Fuel Cell Material and Energy Balance: Testing Station (2021)

An open system (Control Volume) allows mass and energy to cross its boundaries, unlike closed systems. The Control Surface defines the system boundary. The mass balance equation states that mass entering minus mass leaving equals mass accumulation: ṁ_in - ṁ_out = dm_cv/dt. For steady flow processes, no properties change with time, and accumulation is zero, simplifying to ṁ_in = ṁ_out. Mass flow rate can be calculated using ṁ = ρ × A × V, ṁ = ρ × V̇, or ṁ = V̇ / v. The energy balance for open systems includes heat transfer, work, and energy carried by flowing mass. Flow work (Pv) represents the energy required to push fluid across system boundaries. Total energy of flowing systems includes internal energy, kinetic energy, potential energy, and flow work: E_flow = U + KE + PE + Pv. For unit mass: e_flow = u + (1/2)v² + gz + Pv. For steady flow processes, the energy balance simplifies to: Ẇ_in - Ẇ_out = Σṁ × (e_out - e_in). In specific form: q - w = (u₂ - u₁) + (1/2)(v₂² - v₁²) + g(z₂ - z₁) + P₂v₂ - P₁v₁.

This comprehensive section covers the fundamental principles of thermodynamics for open systems. The conservation of mass principle states that mass cannot be created or destroyed, and in an open system with a control volume, the rate of change of mass equals the difference between mass flow rates entering and leaving (dm/dt = m_in - m_out). Similarly, the conservation of energy states that the rate of energy change within the control volume equals the difference between energy flow rates entering and leaving (dE/dt = E_in - E_out). The total energy within a control volume consists of internal energy (energy due to molecular motion), kinetic energy (energy due to motion), and potential energy (energy due to position). Specific internal energy is the internal energy per unit mass. Work and heat transfer are mechanisms by which energy crosses the boundary of a control volume. The comprehensive energy balance for an open system includes all forms of energy transfer: mass flow energy, heat transfer, and work transfer. The steady flow energy equation (SFEE) is a simplified form for open systems under steady flow conditions, where properties at any point remain constant with time. The SFEE states that the energy entering the system equals the energy leaving the system, expressed as m(h + V²/2 + gz) + Q = m(h + V²/2 + gz) + W, where h is specific enthalpy, V is velocity, z is elevation, Q is heat transfer rate, and W is work transfer rate.

Mass balance is based on the Law of Conservation of Mass: Input - Output + Generation - Consumption = Accumulation. Generation/consumption only occur during chemical reactions. In steady state, accumulation is zero. Energy balance for open systems includes energy associated with mass (kinetic, potential, internal) and energy not associated with mass (heat and work). Internal energy depends on temperature and is calculated as mass × specific heat capacity × temperature change. Work of flow (P×V) is required to push mass into or out of open systems. The First Law of Thermodynamics states energy cannot be created or destroyed, only transformed. For open systems: Q - W = ΔH + ΔKE + ΔPE. Enthalpy (H) is defined as internal energy plus flow work: H = u + P×V. For closed systems: Q + W = ΔU. Specific heat capacity indicates how temperature changes with added energy. For water, cb = 1 cal/g·°C. For ideal gases: cp = (7/2)R and cb = (5/2)R, where R = 8.314 J/mol·K. Internal energy change: ΔU = m × cb × ΔT. Enthalpy change: ΔH = m × cp × ΔT.

This segment establishes the fundamental principles for analyzing open thermodynamic systems. The mass balance equation states that mass entering minus mass leaving equals the change in system mass. For systems with no mass entering, mass leaving equals initial mass minus final mass. The energy balance equation states that energy entering minus energy leaving equals the change in system energy. Energy entering includes electrical work and mass enthalpy, while energy leaving includes mass enthalpy. The change in system energy is final internal energy minus initial internal energy. These principles form the foundation for solving thermodynamic problems involving mass flow and energy transfer.

An open system allows free movement of both mass and energy across its boundaries. The fundamental mass balance equation states that the rate of mass change equals mass entering minus mass exiting (dm/dt = m_in_dot - m_out_dot). Mass flow rate is calculated as m_dot = ρAV or equivalently m_dot = AV/v, where ρ is density, A is cross-sectional area, V is velocity, and v is specific volume. In steady state steady flow conditions, mass entering equals mass exiting, and similarly energy entering equals energy exiting, resulting in zero net accumulation. The energy flow in open systems comprises heat transfer (Q_dot), work transfer (W_dot), and energy carried by mass flow.

Fuel cell polarization curves show how voltage decreases with increasing current density. The curve consists of three main regions: open circuit voltage (reversible potential), activation losses, ohmic losses, and concentration losses. Understanding these curves requires modeling cell characteristics including equilibrium voltage (dependent on temperature and gas concentration via Nernst equation), ohmic resistance losses (linear with current density), and electrode overpotentials (non-linear with current density). The complete polarization curve is obtained by subtracting all loss terms from the open circuit voltage.

A polarization curve for a proton exchange membrane fuel cell displays three distinct regions based on current density versus voltage behavior. The activation region at low currents shows a gradual increase in voltage due to kinetic limitations requiring energy to overcome activation barriers. The ohmic region at intermediate currents exhibits a linear relationship between voltage and current following Ohm's law (V = IR), representing resistance losses. The mass transport/diffusion region at high currents shows a sharp drop in voltage as reactant supply becomes limited by diffusion rates, often accompanied by flooding issues that introduce noise into the data. Understanding these regions helps identify which loss mechanism dominates under specific operating conditions.

Proton exchange membrane (PEM) fuel cells convert hydrogen and oxygen chemical energy into electricity through electrochemical reactions. At the anode, hydrogen splits into protons and electrons; protons permeate the polymer membrane while electrons flow externally to create current. At the cathode, oxygen combines with protons and electrons to form water. The polymer membrane must conduct protons without electrons to prevent short-circuiting, resist corrosive environments, and prevent gas crossover. Water management is critical—too much causes flooding, too little causes drying. Platinum is the primary catalyst, but its high cost drives research into alternatives like iron-based catalysts achieving 99 A/cm² at 0.8V. Membrane types range from Nafion (requiring humidification, 80-90°C max) to phosphoric acid-based membranes enabling 120°C operation with improved efficiency. Theoretical maximum efficiency is 83%, but practical efficiency ranges 40-60% due to activation, ohmic, and mass transport losses.

Fuel cell current-voltage (I-V) curves exhibit three distinct polarization regions: at low current densities, voltage loss is dominated by activation/kinetic limitations; in the intermediate range, voltage decreases linearly due to ohmic resistance (IR drop); and at high current densities, voltage drops sharply due to mass transfer limitations from reactant diffusion or convection constraints. Despite different operating temperatures and electrolytes (alkaline at 82°C, PEM at 80°C, SOFC at 800°C), all fuel cell types show similar open circuit voltages around 1.1V and follow this three-region polarization behavior.

A proton exchange membrane (PEM) fuel cell is an electrochemical device that converts chemical energy to electrical energy. Unlike batteries, it requires continuous fuel (hydrogen) and oxidant (oxygen) supplies. At the anode, hydrogen gas decomposes into H+ ions via catalytic reaction, releasing electrons that flow through an external circuit. The H+ ions pass through the proton exchange membrane to the cathode, where they combine with oxygen to form water vapor. This process uses work energy (organized molecular motion) rather than heat energy, enabling efficient energy conversion without combustion.

This comprehensive section covers the foundational principles of process control. It begins with the three main objectives: maintaining safety to prevent accidents, ensuring production quality with correct specifications and quantities, and minimizing environmental emissions. A process is defined as a set of physical or chemical operations receiving raw materials and delivering finished products, often termed 'black boxes' in chemical engineering. Process variables are systematically categorized into output variables (measurable objectives), input variables (manipulable and disturbances), and parameters (constant values). The set point represents the desired value established by the user. Two practical examples illustrate these concepts: maintaining shower water temperature by manipulating hot/cold water flows while ambient temperature changes represent disturbances, and maintaining tank liquid level by identifying which flows are manipulable (with valves) and which are disturbances (without valves). The section concludes by distinguishing between balance of material perspectives and control perspectives, emphasizing that from a control viewpoint, correntes become variables of entry that affect the controlled output.

Process control is the systematic design of systems to maintain selected process variables within predetermined values or ranges to achieve desired objectives, accomplished through either manual operator intervention or automated machine actions based on measurements and feedback.

Mass flow controllers ensure constant air supply to air conditioning packs regardless of engine rpm or intake pressure. They use a piston mechanism with cutouts that modulates airflow based on inlet pressure changes. Temperature control mixes hot air with cooled air from the air cycle machine. Automatic control compares cabin sensor temperature with pilot selection and modulates the hot air valve. Manual control directly positions the valve based on selector switch position.

Process control transforms material and energy through defined steps to generate desired outputs. A process is any operation converting inputs into different outputs, from home appliances to industrial refineries. Process control maintains desired conditions despite disturbances using feedback loops. The fundamental loop architecture includes measurement (sensors detecting variables), comparison to setpoint, decision-making algorithms, and control actions (valves, heaters). Lord Kelvin emphasized that control requires accurate measurement. Process variables include temperature, pressure, flow, level, density, pH, viscosity, and turbidity. Flow measurement uses direct methods (positive displacement, turbine meters) and inferential methods (differential pressure across orifice plates). Pressure equals force per unit area, with common units including PSI and feet of water column. Temperature scales include Fahrenheit, Celsius, Rankine, and Kelvin, which can be converted linearly. Industrial implementation uses standardized P&IDs showing heat exchangers, valves, transmitters, and controllers. The heat exchanger example demonstrates steam flow adjustment based on product temperature measurement, with signals converted through I/P converters for pneumatic valve operation.

Process control regulates process variables to ensure stable, consistent product quality. A process transforms raw materials (liquid, gas, or slurry) into end products through operations like mixing, heating, cooling, filtering, and storing. Process industries include chemical manufacturing, oil and gas, food and beverage, pharmaceuticals, water treatment, and power generation. Two main process types exist: continuous processes (constant material flow, rarely shut down, examples: cement kilns, oil refining) and batch processes (defined start/end points, produce discrete batches, examples: beer brewing). Control approaches include open-loop control (actions taken regardless of conditions, simple but inefficient) and closed-loop control (measures current conditions, compares to set point, corrects deviations). Closed-loop systems consist of sensors (measure process variables), controllers (compare values and calculate corrections), and actuators (physically control the process).