigated, revealing that the movement of metal particles along the axial direction of the blank is the main reason for the formation of bow-collapse. This paper proposes a method to correct the cross-section radius of the blank and thus control for bow-collapse, where the loss coefficient K characterizes the state of metal particle loss in an infinitesimal thickness region on the cross-section. The analytical equation for calculating the corrected value of the cross-section radius is derived, and the corrected value is calculated. Conducted on the modified blank, cold roll-beating FE simulation results show that bow-collapse is effectively controlled, and the loss coefficient K correctly reflects the loss state of metal particles on the cross-section. The simulation results also show that after cold roll-beating, the gear teeth with standard face width and tooth depth can be obtained after two turning end faces and turning tip circle processes. The bow-collapse control method proposed in this paper effectively improves material utilization.

Control and optimization of defects in die casting of complicated right crankcase cover

The die-casting process of ADC12 aluminum alloy right crankcase cover was simulated based on AnyCasting software, and the influence of pouring temperature, initial mold temperature and injection speed on the filling and solidification process of ADC12 right crankcase cover casting was explored by orthogonal experiment method. The optimal process parameters were obtained through optimization, and the die-casting mold was designed. The program was verified in production. The results show that the porosity and shrinkage of the right crankcase cover are mainly concentrated in the thick wall part. The sequence of process parameters that affect the residual melt modulus is pouring temperature, initial mold temperature, and injection speed; The best combination of process parameters: pouring temperature is ∼680 °C, initial mold temperature is ∼200 °C, injection speed is ∼5 m/s. By analyzing the filling process and temperature field simulation results, the casting structure, mold structure and cooling system were optimized, and the process plan was improved. The production verification was carried out according to the optimized process plan. The casting quality is good and has no obvious defects, which meets the actual production needs.

Development of a high-fidelity digital twin using the discrete element method for a continuous direct compression process. Part 2. Validation of calibration workflow

This paper is the second in a series of two that describes the application of discrete element method (DEM) and reduced order modeling to predict the effect of disturbances in the concentration of drug substance at the inlet of a continuous powder mixer on the concentration of the drug substance at the outlet of the mixer. In the companion publication, small-scale material characterization tests, a careful DEM parameter calibration and DEM simulations of the manufacturing process were used to develop a reliable RTD models. In the current work, the same calibration workflow was employed to evaluate the predictive ability of the resulting reduced-order model for an extended design space. DEM simulations were extrapolated using a relay race method and the cumulative RTD was accurately parameterized using the n-CSTR model. By performing experiments and simulations, a calibrated DEM model predicted the response of a continuous powder mixer to step changes in the inlet concentration of an API. Thus, carefully calibrated DEM models was used to guide and reduce experimental work and to establish an adequate control strategy. In addition, a further reduction in the computational effort was obtained by using the relay race method to extrapolate results. The predicted RTD curves were then parameterized to develop reduced order models and used to simulate the process in a matter of seconds. Overall, a control strategy evaluation tool based on high-fidelity DEM simulations was developed using material-sparing small-scale characterization tests.

Influence of hot forging on grain formation in Al0.35CoCrFeNi high-entropy alloy: numerical simulation, microstructure and mechanical properties

One-step (F100) and three-step (F30-60-40) hot forging of Al0.35CoCrFeNi alloy was investigated to achieve a uniform equiaxed grain structure. In the as-cast and forged state, only a single-phase face-centered cubic structure was observed. The formation of twins, recrystallized and partially recrystallized grains in the volume of the samples was observed depending on used forging process. To predict uniform grain-size formation numerical simulation of the hot-forging process was used. The numerical model was calibrated and validated by means of measured compression experimental data of as-cast Al0.35CoCrFeNi alloy before forging. Thermal analysis using finite element analysis was used to simulate cooling of sample during the relocation from the furnace on the lower die. Simulations were run under different thermo-mechanical conditions and the regions for the formation of dynamically recrystallized grains were predicted. Room temperature mechanical properties were evaluated after F100 and F30-60-40 hot-forging process. The F30-60-40 hot forging optimized the grain size, which was evident in the very small dispersion of the room temperature mechanical properties in tension. Elongation after F30-60-40 hot forging increased by 17%. The correlation between temperature, equivalent stress, equivalent plastic strain, microstructure, tensile properties, and strain-hardening behavior is discussed.

Economic feasibility of the biorefinery processing bamboo residues with biphasic phenoxyethanol-acid pretreatment technology: Techno-economic analysis

This study conducted a techno-economic analysis to assess the economic feasibility of a biorefinery converting bamboo residues to bioproducts via phenoxyethanol-acid pretreatment. The analysis is integrated with a rigorous process simulation model with the support of experiment data. The bioproducts include ethanol or polylactic acid (PLA), with lignin-based wood adhesive as the byproduct. The minimum selling price (MSP) is $515-$819 per t ethanol and $1,512-$1,842 per t PLA when biphasic treatment is deployed, compared to the MSP of $2,318-$2,721 per t ethanol and $2,859-$3,211 per t PLA for no biphasic pretreatment. Adopting a ratio of 1:1 phenoxyethanol: acid solution (1%) in pretreatment decreases the final product yield but leads to lower MSP than 4:1 phenoxyethanol: acid solution (1%) due to lower phenoxyethanol consumption. A sensitivity analysis identifies the key drivers of reducing MSP, including increasing economic gain from the lignin-based wood adhesive, lowering the phenoxyethanol cost, and expanding plant capacity.