KR100972938B1 - Method and Apparatus for controlling fuel supplying quantity in fuel cell system - Google Patents

Abstract

The present invention discloses a fuel supply amount control apparatus and method of a fuel cell system. Specifically, the present invention mixes the dilute fuel taken out of the dilution fuel reservoir and the high concentration fuel taken out of the fuel cartridge and supplies it to the fuel cell stack to produce electric energy corresponding to the amount of fuel taken out of the fuel cartridge, In a fuel cell system for returning water and unreacted fuel to the dilution fuel reservoir, the concentration of unreacted fuel (C _AO ) is sensed at the anode outlet of the fuel cell stack, and the density of current produced from the fuel cell stack ( I), the CSTR hypothesis introduced into the unit cell of the fuel cell, and the complete oxidation hypothesis introduced into the cathode, and the crossover of the fuel is substituted by the concentration of the sensed unreacted fuel into the dimensionless crossover model equation derived. After calculation, the fuel consumption corresponding to the current density and the fuel consumption corresponding to the crossover After calculating the supply flow rate of the high-concentration fuel corresponding to the sum of the fuel supply flow rate is adjusted by calculating a supply amount of the high concentration fuel. According to the present invention, the fuel supply amount can be precisely designed by quantitatively evaluating the crossover of the fuel in the fuel cell system, thereby enabling stable operation of the fuel cell system.

 Direct Methanol Fuel Cell, Methanol Crossover, Fuel Flow Control

Description

Method and apparatus for controlling fuel supply of fuel cell system {Method and Apparatus for controlling fuel supplying quantity in fuel cell system}

The following drawings attached to this specification are illustrative of the preferred embodiments of the present invention, and together with the detailed description of the invention to serve to further understand the technical spirit of the present invention, the present invention is a matter described in such drawings It should not be construed as limited to.

1 is a conceptual diagram schematically illustrating a general operation principle of a fuel cell.

2 is a schematic configuration diagram of a direct methanol fuel cell system according to the prior art designed as a circulation process.

3 is a model of a fuel cell unit cell used to derive a crossover model equation for methanol.

4 is a schematic diagram of a fuel cell system used to quantitatively measure methanol crossover.

 5 and 6 are graphs comparing the crossover of methanol and water measured by experiment (dotted line) and the crossover of methanol and water predicted by mathematical modeling according to the present invention (solid line).

7 is a configuration diagram schematically showing a configuration of a fuel supply amount control apparatus of a fuel cell system according to an exemplary embodiment of the present invention.

<Main reference number in drawing>

CT: Fuel Cartridge FT: Dilution Fuel Reservoir

DS: Fuel Dosing Pump CI: Circulation Pump

ST: Fuel Cell Stack AR: Air Pump

HE: Heat Exchanger GLS: Fuel Recovery

MX1: Fuel Mixer MX2: Gas Mixer

S: fuel concentration sensor G: current gauge sensor

C: flow controller MCU: microcontroller

The present invention relates to a method and an apparatus for controlling fuel supply amount of a fuel cell system. More specifically, the fuel cell supply amount introduced into a fuel cell stack may be optimized in consideration of the consumption of fuel that crosses from the anode to the cathode through diffusion. Method and apparatus therefor.

Recently, as the depletion of existing energy resources such as oil and coal is predicted, interest in energy that can replace them is increasing. As one of these alternative energy sources, fuel cells are particularly attracting attention due to their high efficiency, no pollutants such as NO _x and SO _x , and abundant fuel.

A fuel cell is a power generation system that converts chemical reaction energy of a fuel and an oxidant into electrical energy. Hydrogen, a hydrocarbon such as methanol, butane, and the like are typically used as an oxidant.

In a fuel cell, the most basic unit for generating electricity is a membrane-electrode assembly (MEA), which is an electrolyte membrane and a fuel electrode having a catalyst layer coated on both surfaces of the electrolyte membrane and facing the electrolyte membrane. Cathode) and air cathode (anode). Referring to FIG. 1 and Reaction Formula 1 (reaction formula of a fuel cell when hydrogen is used as a fuel) showing the electricity generation principle of a fuel cell, an oxidation reaction of a fuel occurs in a catalyst layer coated on a surface of a fuel electrode, thereby generating hydrogen ions and electrons. The hydrogen ions then move to the cathode through the electrolyte membrane. In the cathode, water is generated by reaction between oxygen (oxidant) and hydrogen ions delivered through the electrolyte membrane and electrons in the catalyst layer coated on the surface. By this reaction, current is generated while electrons move in the external circuit.

Scheme 1

^{_{Anode: H 2 → 2H + + 2e}} -

^{_{Cathode: 1 / 2O 2 + 2H +}} + 2e - → H 2 O

Total reaction: H ₂ + 1 / 2O ₂ → H ₂ O

Fuel cells include polymer electrolyte fuel cells (PEMFC), direct methanol fuel cells (DMFC), phosphoric acid fuel cells (PAFC), alkaline fuel cells (AFC), molten carbonate fuel cells (MCFC), and solid oxide fuels. Batteries (SOFC) and the like. Among them, the polymer electrolyte fuel cell has advantages of high energy density and high output, but has a problem of requiring additional equipment such as a reforming device for reforming fuel such as methane or methanol. On the contrary, the direct methanol fuel cell has the disadvantage of low energy density, low power, and a large amount of catalyst, compared to a polymer electrolyte fuel cell due to a slow reaction rate, but does not require a separate reforming device. The liquid fuel is easy to handle and has an advantage of low operating temperature. Therefore, recently, researches on fuel cells using liquid fuels including methanol have been actively conducted.

In the direct methanol fuel cell, methanol and water react at the anode to produce carbon dioxide, and hydrogen and oxygen react at the cathode to generate water, thereby generating electricity as a whole. In addition, the power generation system including a direct methanol fuel cell stacks a direct methanol fuel cell in units of cells to form a fuel cell stack, and then recovers unreacted methanol emitted from the anode of each cell, and is generated at the cathode of each cell. It is designed as a circulation process to recycle water.

      Scheme 2

_{Anode: CH 3 OH + H 2 O} → CO 2 + 6H + + 6e -

^{_{Cathode: 3 / 2O 2 + 6H +}} + 6e - → 3H 2 O

Total reaction: CH ₃ OH + 3 / 2O ₂ → CO ₂ + 2H ₂ O

2 is a schematic configuration diagram of a direct methanol fuel cell system according to the prior art designed as a circulation process. Referring to the drawings, the direct methanol fuel cell system includes a fuel cell stack ST in which a plurality of fuel cell cells are stacked, a fuel cartridge CT in which high concentration methanol of 100% purity is stored, and a fuel cartridge CT. A fuel dosing pump (DS) for extracting a high concentration of methanol from the distillate, a dilution fuel reservoir (FT) storing dilution methanol to be mixed with the high concentration methanol, and a withdrawal from the dilution fuel reservoir (FT) Fuel mixer MX1 for mixing dilute methanol and high concentration methanol supplied through the fuel dosing pump DS, and fuel forcing convection of methanol by injecting mixed methanol into the fuel inlet of the fuel cell stack ST. A fuel recoverer (GL) for recovering unreacted methanol by removing carbon dioxide from the circulation by-product (CI) and the reaction by-products discharged from the anode outlet of the fuel cell stack (ST). S); An air pump AR for supplying air in the air to the cathode inlet of the fuel cell stack ST, and a heat exchanger for recovering water by liquefying hot vapor discharged from the cathode outlet of the fuel cell stack ST. ), A gas mixer MX2 for mixing air discharged from the heat exchanger HE and carbon dioxide discharged from the fuel recovery unit GLS, and a gas discharger VT for discharging the gas discharged from the gas mixer MX2 to outside air. ).

When the above-described direct methanol fuel cell system operates ideally, the fuel cell stack ST generates power corresponding to the amount of the high concentration methanol extracted from the fuel cartridge CT. The concentration of the diluted methanol and the level of the methanol stored in the diluted fuel reservoir FT by the unreacted methanol and water returning to the diluted fuel reservoir FT are kept constant. However, in each fuel cell unit cell included in the fuel cell stack ST, a crossover of methanol and water occurs, and a portion of the methanol and water moves from the anode to the cathode through the membrane-electrode assembly included in the fuel cell unit cell. Therefore, in the operation of the actual fuel cell system, a part of the supply of high concentration methanol is not converted into electrical energy but is consumed by crossover. Therefore, for stable operation of the direct methanol type fuel cell system, the amount of methanol converted into electric energy and the amount of methanol consumed by crossover are quantitatively calculated to precisely supply the high flow rate of methanol extracted from the fuel cartridge (CT). Need to be controlled.

By the way, the amount of methanol consumed by the electrochemical reaction can be accurately predicted by detecting the current density produced. However, the amount of methanol consumed by the crossover is difficult to accurately calculate due to the lack of proper mathematical modeling. Therefore, conventionally, the supply of high concentration methanol was designed based on a simple polynomial depending on trial and error or the main variables of the fuel cell (for example, current density, active area, number of cells, etc.) as shown in Equation 1 below. . However, this method has a limitation in the stable operation of the fuel cell system because it requires resetting the coefficient of the polynomial which defines the amount of methanol fuel supplied even with a slight change in operating conditions. For reference, in Equation 1, I _load is the current density produced in the fuel cell system, A _active is the area of the fuel cell unit in which the electrochemical reaction occurs, and N _{cell #} is the fuel cell stack (ST). The number of fuel cell unit cells included.

       [Equation 1]

Therefore, in the technical field of the present invention, the functional relationship between the crossover of methanol and operating condition variables and the supply design method of methanol reflecting the same are continuously studied.

SUMMARY OF THE INVENTION The present invention has been made under the background of the prior art as described above. In a fuel cell system designed in a circulating process such as a direct methanol fuel cell system, the fuel consumption by crossover is accurately predicted by mathematical modeling for electrochemical reaction. It is an object of the present invention to provide a fuel supply amount control method and apparatus capable of setting a stable fuel supply amount in consideration of fuel consumption amount and fuel consumption amount due to crossover.

A fuel supply amount control apparatus of a fuel cell system according to the present invention for achieving the above technical problem, a mixture of the dilute fuel taken out of the dilution fuel reservoir and the high concentration fuel taken out of the fuel cartridge is supplied to the fuel cell stack to supply a fuel cartridge An apparatus for controlling the supply of high concentration fuel in a fuel cell system that produces electrical energy corresponding to the amount of fuel taken out from the fuel and returns water and unreacted fuel, which are reaction by-products, to the dilution fuel reservoir. A mixer for mixing; A fuel concentration sensor configured to sense a concentration (C _AO ) of the unreacted fuel at an anode outlet of the fuel cell stack; A current gauge sensor for sensing a density I of current produced from the fuel cell stack; A fuel dosing pump which extracts a high concentration of fuel from the fuel cartridge and supplies the same to the mixer; And a flow rate controller for controlling a fuel supply flow rate Q _DS of the fuel dosing pump. The concentration of the unreacted fuel is input to the dimensionless crossover model equation derived by receiving data on the concentration and current density of the unreacted fuel from the fuel concentration sensor and the current gauge sensor, and introducing the CSTR hypothesis and the complete oxidation hypothesis of hydrogen. Calculate the crossover of the fuel by substituting and calculate the supply flow rate of the high concentration fuel corresponding to the sum of the fuel consumption corresponding to the current density and the fuel consumption corresponding to the crossover, and control the flow controller to control the fuel flow rate through the fuel dosing pump. And a microcontroller that adjusts the supplied fuel supply flow rate to the calculated fuel supply flow rate.

에 의해 계산된다. 그리고, 상기

와

는 연료가 "기체확산층(-)/막-전극 접합체/기체확산층(+)"을 통해 확산하여 크로스오버되고 연료전지 단위 셀에 CSTR 가정을 적용하고 공기극에 완전 산화 가정을 적용하여 유도되는 계수로서 연료가 확산되는 경로상에 배치된 각 물질막의 두께와 각 물질막을 기준으로 산출한 연료의 확산 계수로 표현된다.Preferably, the crossover I _xover of the fuel is

Is calculated by. And,

Wow

Is a coefficient derived from the diffusion of fuel through the "gas diffusion layer (-) / membrane-electrode assembly / gas diffusion layer (+)", crossover and application of the CSTR hypothesis to the fuel cell unit cell and the application of the full oxidation hypothesis to the cathode. It is expressed by the thickness of each material film disposed on the path where the fuel is diffused and the diffusion coefficient of the fuel calculated on the basis of each material film.

와

는 각각

및

이고, δ_AD, δ_AC, δ_ME는 각각 연료가 확산되는 경로 상에 배치된 기체확산층, 촉매층 및 멤브레인층의 두께이고, D_AD, D_AC, D_ME는 각각 연료가 확산되는 경로 상에 배치된 기체확산층, 촉매층 및 멤브레인층에서의 연료 확산 계수이고,

는 연료의 반응속도와 크로스오버에 의한 연료의 전달 속도 비이다. According to the invention, the

Wow

Respectively

And

Δ _AD , δ _AC , and δ _ME are the thicknesses of the gas diffusion layer, catalyst layer, and membrane layer respectively disposed on the path through which the fuel is diffused, and D _AD , D _AC , D _ME , respectively, are disposed on the path through which the fuel is diffused. Fuel diffusion coefficients in the gas diffusion layer, catalyst layer and membrane layer,

Is the ratio of the fuel reaction rate and the fuel delivery rate due to the crossover.

는 패러데이 상수 F를 포함하여

로 정의되고, I_c, L_c, C_c 및 D_c는 각각 크로스오버 모델 방정식을 무차원하기 위한 전류 밀도, 길이, 농도 및 확산계수의 특성값이다.Preferably, the

Including the Faraday constant F

Where I _c , L _c , C _c and D _c are the characteristic values of current density, length, concentration and diffusion coefficient for dimensionless crossover model equations, respectively.

이고, Da_s는

(여기서, 분자는 연료전지 스택의 총반응면적, 분모의 F는 패러데이 상수)이고, C_CT는 고농도 연료의 농도이다. Preferably, the supply flow rate Q _DS of the high concentration fuel is

And Da _s is

Where num is the total reaction area of the fuel cell stack, F is the Faraday constant, and C _CT is the concentration of the high concentration fuel.

In order to achieve the above technical problem, a fuel supply amount control method of a fuel cell system according to the present invention comprises mixing a diluted fuel taken out of a diluted fuel reservoir with a high concentration fuel taken out of a fuel cartridge and then supplying the fuel cell stack to a fuel cell stack. A method of controlling the supply of high concentration fuel in a fuel cell system that produces electrical energy corresponding to the amount of fuel taken out and returns the byproduct water and unreacted fuel to the diluted fuel reservoir, the method comprising: (a) Sensing the concentration (C _AO ) of the unreacted fuel at the anode exit; (b) sensing the density (I) of the current produced from the fuel cell stack; And (c) calculating the fuel crossover by substituting the concentration of the sensed unreacted fuel in a dimensionless crossover model equation derived by introducing a CSTR hypothesis into a unit cell of a fuel cell and introducing a complete oxidation hypothesis into the cathode. And calculating the supply flow rate of the high concentration fuel corresponding to the sum of the fuel consumption amount corresponding to the post current density and the fuel consumption amount corresponding to the crossover, and then adjusting the supply amount of the high concentration fuel to the calculated fuel supply flow rate. Here, the steps (a) to (c) is preferably repeated periodically.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. Prior to this, terms or words used in the specification and claims should not be construed as having a conventional or dictionary meaning, and the inventors should properly explain the concept of terms in order to best explain their own invention. Based on the principle that can be defined, it should be interpreted as meaning and concept corresponding to the technical idea of the present invention. Therefore, the embodiments described in the specification and the drawings shown in the drawings are only the most preferred embodiment of the present invention and do not represent all of the technical idea of the present invention, which can be replaced at the time of the present application It should be understood that there may be various equivalents and variations.

On the other hand, in the following embodiment, a fuel supply amount control method and apparatus thereof according to the present invention will be described using a direct methanol fuel cell system as an example. However, the present invention can be applied to any system as long as it is a fuel cell system designed in a circulation process.

Here, a fuel cell system designed as a circulating process is a dilution fuel stored in a dilution fuel reservoir by mixing a high concentration fuel and a dilution fuel, supplying it to a fuel cell stack, and returning unreacted fuel and water derived from reaction byproducts to a dilution fuel reservoir. It means a fuel cell system that maintains a constant concentration and level of. For this, reference may be made to the fuel cell system shown in FIG. 2.

First, in order to precisely control the supply of high concentration methanol supplied by the fuel dosing pump in a direct methanol fuel cell system, the crossover of methanol diffused from the anode of the fuel cell unit cell included in the fuel cell stack to the cathode is quantified. We need a mathematical model to do this.

The crossover is determined by diffusion due to the difference in methanol concentration between the anode and the cathode. The present invention introduces a complete mixing after reaction (CSTR) assumption for each fuel cell unit cell included in the fuel cell stack. The 1D dimensionless model of Equation 2 is derived for the methanol crossover (I _{m , xover} ) by introducing a complete oxidation) assumption. For convenience of explanation, the dimensionless model according to Equation 2 below is called a crossover model equation.

 &Quot; (2) &quot;

In Equation 2, C _{M, AO} is the concentration of unreacted methanol discharged to the anode outlet of the fuel cell stack, I is the current density, I _{m , xover} is the crossover of methanol, δ _AD , δ _AC , δ _ME Effective diffusion coefficent of methanol in the diffusion layer, the catalyst layer, and the electrolyte membrane layer that transfers hydrogen ions to the cathode side, respectively, included in the fuel cell unit cell And δ _AD , δ _AC , δ _ME are the thickness of each layer. The characteristic values for constructing the dimensionless model are D _C = 1E-6 [cm ² / s], I _C = 1 [A / cm ² ], C _C = 1 [M], M _C = 1 [ g / mole], Q _C = 1 [ccm], M _C = 1 [g / mole], ρ _C = 1 [g / liter], Cell # = 5, A _C = 50 [cm ² ], L _C = 0.01 [cm]. In addition, the dimensionless variable Da _{C, which} represents the ratio of the methanol reaction rate and the delivery rate, was defined as Da _C = (I _C L _C ) / (6FC _C D _C ) including the Faraday constant F.

3 is a model of a fuel cell unit cell used to derive a crossover model equation of methanol according to Equation 2 above.

In the figure, 'anode' represents the anode, 'cathode' represents the cathode, Z ₀ to Z ₁ are gas diffusion layers on the anode side, Z ₁ to Z ₂ are catalyst layers on the anode side, and Z ₂ to Z ₃ are electrolyte membrane layers. , Z ₃ to Z ₄ are catalyst layers on the cathode side, and Z ₄ to Z ₅ are gas diffusion layers on the cathode side.

Referring to FIG. 3, a process of deriving a crossover model equation of methanol is introduced. First, a CSTR hypothesis is introduced into a fuel cell unit cell, and a complete oxidation hypothesis is introduced at the cathode. The concentration of methanol at the Z ₀ point can then be calculated, the methanol concentration at the Z ₃ point can be ignored, and the molar flux of methanol through the membrane-electrode assembly (Z ₀ to Z ₅ ) is It can be represented by Equation 3. In Equation 3, C represents concentration, D represents diffusion coefficient, and δ represents thickness. Subscripts AD, AC, and ME represent the gas diffusion layer, the catalyst layer, and the electrolyte membrane layer on the anode side, respectively.

&Quot; (3) &quot;

When a characteristic scale for dimensionlessness is applied to Equation 3, Equation 4 is derived. The characteristic value scale factors applied are D _c , L _c , I _c , C _c and J _c = D _c C _c / L _c .

&Quot; (4) &quot;

는 메탄올의 반응속도와 확산에 의한 전달 속도의 비로서,

이다.here,

Is the ratio of the reaction rate of methanol and the delivery rate by diffusion,

to be.

By arranging Equation 4 by the algebraic operation, a dimensionless crossover model equation for methanol is derived as in Equation 5 below. In contrast with Equation 2 and Equation 5 below, C _{M, AO} Is C _ZO , and α ₀ and α ₁ are the coefficients of C _ZO and I.

[Equation 5]

The core of the above methanol crossover model equation is that the methanol crossover is expressed using the membrane and catalyst layers included in the membrane-electrode assembly, the methanol diffusion coefficient in the gas diffusion layer, and the thickness of each material layer. In the embodiment of the present invention, δ _AD , δ _AC , δ _ME are set to 200 micro-m, 50 micro-m, and 175 micro-m, respectively. However, the present invention is not limited thereto. Meanwhile, the diffusion coefficient preferably reflects the temperature influence of the fuel cell stack through Equation 6 below.

&Quot; (6) &quot;

Here, the model variable of the diffusion coefficient is adjusted through a verification experiment after referring to the literature value. The variable values used in the embodiment of the present invention are summarized as follows.

As seen in Equation 2, the crossover model equation of methanol proposed by the present invention is expressed by the linear relationship between the concentration of unreacted methanol, C _{M, AO} and current density discharged from the anode outlet of the fuel cell stack. The coefficients used in this study consisted of the diffusion coefficient and the thickness of the material layer constituting the membrane-electrode assembly. However, the current density can be measured, and the coefficient can also be calculated from the diffusion coefficient and thickness of the material layer. Therefore, it is possible to quantify the crossover of methanol by measuring the concentration of unreacted methanol, C _{M and AO} . Therefore, it is possible to design an accurate methanol feed process that reflects the consumption of methanol by electrochemical reactions and crossovers.

On the other hand, in order to confirm the accuracy of the crossover model equation of methanol according to the present invention through an experiment is also required a mathematical model of the crossover of water. The present invention models water crossover by the following equation 7 in consideration of the electroosmotic pressure and evaporation of water.

[Equation 7]

)을 구하여 사용한다. 본 발명의 실시예에서는, 'under-relaxation' 법을 사용하여 수렴 해(

)를 구하여 x_{A , amb}으로 사용한다. 하지만 본 발명이 이에 한하는 것은 아니다.In Equation 7, x _{A , amb} is the mole fraction of the vapor contained in the gas of the cathode, and x _A0 is the mole fraction of the vapor characteristic near the gas interface with condensed water, generally x _A0 = P _vap (T) / It can be obtained as P. x _A0 = P In _vap (T) / P, if P is set to atmospheric pressure, x _A0 The value varies depending on the stack temperature T of the fuel cell. Through repeated experiments, the value of x _A0 according to the temperature T can be predefined. k is a dimensionless mass transfer coefficient affected by water flow conditions in the anode, and the present invention assumes a constant value and calculates it based on 0.01 [mole / cm ² / min]. x _{A and amb} have a relationship that mutually affects the crossover of water according to Equation (7). Therefore, the value converged through proper iteration calculation (

Obtain and use). In an embodiment of the present invention, the convergence solution is performed using the 'under-relaxation' method.

) And use it as x _{A , amb} . However, the present invention is not limited thereto.

Then, the case of calculating the crossover of methanol and water according to the mathematical model proposed by the present invention and the case measured through actual experiments will be compared with each other.

First, in order to quantify the methanol crossover through experiments, it is necessary to know the methanol concentration at the anode exit side of the fuel cell stack. However, since the methanol concentration at the outlet side of the anode is affected by the amount of methanol crossover, the equation development process using the mass balance equation of methanol and water input or output through the anode is required to obtain the methanol crossover through the experiment. need.

In the present invention, the CSTR assumption is introduced for the fuel cell stack. Therefore, the mass balance equation of Equation 8 can be obtained for methanol and water at the anode. In Equation 8, C _{W , AI} is the concentration of water entering the anode inlet of the fuel cell stack, C _{W , AO} is the concentration of water discharged from the anode outlet of the fuel cell stack, Q _AI is the anode inlet of the fuel cell stack The flow rate of the incoming methanol, Q _AO is the flow rate of unreacted methanol released from the anode outlet of the fuel cell stack, I is the current density produced in the fuel cell stack, I _{m , xover} is the methanol crossover, I _{w , xover} is It is a crossover of water.

[Equation 8]

The two-species mixture according to Equation 9 is applied to the mass balance equation for water in the mass balance equation of Equation 8, and then the outlet flow rate Q _AO of the anode. In summary, the following equation (10) is obtained.

[Equation 9]

 Heterogeneous Mixed Homes:

[Equation 10]

Substituting the equation for Q _AO obtained above into the mass balance equation of methanol in the mass balance equation of Equation 8, and substituting I _{m , xover} as C _{m and AO} according to Equation 2, C _{m Since the} quadratic equation for _AO is obtained, the equations of the quadratic equation are determined after the temperature conditions of a given stack and the measurable C _{m, AI} , C _{w , AI} , Q _AI , and I (current density). When solved, C _{m and AO} can be obtained. When C _{m and AO} are obtained, α ₀ , α ₁ , β ₀ , β ₁ can be calculated, and thus the crossover of methanol and water can be calculated quantitatively by mathematical modeling.

Then, below, it will be confirmed by experiment whether the crossover of methanol and water calculated by the mathematical modeling proposed by the present invention follows the crossover measured through the actual experiment.

4 is a schematic diagram of a fuel cell system used for an experiment. Referring to the drawings, in order to perform the experiment, the fuel cell stack 10 was shielded by an insulating member, and then the methanol supply pump 20 was connected to the anode inlet of the fuel cell stack 10. At this time, in order to control the temperature of the fuel cell stack 10, a preheater 30 was installed between the methanol supply pump 20 and the inlet of the anode to adjust the temperature of the fuel methanol to a desired temperature. The temperature of the regulated methanol corresponds to the temperature of the fuel cell stack 10. The methanol supply pump 20 extracts methanol from the fuel methanol storage container 40 and supplies methanol to the preheater 30. The preheater 30 then heats methanol to the control target temperature and supplies it to the inlet side of the anode. On the outlet side of the anode, a fuel methanol recovery vessel 50 for recovering unreacted fuel methanol is provided, and the concentration (C _{M, AO} ) and the flow rate of methanol discharged through the outlet side of the anode using a methanol flow meter and a concentration meter ( Q (AO)) was measured. On the other hand, an air pump 60 is mounted on the inlet side of the cathode to supply a sufficient amount of air so that a complete oxidation reaction occurs at the cathode. An ice chamber 70 is installed on the outlet side of the cathode to provide a gas mixture discharged from the outlet side. After condensation, the flow rate of the coagulated water (Q (CO)) was measured. Then, the data obtained through the measurement was substituted into the above-described mass balance equation of methanol and water, and the binary first-order equation was solved to calculate the crossover of methanol and water. Apart from this, the crossover of methanol and water was quantitatively calculated based on the mathematical modeling proposed by the present invention. Since the detailed calculation process has already been described above, repetitive description is omitted. On the other hand, the basic operating conditions of the fuel cell stack under the experimental conditions described above are as follows.

[Operation conditions]

Number of fuel cell: 5

Area of reaction zone: 50 cm ²

Methanol anode concentration: 0.5M

Air supply flow rate through air cathode: 2500 ccm

5 and 6 are graphs comparing the crossover of methanol and water measured by experiment (dotted line) and the crossover of methanol and water predicted by mathematical modeling according to the present invention (solid line). The crossovers of methanol and water were obtained from experimental and predicted values under three conditions. In the first to third conditions, the concentration, temperature, and supply flow rate of methanol supplied to the anode are 0.5 M, 60 degrees, and 15 ccm, respectively; 0.5 M, 60 degrees, 30 ccm; 0.5, 70 degrees, and 30 ccm were set.

Referring to FIG. 5, the crossover of methanol shows a tendency to decrease as the current density increases in both the experimental value and the predicted value. And it can be seen that the methanol crossover value at a relatively low current density increases as the stack temperature rises. This is because the diffusion of methanol, which is the main mechanism causing methanol crossover, is activated. In addition, as the flow rate of methanol supplied to the anode increases, the decrease of the methanol crossover with the increase of the current density decreases because the methanol concentration at the anode remains high as the methanol supply flow rate increases.

Next, referring to FIG. 6, the water crossover tends to increase as the current density increases, since the crossover mechanism is due to the electro-osmotic drag of the water, unlike in the case of methanol. . In addition, the change in the supply flow rate of methanol supplied to the anode does not significantly affect the crossover of water, but it can be seen that the crossover of water also increases as the temperature of methanol rises.

According to the graphs shown in FIGS. 5 and 6, the crossover of methanol and water actually measured by the experiment and the crossover between methanol and water calculated by the mathematical modeling according to the present invention are almost identical. Therefore, it can be confirmed that the mathematical modeling proposed by the present invention is a model that can be usefully applied to the fuel supply design of the fuel cell system.

Hereinafter, a method and apparatus for controlling fuel supply amount of a fuel cell system to which the mathematical model proposed by the present invention is applied will be described in detail.

7 is a configuration diagram schematically showing a configuration of a fuel supply amount control apparatus of a fuel cell system according to an exemplary embodiment of the present invention.

Referring to the drawings, the fuel supply amount control apparatus mixes the dilute fuel taken out from the dilution fuel reservoir FT and the high concentration fuel taken out from the fuel cartridge CT, and then supplies the fuel cartridge CT to the fuel cell stack ST. Is a device that controls the supply of high concentration fuel in the fuel cell system according to the circulation process of producing electrical energy corresponding to the amount of fuel taken out from the) and returning the by-product water and unreacted fuel to the diluted fuel reservoir (FT). .

The basic configuration of the fuel supply amount control device is the same as that of the direct methanol fuel cell system illustrated in FIG. 2, but includes a fuel concentration sensor configured to sense the concentration (C _AO ) of the unreacted fuel at the outlet of the fuel cell stack ST. S), a current gauge sensor G for sensing the density I of the current produced from the fuel cell stack ST, and a flow rate controller for adjusting the fuel supply flow rate Q _DS of the fuel dosing pump DS. (C) and from the fuel concentration sensor (S) and the current gauge sensor (G) receive data on the concentration and current density of the unreacted fuel and introduce the CSTR hypothesis and the fully oxidized hypothesis of hydrogen to be derived dimensionless. Calculate the crossover of the fuel by substituting the concentration of the unreacted fuel in the crossover model equation, and then the high concentration corresponding to the fuel consumption calculated by the current density and the fuel consumption consumed by the crossover. A microcontroller (MCU) which calculates a supply flow rate of the fuel by Equation 11 and controls the flow controller C to adjust the fuel supply flow rate supplied through the fuel dosing pump DS to the calculated fuel supply flow rate; It includes.

 [Equation 11]

에 의해 계산한다. 여기서, 계수

와

는 연료가 "기체확산층(-)/막-전극 접합체/기체확산층(+)"을 통해 확산하여 크로스오버되고 연료전지 단위 셀에 CSTR 가정을 도입하고 공기극에서 완전 산화 가정을 적용하여 유도되는 계수로서 연료가 확산되는 경로상에 배치된 각 물질막의 두께와 각 물질막을 기준으로 산출한 연료의 확산 계수로 표현된다.The crossover I _xover of the fuel is

Calculate by Where coefficient

Wow

Is a coefficient derived from fuel spreading through the "gas diffusion layer (-) / membrane-electrode assembly / gas diffusion layer (+)", crossover and introducing the CSTR hypothesis into the fuel cell unit cell and applying the full oxidation hypothesis at the cathode. It is expressed by the thickness of each material film disposed on the path where the fuel is diffused and the diffusion coefficient of the fuel calculated on the basis of each material film.

와

는, 각각

및

이다. 여기서, δ_AD, δ_AC, δ_ME는 각각 연료가 확산되는 경로 상에 배치된 기체확산층, 촉매층 및 멤브레인층의 두께이고, D_AD, D_AC, D_ME는 각각 연료가 확산되는 경로 상에 배치된 기체확산층, 촉매층 및 멤브레인층에서의 연료 확산 계수이다.

는 연료의 반응속도와 크로스오버에 의한 연료의 전달 속도 비이다. 연료로서 메탄올이 사용되는 경우, 상기

는 패러데이 상수 F를 포함하여

로 정의되고, I_c, L_c, C_c 및 D_c는 각각 크로스오버 모델 방정식을 무 차원하기 위한 전류 밀도, 길이, 농도 및 확산계수의 특성값이다. 아울러, 연료로서 메탄올이 사용되는 경우, 상기 수학식 11에서, Da_s는

(여기서, 분자는 연료전지 스택의 총반응면적, 분모의 F는 패러데이 상수)이고, C_CT는 연료 카트리지(CT)로부터 취출되는 고농도 연료의 농도이다.Preferably, the

Wow

Are each

And

to be. Here, δ _AD , δ _AC , δ _ME are the thicknesses of the gas diffusion layer, catalyst layer and membrane layer respectively disposed on the path through which the fuel is diffused, and D _AD , D _AC , D _ME are respectively disposed on the path through which the fuel is diffused. Fuel diffusion coefficients in the gas diffusion layer, catalyst layer and membrane layer.

Is the ratio of the fuel reaction rate and the fuel delivery rate due to the crossover. When methanol is used as fuel,

Including the Faraday constant F

Where I _c , L _c , C _c and D _c are the characteristic values of current density, length, concentration and diffusion coefficient, respectively, for dimensionless crossover model equations. In addition, when methanol is used as the fuel, in Equation 11, Da _s is

Where molecule is the total reaction area of the fuel cell stack, F is the Faraday constant, and C _CT is the concentration of high concentration fuel taken out of the fuel cartridge (CT).

Next, the operation of the fuel supply amount control device having the above-described configuration will be described. First, the microcontroller (MCU) is produced from the fuel cell stack (ST) and the concentration of unreacted fuel periodically discharged from the fuel concentration sensor (S) and the current gauge sensor (G) to the anode outlet side of the fuel cell stack (ST). Input the density of the current to be received. Then, the fuel supply flow rate of the fuel dosing pump DS is calculated by Equation 11. In the calculation of the fuel supply flow rate, the fuel crossover is calculated based on the fuel concentration measured by the fuel concentration sensor S and the current density measured by the current gauge sensor G, and then the crossover of the calculated fuel is calculated. And the flow rate of fuel is calculated by using Equation 11 using the measured current density and constant values (α ₀ , α _1, etc.) stored in the memory. When the fuel supply flow rate is calculated, the flow rate controller C of the fuel dosing pump DS is controlled to change the fuel supply flow rate to the fuel supply flow rate calculated by Equation (11). Then, fuel can be precisely supplied to the fuel cell stack ST as consumed by the electrochemical reaction and crossover, thereby enabling stable fuel cell system operation.

As described above, although the present invention has been described by way of limited embodiments and drawings, the present invention is not limited thereto, and the technical spirit of the present invention and the following will be understood by those skilled in the art to which the present invention pertains. Various modifications and variations are possible, of course, within the scope of equivalents of the claims to be described.

According to the present invention, since the fuel supply amount can be set in consideration of not only the amount of fuel consumed by the electrochemical reaction in the fuel cell but also the amount of fuel crossover from the anode to the cathode, the operation of the fuel cell system can be optimized. .

Claims (11)

Diluted fuel taken out of the dilution fuel reservoir and high concentration fuel taken out of the fuel cartridge are mixed and supplied to the fuel cell stack to produce electric energy corresponding to the amount of fuel taken out of the fuel cartridge. An apparatus for controlling the supply amount of high concentration fuel in a fuel cell system to return to the diluted fuel reservoir, A mixer for mixing the diluted fuel and the high concentration fuel; A fuel concentration sensor configured to sense a concentration (C _AO ) of the unreacted fuel at an anode outlet of the fuel cell stack; A current gauge sensor for sensing a density I of current produced from the fuel cell stack; A fuel dosing pump which extracts a high concentration of fuel from the fuel cartridge and supplies the same to the mixer; And a flow rate controller for controlling a fuel supply flow rate Q _DS of the fuel dosing pump. A dimensionless crossover model equation derived by inputting data on the concentration and current density of the unreacted fuel from the fuel concentration sensor and the current gauge sensor, and introducing a complete mixing after reaction (CSTR) hypothesis and a perfect oxidation hypothesis of hydrogen ( Calculates a crossover of fuel by substituting the concentration of the unreacted fuel and the current density into the unreacted ethanol concentration and the current density as a variable, and then corresponds to the fuel consumption and crossover corresponding to the current density. And a microcontroller for controlling the flow rate of the fuel by controlling the flow rate controller so as to correspond to the sum of fuel consumption. The method of claim 1, The crossover I _xover of the fuel is

Is calculated by remind

Wow

Is a coefficient derived from the diffusion of fuel through the "gas diffusion layer (-) / membrane-electrode assembly / gas diffusion layer (+)", crossover and application of the CSTR hypothesis to the fuel cell unit cell and the application of the full oxidation hypothesis to the cathode. A fuel supply amount control apparatus for a fuel cell system, characterized in that it is expressed by the thickness of each material film disposed on the path where the fuel is diffused and the diffusion coefficient of the fuel calculated on the basis of each material film. The method of claim 2, remind

Wow

Quot; each

And

ego, δ _AD , δ _AC , δ _ME are the thicknesses of the gas diffusion layer, catalyst layer and membrane layer disposed on the path where the fuel is diffused, respectively, and D _AD , D _AC , D _ME are the gases disposed on the path where the fuel is diffused, respectively. Fuel diffusion coefficients in the diffusion layer, catalyst layer and membrane layer,

The fuel supply amount control device of the fuel cell system, characterized in that the ratio of the reaction rate of the fuel and the delivery rate of the fuel by the crossover. The method of claim 3, remind

Including the Faraday constant F

Defined as I _c , L _c , C _c and D _c are fuel supply system control apparatuses for the fuel cell system, characterized in that the characteristic values of current density, length, concentration and diffusion coefficient for dimensionless crossover model equations, respectively. The method of claim 2, The supply flow rate Q _DS of the high concentration fuel is calculated by the following equation,

In the above equation Da _s is

Wherein the molecule is the total reaction area of the fuel cell stack and the denominator F is a Faraday constant, and the C _CT is the concentration of the high concentration fuel. Diluted fuel taken out of the dilution fuel reservoir and high concentration fuel taken out of the fuel cartridge are mixed and supplied to the fuel cell stack to produce electric energy corresponding to the amount of fuel taken out of the fuel cartridge. In the fuel cell system for returning to the diluted fuel reservoir in a method for controlling the supply amount of high concentration fuel, (a) sensing a concentration (C _AO ) of the unreacted fuel at an anode outlet of the fuel cell stack; (b) sensing a current density (I) produced from the fuel cell stack; And (c) A dimensionless crossover model equation derived from the introduction of the Complete Mixing After Reaction (CSTR) hypothesis into the unit cell of the fuel cell and the introduction of the complete oxidation hypothesis into the cathode (which is a function of the concentration of the unreacted fuel and the current density). Calculate the crossover of the fuel by substituting the sensed concentration of the unreacted fuel and the current density, and correspondingly to the sum of the fuel consumption corresponding to the current density and the fuel consumption corresponding to the crossover. Adjusting the supply flow rate; Fuel supply amount control method of a fuel cell system comprising a. The method of claim 6, The fuel supply amount control method of the fuel cell system, characterized in that step (a) to (c) is repeated periodically. The method of claim 6, The crossover I _xover of the fuel is

Is calculated by remind

Wow

Is a coefficient derived from the fuel spreading through the "gas diffusion layer (-) / membrane-electrode assembly / gas diffusion layer (+)" and crossover, introducing the CSTR hypothesis into the fuel cell unit cell, and introducing the complete oxidation hypothesis into the cathode. A fuel supply amount control method for a fuel cell system, characterized by the thickness of each material film disposed on a path through which fuel is diffused and the diffusion coefficient of the fuel calculated based on each material film. The method of claim 8, remind

Wow

Quot; each

And

ego, δ _AD , δ _AC , δ _ME are the thicknesses of the gas diffusion layer, catalyst layer and membrane layer disposed on the path where the fuel is diffused, respectively, and D _AD , D _AC , D _ME are the gases disposed on the path where the fuel is diffused, respectively. Fuel diffusion coefficients in the diffusion layer, catalyst layer and membrane layer,

The fuel supply amount control method of the fuel cell system, characterized in that the ratio of the reaction rate of the fuel and the delivery rate of the fuel by the crossover. 10. The method of claim 9, remind

Including the Faraday constant F

Defined as I _c , L _c , C _c and D _c are fuel supply system control methods, characterized in that the characteristic values of current density, length, concentration and diffusion coefficient for dimensionless crossover model equations, respectively. The method of claim 8, The supply flow rate Q _DS of the high concentration fuel is calculated by the following equation,

In the above equation Da _s is

Where the molecule is the total reaction area of the fuel cell stack and the denominator F is the Faraday constant, and the C _CT is the concentration of the high concentration fuel.

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