Combustor air flow control method for fuel cell apparatus

A method for controlling the heat output of a combustor in a fuel cell apparatus to a fuel processor where the combustor has dual air inlet streams including atmospheric air and fuel cell cathode effluent containing oxygen depleted air. In all operating modes, an enthalpy balance is provided by regulating the quantity of the air flow stream to the combustor to support fuel cell processor heat requirements. A control provides a quick fast forward change in an air valve orifice cross section in response to a calculated predetermined air flow, the molar constituents of the air stream to the combustor, the pressure drop across the air valve, and a look up table of the orifice cross sectional area and valve steps. A feedback loop fine tunes any error between the measured air flow to the combustor and the predetermined air flow.

FIELD OF THE INVENTION
 The present invention relates, in general, to electrochemical fuel cells
 and, more specifically, to combustors for heating a fuel processor.
 BACKGROUND OF THE INVENTION
 Fuel cells have been used as a power source in many applications. Fuel
 cells have also been proposed for use as a vehicular power plant to
 replace the internal combustion engine. In proton exchange membrane (PEM)
 type fuel cells, hydrogen is supplied to the anode side of the fuel cell
 and air or oxygen is supplied as the oxidant to the cathode side. PEM fuel
 cells include a "membrane electrode assembly" (a.k.a. MEA) comprising a
 thin, proton transmissive, solid polymer membrane-electrolyte having the
 anode on one of its faces and the cathode on the opposite face. The MEA is
 sandwiched between a pair of electrically conductive elements which (1)
 serve as current collectors for the anode and cathode, and (2) contain
 appropriate channels and/or openings therein for distribution the fuel
 cell's gaseous reactants over the surfaces of the respective anode and
 cathode catalysts. A plurality of individual cells are commonly bundled
 together to form a PEM fuel cell stack.
 For vehicular applications, it is desirable to use a liquid fuel such as an
 alcohol (e.g., methanol or ethanol), or hydrocarbons (e.g., gasoline) as
 the fuel for the vehicle owing to the ease of on-board storage of liquid
 fuels and the existence of a nationwide infrastructure for supplying
 liquid fuels. However, such fuels must be dissociated to release the
 hydrogen content thereof for fueling the fuel cell. The dissociation
 reaction is accomplished heterogeneously within a chemical fuel processor,
 known as a fuel processor, that provides thermal energy throughout a
 catalyst mass and yields a reformate gas comprising primarily hydrogen and
 carbon dioxide. For example, in the steam and methanol reformation
 process, methanol and water (as steam) are ideally reacted to generate
 hydrogen and carbon dioxide according to this reaction:
EQU CH.sub.3 OH+H.sub.2 O.fwdarw.CO.sub.2 +3H.sub.2.
 The reforming reaction is an endothermic reaction that requires external
 heat for the reaction to occur. The heat required to produce enough
 hydrogen varies with the demand put on the fuel cell system at any given
 point in time. Accordingly, the heating means for the fuel processor must
 be capable of operating over a wide range of heat outputs. Heating the
 fuel processor with heat generated externally from either a flame
 combustor or a catalytic combustor is known. U.S. patent applications Ser.
 Nos. 08/975,422 and 08/980,087 filed in the name of William Pettit in
 November, 1997, and assigned to the assignee of the present invention,
 disclose an improved catalytic combustor, and the integration thereof with
 a fuel cell system which fuels the combustor with unreformed liquid fuel,
 hydrogen-containing anode exhaust gas from the fuel cell, or both. The
 operating cycle depends on many factors, such as anode stoichiometry,
 steam/carbon ratio, electrical demand placed on the system, etc.
 Load changes placed on the fuel cell resulting in greater or lower power
 output requirements, results in the fuel processor generating more or less
 hydrogen. Correspondingly, since the combustor generates whatever heat
 input is required to sustain the chemical reactions within the fuel
 processor, the combustor likewise must generate more or less heat to
 maintain the required reaction temperatures within the fuel processor. The
 temperature control of the combustor is dependent upon several parameters,
 an important one being the air flow to the combustor.
 What is needed in a vehicular fuel cell application is a fast response to
 fuel cell load changes. However, air flow control devices using simple
 feedback to control the air flow to the combustor demonstrate slow
 response times.
 Another problem results from the use of cathode effluent as an air source
 to the combustor. Such cathode effluent is typically oxygen depleted after
 exiting the fuel cell such that the actual constituent makeup of the
 cathode effluent, in terms of water, nitrogen and oxygen differs from that
 found in normal air. As the air to the combustor is taken from two
 different sources depending upon the mode of operation of the fuel cell
 apparatus, i.e., start-up, warm-up, normal operating run mode, etc.,
 conventional sensors which merely measure air or mass flow rates do not
 take into account the constituent makeup of such air which may have a
 deleterious effect on the temperature in the combustor.
 Thus, it would be desirable to provide an air flow control method for a
 fuel cell apparatus which has a fast response to load changes, utilizes
 closed loop control with conventional automotive sensors and actuators and
 automatically compensates for molar fraction deviations of oxygen depleted
 air in the air flow stream to the combustor.
 SUMMARY OF THE INVENTION
 A method of operating a combustor to heat a fuel processor in a fuel cell
 apparatus in which the fuel processor generates hydrogen from a
 hydrocarbon fuel for supplying a fuel cell, the fuel cell discharging an
 anode effluent containing hydrogen and a cathode effluent containing
 oxygen, the method comprising the steps of:
 providing a fuel stream to the combustor;
 providing an air flow stream to the combustor, the air flow stream
 including at least one of a first air source and cathode effluent from the
 fuel cell;
 determining the power input requirement of the fuel processor;
 determining the output power of the combustor to support the determined
 power requirement of the fuel processor; and
 regulating the air flow stream to the combustor to control the temperature
 of the combustor.
 In one aspect, the regulation step comprises controlling the direction of
 air flow. Preferably, this is accomplished by directing the air either
 primarily through the cathode portion of the stack and to the combustor,
 or primarily directing the air in a path directly to the combustor. The
 later is referred to as stack-bypass.
 In another aspect, the regulating step comprises the step of controlling
 the cross sectional area of an orifice of an air flow regulator or valve
 in the air stream in response to the constituent makeup of the air stream.
 The control method also includes the step of limiting the cross sectional
 area of an air flow regulator orifice to a maximum or a minimum cross
 sectional area.
 In still another aspect of the present method, the regulating step includes
 connecting an air flow valve to an external exhaust to bleed air from the
 air stream input to the combustor.
 According to one aspect, the air flow regulator or valve is an air flow
 device having a variable cross sectional orifice which can be varied in a
 discrete number of steps by a stepper motor operator between full valve
 open and full valve closed positions. The orifice has a known cross
 sectional area at each discrete step. The inventive method determines the
 desired air flow through the valve based on certain input parameters,
 sensors and empirically obtained daita, to adjust the orifice to the cross
 sectional area which is capable of supplying the desired air flow.
 Finally, in the present control method, the method also includes the step
 of summing the first cross-sectional area of the orifice of the air flow
 regulator with an error signal representing the difference between the
 measured actual air flow to the combustor and the predetermined air flow.
 Preferably, according to one aspect of the invention, the error signal is
 generated by a PID controller.

DESCRIPTION OF THE PREFERRED EMBODIMENTS
 The invention is hereafter described in the context of a fuel cell fueled
 by a methanol (MeOH) fuel processor. However, it is to be understood that
 the principles embodied herein are equally applicable to fuel cells fueled
 by other fuels, such as ethanol or gasoline, which utilize a fuel
 processor for conversion into a hydrogen rich stream.
 As shown in FIG. 1, a fuel cell apparatus includes a fuel processor 2 for
 catalytically reacting methanol from a methanol stream 6 and water or
 steam from a water stream 8 in a recirculating bed 10 and a catalytic bed
 12 to form a hydrogen-rich reformate gas stream. A heat exchanger 14 is
 interposed between the catalytic bed 12 and a preferential oxidation
 (PROX) reactor 16. The reformate output gas stream comprises primarily
 H.sub.2 and CO.sub.2, but also includes N.sub.2, CO and water. The
 reformate stream passes through the preferential oxidation (PrOx) reactor
 16 to reduce the CO-levels therein to acceptable levels (i.e., below 20
 ppm). The H.sub.2 rich reformate 20 is then fed into the anode chamber of
 a fuel cell 22. At the same time, oxygen (e.g., air) from an oxidant
 stream 24 is fed into the cathode chamber of the fuel cell 22. The
 hydrogen from the reformate stream 20 and the oxygen from the oxidant
 stream 24 react in the fuel cell 22 to produce electricity.
 Exhaust or effluent 26 from the anode side of the fuel cell 22 contains
 some unreacted hydrogen. The exhaust or effluent 28 from the cathode side
 of the fuel cell 22 contains some unreacted oxygen. The terms effluent and
 exhaust are used herein interchangeably. Air for the oxidant stream 24 is
 provided by a compressor 30 and is directed to the fuel cell 22 by a valve
 32 under normal operating conditions. During start-up, however, the valve
 32 is actuated to provide air to the input of a combustor 34 used to heat
 the fuel processor 2, as will be described in more detail hereinafter.
 Heat from the heat exchanger 14 heats the catalyst bed(s) 10 and 12 in the
 fuel processor 2 and also heats the PROX 16. In this regard, the H.sub.2
 O--MeOH mixture supplied to the fuel processor 2 will be vaporized and
 preferably be recirculated/refluxed several times (e.g., 20.times.)
 through the recirculating bed 10 in the fuel processor 2, the heat
 exchanger side of the bed 12, the PROX 16 and the heat exchanger 14 such
 that the mixture also functions as a heat transfer medium for carrying
 heat from the heat exchanger 14 into the beds 10 and 12 of the fuel
 processor 2 and to the PROX 16.
 The heat exchanger 14 itself is heated from exhaust gases 36 exiting the
 catalytic combustor 34. The gases 36 exiting the heat exchanger 14 are
 still hot and could be passed through an expander, not shown, which could
 drive the compressor 30 or utilized in another manner. In the present
 implementation, as shown in FIG. 1, the exhaust gases from the combustor
 34 are used to heat the fuel processor 2 pass through a regulator 38, a
 shutoff valve 140 and a muffler 142 before being dumped to atmosphere.
 MeOH vapor 40 emanates from a vaporizer 41 nested in the exhaust end 44 of
 the combustor 34. The vaporizer 41 is a heat exchanger that extracts heat
 from the combustor 34 exhaust to vaporize a first fuel stream, such as
 liquid MeOH 46 provided o the vaporizer 41 by fuel metering device 43 from
 the vehicle's fuel tank. The MeOH vapor 40 exiting the vaporizer 41 and
 the anode effluent 26 are reacted in a catalyst section 48 of the
 combustor 34 lying intermediate the inlet and exhaust ends 42 and 44
 respectively of the combustor 34. Oxygen is provided to the combustor 34
 either from the compressor 30 (i.e., via valve 32) or from a second air
 flow stream, such as a cathode effluent stream 28 depending on system
 operating conditions. A valve 50 permits dumping of the combustor exhaust
 36 to atmosphere when it is not needed in the fuel processor 2.
 Further details concerning the construction of the combustor 34 can be had
 by referring to pending U.S. patent applications Ser. Nos. 08/975,422 and
 08/980,087 filed in the name of William Pettit in November 1997, the
 entire contents of which are incorporated herein by reference.
 An electric heating element (EHC) 52 is provided upstream of the catalyst
 bed 48 in the combustor 34 and serves to vaporize the liquid fuel 46
 entering the combustor 34, heat the gas entering the bed 48 as well as
 preheating the bed 48 during start-up of the combustor 34. The heating
 element 52 may or ray not be catalyzed. After start-up, as described
 hereafter, the electric heater 52 is no longer required since the fuel
 will be vaporized by the exhaust gases emanating from the exhaust end 44
 of the combustor 34. A preferred electric heater 52 comprises a
 commercially available, uncatalyzed extruded metal monolith resistance
 element such as is used to light off the catalyst of a catalytic converter
 used to treat IC engine exhaust gases.
 The exhaust end 44 of the combustor 34 includes a chamber that houses the
 vaporizer 41 which is a coil of metal tubing which is used to vaporize
 liquid fuel to fuel the combustor 34. More specifically, under normal
 post-start-up conditions, air or cathode effluent 28 may be introduced
 into the inlet end of the coil and mixed with liquid fuel sprayed into the
 inlet end via a conventional automotive type fuel injector. The airborne
 atomized fuel passes through the several turns of the heated coil tube,
 and therein vaporizes and exits the tube at an outlet which is located in
 the cathode effluent supply conduit. This vaporized first fuel stream
 supplements a second fuel stream or anode effluent 26 as fuel for the
 combustor 34 as may be needed to meet the transient and steady state needs
 of the fuel cell apparatus. The vaporizer coil is sized to vaporize the
 maximum flow rate of fuel with the minimum combustor exhaust flow rate,
 and is designed to operate at temperatures exceeding the autoignition
 temperature of the MeOH-air mixture therein throughout its fuel
 operational range. Autoignition within the vaporizer is avoided, however,
 by insuring that the velocity of the mix flowing through the coil
 significantly exceeds the worst-case flame speed of the mixture which
 varies with the composition of the inlet streams.
 As shown in FIG. 1, ant as described in greater detail hereafter, the
 amount of heat demanded by the fuel processor 2 which is to be supplied by
 the combustor 34 is dependent upon the amount of fuel and water input to
 the fuel processor 2. The greater the supply of fuel and water, the more
 heat energy the reformer will need. To supply the heat demand of the fuel
 processor 2, the combustor 34 utilizes all anode exhaust or effluent and
 potentially some liquid fuel. Enthalpy equations are used to determine the
 amount of cathode exhaust or air to be supplied to the combustor 34 to
 meet the desired temperature requirements of the combustor 34, and the
 combustor 34 ultimately satisfies the heat demanded by the fuel processor
 2. The oxygen, air, or air like stream provided to the combustor 34
 includes one or both of cathode effluent exhaust 28 which is typically a
 percentage of the total oxygen supplied to the cathode of the fuel cell 22
 and a compressor output air stream depending on whether the apparatus is
 operating in a start-up mode wherein the compressor air stream is
 exclusively employed or in a run mode using the cathode effluent 28 and/or
 compressor air. In the run mode, any total air, oxygen or diluent demand
 required by the combustor 34 which is not met by the cathode effluent 28
 is supplied by the compressor 30 in an amount to balance the enthalpy
 equations, and to satisfy the temperature and heat demanded by the
 combustor 34 and the fuel processor 2, respectively.
 The air quality control is implemented via an air dilution valve 47 which
 is a stepper motor driven valve having a variable orifice to control the
 amount of bleed-off of cathode exhaust supplied to the combustor 34 and
 potentially the system exhaust, which bled-off air is dumped to atmosphere
 through the regulator 38, the valve 140, and the muffler 142. A further
 description of the air dilution valve 47 will be presented hereafter in
 conjunction with the various modes or sequences of operation of the
 combustor 34.
 The fuel cell apparatus of the present invention operates as follows. At
 the beginning of operations when the fuel cell apparatus is cold and
 starting up: (1) the compressor 30 is driven by an electric motor
 energized from an external source (e.g., a battery) to provide the
 necessary system air; (2) air is introduced into the combustor 34 as well
 as the input end of the vaporizer 41; (3) liquid fuel 46 (e.g., MeOH) is
 injected into the inlet end of the vaporizer 41 via a fuel injector, and
 atomized as fine droplets with the air flowing therein; (4) the air-MeOH
 droplet mix exits the vaporizer 41 and mixes with compressor air
 introduced into the combustor 34, and is then introduced into the input
 end 42 of the combustor 34; (5) the mix passes through a flame arrestor in
 the front of the combustor 34; (6) the mix is then heated by the heater 52
 to vaporize the liquid droplets and heat the mixture; (7) the preheated
 vaporous mix then enters a mixing-media bed for still further intimate
 mixing before contacting the light-off catalyst bed; (8) upon exiting the
 mixing-media bed, the mix begins oxidizing on the light-off catalyst bed
 just before it enters a primary catalyst bed 48, or reacting section of
 the combustor 34, where substantially complete combustion of the fuel is
 effected; and (9) the hot exhaust gases exiting the catalyst bed are
 conveyed to the heat exchanger 14 associated with the fuel processor 2.
 Once the fuel processor's temperature has risen sufficiently to effect and
 maintain the reformation process: (1) valve 32 is activated Ho direct air
 to the cathode side of the fuel cell 22; (2) MeOH and water are fed to the
 fuel processor 2 to commence the reformation reaction; (3) reformate
 exiting the fuel processor 2 is fed to the anode side of the fuel cell 22;
 (4) anode effluent 26 from the fuel cell 22 is directed into the combustor
 34; (5) cathode effluent 28 from the fuel cell 22 is directed into the
 combustor 34; (6) air is introduced into the vaporizer 41; (7) liquid
 methanol is sprayed into the vaporizer 41; (8) the methanol-air mix
 circulates through the heated vaporizer coil where the MeOH vaporizes; (9)
 the methanol-air mix along with the cathode effluent 28 then mixes with
 the anode effluent 26; and (10) the mix is burned on the catalyst bed of
 the combustor 34.
 During normal (i.e., post start-up) operating conditions, the heater 52 is
 not used as the vaporizer 41 alone vaporizes the MeOH and preheats the
 MeOH-air mix. Under certain conditions, as described hereafter, the
 combustor 34 could operate solely on the anode and cathode effluents,
 without the need for additional MeOH fuel from the vaporizer 41. Under
 such conditions, MeOH injection to the combustor 34 is discontinued. Under
 other conditions, e.g., increasing power demands, supplemental fuel is
 provided to the combustor 34.
 As described above, the combustor 34 receives multiple fuels, such as a
 methanol-air mix as well as anode effluent 26 from the anode of the fuel
 cell 22. Oxygen depleted exhaust air 28 from the cathode of the fuel cell
 22 and air from the compressor 30 are also supplied to the combustor 34.
 According to the present invention, a controller 150 shown in FIG. 1
 controls the operation of the combustor 34. Anode exhaust or effluent plus
 a liquid fuel, i.e., methanol, if required, support the energy
 requirements of the combustor 34. An enthalpy balance maintains the
 desired reaction temperature by controlling the amount of air and/or
 cathode exhaust supplied to the combustor 34 to meet all fuel processor
 heat requirements.
 It should be noted that the energy requirements of the apparatus components
 are expressed herein in terms of power. This is for convenience and is
 meant to express an energy rate, often in units of kilowatts, rather than
 BTU per second.
 The controller 150 may comprise any suitable microprocessor,
 microcontroller, personal computer, etc., which has central processing
 unit capable of executing a control program and data stored in a memory.
 The controller 150 may be a dedicated controller specific to the combustor
 34 or implemented in software stored in the main vehicle electronic
 control module. Further, although the following description describes a
 software based control program for controlling the combustor 34 in various
 modes of operation or sequence, it will also be understood that the
 combustor control can also be implemented in part or whole by dedicated
 electronic circuitry.
 According to the present invention, the controller 150 controls the
 operation of the combustor 34 in six different modes or sequences of
 operation. The separate modes of operation include (1) combustor start-up,
 (2) combustor operation during fuel processor warm-up, (3) combustor
 operation during fuel processor start-up, with the fuel cell off-line, (4)
 combustor operation during fuel processor run mode with the fuel cell
 stack on-line, and (5) combustor shut down. Each of these control
 sequences will be described with reference to the figures and to the
 equations in Table 1.
 The various sensors, actuators, and devices which supply input signals to
 the controller 150 or are controlled by output signals from the controller
 150 will be described in conjunction with the appropriate sequence step
 described hereafter.
 Combustor Start-Up
 Turning now to FIG. 2, there is depicted the sequence of program steps
 performed by the controller 150 to control the combustor 34 during a
 start-up mode or sequence.
 Initially, the controller 150 in step 152 selects the start-up combustor
 power level and reaction temperature. These values are base on a
 particular combustor performance and overall system requirements for
 warm-up times since, at this point in the operation of the engine, the
 fuel processor 2 and the fuel cell 22 are inactive and there is no
 hydrogen available at start-up of the combustor 34 from the fuel cell 22
 or from the fuel processor 2. Other methods include a quick start fuel
 processor and stack or on-board hydrogen or reformate storage.
 The controller 150 switches the air bypass valve 32 to a position diverting
 all air output flow from the compressor 30 to the combustor 34. The
 controller 150 regulates the compressor 30 to provide the desired air flow
 to the combustor 34 for the selected power level and reaction temperature
 in step 154. The controller 150 also controls the orifice size of the
 stepper motor, as described hereinafter, driven air dilution valve 47 to
 provide selected bleed-off of the air supplied to the combustor 34 in
 order to balance the enthalpy of the reaction in the combustor 34 by
 determining the amount of air flow required in the combustor 34 to create
 a desired reaction temperature within the combustor given the heat
 requirements demanded by the fuel processor 2.
 Since no hydrogen is available at combustor start-up, all power for
 combustor operation must come from another fuel, such as methanol. The
 controller 150 uses equations 1, 2, and 16 in Table 1 to determine the
 desired methanol flow and air flow required to obtain the combustor
 reaction temperature calculated using equations 4-15 in Table 1.
 The controller 150 in step 156 then compares the air flow to the compressor
 30 as measured by a mass flow meter with a minimum combustor air flow. If
 the measured air flow is less than the preset minimum combustor air flow,
 the controller 150 enters a timeout loop in step 158 which sets a time
 limit for the combustor 34 to reach the desired air flow level. If time
 expires in the timeout loop in step 156, the controller 150 switches to a
 combustor shutdown sequence described hereafter.
 When the measured air flow exceeds the preset minimum combustor air flow,
 the controller 150 in step 160 checks a sensor or thermocouple 151 to
 determine the temperature of the catalyst bed 48 in the combustor 34. If
 the temperature of the bed 48 exceeds the heater 52 preset turnoff
 temperature, the controller 150 turns off the heater 52 in step 162. If
 the temperature of the bed in step 160 is less than the heater turnoff
 temperature, the controller 150 turns on the heater in step 164.
 Next, in step 166, the controller 150 determines the vaporizer air flow
 from the output of a mass flow meter 167 and compares the measured air
 flow with a minimum air flow set point. If the measured vaporizer air flow
 is less than the set point, the combustor shutdown sequence is executed.
 However, if the vaporizer air flow is above the minimum air flow set
 point, the controller 150 next determines if the temperature of the
 catalyst bed 48 in the combustor 34, as measured by sensor 151, exceeds a
 minimum temperature set point. If the temperature of the bed is less than
 the minimum temperature set point, a timeout loop in step 170 is executed
 which routes control back through steps 160-168 as long as time remains in
 the timeout period. Eventually, if the timeout period in the timeout loop
 in step 170 is exceeded and the temperature of the combustor bed has not
 reached the set point temperature, the controller 150 executes the
 combustor shutdown sequence.
 When the measured temperature of the combustor bed 48 equals or exceeds the
 minimum set point temperature, the controller 150 turn the methanol fuel
 flow on via fuel injector 43 at a desired combustion power level as set in
 step 172.
 The controller 150 then measures the vaporizer 41 temperature in step 174
 from sensor Tvap and compares the measured vaporizer temperature with a
 set point temperature for running the combustor 34 at full power. If the
 vaporizer temperature is less than the set point run temperature, a
 timeout loop 176 is entered to allow time for the vaporizer temperature to
 come up to set point. Eventually, if the timeout: period is exceeded
 without a temperature match, the combustor shutdown sequence is executed.
 Fuel Processor Warm-up
 When the temperature of he vaporizer 41 equals or exceeds the minimum set
 point run temperature in step 174, the combustor start-up sequence is
 completed and the controller then executes the fuel processor warm-up
 sequence shown in FIG. 3. In step 180, the controller 150 sets the
 combustor power level and reaction temperature based on the system
 requirements for warming up the fuel processor 2 to a preset temperature.
 If stored hydrogen is not available, all of the combustor power comes from
 the liquid fuel. The controller 150 uses equations, 1, 2, and 16 to
 calculate the methanol flow. The air flow required to obtain the desired
 combustor reaction temperature is calculated by the controller 150 in step
 182 using equations 4-15 and controlled by the air dilution valve 47.
 The controller 150 using feedback from the fuel processor 2 then determines
 in step 184 if the output power of the combustor 34 is desired to be
 increased. If not so desired, then in step 185 it is determined whether
 combustor power is decreasing. If not, the fuel processor is started at
 step 198. If combustor power is decreasing, then proceed to step 192.
 If in step 184 it is desired that combustor power be increasing, then at
 step 186 the controller 150 increases the air flow to the combustor 34 in
 step 186 and then waits in step 188 for the air flow to increase as
 measured by a change in the combustor exhaust temperature from a sensor or
 thermocouple 116. This wait period can be a programmed time delay, or a
 period based on feedback from either an air flow meter, a temperature
 decrease in the combustor catalyst bed, or a pressure increase in the
 combustor manifold. Once the wait period has been exceeded, the controller
 150 then increases the methanol flow to the combustor 34 in step 190.
 In the event that the controller 150 determines that the combustor power is
 decreasing in step 185, the controller 150 decreases the methanol flow to
 the combustor 34 in step 192. Another await period 194 is executed for the
 fuel flow to decrease to the set amount. This wait period can be a
 programmed time delay, or based on feedback from either a methanol flow
 meter, a temperature decrease in the combustor catalyst bed, or a pressure
 decrease in the combustor manifold. Once the desired fuel flow decrease
 has occurred, the controller 150 in step 196 decreases the air flow to the
 combustor 34 for proper reaction power and temperature.
 At the end of either step 185, 190 or 196, the controller 150 determines in
 step 108 if the fuel processor 2 is ready for start-up. If not, steps 180
 through 196 are re-executed as described above until the fuel processor 2
 is ready for start-up.
 As can be seen from the above steps, a change in air flow leads a change in
 fuel flow when power is increasing and a change in fuel flow leads a
 change in air flow when power is decreasing.
 Fuel Processor Start-up--Fuel Cell Offline
 At this point, control switches to the fuel processor start-up sequence
 shown in FIG. 4. In step 200, the fuel processor requirements, such as the
 operating temperature of the fuel processor catalyst and the desired fuel
 processor output power (equivalent kilowatts of hydrogen production), are
 used to determine the combustor power and reaction temperature required to
 meet the system requirements to start-up the fuel processor 2 to a steady
 state run temperature. During fuel processor 2 start-up, the fuel
 processor 2 is operated at an output (hydrogen/effluent production) level
 that the combustor 34 can consume.
 As is conventional, during fuel processor 2 start-up, water and fuel (i.e.,
 methanol) are injected into the fuel processor 2 which produces hydrogen
 and CO, plus other effluent gases, such as H.sub.2 O and CO.sub.2. Also,
 air is injected into the PrOx 16, which consumes some of the gases and,
 particularly, hydrogen, produced in the fuel processor 2. Thus, a power
 equivalent of H.sub.2 and CO is able to be calculated and it is this
 output which is circulated to the combustor 34 when the quantity of CO is
 unacceptable for use by the fuel cell stack 22.
 Since, at start-up, the temperature of the fuel processor 2 is not up to a
 steady state run temperature causing higher than desirable carbon monoxide
 levels to be present in the reformate, the entire output of the fuel
 processor 2 is recirculated to the combustor 34 as fuel through a fuel
 bypass valve 201 which supplies the fuel processor output gas stream to a
 second inlet on the combustor 34. Bypass air is also supplied to the
 combustor 34 through air bypass valve 32 to cause combustion of the
 reformate from the fuel processor 2. Preferably valve 32 is a proportional
 air bypass valve. The total amount of air from the compressor 30 supplied
 to the combustor 34 is regulated by one or more of the following: variable
 compressor speed; the position of the proportional air bypass valve 32;
 and the diameter of the air dilution valve 47; or the position of valve
 47. Thus, the output flow of valve 47 is preferably adjusted by
 controlling the diameter of an output flow orifice of valve 47. The air
 supplied to the combustor is also controllable by changing the position of
 valve 32 in the valve body from open to closed or to an intermediate
 position such as partially open or partially closed. In that regard,
 equations 1-16 are useful.
 The amount of hydrogen in the reformate stream which is supplied to the
 combustor 34 is calculated by the controller 150 in step 202 based on a
 given amount of fuel and water injected into the fuel processor 2 which
 react to make a given amount of hydrogen, carbon monoxide, carbon dioxide
 and water. The controller 150 also takes into account the injection of a
 certain amount of air into the PrOx reactor 16 and, based on the amount of
 air input to the PrOx reactor 16, a determination is made of how much
 hydrogen generated by the fuel processor 2 is consumed by the PrOx 16.
 From these calculations, the controller 150 determines the equivalent
 power (i.e., hydrogen) output from the fuel processor 2.
 The controller 150 then compares the calculated or determined hydrogen
 quantity generated by the fuel processor 2 and supplied to the combustor
 34 with the calculated fuel processor start-up power and reaction
 temperature requirements, taking into account heat generated by the PrOx
 16, and, in step 204, calculates the supplemental amount of methanol and
 oxidant stream flow rates to the combustor using equations 1-16 in Table
 1, with the diameter of the orifice of the air dilution valve 47
 controlled to balance the enthalpy of the combustor reaction. For example,
 assuming that, on start-up, the fuel processor 2 produces 30 kilowatts
 equivalent of hydrogen which is supplied to the combustor 34. However, if
 the fuel processor 2 is demanding 35 kilowatts equivalent since it is not
 up to a steady state temperature, the combustor power requirement is also
 35 kilowatts, and the combustor 34 will use 30 kilowatts of equivalent
 fuel from the fuel processor 2 and will require 5 kilowatts of additional
 methanol. Equations 1-16 are solved to determine how much air is required
 to generate a desired gas stream temperature at this amount of power. The
 control program insures that the maximum power possible is obtained first
 from the output of the fuel processor 2, including any heat generated by
 the PrOx 16, before additional quantities of methanol are used.
 It should be noted that the fuel processor warm-up and fuel processor
 start-up control sequences for the combustor 34 can be utilized from an
 initial cold start of the fuel cell apparatus where the engine has been
 sitting idle for a long period of time and has reached ambient temperature
 or employed when the engine has been turned off only for a short period of
 time such that residual heat remains in the fuel processor and combustor
 catalyst beds. During a quick restart of the engine, it is possible that
 the fuel processor 2 could generate acceptable levels of reformate, e.g.,
 low amounts of carbon monoxide, from the start.
 Referring again to FIG. 4, in step 206 the controller 150 checks if the
 hydrogen level supply to the combustor 34 exceeds the fuel processor heat
 requirement or the combustor maximum design power output. If there is
 excess hydrogen, the controller 150 switches to the combustor shutdown
 sequence. Alternatively, the fuel processor power could be reduced. If
 there is not excess hydrogen in step 206, a determination is made in step
 208 if there is a sufficient quantity of hydrogen supplied from the fuel
 processor 2 to the combustor 34. If there is insufficient hydrogen, the
 controller 150 in step 210 calculates the supplemental amount of methanol
 required to obtain the desired fuel processor temperature. Again, maximum
 power is obtained first from the output of the fuel processor 2 and then
 from methanol. In making this calculation, the controller executes
 equations 1-3 and 16 in Table 1. Based on the calculated values in step
 210, the controller 150 adjusts the air flow to the combustor 34 by
 changing the cross section of the orifice of the valve 47 in step 212,
 waits for the desired air flow change, and then increases liquid methanol
 fuel flow in step 214 to the combustor 34. The controller 150 adjusts the
 fuel flow rate in step 214 using the equations in Table 1 based on the
 fuel energy content.
 Next, in step 218, the controller 150 determines if the combustor power
 output is greater than the fuel processor power requirement. If the answer
 is no, the controller 150 checks in step 220 if the system is ready to
 enter a run mode for fuel cell operation. If not, control switches back to
 step 200 and steps 200-220 are re-executed.
 If the combustor power output is greater than the fuel processor
 requirement, the controller 150 in step 222 open s the combustion exhaust
 diverter valve 50 to divert or dump combustor exhaust to atmosphere.
 Referring back to step 208, if there is enough hydrogen to support fuel
 processor operation, the controller in step 224 determines if there is
 methanol fuel flow to the combustor 34. If the answer is yes, the
 controller 150 in step 226 decreases the amount of the liquid fuel flow to
 the combustor 34 to a level required to meet fuel processor combustion
 power requirements. A wait period is executed in step 228 for a fuel flow
 is change, which can be a programmed time delay, or based on feedback from
 a fuel flow meter, or a temperature decrease in the combustor catalyst
 bed, or a pressure decrease in the combustor manifold. Steps 216-222 are
 then executed as described above.
 Combustor Run Mode
 FIG. 5 depicts the run mode or sequence of operation of the combustor 34
 when the fuel processor 2 is in a run mode. In step 230, the system
 developed equations are used to calculate the compositions of the anode
 exhaust streams and the cathode exhaust streams from the fuel cell 22
 which are supplied to the combustor 34 as described above. Next, in step
 232, the required fuel processor power and reaction temperatures are used
 to calculate the methanol fuel flow rate and cathode exhaust flow rate to
 the combustor 34 using the anode exhaust flow rate and composition and the
 cathode stream composition. Equations 1-16 in Table 1 are used to maintain
 an enthalpy balance of the reaction by controlling the oxidant stream via
 regulating the orifice diameter of the air dilution valve 47 and/or the
 compressor speed.
 Next, the fuel processor temperature is checked in step 234, via the output
 of a temperature sensor thermocouple 235 located between the output of the
 heat exchanger 14 and the plug flow bed 12 within the fuel processor 2, to
 determine if it is below a steady state run temperature. If the fuel
 processor temperature is low, the controller 150 in step 236 increases the
 combustor output power and recalculates air and fuel flow to the combustor
 34 to raise the fuel processor 2 temperature to the steady state set
 point. In order to increase the combustor power, the controller 150 in
 step 238 increases the air flow by adjusting the orifice diameter of valve
 47 and waits in step 240 for the desired change in the air flow to take
 effect. The wait period can be a programmed time delay, or based on
 feedback from the air flow meter, a temperature decrease in the combustor
 catalyst bed, or a pressure increase in the combustor manifold. Next, the
 controller 150 increases the methanol fuel flow to the combustor 34 in
 step 242.
 Alternately, if the fuel processor steady state temperature is above the
 steady state run temperature, i.e., not low, in step 234, the controller
 150 determines if the fuel processor steady state temperature is high or
 exceeds the desired steady state temperature in step 244. If the fuel
 processor temperature as determined in step 244 is higher than the set
 point, the controller 150 then determines in step 246 if the methanol fuel
 flow is turned on to the combustor 34. If the liquid fuel flow is not on,
 the controller 150 activates the exhaust dump valve 50.
 If the methanol fuel flow is on as determined in step 246, the controller
 150 decreases combustor power in step 248 and recalculates the desired
 methanol fuel flow and air flow to the combustor 34 using the enthalpy
 balance equations 1-16 in Table 1. The controller 150 then decreases
 methanol fuel flow to the combustor 34 in step 250 and waits a
 predetermined time for a change in the fuel flow in step 252. Again, the
 wait period can be a programmed time delay, or based on feedback from the
 fuel flow meter, a temperature decrease in the combustor catalyst bed, or
 a pressure decrease in the combustor manifold. In step 254, the controller
 150 then adjusts the air flow to the combustor 34 for the decreased liquid
 fuel flow rate.
 At the completion of steps 242 or 254, the controller 150 determines if the
 system is to remain in a continuous run mode and, if so, control switches
 back to step 230. If system operation is not to be continued, the
 controller 150 enters a shutdown sequence as described hereafter and shown
 in FIG. 6.
 Shutdown
 The control sequence for shutting down the combustor 34 is initiated by a
 shutdown command or when the controller 150 reaches a shutdown sequence as
 shown in FIG. 6. The sequence begins at step 259 where the shutdown
 command initiates the turning off of liquid fuel to the combustor.
 In step 260 shown in FIG. 6, the controller 150 determines if the fuel
 processor fuel supply is turned off. If it is, the controller 150 in step
 262 sets the air flow to the combustor 34 to a preset shutdown flow rate.
 Next, in step 264, the controller 150 determines if the combustor 34 has
 reached a preset shutdown temperature. If not, the controller 150 executes
 a wait period 266 and loops through steps 264 and 266 until the combustor
 temperature has reached its desired shutdown temperature. The controller
 150 then shuts off air flow to the combustor 34 in step 268 to complete
 the combustor shutdown sequence.
 Referring back to step 260, if the fuel processor fuel supply has not been
 turned off, hydrogen and exhaust air are still being supplied to the
 combustor 34. In this event, the controller 150 in step 270 determines the
 remaining energy and composition by calculating the anode and cathode
 exhaust compositions from the fuel cell 22. In step 272, the controller
 150 calculates the cathode flow rate and oxidant flow rate from the fuel
 cell 22 required for the combustor 34 to consume all of the remaining fuel
 in the apparatus. The controller 150 then adjusts the air flow rate to the
 combustor 34 in step 274 via air valve 47 as required by the results of
 step 272 and returns to step 260 until all of the fuel remaining in the
 apparatus has been consumed. It should be noted that if the energy content
 remaining in the apparatus is high, the controller 150 may cause the
 combustor 34 to exhaust the remaining fuel content energy through the
 system dump valve 50.
 Referring now to FIG. 7, there is depicted a control method used to control
 the effective or cross sectional area of the orifice of the air valve 47,
 as described above, to control the air flow rate and the oxygen quantity
 to the combustor 34.
 It will be understood that although the flow control method is depicted in
 block form, the control method can be implemented in either hardware
 elements or, preferably, software via a control program stored in the
 memory of the electronic control module of the fuel cell apparatus.
 In general, the control method of the present invention utilizes a feed
 forward control which quickly sets the effective or cross sectional
 opening of the orifice of air dilution valve 47 for a predetermined air
 flow rate based on the nitrogen, oxygen and water molar constituents of
 the air, including atmospheric air and fuel cell cathode effluent which
 generally is depleted oxygen air, the partial pressures of the
 constituents of atmospheric air and the expected output of cathode
 effluent of the fuel cell, as well as a table of valve cross-sectional
 orifice area versus opening size in a number of discrete steps. In
 addition, a conventional PID feedback loop is used to implement the final
 setting of the orifice diameter of the air dilution control valve 47.
 As shown in FIG. 7, a combustor air valve math model 300 is implemented by
 a control program executed by the ECM of the fuel cell apparatus. The math
 model 300 receives inputs 302, 304 and 306 representing the mole
 constituents of oxygen, nitrogen and water, respectively, in the cathode
 effluent of the fuel cell. These molar constituents can be calculated in a
 separate processor in the fuel cell apparatus or in the ECM which contains
 the math model 300 (FIG. 7) and by example are: 10% for O.sub.2, 75% for
 N.sub.2 and 15% for H.sub.2 O. Also input to the math model 300 are the
 partial pressures of the mole fractions of oxygen 308, nitrogen 310 and
 water 312 in the cathode effluent from the fuel cell. Again, these values
 are calculated based on the expected cathode effluent constituent make-up
 of the fuel cell during normal run mode and each other mode of operation
 of the fuel cell apparatus.
 Sensor inputs to the math model 300 include the cathode effluent pressure
 314 upstream of valve 47, the pressure 316 downstream of the valve 47 and
 the cathode effluent temperature 318 upstream of valve 47. These input
 values are measured by conventional pressure and temperature sensors
 placed at appropriate locations in the cathode effluent flow line.
 Calibrations are also supplied to the math model for the particular
 mechanical characteristics of the air depletion valve 47 used in the fuel
 cell apparatus. A constant labeled K_COMB_AIR_VLV_K_CONSTANT 322 is input
 to the math model 300 to provide an indication of the flow characteristics
 of the orifice between full open and full closed. For the present example,
 this constant was 2.0. The K.sub.--COMB.sub.--AIR.sub.--VLV.sub.--K
 _CONSTANT can also be obtained from a look-up table if the constant
 changes with valve position.
 Finally, another variable input to the math model 300 is the desired
 combustor air flow 324 which is supplied by solving the enthalpy balance
 equations as described above.
 In the various modes of operation of the combustor described above, the
 combustor receives either atmospheric air from the compressor 30 or
 cathode effluent from the fuel cell 22. Based in the particular fuel cell
 stoichiometry, excess air, typically on the order of double the amount
 normally required, is supplied to the fuel cell to support fuel cell
 operation. It is conceivable that different fuel cells may have different
 cathode stoichiometries such that the amount of oxygen contained in the
 cathode effluent may be so low as to require air from the compressor to
 support combustor operation in the run mode.
 In one aspect, the math model 300 uses two sets of molar constituents and
 mole fraction partial pressures. One set is for normal atmospheric air
 supplied by the compressor during combustor start-up, fuel processor
 warm-up and fuel processor start-up modes described above. There is a
 second set of molar constituents and mole fraction partial pressures using
 oxygen depleted air in the cathode effluent during the normal combustor
 run modes and combustor shutdown modes of operation (see FIG. 7, 302-312).
 Preferably, a second model is used to determine values 302 to 312 and
 supply them to the model 300, shown in FIG. 7.
 Thus, in operation, in any of the modes described above, a particular fuel
 processor output will be calculated. A combustor output heat requirement
 will then be determined to support the required fuel processor operating
 temperature. Solution of enthalpy balance equations provides a desired air
 flow to the combustor 34 to support combustor operation in supplying the
 required fuel processor heat requirements.
 As noted above, any conventional air dilution valve 47 having a variable
 cross section orifice may be employed in the present control method. A
 stepper motor controlled air dilution valve 47 is preferred due to precise
 discrete steps of orifice cross section. The orifice shape may be any
 conventional orifice shape, including a knife edge orifice, a tube
 orifice, or an orifice with round edges. etc.
 In operation, upon receiving a desired air flow rate 324, the math model
 300, using the sensor inputs, the variable inputs and the calibrations
 described above, will calculate an orifice cross-sectional area to support
 the desired air flow rate:
 ##EQU1##
 The math model 300 generates an output 331 labeled
 COMB_AIR_VLV_POS_DES_VIRTUAL which is used to generate a command position
 signal 332 specifying a step number for the stepper motor of the air
 dilution valve 47 which adjusts the orifice cross section to provide the
 desired air flow rate to the combustor 34. The manufacturer of each valve
 47 will supply orifice cross sectional area versus stepper motor steps as
 part of the design data of the stepper motor operated valve 47. This data
 is stored in memory in the math model 300 as a lookup table wherein the
 desired valve area (Av), as calculated above, acts as an address to the
 lookup table, the output of which is the number of steps for the stepper
 motor to adjust the orifice of the valve for the desired air flow. The
 output 331 from the math model 300 is the determined valve step number.
 The fast response of the math model 300 results in a fast repositioning of
 the valve orifice cross section so as to make the valve orifice
 cross-sectional changes quickly in response to variable load changes on
 the fuel cell 22, fuel processor 2, and combustor 34.
 While the command position signal 332 specifying a desired orifice
 cross-sectional area in the valve 47 may be the exact cross-sectional area
 required to support a desired air flow to the combustor 34, it is
 possible, and probably typical, due to valve tolerances, fuel cell
 operation variations, etc., for the actual air flow to the combustor 34,
 as measured by the mass flow meter 157, to vary from the desired or
 calculated predetermined air flow rate. Thus, the output 331 from the math
 model 300 is considered an initial set point for the air dilution valve
 orifice cross section, but a set point which is quickly achieved due( to
 the feed forward structure of the math model 300.
 In order to fine tune the cross-sectional area of the orifice to support a
 desired air flow rate to the combustor 34, any error between the actual
 flow rate and the predetermined or calculated air flow rate is determined
 in step 340. This error is supplied to a feedback loop 342 to generate
 signals to the stepper motor of the valve 47 to make fine changes in the
 cross-sectional area of the orifice to reduce the error to zero.
 Although, any control feedback may be employed which compares a set point
 or actual desired air flow rate with a measured air flow rate to develop
 an error signal, with the error signal used to adjust the cross sectional
 area of the orifice of the valve 47 to reduce the error signal to zero, a
 PID control loop, shown in FIG. 7 is preferred.
 The PID loop 342 includes proportional, integral and derivative terms 344,
 346 and 348, respectively, which are added to or subtracted from the error
 signal to develop the desired output control signal. More specifically,
 the D term has two parts, 348 and 350, which is designated as 349.
 Conventional PID control loops may be implemented in either hardware or
 software. For example, in a conventional hardware implementation, the PID
 terms 344, 346 and 349 may be provided by separate amplifier, integrator
 and differentiator circuits. Alternately, and preferred in the present
 invention, these terms are used in a software implementation of the ECM by
 a conventional algorithm to generate values for the control signal in
 response to applied values for measurement and set point inputs of the
 orifice cross-sectional area.
 The proportional term 344 represents a linear gain factor related to the
 magnitude of the error signal and the magnitude of the control signal
 necessary to achieve the desired orifice cross-sectional area. The
 integral term 346 is a long time constant linear gain term related to the
 integral of the error signal used to reduce to the residual error that
 would otherwise occur in a proportional only control loop between the set
 point and measured air flow values. The derivative term 349 is the
 derivative of the error signal and enhances system response to short term
 transients without reducing the long term accuracy benefits of the
 integral term.
 Further, as is conventional in PID control loops, calibrations or gains are
 supplied to each term 344, 346 and 349 to trim the operation of the PID
 loop 342.
 As shown in FIG. 7, the outputs of the multipliers 350 and 344 and the
 integral term 346 are summed in a summing junction 352 along with a K_COMB
 MAF_TRIM_LOOP_BIAS gain term 354. This calibration or gain term 354
 defines the default position of the valve 47 when no error exists between
 the actual air flow to the combustor 34 and the predetermined desired air
 flow to the combustor 34. The calibration term 354 inputs a number into
 the FID control loop 342, preferably into the summing junction 352. In one
 aspect, the calibration term 354 inputs a number into the PID control loop
 342 when the outputs of the proportional, integral and derivative terms
 344, 346 and 349 are zero.
 The output of the summing junction 352 is input to a scaler or divider 356
 which divides the summer output by 100.
 The output of the scaler 356 is adjusted by K_COMB_MAF_TRIM_ADJ_MIN and
 K_COMB MAF_TRIM_ADJ_MAX constants which define the minimum and maximum
 limits for the error signal adjustment signal. In general, these limits
 stop the integrator 346 from Charging up or charging down too far.
 After the limit control, the output of the divider 356 is summed in step
 330 with the output 331 of the math model 300.
 As the PID control loop 342 has a slower response time than the quicker
 response of the generatxon of the command position signal 331 from the
 math model 300, the cross-sectional area of the orifice of the air
 dilution valve 47 will be quickly adjusted to the command position set by
 the output 331 of the math model 300 and then more slowly adjusted by the
 PID loop 342 to eliminate any error between the actual air flow to the
 combustor 34 as measured by the mass flow meter 157 and the desired or
 predetermined air flow to the combustor 34 as established by the enthalpy
 balance equations described above.
 In summary, there has been disclosed a unique combustor air flow control
 method which provides quick response in establishing a predetermined air
 flow to the combustor over varying power requirements imposed on the
 combustor. The control method applies a feed forward control output with a
 conventional FID control loop error output to precisely control the
 cross-sectional area of the orifice of the air dilution valve to control
 the air flow to the combustor. The present control methodology also
 compensates for molar fraction deviations of oxygen depleted air in the
 cathode effluent from the fuel cell to support the desired heat output of
 the combustor.
 TABLE 1
 Operating Equations
 (1) P.sub.C = P.sub.MeOH + P.sub.H2 (KW)
 where: P.sub.C = combustor power, P.sub.MeOH =
 power from MeOH, P.sub.H2 = power from hydrogen
 (2) P.sub.MeOH = 636 n.sub.MeOH
 where: n.sub.MeOH = molar flow of MeOH
 (3) P.sub.H2 = 242 n.sub.H2
 where: n.sub.H2 = molar flow of hydrogen
 (4) n.sub.CATH = (n.sub.MeOH .multidot. dh(MeOH) + nCO.sub.2
 .multidot.
 dh(CO.sub.2) + n.sub.H2 .multidot. dh(H.sub.2) +
 nH.sub.2 O .multidot. dh(H.sub.2 O) + n.sub.N2 .multidot.
 dh(N.sub.2))/dh(CATH)
 where: n.sub.CATH = molar flow of cathode input to
 combustor; nCO.sub.2, n.sub.H2, nH.sub.2 O, n.sub.N2 = molar
 flows of CO.sub.2, H.sub.2, H.sub.2 O, and N.sub.2,
 respectively, in the anode input to the
 combustor; dh(X) = difference of the
 enthalpy for given component X from inlet
 of combustor to outlet of combustor.
 (5) dh(MeOH) = H(MeOH, T.sub.MeOH) - H(CO.sub.2, T.sub.CRT) -
 2 .multidot. H(H.sub.2 O, T.sub.CRT) + 1.5 .multidot. ,
 H(O.sub.2 - T.sub.CRT)
 where: H(X, T.sub.y) = enthalpy of component X at
 temperature T.sub.y, T.sub.MeOH = temperature of
 liquid MeOH supplied to vaporizer, T.sub.CRT =
 combustor reaction temperature (combustion
 out temperature)
 (6) dh(CO.sub.2) = H(CO.sub.2, Tan) - H(CO.sub.2, T.sub.CRT)
 where: Tan = anode temperature into combustor
 (7) dh(H.sub.2) = H(H.sub.2, Tan) + 0.5 .multidot. H(O.sub.2,
 T.sub.CRT) - H(H.sub.2 O, T.sub.CRT)
 (8) dh(H.sub.2 O) = H(H.sub.2 O, Tan) - H(H.sub.2 O, T.sub.CRT)
 (9) dh(N.sub.2) = H(N.sub.2, Tan) - H(N.sub.2, T.sub.CRT)
 (10) dh(CATH) = % O.sub.2 .multidot. dh(CATH O.sub.2) +
 % N.sub.2 .multidot. dh(CATH N.sub.2) +
 % H.sub.2 O .multidot. dh(CATH H.sub.2 O)
 where: % O.sub.2, % N.sub.2 and % H.sub.2 O are mole fractions
 (percentages) of oxygen, nitrogen and
 water, respectively, in the cathode input.
 (11) dh(CATH O.sub.2) = H(O.sub.2, T.sub.CA) -
 H(O.sub.2, T.sub.CRT)
 where: T.sub.CA = Cathode Input Temperature
 (12) dh(CATH N.sub.2) = H(N.sub.2, T.sub.CA) -
 H(N.sub.2, T.sub.CRT)
 (13) dh(CATH H.sub.2 O) = H(H.sub.2 O, T.sub.CA) -
 H(H.sub.2 O, T.sub.CRT)
 (14) m.sub.CATH = n.sub.CATH .multidot. mw.sub.CATH
 where: mw.sub.CATH = molecular weight of cathode input
 stream
 (15) mw.sub.CATH = % O.sub.2 .multidot. mw.sub.O2 + % N.sub.2
 .multidot. mw.sub.N2 +
 % H.sub.2 O .multidot. mw.sub.H2O
 (16) m.sub.MeoH = n.sub.Me0H .multidot. mw.sub.MeoH