Method and apparatus for controlling combustion process systems

Abstract

Procedure comprising: monitoring an actual fuel flow (234) into a combustion process; Calculating a relative heat release value corresponding to the fuel in the combustion process; and Determining a fuel requirement for the combustion process based on the relative heat release value.

Description

FIELD OF DISCLOSUREThis disclosure relates generally to process control, and more particularly to methods and apparatus for controlling combustion process systems.BACKGROUNDCombustion processes such as those used in process fired heaters, boilers, and the like are extensively used across many industries for heating, vaporizing, or thermally cracking various process fluids. Operating and servicing these combustion processes is challenging because incomplete or variable combustion may result in product variability, thermal loading of equipment, environmental hazards, and, if severe, equipment explosion.Document DE 690 14 308 T2 discloses a method for controlling the fuel / air ratio in a heating system and comprises measuring the fuel supply to the heating system and is characterized by measuring parameters which are characteristic of certain properties which characterize the composition of the fuel for the heating system. These parameters include the thermal conductivity as well as the specific heat of the fuel. The method further comprises determining combustion characteristics of the fuel composition according to the measured parameters, determining the power supply to the heating system based on the fuel supply and the determined combustion characteristics, and measuring the combustion air flow in the heating system and controlling the fuel / air ratio as a function of the power supply and the measured air flow.Document US 4 742 783 A relates to the combustion of hazardous waste. In one aspect, it relates to an apparatus for controlling the combustion air supplied to a combustion plant. In another aspect, it relates to a method of automatically controlling the combustion air supplied to a hazardous waste incinerator to maintain an air supply in sufficient quantity as required by the governmental and / or federal regulations for the particular waste burned.Document US 4 498 428 A discloses a method and apparatus for controlling a boiler combustion process in which a low caloric exhaust gas is used as the main fuel so that all the exhaust gas is burned without sacrificing process requirements.Document US 4 576 570 A discloses a method and apparatus for controlling the combustion of multiple fuels having different combustion air requirements by adjusting the fuel and air flow rates. A heating power demand signal indicative of the desired heating power is generated and compared to a fuel-based heating power signal, the larger value being selected as an air demand signal and serving as a set point for a combustion air regulator. The fuel flow rates are monitored, scaled and summed to determine the heating power. Adjustments are made to ensure optimum combustion air delivery using a pilot signal and an equivalent air heating power signal.The object of the present invention is to provide an improved method and an improved device for controlling combustion process systems. This object is achieved by the independent claims 1 and 9. Further advantageous embodiments of the invention are set forth in the dependent claims.Example methods and apparatus for controlling combustion process systems are disclosed. An example method includes monitoring a current fuel flow to a combustion process, calculating a relative heat release value corresponding to the fuel in the combustion process, and determining a fuel demand for the combustion process based on the relative heat release value.An example apparatus includes a sensor for monitoring a current fuel flow into a combustion process, a heat release calculator for calculating a relative heat release value corresponding to the fuel in the combustion process, and a cross limiting calculator for determining a fuel demand for the combustion process based on the relative heat release value. FIG. 1 illustrates an example combustion process system in which the teachings disclosed herein may be implemented. FIG. 2 is a block diagram of the example control system of FIG. 1 constructed in accordance with the teachings disclosed herein. FIG. 3 illustrates an example table and corresponding curve indicating a ratio of percent oxygen to excess air for an example fuel used in the combustion process system of FIG. 1. FIGS. 4-11 are flowcharts representative of example processes for implementing the example control system of FIGS. 1 and / or 2. FIG. 12 is a schematic diagram of an example processor platform that may be used and / or programmed to perform the example process of FIGS. 4-11 and / or, more generally, implement the example control system of FIGS. 1 and / or 2.The goal for a fired heater is to heat a process fluid to a desired temperature. Maintaining a constant exit temperature is important to the process. Changes in the outlet temperature introduce variability into the overall process. Although optimum operation of a fired heater is typically close to constraints (e.g., maximum tube temperatures, minimum excess air), a change in the process will cause operators to move away from the actual limit to provide a buffer or safety margin to deal with any unexpected process disturbances. As a result, manufacturers are not always able to maximize the throughput of their plants or otherwise increase their efficiency.Process fired heaters generally utilize waste fuel from the process, which may have a widely varying heating value. Changes in fuel heating value pose a challenge to control air and fuel demands. In many cases, the air and fuel ratio is handled with a substantial excess air safety buffer to reduce risks associated with incomplete combustion. This strategy of providing a significant safety buffer may result in insufficient operation and / or increased emissions. Significant changes in fuel heating value may also result in changes in end product quality or ssubstoichiometric conditions.Previous control solutions include proportional / integral / derivative (PID) control of product temperature and constraints with fixed mathematical algorithms to estimate the fuel energy changes necessary to handle the fuel and air ratio. Typical fuel control solutions involve empirically derived air / fuel curves based on matching the mass of air with the mass of fuel to achieve a desired excess amount of air. However, these solutions are difficult to handle. Typically, the PID controls cannot cope properly with multiple interactions of control, manipulated variable, and condition variables. Empirical combustion curves must be generated by manually adjusting the air flow across all possible fuel energy changes. This is often impossible to coordinate in an actively operating installation. Additionally, a mass flow rate based on calculations and / or curves may not compensate for composition changes of exhaust gas associated with hydrogen, carbon dioxide, or inert gas.Examples disclosed herein implement a strategy of simultaneously controlling combustion, throughput, and end product temperature of fired equipment to improve the safety and operation of these devices. The examples disclosed herein may be implemented in connection with any fired application (e.g., process fired heaters, thermal oxidation units, rotary fired dryers, lime furnaces, reformers, cracking furnaces) that uses waste fuel and / or variable energy content fuel (e.g., ethylene furnaces and / or steam methane reformers). The examples disclosed herein eliminate the fuel-air curves used during the last sixty years in automatic combustion control by using an algorithm disclosed herein to coordinate the combustion air with the fuel for optimal and safe combustion. The examples disclosed herein determine an air demand based on a fuel flow (either directly measured or inferred) and adjust the fuel flow target to compensate for varying heat content in the fuel.The examples disclosed herein determine the air demand based on the energy in the fuel (heat rate). The examples disclosed herein adjust the fuel heating value to compensate for the varying heat content in the fuel. The adjusted heating value is then used to determine the fuel flow target. This control strategy or technique, while minimizing excess air, provides a consistent product temperature for improved efficiency and stable, consistent production overall within the configured constraints. Maintaining an optimum excess of air has the added advantage of reduced emissions.The examples disclosed herein may be used in situations where, for example, the heating value is not measured directly, but a typical value is known. In some examples, the heating value of the fuel is derived using specific gravity and / or chromatography. In such cases, the measured value is adjusted based on the example algorithms disclosed herein, resulting in a further refinement to the combustion air demand.According to the examples disclosed herein, the ratio between percent oxygen in the flue gas and percent excess combustion air is determined based on the fuel type. This strategy ensures the proper amount of air for combustion even when the fuel varies in caloric value.When a process-fired heater is fired with purchased gas (e.g., "city gas"), the energy savings may be significant from an improved efficiency provided by the examples disclosed herein. Even more significant savings can be realized by using available exhaust gas for relatively more expensive purchased gas. Exhaust gas in refinery and petrochemical plants typically varies dramatically in composition depending on which process unit is delivering to the fuel system. Large changes in hydrogen, nitrogen and hydrocarbon distribution are common for these waste streams. When the exhaust gas has a highly variable caloric value, it often cannot be used in critical units. However, examples disclosed herein provide a combustion strategy, as will be described in detail below, that balances a widely varying caloric value, thus enabling fuel replacement that can result in significant savings and / or increases in efficiency. In addition, by enabling increased (e.g., maximum) capture of the available heat in the fuel with less variability, the combustion strategy provided by the examples disclosed herein reduces greenhouse gas emissions, makes the fuel available for other uses such as boilers or heating plants, and enables more throughput in a capacity-shortage situation.In addition to coordinating fuel and air, while compensating for varying energy content in the fuel, the examples disclosed herein utilize model predictive control (MPC) to achieve the complex objective of stabilizing end product quality. That is, the examples disclosed herein combine improved combustion controls with MPC. The improved combustion controls disclosed herein ensure safe, stable combustion, and the MPC utilization of the examples disclosed herein provides optimal product control within process limits such as emissions, maximum firing inputs, equipment constraints, etc. In some examples, the utilization of MPC by the examples disclosed herein eliminates the use of multiple PID controls or PID counterparts for the same or better functionality.Thus, the examples disclosed herein eliminate the need for empirical air and fuel curves, provide methods and apparatus that compensate for varying fuel energy content and / or combustion air requirements, improve plant safety, efficiency, and throughput of, for example, process fired heaters, while at the same time reducing product variability and emissions. Moreover, the examples disclosed herein provide the capability to determine the relative energy changes of any (e.g., solid, liquid, or gaseous) fuel on a real-time basis without taking a sample from the fuel stream. By defining the fuel energy content on a real-time basis, the total combustion air can be matched to the energy requirements, thereby lowering emissions and increasing the safety of operations. By defining the energy content of each fuel, the examples disclosed herein normalize all fuels so that the same combustion concept and / or solution can be used on each device (e.g., a process-fired heater). Matching the energy demand with the accurate (e.g., within a negligible threshold) amount of energy in the combustion reduces variability and cost.FIG. 1 is a diagram representative of an example combustion process system 100. The example combustion process system 100 is a process-fired heater system that may be used to heat a process feed that flows through tubes disposed within the heater. Although a fired heater system is shown in FIG. 1 and the following explanation is presented in the context of a fired heater, the teachings disclosed herein may be applied to any other combustion process such as, for example, a boiler, fired rotary dryers, etc. The example systems and methods are described herein as being advantageously applicable to controlling process heaters that use fuel with a variable heating value (e.g., due to a composition of the fuel varying over time). In particular, the example combustion process system 100 is described below as using a waste fuel that may contain hydrogen (e.g., in some cases, the hydrogen concentration may range from 25% to 75%), a mixture of light end hydrocarbons, incremental natural gas, or excess butane. However, in alternative implementations, the example systems and methods described herein may be used to control combustion / production systems that use any type of fuel.As shown in FIG. 1, the example system 100 includes a fired heater 102 that receives fuel gas from a fuel supply 104 that is mixed with air and burned in a furnace 106 of the heater 102. In the illustrated example, tubes 108 transport a process feed or product fluid from a process feed product supply 110 through the furnace 106. The example tubes 108 of the illustrated example are shown in a 2-pass arrangement. In other examples, the system 100 may alternatively be configured with a single pass fired heater 102. In other examples, the system 100 may be configured with more than 2 passes (e.g., 4, 8, or 16). As the feed passes through the fired heater 102, the heat generated by the burning fuel is transferred to the feed. Any excess heat, exhaust air and / or emissions from the combustion process of the illustrated example are released via a chimney or flue 112 on top of the heater 102.The example system 100 also includes an example control system 116 for detecting and monitoring various operating conditions (e.g., fuel flow, airflow product flow, product temperature, etc.) of the example combustion system 100 to determine configuration settings (e.g., fuel flow and airflow) that may be used to operate the combustion system 100 within a predetermined, required, and / or desired operating range (e.g., heat coil outlet temperature associated with the product), while maintaining other operating characteristics (e.g., fuel-air ratios, emissions, etc.) within predetermined, required, or desired operating ranges. As will be described in more detail below in connection with FIG. 2, the example control system 116 uses model predictive rules to predict configuration settings to substantially reduce or eliminate instances (or time) during which (the) the example system 100 is operating in an improper (and potentially inefficient and / or unsafe) state. More specifically, the control system 116 uses measurements of present and / or previous operating conditions to perform analyses to predict how the exemplary system should operate in the near or far future, and based on these analyses generates product feed stream configuration settings that are future directed to prevent the combustion system 100 from operating outside the predetermined, required, or desired operating range or ranges. Additionally, the example control system 116 employs measurements that monitor the current heat release of the combustion process to control the fuel firing rate for a consistent furnace temperature. More specifically, the fuel flow and a corresponding heating value (based on the monitored heat release) of the fuel are monitored to determine a target air flow for the combustion process, while the air flow and heating value of the fuel are used to determine or adjust a target fuel flow or target fuel demand. That is, the fuel flow and the air flow are analyzed via a cross-limiting strategy in conjunction with a corresponding heat release determined from the combustion of the associated fuel and air. In this manner, a controlled combustion environment is achieved to provide a more consistent product temperature than other known fired heaters, while reducing (e.g., minimizing) excess air used in the system 100 for improved efficiency and a stable, consistent product. Moreover, the example control system 116 monitors configured constraints to maintain the example system 100 within allowable limits to ensure system safety and quality of the product.As shown in FIG. 1, the example control system 116 communicates with a fuel flow valve 118 to regulate the fuel flow rate into the fired heater 102, product flow valves 120, 122 to regulate the flow rate or feed rate of product through the fired heater 102 via the tubes 108, and a chimney flap 124 to regulate the amount of air introduced into the heater 102 and, accordingly, the amount of air and / or exhaust air released from the heater 102. Additionally or alternatively, in some examples, the example control system 116 communicates with a fan, blower, and / or an associated flap to regulate the flow of air through the heater 102. To measure the feed rates or flow rates of each of the supplies (e.g., fuel, feed, airflow), the control system 116 of the illustrated example may be communicatively connected to multiple sensors and / or other measurement devices.In particular, an oxygen sensor 126 and a carbon monoxide sensor 128 are communicatively coupled to the example control system 116 to monitor the state of the exhaust air and emissions leaving the heater 102 via the chimney 112. Specifically, oxygen and carbon monoxide indicate the combustion state in the heater 102 substantially in real time. By monitoring the combustion process in this manner, in some examples, the control system 116 determines settings to be made to the process to stabilize the unit, improve efficiency, and / or reduce emissions. In some examples, other sensors are included in addition to oxygen sensor 126 and carbon monoxide sensor 128 to monitor other emissions (e.g., nitrogen oxides, sulfur dioxide, particulate matter, carbon dioxide, etc.) on a real-time basis to meet environmental regulations and / or add constraints to the operation of the process system.In some examples, a draft pressure sensor 132 to be used to detect flame stability in the heater 102 is communicatively coupled to the example control system 116. In many cases, one challenge in operating a fired heater is the instability of burner flames, which is particularly relevant when there are large and / or rapid changes in the heating value or energy content of the fuel (e.g., due to refinery disturbances that cannot adequately compensate for combustion regulations). If a flame is unstable, it may flicker or extinguish, which is a dangerous condition that may cause unburned fuel to remain in the furnace. Some techniques may be used to avoid such conditions. However, these techniques are often subject to false alarms, may not detect conditions until the flame is off, and / or may be cost prohibitive to service and / or install. Accordingly, in some examples, flame stability is monitored and detected based on the train air pressure measured via the train air pressure sensor 132. In such examples, flame stability detection is based on the premise that dynamic processes under normal conditions have a unique noise or variation signal, such that changes in these characteristic signatures indicate a change in the process. As such, in some cases, the draft air pressure is monitored to make changes incompatible with the combustion process occurring under a stable flame to warn and / or adjust the system of the furnace being extinguished and shut down.In some examples, a chimney temperature sensor 130, a flap position sensor 134, and an airflow sensor 136 are communicatively coupled to the example control system 116 to monitor the state of airflow exiting the heater 102 via the chimney 112. Specifically, in some examples, such measurements are used to maintain safe and stable firing and improve (e.g., optimize) the combustion process in real time for a more consistent product temperature, higher efficiency, and / or reduced emissions. How the air flow measurement is obtained depends in some examples on the type of oven in question and the particular on-site equipment. For example, fired heaters may typically be classified into a forced draft air-based heater, a balanced draft air-based heater, and a natural draft air-based heater. In the forced draft or balanced draft heater processes, an air flow can be controlled by controlling the speed of a forced draft fan with, for example, a variable speed drive to enable precise and repeatable air flow control over a wide range at a reduced cost due to reduced power consumption. Alternatively or in some examples, in addition to modulating blower speed, an associated airflow control door may be modulated. In such examples, to measure airflow, a sensor may be used at either the inlet of a forced air blower or in an air duct between the forced air blower and the heater 102. In some cases, the sensor uses averaging trap tube (APT) technology (APT) to overcome challenges resulting from channel shape, lack of straight traces, lack of external separation, flow stratification in the channel, etc. In natural draft processes (such as the example process system 100 shown in FIG. 1), the airflow is adjusted by modulating the flap 124 in the chimney 112. Typically, the air flow is not measured directly in natural draft-based heaters, as such measurements are challenging because there is neither a blower nor a duct in which a sensor could be placed. However, in the illustrated example, the airflow sensor 136 is inserted into the chimney 112 and incorporates the APT technology described above to monitor a flow of flue gas as it varies based on the position of the chimney flap 124. A flue gas flow may be used to derive an air flow. In some examples, the door 124 is actuated with a digital controller with calibration, configuration, and diagnostic functionality running online to enable accurate positioning of the door 124 as well as ensure reliability and repeatability of door movement over time.In the illustrated example of FIG. 1, a burner pressure sensor 138 and a furnace temperature sensor 140 are communicatively coupled to the control system 116 to monitor conditions inside the furnace 106 of the heater 102. Such measurements are used in some examples as constraints imposed on the control process disclosed herein to ensure a safe and stable process environment.Additionally, in some examples, a total flow sensor 142, product outlet temperature sensors 144, 146, and a heater coil outlet temperature sensor 148 are communicatively coupled to the control system 116 to monitor the conditions of the feed product entering and exiting the heater 102. In some examples, the total flow rate corresponds to the total feed stream passing through heater 102 over all passes. In some examples, the heating coil outlet temperature corresponds to the combined temperature of the feed product in each pass as it exits the heater 102 (e.g., as determined by each product outlet temperature sensor 144, 145). Often, a process goal is to control the process to achieve a target coil outlet temperature of the material exiting the furnace. Accordingly, in some examples, the heater coil outlet temperature and total flow rate are used as primary or main inputs or set points used to define the required heat release from the combustion process in heater 102. In particular, a balance must often be found between increasing the heater outlet temperature (e.g., to the coking limit) to improve yields and decreasing the temperature to extend the life of the combustion process (e.g., before the heater needs to be decoked). Accordingly, in some examples, the control system 116 uses the above parameters in conjunction with MPC to maintain the outlet temperature of each product pass substantially the same (e.g., pass compensation), thereby reducing the likelihood that one set of tubes 108 will coke more quickly in the heater 102 than the others to increase (e.g., maximize) an operating run length while improving (e.g., maximizing) the quality of the process yield with reduced variability. Maintaining a relatively constant temperature across all furnace tubes also reduces the likelihood of hot spots on tubes overheating. Moreover, such technical control methods also increase (e.g., maximize) the total feed or throughput processed by the system without exceeding heater constraints and / or limits.Further, a fuel heating value sensor 150, a fuel temperature sensor 152, and a fuel pressure sensor 154 are communicatively coupled to the control system 116 to monitor the conditions of the fuel supplied to the heater 102, which is one of the primary parameters used in the combustion control system described herein. Specifically, disclosed examples calculate heat release in the combustion process to derive a BTU (energy) content or heating value of the fuel, which, when combined with the flow rate of the fuel, may be used in the combustion process system 100 to calculate and control the flow of air into the system to maintain a stable, safe, and efficient combustion process. In some examples, the temperature and pressure sensors 152, 154 may be used to calculate a mass flow of the fuel. Additionally or alternatively, in some examples, a Coriolis flowmeter may be used to measure a mass flow that may be correlated with the mass-based heating value of the fuel. Moreover, in some examples, other types of flow measurement devices are employed. For example, nozzle disks with differential pressure transmitters or vortex meters can be used to monitor the flow of fuel. In some examples, a specific gas density measurement device may be installed to derive a value of the BTU content of the fuel on a real-time or substantially real-time basis.Although not shown, other additional sensors (e.g., temperature sensors, current / delivery sensors, pressure sensors, etc.) distributed throughout the example combustion process system 100 may be communicatively coupled to the control system 116 to obtain measurements for use in implementing the example systems and methods described herein. Moreover, particular locations of any of the sensors described herein and / or the parameters monitored by the sensors may be adjusted based on the needs of the particular application in which the teachings of this disclosure are practiced.FIG. 2 is a detailed block diagram of the example control system 116 of FIG. 1. the control system 116 may utilize predictive technical control methods for controlling the operation of the example combustion system 100 by determining future directed or predicted configuration settings based on conditions being monitored at the present time. In this manner, the control system 166 may proactively respond to the monitored conditions by changing or adjusting configuration settings to reduce or prevent the likelihood that the example system 100 will operate outside predetermined, desired, or required operating conditions (e.g., a coil outlet temperature associated with product delivery).In the illustrated example, the control system 116 includes a model predictive control (MPC) optimizer 202, a cross-limiting calculator 204, an airflow controller 206, a fuel heat release calculator 208, and a fuel controller 210. In an exemplary implementation, MPC optimizer 202 may be implemented using an MPC available in the Delta V control system developed and sold by Emerson Process Management, Austin, Texas. The MPC optimizer 202 is configured to regulate a flow rate of a product feed passing through the fired heater 102 in response to a heater coil outlet temperature 212 and product flow rates 214, 216 corresponding to each product flow valve (e.g., the product flow valves 120, 122 of FIG. 1 ). More specifically, in some examples where the combustion process system 100 includes a multi-pass heater (e.g., heater 102 in FIG. 1, shown as a 2-pass heater), the MPC optimizer 202 is configured to balance the outlet temperature of the product for each pass while maintaining the total heater coil outlet temperature at a desired set point. That is, the MPC optimizer 202 of the illustrated example provides each product flow valve 120, 122 with a control signal for controlling the product flow through each pass to maintain a substantially consistent outlet temperature within each pass as well as a consistent heater coil outlet temperature.In addition to controlling the product flow through each pass of the heater 102, the MPC optimizer 202 of the illustrated example also uses, in some examples, the heater coil outlet temperature 212 and a total flow rate (e.g., the total product flow through all passes in the heater) to regulate the fuel firing rate to the furnace 106 of the heater 102. In some examples, the MPC optimizer 202 uses the heating coil outlet temperature and total mass flow rate to provide an initial or main set point for fuel demand to be provided to the combustion and fuel systems (e.g., the airflow controller 206 and the fuel controller 210) based on a cross-limiting strategy, which is described in more detail below. In some examples, to account for variations in total mass flow (e.g., resulting from changes from the multiple pass compensation control of the MPC optimizer 202), a feedforward strategy is employed that builds on total mass flow. In other examples, the MPC optimizer 202 generates the starting fuel demand parameter in conjunction with flow balancing of the feed product flowing through the tubes 108 of the heater 102. In such examples, the output fuel demand generated directly by the MPC calculations may avoid a fuel demand calculation based on the heating coil outlet temperature and the total mass flow rate.To prevent the process from running under unstable, unsafe, and / or otherwise undesirable conditions, the example MPC optimizer 202 is also provided with a plurality of constraint values 218 (e.g., burner pressure, furnace temperature, etc.) that limit heater demand. In some cases, the MPC optimizer 202 calculates separate fuel demands for the combustion process based on a high burner pressure and a low burner pressure (measured via the burner pressure sensor 138) with respect to user-specified burner pressure setpoints. Additionally, the MPC optimizer 202 calculates a fuel demand based on the furnace temperature (measured via the furnace temperature sensor 140) with respect to a user specified furnace temperature set point. In some examples, the burner pressure ranges from 0 to 15 pounds per square inch (psig) and the furnace temperature ranges from 50° F. to 1600° F. In some cases, to determine a forced fuel demand, the MPC optimizer 202 uses the required starting fuel demand (e.g., based on the coil outlet temperature) to predict whether that demand will violate the low or high burner pressure specifications. In some examples, the MPC optimizer 202 will set the required starting fuel demand to a pressure-constrained fuel demand so that the burner pressure constraint conditions are not violated. In some such examples, the MPC optimizer 202 will also compare the pressure constrained fuel demand to the furnace temperature constraint and predict whether a damage will occur, and accordingly adjust to a final constrained fuel demand used as an input to the cross-limiting calculator 204.In the illustrated example, the example control system 116 is equipped with the cross-limiting calculator 204 to implement a cross-limiting strategy, described in more detail below, that regulates both airflow and fuel flow based on airflow and fuel flow monitoring values. Additionally, in the illustrated example of FIG. 2, the cross-limiting calculator 204 is provided with a plurality of exhaust gas values 220 that indicate the presence of oxygen (as measured, e.g., by the oxygen sensor 126) and carbon monoxide (as measured, e.g., via the carbon monoxide sensor 128) in the flue or chimney 112 of the heater 102 of FIG. 1, which are also used as inputs to the cross-limiting calculations described below. In some examples, the oxygen in the chimney 112 is 0% to 10% (e.g., by volume) of the exhaust air leaving the heater 102, and the carbon monoxide in the chimney is 0 to 100 particles per million (ppm). In the illustrated example, the measured amount of oxygen is used to balance the combustion air in the heater 102 to maintain a desired amount of excess air to achieve a safe environment while improving (e.g., maximizing) efficiency. In some examples, the cross-limiting calculator 204 includes the functionality of an oxygen balance regulator configured to calculate an oxygen balance factor based on the measured oxygen with respect to a user-specified baseline oxygen setpoint. Additionally, in some examples, the cross-limiting calculator 204 is configured to operate in a cascade mode with a cascade set point provided via a bias / gain station. In some examples, when the bias / gain station is auto-tuned, a user has the ability to up or down the baseline oxygen setpoint by 2%. When the bias / gain station is cascaded, the oxygen bias is calculated based on the amount of carbon monoxide measured in chimney 112. For example, as the level of fuels (e.g., carbon monoxide) increases, the oxygen setpoint bias becomes higher to decrease carbon monoxide emissions. In some such examples, the influence on the basic oxygen setpoint is 0% to 5%. In the illustrated example, the bias value, either user specified (auto) or calculated from the carbon monoxide measurement (cascade), is summed with the user specified base oxygen setpoint for a final oxygen setpoint used to determine the oxygen balance factor.In some examples, the cross-limiting calculator 204 controls an air flow to the heater 102 (via the air flow controller 206, as described in more detail below) by matching the target air flow with the calculated oxygen matching factor. In some examples, the oxygen trim factor is 80% to 120%, which corresponds to a total air area trim of plus or minus 20%. Additionally, in some examples, the cross-limiting calculator 204 uses the actual oxygen in the chimney 112 to determine the actual excess air (AEA) 224 used to calculate the heat release of the fuel to further control the combustion process (via the fuel heat release calculator 208, as described in more detail below). Similarly, the cross-limiting calculator 204 uses the oxygen set point to determine a target excess air (TEA) 222 (e.g., the total amount of excess air desired in the combustion process) that is also provided to the fuel heat release calculator 208. The AEA and TEA are determined based on the ratio of a known oxygen level (e.g., the oxygen set point and / or the measured actual oxygen) and excess air. In particular, for any particular fuel composition, there is a corresponding ratio between excess air and oxygen levels resulting from a combustion process involving the fuel. For example, FIG. 3 depicts an example table 300 and corresponding plot 302 with a curve 304 representative of the ratio of oxygen to excess air. In the illustrated example of FIG. 3, oxygen is expressed as a percentage (e.g., by volume) of the flue gas exiting the combustion system, and the excess air is expressed as a percentage (e.g., by volume) of the total air that has entered the combustion process. Corresponding curves can be generated for each fuel composition. Accordingly, in the illustrated example, a characteristic fuel composition may be assumed and the resulting curve used to calculate the TEA and AEA. More specifically, TEA corresponds to the value of the excess air on the curve associated with the oxygen set point. Similarly, AEA corresponds to the value of the excess air on the curve associated with the oxygen measured in chimney 112 of heater 102.Returning to FIG. 2, as described above, in some examples, the composition of a fuel provided in the combustion process may vary over time. As a result, the heating value or energy content of the fuel also varies with time. To accommodate such changes, the example control system 116 includes the fuel heat release calculator 208 for calculating a BTU (British Heat Unit) adjustment factor to adjust the fuel demand. The use of BTUs as a specific metric or unit of energy is provided in the explanation of the teachings disclosed herein for clarity. Accordingly, where specific example values and their corresponding units are provided for particular parameters used in connection with the systems and methods disclosed herein, such values and corresponding units may be converted to any other set of metrics or units based on the appropriate conversion factor or factors, respectively. It is generally known that at a certain BTU content, the fuel consumes a stoichiometric amount of air in a combustion process. Moreover, as the heating value (e.g., BTU content) of the fuel changes, the amount of stoichiometric air consumed during combustion also changes. Accordingly, in some examples, the fuel heat release calculator 208 determines a relative heat release value corresponding to the ratio of an actual (e.g., measured) stoichiometric air demand (ASAD) in a combustion process to a predicted (e.g., targeted or expected) stoichiometric air demand (PSAD). The relative heat release value can be expressed as follows:The ratio of Equation 1 provides an indication of the relative difference between the predicted stoichiometric air demand (e.g., predicted based on a given air-fuel ratio) and the actual stoichiometric air demand (e.g., based on variability in the heat content of the fuel). In some examples, the actual stoichiometric air demand (ASAD) may not be known, but is related to an actual air flow (AAF) 226 (as measured by the air flow sensor 136 of FIG. 1 ) into the combustion process and to the actual excess air (AEA) 224 exiting the combustion process (as determined based on the oxygen measured by the oxygen sensor 126, as described above). In some examples, the actual excess air corresponds to an excess air factor between 1 and 2. the ratio between ASAD, AAF, and AEA may be expressed as follows:Thus, although the actual stoichiometric air demand may be unknown, it may be resolved as follows by rewriting Equation 2:Accordingly, although the predicted stoichiometric air demand may not be known, it is related to a desired or target air flow (TAF) 228 (determined via the cross-limiting calculator 204, as will be described in more detail below) in the combustion process and the target excess air (TEA) 222 (determined based on the oxygen set point, as described above). In some examples, the target excess air corresponds to an excess air factor between 1 and 2. the ratio between PSAD, TAF, and AEA may be expressed as follows:Although the predicted stoichiometric air demand may be unknown, it may be appropriately resolved by rewriting Equation 4 as follows:Substituting Equations 3 and 5 into Equation 1, the following results:Equation 6 may then be rewritten as the ratio of the actual air flow to the target air flow multiplied by the ratio of the target excess air to the actual excess air as follows:Based on the relative heat release value calculated from Equation 7, the fuel heat release calculator 208 may determine the amount of change in the heating value (e.g., BTU content) of the fuel without considering changes in the airflow. In some examples, a baseline or baseline heating value for the fuel (e.g., based on an assumed composition of the fuel) may be assumed, and the relative heat release value may be used to determine a BTU adjustment factor to adjust or adjust the assumed heating value of the fuel to compensate for changes in the composition of the fuel when burned in the combustion system. In some examples, the baseline heating value is measured (e.g., via fuel heating value sensor 150 shown in FIG. 1 ). In some examples, at a set point of 1, the relative BTU values are 0 to 2. for example, if the actual fuel heating value is equal to the predicted heating value of the fuel, the relative BTU value is 1. however, if the heating value of the fuel changes by, for example, increasing by 10%, the stoichiometric amount of air consumed will correspondingly increase by 10%, resulting in a relative BTU value of 1.1. In the illustrated example, the fuel heat release calculator 208 also functions as a BTU compensation controller for adjusting (adjusting) the fuel heating value to bring the relative BTU value to the target value of 1. In this example, the fuel heat release calculator 208 will determine a BTU adjustment factor to increase the output heating value by 10%. The adjusted heating value is then used in such an example to regulate the fuel flow to provide the proper amount of fuel (based on its energy content) in the combustion process. If, on the other hand, the heating value of the fuel is not matched, the heat released by the fuel will not be correctly known and the resulting fuel flow is not controlled as desired, causing process disturbances. More specifically, in some examples, the resulting adjusted fuel heating value is multiplied by the flow rate of the fuel (e.g., as measured via fuel pressure and temperature sensors 152, 154, and / or any other flow sensor) to calculate an adjusted fuel flow provided to cross-limiting calculator 204 for performing the air-fuel cross-limiting calculations.In the illustrated example, the control system 116 is provided with the cross-linking calculator 204 to implement a cross-limiting strategy to ensure that air supplies fuel ahead as the fuel demand increases and supplies fuel in a retarding manner as the fuel demand decreases. In the illustrated examples, the feed forward fuel demand is calculated based on the forced fuel demand (as determined by the MPC optimizer 202 described above) and the fuel demand based on the air actually available for combustion. The feed forward air demand is calculated based on the desired percentage of oxygen in the chimney 112 (e.g., the oxygen set point determined by the cross limiting calculator 204) and the larger of the two forced fuel demand values (as determined by the MPC optimizer 202 described above) and the matched heating value of the fuel (as determined by the fuel heat release calculator 208 described above).More specifically, in the illustrated example, the feed forward air demand may be expressed as: where XAD is the feed forward air demand, FDmax is the maximum fuel demand calculated for the combustion system (e.g., as between the feed forward fuel demand and the adjusted fuel heating value), AFR is the air-fuel ratio, and TEA is the target excess air. The feed forward air demand (XAD) corresponds to the target air flow (TAF) provided to the fuel heat release calculator 208 to determine the BTU trim factor as described above. Further, the BTU adjustment factor is used to calculate the adjusted heating value used in determining FDmax, as described above. Accordingly, through implementation of the teachings disclosed herein, the XAD (or TAF) returns to itself, thereby allowing a constant update of the target airflow to continually adjust the system to address changing circumstances (e.g., a change in fuel composition). In some examples, the forced fuel demand is a scaled value expressed in terms of maximum heater load. Accordingly, in some examples, when comparing the forced fuel demand to the matched heating value, the cross-limiting calculator 204 first converts the forced fuel demand parameter in units of millions of metric BTUs per hour (MMBtu / h) using a scaler corresponding to 100% of the heater load (expressed in MMBtu / h). For example, if the maximum load of a heater is 75 MMBtu / hr, this value is used to convert the forced fuel demand in units corresponding to the adjusted heating value of the fuel. The air-fuel ratio (AFR) used in the above equation 8 is an adjustable value set by a user. Typically, the AFR is made up with about 0.70 thousand pounds of air to million BTUs fuel (Mlb air / MMBtu fuel). The target excess air (TEA) corresponds to the target excess air provided to the fuel heat release calculator 208 as described above.As described above, the feed forward fuel demand is based on the smaller of the forced fuel demand and the fuel demand based on air actually available for combustion. The fuel demand based on actually available air (FDA) may be expressed as: where DB is the dead band, AAF is the actual air flow into the heater, OTS is the oxygen balance signal, AFR is the air-fuel ratio, and TEA is the target excess air. The actual airflow (AAF) corresponds to the actual airflow measured by the airflow sensor 136 and provided to the fuel heat release calculator 208 as described above for determining the relative heat release value and BTU trim factor. The oxygen balance signal (OTS) corresponds to the above-described oxygen balance factor, except that the OTS is expressed on a scale of 0.8 to 1.2 and not on a scale of 80% to 120% (i.e., OTS corresponds to the oxygen balance factor divided by 100). The air-fuel ratio (AFR) and the target excess air (TEA) are the same as described above with respect to Equation 8.The resulting fuel demand of Equation 9, which is based on actually available air (FDA), is in units of MMBtu / hr (e.g., FDA is an expression of the heat rate of fuel in the combustion system based on the actually available air). Accordingly, in some examples, to compare the FDA to the forced fuel demand, the cross-limiting calculator 204 converts the forced fuel demand parameter into corresponding units using the scaler as described above. In some such examples, the feed forward fuel demand is designated as the lower of the two values. In some examples, the feed-forward fuel demand is converted back to a flow rate (e.g., thousand standard cubic feet per hour (MSCPH)) and provided to the fuel regulator 210 as a cascade set point or target fuel flow. In some examples, the adjusted heating value for the fuel is used as a conversion factor.In the illustrated example, the fuel regulator 210 monitors a fuel flow 234 and actuates and / or regulates a corresponding fuel flow valve 118 to adjust the flow of fuel based on a monitored fuel flow 234 with respect to the feed forward fuel demand. In this way, a controlled rate of heat of the fuel is possible even when the BTU content of the fuel changes over time. In some examples, the fuel regulator set point may be user specified to run independently of the remainder of the control system 116. In some examples, the fuel flow valve 118 is configured to switch to a closed position such that fuel flow is stopped when there is a loss of communication with the control system 116 and / or any other problem. Additionally, in some examples, the fuel regulator 210 has the capability for latches that open (or close) the valve 118. In such examples, the locks (with the user's appropriate account privilege) may be bypassed for testing on a bypass route.Moreover, in the illustrated example, the control system 116 is equipped with the airflow controller 206 for controlling the flow of air into and / or out of the combustion process system 100. As described above, the cross-limiting calculator 203 determines the optimum value determined air demand (XAD) corresponding to the target air flow (TAF) used by the heat release calculator 208. In some examples, the feed forward air demand (XAD) or the target air demand (TAF) is also provided to the airflow controller 206 by multiplying the value by the oxygen balance factor to become a balanced target airflow that is used as the output cascade set point for the airflow controller 206. In some examples, the airflow regulator 204 also includes the functionality of a train air pressure regulator that monitors a train air pressure 230 and may be used as a prime or override regulator for the chimney flap 124. That is, in some examples, the airflow controller 206 calculates a first demand for the flap 124 based on the AAF 226 and a second demand for the flap 124 based on the draft air pressure 230. In such examples, the airflow controller 206 selects the higher value between the first and second demands as the final set point used to control a position 232 of the door 124. In some such examples, the selected setpoint for the door 124 is characterized by counteracting process response nonlinearity to changes in door position. In some examples, the chimney door 124 is configured not to transition to an open state when there is a loss of an instrument signal from the control system 116. Additionally, in some examples, the airflow regulator 206 has the capability for latches that open (or close) the flap 124. In such examples, the locks (with the user's appropriate account privilege) may be bypassed for testing on a bypass route.While an example manner of implementing the example control system 116 of FIG. 1 is illustrated in FIG. 2, one or more of the elements, processes, and / or devices shown in FIG. 2 may be combined, shared, reordered, omitted, eliminated, and / or implemented in any other manner. Moreover, the MPC optimizer 202, the example cross-limiting calculator 204, the example airflow controller 206, the example fuel heat release calculator 208, the example fuel controller 210, and / or, more generally, the example control system 116 of FIG. 2 may be implemented by hardware, software, firmware, and / or any combination of hardware, software, and / or firmware. Thus, for example, the example MPC optimizer 202, the example cross-limiting calculator 204, the example airflow controller 206, the example fuel heat release calculator 208, the example fuel controller 210, and / or, more generally, the example control system 116 of FIG. 2 could be implemented by a / n or more analog or digital circuit / s, logic circuit / s, programmable processor / s, application specific integrated circuit / s (ASIC / s), programmable logic device / s (PLD / s), or field programmable logic device / s (FPLD / s). When any of the apparatus or system claims of this patent states that a purely software and / or firmware implementation is covered, the example MPC optimizer 202, the example cross-limiting calculator 204, the example airflow controller 206, the example fuel heat release calculator 208, and / or the example fuel controller 210 is / is hereby expressly defined to include a tangible, computer readable storage device or storage disk, such as a data storage, a digital versatile disk (DVD), a compact disk (CD), a blue ray disk, etc., that stores the software and / or firmware. Still further, the example control system 116 of FIG. 1 may include one or more element / s, process / s, and / or component / s in addition to or in place of that shown in FIG. 2, and / or may include more than one / any of any or all of the shown elements, processes, components.Flowcharts representative of example methods for implementing the example control system 116 of FIG. 2 are shown in FIGS. 4-11. In this example, the methods may be implemented using machine readable instructions comprising a program for execution by a processor, such as processor 1212 shown in example processor platform 1200 discussed below in connection with FIG. 12. The program may be included in software stored on a tangible computer readable storage medium such as a CD-ROM, a floppy disk, a hard disk, a digital versatile disk (DVD), a blue-ray disk, or a data storage connected to the processor 1212, but the entire program and / or parts thereof could alternatively be executed on a device other than the processor 1212 and / or firmware or dedicated hardware. Moreover, although the example program is described with reference to the flowcharts illustrated in FIGS. 4-11, many other methods of implementing the example control system 116 may alternatively be employed. For example, the execution order of the blocks may be changed and / or some of the described blocks may be changed, eliminated, or combined.As described above, the example methods of FIGS. 4-11 may be implemented using coded instructions (e.g., computer and / or machine readable instructions) stored on a tangible computer readable storage medium such as a hard disk drive, flash memory, read only memory (ROM), compact disk (CD), digital versatile disk (DVD), cache, random access memory (RAM), and / or any other storage device or storage disk in which information is stored for any duration (e.g., for long periods of time, permanently, temporarily, for temporarily buffering, and / or for caching the information). As used herein, the term "tangible computer readable storage medium" is expressly defined to include any type of computer readable storage device and / or storage disk and to exclude propagating signals. As used herein, "tangible computer readable storage medium" and "tangible computer readable storage medium" are used interchangeably. Additionally or alternatively, the example methods of FIGS. 4-11 may be implemented using coded instructions (e.g., computer and / or machine readable instructions) stored on a non-transitory computer and / or machine readable storage medium such as a hard disk drive, flash memory, read-only memory, compact disk, digital versatile disk, cache, random access memory, and / or any other storage device or storage disk in which information is stored for any duration (e.g., for long periods of time, permanently, temporarily, for temporarily buffering, and / or for caching the information). As used herein, the term "non-transitory computer readable storage medium" is expressly defined to include any type of computer readable device and / or disk and to exclude propagating signals. When the phrase "at least" as used herein is used as the transitional term in a preamble of a claim, it is open in the same manner as the term "comprising" is open.The example method of FIG. 4 begins at a block 400 where the example MPC optimizer 202 controls a flow of product through a fired heater, as will be described in detail below in connection with the flowchart of FIG. 5. Although, as described above, the following figures are described in the context of a fired heater, the example methods described herein may also be implemented with respect to any type of combustion process. At a block 402, the example MPC optimizer 202 determines a forced fuel demand, which is described in more detail below in connection with the flowchart of FIG. 6. In a block 404, the example cross-limiting calculator 204 monitors exhaust air from the heater to determine an oxygen balance, actual excess air, and target excess air, which will be described in detail below in connection with the flowchart of FIG. 7. At a block 406, the example fuel heat release calculator 208 determines a BTU adjustment factor, which will be described in detail below in connection with the flowchart of FIG. 8. At a block 408, the example fuel heat release calculator 208 determines the adjusted heat rate and the adjusted heating value of the fuel, which will be described in detail below in connection with the flowchart of FIG. 9.In a block 410, the example cross-limiting calculator 204 calculates an optimum determined air demand. As described above, the optimum determined air demand is calculated based on the desired percentage of oxygen in the chimney 112 and the larger of the forced fuel demand and matched fuel heating values, respectively, according to Equation 8 described above. In the example method of FIG. 4, the desired percentage of oxygen corresponds to the oxygen set point used to calculate the target excess air (TEA) used in Equation 8. Determining the oxygen set point and corresponding TEA will be described in more detail below in connection with FIG. 7, which corresponds to block 404 of the example method of FIG. 4. The forced fuel demand is determined at block 402, which is described in more detail below in connection with FIG. 6. The adjusted heating value of the fuel is determined at block 408, which is described in more detail below in connection with FIG. 9.In a block 412, the example cross-limiting calculator 204 calculates an optimum determined fuel demand. The feed forward fuel demand is calculated based on the smaller of the forced fuel demand (e.g., determined in block 402) and the fuel demand based on air actually available for combustion. As described above, the actual available air (FDA) fuel demand is calculated based on Equation 9 and takes into account the actual air flow (AAF), the oxygen trim signal (corresponding to the oxygen set point), and the TEA, as well as several user specified parameters (e.g., the dead band and the air-fuel ratio). In the example method of FIG. 4, the AAF is determined at block 406 as described in more detail below in connection with FIG. 8. The oxygen set point and the TEA are the same as described above in connection with block 410.In a block 414, the example fuel flow controller 210 regulates a flow of fuel into the heater, as will be described in detail below in connection with the flowchart of FIG. 10. At a block 416, the example airflow controller 206 controls airflow into the heater, as will be described in detail below in connection with the flowchart of FIG. 11. In a block 418, the example control system 116 determines whether to end the control process. For example, if a user or any other control system (e.g., a safety control system) makes a stop request arrive at the control system 116, the control system 116 terminates the control process and / or returns control to a calling process or function, such as a shutdown process, an idle process, etc., in response to the stop request. If the control system 116 determines that it should not end the control process, control otherwise returns to block 400.FIG. 5 is a flow diagram representative of an example method that may be employed to implement the operation of block 400 of FIG. 4 to regulate the product flow through a fired heater. The example method of FIG. 5 begins in a block 500 in which the example MPC controller determines whether a specified operating time has elapsed. The specified operating time is specified by the example MPC optimizer 202 each time it generates a predicted path set output for controlling the product feed stream through the heater, and is related to the amount of time that the combustion system 100 may operate within operating constraints (e.g., maintain a consistent heater coil outlet temperature) without requiring updates to the predicted path set output values to maintain operation within the operating constraints. The operating time may be based on a timer or time of day (e.g., a real-time clock).If the MPC optimizer 202 determines that the operating deadline has not expired, the example MPC optimizer 202 continues to check whether the operating deadline has expired (block 500) until the deadline expires or until the control system 116 receives an interrupt or command to proceed otherwise. If the example MPC optimizer 202 determines that the operating deadline has expired at block 500, control proceeds to block 502 where the example MPC optimizer 202 receives a measured product stream for each pass. Such flow measurements correspond to the flow controlled by each product flow valve (e.g., valves 120, 122 of FIG. 1 ). In a block 504, the example MPC optimizer 202 calculates a total mass flow rate. In some examples, the total flow rate corresponds to the combined product flow rate flowing through each pass in the heater.In a block 506 of the example method of FIG. 5, the example MPC optimizer 202 obtains a measured outlet temperature for each pass. In some examples, such temperature measurements are obtained from corresponding outlet temperature sensors (e.g., sensors 144, 146 of FIG. 1 ). In a block 508, the example MPC optimizer 202 calculates a heating coil outlet temperature. In a block 510, the example MPC optimizer 202 obtains a product flow setpoint for each pass. In some examples, the product flow setpoint is calculated via a linear program optimizer connected to the MPC optimizer. In such cases, the linear program optimizer calculates a flow rate for each pass such that the temperature increase in each pass (e.g., the outlet temperature at each pass) is substantially equivalent. That is, the linear program optimizing section achieves run compensation between plural runs. In a block 512, the example MPC optimizer 202 actuates the product flow valves to adjust the product flow for each pass based on the model predictive control. For example, after the example MPC optimizer 202 activates the product flow valves, the control returns to a calling function, such as the example method of FIG. 4.FIG. 6 is a flow diagram representative of an example method that may be employed to implement the operation of block 402 of FIG. 4 to determine a forced fuel demand. The example method of FIG. 6 begins at a block 600 at which the example MPC optimizer 202 determines whether a baseline fuel demand is provided via model predictive control. In addition to using the MPC to achieve run leveling of a product feed that passes through separate passes of the heater, as described above in connection with FIG. 5, in some examples, the MPC also generates a source or main fuel demand that may be introduced into the combustion control process. If such a fuel demand value is provided, a calculation of the output fuel demand based on the heater coil outlet temperature and the total mass flow rate may be bypassed so that control proceeds to a block 608. However, if the MPC optimizer 202 determines that no baseline fuel demand is provided via the model predictive control (block 600), control proceeds to a block 602, in which the example MPC optimizer 202 obtains the heating coil outlet temperature (e.g., based on the heating coil outlet temperature calculated at block 508 of FIG. 5 ). At a block 604, the example MPC optimizer 202 obtains the total mass flow rate (e.g., based on the total mass flow rate calculated at the block 504 of FIG. 5 ). In a block 606, the example MPC optimizer 202 calculates a baseline fuel demand. In some examples, the output fuel demand is based on the heating coil outlet temperature and the total mass flow rate.Whether the initial target flow rate is calculated (block 606) or provided via the MPC (block 600), the example method of FIG. 6 at any rate advances to a block 608 in which the example MPC optimizer 202 receives a measured burner pressure (e.g., via the burner pressure sensor 138 of FIG. 1 ). In a block 610, the example MPC optimizer 202 obtains a burner pressure set point. In some examples, the burner pressure set point is user specified. In a block 612, the example MPC optimizer 202 obtains a furnace temperature measured (e.g., via the furnace temperature sensor 140 of FIG. 1 ). In a block 614, the example MPC optimizer 202 obtains a furnace temperature set point. In some examples, the oven temperature set point is user specified.At a block 616, the example MPC optimizer 202 calculates a forced fuel demand based on constraint factors. More specifically, in some examples, the MPC optimizer 202 calculates various fuel demands based on a high burner pressure, a low burner pressure, and the furnace temperature, each of which may be a constraint factor in calculating the forced fuel demand. In some examples, the low and high burner pressure constraints are compared to the baseline fuel demand (e.g., calculated at block 606 or provided via the MPC as described at block 600). In such examples, the MPC optimizer 202 predicts a constraint violation and makes a setting if necessary, and then compares the resulting pressure constrained demand with the oven temperature constraint. The MPC optimizer 202 predicts a constraint violation and adjusts the demand to a final constraint fuel demand for the cross-limiting calculation, if necessary. For example, after the example MPC optimizer 202 calculates the forced fuel demand in this manner, control returns to a calling function or process such as the example method of FIG. 4.FIG. 7 is a flow diagram representative of an example method that may be employed to implement the operation of block 404 of FIG. 4 for monitoring exhaust air from the heater to determine an oxygen balance, actual excess air, and target excess air. The example method of FIG. 7 begins at a block 700 at which the example cross-limiting calculator 204 receives an amount of carbon monoxide measured in the chimney of the fired heater (e.g., via the carbon monoxide sensor 128 of FIG. 1 ). In a block 702, the example cross-limiting calculator 204 obtains an amount of oxygen measured in the chimney of the fired heater (e.g., via the oxygen sensor of FIG. 1 ).In a block 704, the example cross-limiting calculator 204 obtains an oxygen set point. In some examples, the oxygen setpoint is used to calculate an oxygen balance factor. In some examples, the oxygen set point is based on a user-specified base set point combined with an impact value. In some examples, the bias value is also set by a user. In some examples, the impact value is based on the carbon monoxide measured in the chimney of the heater (e.g., at block 700). In a block 706, the example cross-limiting calculator 204 determines an oxygen balance factor. As described above, in some examples, the oxygen balance factor is based on the oxygen set point (block 704) and the measured amount of oxygen in the chimney (block 702). In some examples, the oxygen balance factor is scaled to between 80% and 120%.In a block 708, the example cross-limiting calculator 204 determines an actual excess air (AEA). In some examples, the AEA is based on the known ratio between oxygen in the chimney and excess air in the heater for a particular fuel composition. In some examples, the ratios are defined by a curve (e.g., curve 304 of FIG. 3 ) corresponding to an assumed composition of the fuel in the combustion process. Thus, the example cross-limiting calculator 204 introduces the measured amount of oxygen in the chimney (block 702) into the curve to result in a resulting excess air corresponding to the AEA. In a block 710, the example cross-limiting calculator 204 determines a target excess air (TEA). In some examples, the example cross-limiting calculator 204 determines the TEA in the same manner as the AEA (e.g., via curve 304), except that the input oxygen level used is the oxygen set point (block 704). For example, after the example cross-limiting calculator 204 determines the oxygen balance factor (block 706), the AEA (block 708), and the TEA (block 710), the controller returns to a calling function or process such as the example method of FIG. 4.FIG. 8 is a flow diagram representative of an example method that may be employed to implement the operation of block 406 of FIG. 4 to determine a BTU adjustment factor. The example method of FIG. 8 begins at a block 800 at which the example fuel heat release calculator 208 obtains an actual airflow (AAF) (e.g., via the airflow sensor 136 of FIG. 1 ). In a block 802, the example fuel heat release calculator 208 calculates a target air flow (TAF). In some examples, the TAF corresponds to the feed forward air demand calculated at block 410 of FIG. 4 as described above. However, in the example methods described herein, the TAF is an input value used in calculating the feed forward air demand. Thus, the TAF is a feedback input to its own subsequent computation that adjusts when the example method cycles through multiple repetitions. In some examples, the TAF is defined as being equivalent to the AAF as the initial start point. Once the example method has undergone the first iteration, all parameters will be known to then calculate a TAF, which may then deviate from the AAF, thereby requiring adjustments to the combustion process.In a block 804, the example fuel heat release calculator 208 calculates a relative heat release value. In some examples, the relative heat release value corresponds to the ratio of the actual airflow (block 800) to the target airflow multiplied by the ratio of target excess air (block 710) to actual excess air (block 708) (block 802). The relative heat release value is expressed in Equation 7 described above. At block 804, the example fuel heat release calculator 208 calculates the BTU trim factor. In some examples, the BTU adjustment factor has a set point of 1 and is determined based on the relative heat release value. In some examples, the BTU adjustment factor is scaled between 80% and 120%. For example, after the example fuel heat release calculator 208 determines the BTU trim value, the controller returns to a calling function or process such as the example method of FIG. 4.FIG. 9 is a flow diagram representative of an example method that may be employed to implement the operation of block 408 of FIG. 4 to determine a matched heat rate and a matched heating value of the fuel. The example method of FIG. 9 begins at a block 900, where the example fuel heat release calculator 208 obtains the actual fuel flow (e.g., via the fuel temperature and fuel pressure sensors 152, 154 of FIG. 1 ). In a block 902, the example fuel heat release calculator 208 obtains a baseline heating value of the fuel. In some examples, the baseline heating value is an assumed constant value specified by a user corresponding to an assumed composition of the fuel. In other examples, the baseline heating value may be measured (e.g., via fuel heating value sensor 150). In a block 904, the example fuel heat release calculator 208 calculates the adjusted heating value of the fuel. In some examples, the adjusted heating value corresponds to the baseline heating value multiplied by the BTU adjustment factor (block 806 of FIG. 8 ) (block 902). At block 904, the example fuel heat release calculator 208 calculates the adjusted heat rate of the fuel. In some examples, the adjusted heat rate corresponds to the adjusted heating value of the fuel multiplied by the actual fuel flow (block 900) (block 904). For example, after the example fuel heat release calculator 208 calculates the matched heating value and the matched heat rate of the fuel, the controller returns to a calling function or process such as the example method of FIG. 4.FIG. 10 is a flow diagram representative of an example method that may be employed to implement the operation of block 414 of FIG. 4 to control a flow of fuel into the heater. The example method of FIG. 10 begins at a block 1000, at which the example fuel flow controller 210 obtains an actual fuel flow (e.g., the fuel flow obtained at block 900 of FIG. 9 ). In a block 1002, the example fuel flow controller 210 receives a target fuel flow. In the example method of FIG. 9, the target fuel flow corresponds to the feed forward fuel demand calculated in block 412 of FIG. 4. In a block 1004, the example fuel flow controller 210 actuates the fuel flow valve to adjust the fuel flow. For example, after the example fuel flow controller 210 actuates the fuel flow valve, the controller returns to a calling function or process such as the example method of FIG. 4.FIG. 11 is a flow diagram representative of an example method that may be employed to implement the operation of block 416 of FIG. 4 to control airflow into the heater. The example method of FIG. 11 begins at a block 1100, at which the example airflow controller 206 obtains an actual airflow (AAF) (e.g., via the airflow sensor 136). In some examples, the AAF corresponds to the AAF obtained in block 800 of FIG. 8. In a block 1102, the example airflow controller 206 calculates a matched airflow setpoint. In some examples, the adjusted airflow setpoint (or adjusted TAF) corresponds to the target airflow (TAF) (calculated at block 802 of FIG. 7 ) multiplied by the oxygen adjustment factor (determined at block 706 of FIG. 7 ).In a block 1104, the example airflow controller 206 receives a train air pressure (e.g., via the train air pressure sensor 132). At a block 1106, the example airflow controller 206 receives a flap position (e.g., via the flap position sensor 134). In a block 1108, the example airflow controller 206 calculates a demand for the door. In some examples, the demand for the door corresponds to the greater of a demand based on the AAF relative to the adjusted airflow setpoint or a demand based on the draft air pressure, respectively. In a block 1110, the example airflow controller 206 actuates the door to adjust the airflow. For example, after the example airflow controller 206 actuates the door, the controller returns to a calling function or process such as the example method of FIG. 4.FIG. 12 is a block diagram of an example processor platform 1200 capable of executing the instructions of FIGS. 4-11 to implement the control system 116 of FIG. 2. The processor platform 1200 may be, for example, a server, a personal computer, a mobile device (e.g., a cell phone, a smart phone, a tablet such as a iPad™), or any other type of computing device.The processor platform 1200 of the illustrated example includes a processor 1212. The processor 1212 of the illustrated example is in hardware. For example, processor 1212 may be implemented by one / n or more integrated circuit / s, logic circuit / s, microprocessor / s, or controllers from any desired family or manufacturer.The processor 1212 of the illustrated example includes a local memory 1212 (e.g., a cache memory). The processor 1212 of the illustrated example is in communication with a main memory including a volatile memory 1214 and a nonvolatile memory 1216 via a bus 1218. The volatile memory 1214 may be implemented by synchronous dynamic random access memory (SDRAM), dynamic random access memory (DRAM, dynamic RAMBUS random access memory (RDRAM), and / or any other type of random access memory device. The non-volatile memory 1216 may be implemented by flash memory and / or any other desired type of storage device. Access to main memory 1214, 1216 is controlled by a memory controller.The processor platform 1200 of the illustrated example also includes an interface circuit 1220. The interface circuit 1220 may be implemented by any type of interface standard such as an Ethernet interface, a universal serial bus (USB), and / or a PCI express interface.In the illustrated example, one or more input devices 1222 are connected to the interface circuit 1220. The input device / s 1222 enables / enables a user to input data and commands to the processor 1212. The input device / s 1222 may be implemented, for example, by an audio sensor, a microphone, a (still or video) camera, a keyboard, a key, a mouse, a touch screen, a trackpad, a trackball, isopoint, and / or a voice recognition system.One or more output device / s 1224 is / are also connected to the interface circuit 1220 of the illustrated example. The output devices 1224 may be implemented, for example, by display devices (e.g., a light emitting diode (LED), an organic light emitting diode (OLED), a liquid crystal display, a cathode ray tube display (CRT), a touch screen, a tactile output device, a light emitting diode (LED), a printer, and / or speaker). The interface circuit 1220 of the illustrated example thus typically includes a graphics driver card, a graphics driver chip, or a graphics driver processor.The interface circuit 1220 of the illustrated example also includes a communication device such as a transmitter, a receiver, a transmit / receive unit, a modem, and / or a network interface card to facilitate exchanging data with external machines (e.g., computing devices of any type) via a network 1226 (e.g., an Ethernet connection, a digital subscriber line (DSL), a telephone line, a coaxial cable, a cellular telephone system, etc.).The processor platform 1200 of the illustrated example also includes one or more mass storage device / s 1228 for storing software and / or data. Examples of such mass storage devices 1228 include floppy disk drives, hard disks, CD drives, Blue Ray disk drives, RAID systems, and DVD drives.Encoded instructions 1232 for implementing the methods of FIGS. 4-11 may be stored in mass storage device 1228, volatile memory 1214, nonvolatile memory 1216, and / or on a removable, tangible computer readable storage medium such as a CD or DVD.Although certain example methods, apparatus, and articles of manufacture have been disclosed herein, the scope of coverage of this patent is not limited thereto. Rather, this patent covers all methods, apparatus and articles of manufacture that fall appropriately within the scope of the claims of this patent.

Claims

A method comprising: monitoring an actual flow of fuel (234) into a combustion process; calculating a relative heat release value corresponding to the fuel in the combustion process; and determining a fuel demand for the combustion process based on the relative heat release value.The method of claim 1, further comprising: monitoring an actual air flow (226) of air into the combustion process; determining the fuel demand for the combustion process based on the actual air flow (226); and determining a target air flow (228) for the combustion process based on the greater value of the actual fuel flow (234) or the fuel demand.The method of claim 2, further comprising: determining a target excess air (222) for the combustion process; determining an actual excess air (224) in the combustion process; determining a relative heat release value based on the target air flow (228), the actual air flow (226), the target excess air (222), and the actual excess air (224).The method of claim 3, further comprising: monitoring an amount of oxygen in an exhaust air of the combustion process; receiving an oxygen set point indicative of a desired amount of oxygen in the exhaust air of the combustion process; determining the target excess air (222) based on the oxygen set point; and determining the actual excess air (224) based on the amount of oxygen in the exhaust air of the combustion process.The method of claim 4, further comprising monitoring an amount of carbon monoxide in the exhaust air of the combustion process, wherein the oxygen setpoint is based on the amount of carbon monoxide.The method of claim 1, wherein the fuel has a heating value that varies over time.The method of claim 1, wherein calculating the relative heat release value comprises multiplying a ratio of an actual air flow (226) of air into the combustion process to a target air flow (228) and a ratio of a target excess air (222) for the combustion process to an actual excess air (224).The method of claim 1, further comprising: determining a BTU trim factor based on the relative heat release value; calculating a adjusted heating value for the fuel; and determining the fuel demand based on the adjusted heating value.An apparatus comprising: a sensor for monitoring an actual flow of fuel (234) into a combustion process; a heat release calculator (208) for calculating a relative heat release value corresponding to the fuel in the combustion process; and a cross-limiting calculator (204) for determining a fuel demand for the combustion process based on the relative heat release value.The apparatus of claim 9, further comprising an airflow sensor (136) for monitoring an actual airflow (226) of air into the combustion process, wherein the fuel demand for the combustion process is to be based on the actual airflow (226), wherein the cross-limiting calculator (204) is to determine a target airflow (228) for the combustion process based on the larger of the actual fuel flow (234) or the fuel demand.The apparatus of claim 10, further comprising: a controller to determine a target excess air (222) for the combustion process and an actual excess air (224) in the combustion process, wherein the relative heat release value is to be based on the target air flow (228), the actual air flow (226), the target excess air (222), and the actual excess air (224).The apparatus of claim 11, further comprising an oxygen sensor (126) for monitoring an amount of oxygen in an exhaust air of the combustion process, wherein the controller is to determine the actual excess air (224) based on the amount of oxygen in the exhaust air of the combustion process and to determine the target excess air (222) based on a set point of oxygen that indicates a desired amount of oxygen in the exhaust air of the combustion process.The apparatus of claim 12, further comprising a carbon monoxide sensor (128) for monitoring an amount of carbon monoxide in the exhaust air of the combustion process, wherein the oxygen setpoint is to be based on the amount of carbon monoxide.The apparatus of claim 9, wherein the fuel has an unknown composition that varies over time.The apparatus of claim 9, wherein the relative heat release value corresponds to the product of a ratio of an actual air flow (226) of air into the combustion process to a target air flow (228) and a ratio of a target excess air (222) for the combustion process to an actual excess air (224).The apparatus of claim 9, wherein the heat release calculator (208) is configured to: determine a BTU trim factor based on the relative heat release value; and calculate a adjusted heating value for the fuel, wherein the fuel demand is to be based on the adjusted heating value.A tangible machine-readable storage medium comprising instructions (1232) that, when executed, cause an engine to at least: monitor an actual fuel flow (234) in a combustion process; calculate a relative heat release value corresponding to the fuel in the combustion process; and determine a fuel demand for the combustion process based on the relative heat release value.The storage medium of claim 17, wherein the instructions (1232), when executed, further cause the engine to: monitor an actual airflow (226) of air into the combustion process; determine the fuel demand for the combustion process based on the actual airflow (226); and determine a target airflow (228) for the combustion process based on the larger of the actual fuel flow (234) or the fuel demand.The storage medium of claim 18, wherein the instructions (1232), when executed, further cause the engine to: determine a target excess air (222) for the combustion process; determine an actual excess air (224) in the combustion process; determine the relative heat release value based on the target air flow (228), the actual air flow (226), the target excess air (222), and the actual excess air (224).The storage medium of claim 19, wherein the instructions (1232), when executed, further cause the engine to: monitor an amount of oxygen in an exhaust of the combustion process; receive an oxygen set point indicative of a desired amount of oxygen in the exhaust of the combustion process; determine the target excess air (222) based on the oxygen set point; and determine the actual excess air (224) based on the amount of oxygen in the exhaust of the combustion process.The storage medium of claim 20, wherein the instructions (1232), when executed, further cause the engine to monitor an amount of carbon monoxide in the exhaust air of the combustion process, wherein the oxygen set point is based on the amount of carbon monoxide.The storage medium of claim 17, wherein the fuel has a heating value that varies over time.The storage medium of claim 17, wherein calculating the relative heat release value comprises multiplying a ratio of an actual air flow (226) of air into the combustion process to a target air flow (228) and a ratio of a target excess air (222) for the combustion process to an actual excess air (224).The storage medium of claim 17, wherein the instructions (1232), when executed, further cause the engine to: determine a BTU adjustment factor based on the relative heat release value; calculate an adjusted heating value for the fuel; and determine the fuel demand based on the adjusted heating value.

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