Design Program for Power Generation by Biomass Gasification Version 3 Greenwood

Introduction

As introduced in Biomass Gasification Project, it was Mr. Greenwood's responsibility to make basic design calculations to determine operating condition and equipment specifications. For this purpose, he had to make chemical equilibrium calculation, stoichiometric calculation, enthalpy calculation and engineering calculation. He has developed a computer program of 676kb, 28sheets size using MS Excel. Using this program, he designed and made studies for:

(1) Wood Gas Cart

(2) Comparison of Wood v.s. Charcoal

(3) Hardwood Power Generation

During times of the World War II, biomass gasification technology was developed to fill shortage of petroleum.

Gasifier used in Denmark in war time (photo by Mr. Cooper)

According to a design manual published by Forestry Department of FAO (Food Agricultural Organization) of UN. there are four types of reactor design.

(1) Up-draught or counter current gasifier

(2) Cross-draught gasifier

(3) Downdraught or co-current gasifier

(4) Fluidized bed gasifier

Downdraught or co-current gasifier is most suited for supplying gas to reciprocating engine. There are 3 different types among Downdraught or co-current gasifier.　

Following table shows appropriate "Hearth Load" for each type.

Further recommendations by the manual by FAO are:

-nozzle air inlet velocities should be around 30-35m/sec

-throat inclination should be around 45-60^o

-height of the lower hearth (expanding zone) below throat (narrowest constriction) should be more than 20cm.

-height of the air inlet nozzle plane above throat should be 10cm above narrowest constriction of the height determined by following equation.

(nozzle height)/(throat dia.)=19.6*(throat dia.)^-0.64

-hearth diameter at air inlet height should be 10cm larger than throat diameter in case of single throat and about 20 cm larger than the throat diameter of the throat dia. in case of double throat design.

1. Input Data (Input Sheet)

<Biomass Composition>

Carbon/hydrogen/oxygen element ratio (CHO elemental ratio) of the dry biomass was calculated from cellulose(C₆H₁₀O₅)n and lignin (C₁₈H₂₄O₁₁)n. It was assumed that 70% is cellulose and remaining 30% is lignin. The average formula becomes(C₆H_9.4O_4.6)n. Biomass composition is calculated from CHO elemental ratio. Chemical formula for biomass were taken from Reference 1. Water and ash content were assumed 30 wt% and 3 wt% respectively.

Input Biomass Data 

Blue figures are input data, yellow figures are calculated from (C₆H_9.4O_4.6)n

<Process Flow Scheme>

The basic process flow scheme was established as follow.

Process Flow Scheme

Biomass is charged batch wise into the container. Ashes and condensate will also be discharged batch wise.

When water content of biomass is more than 30wt% and when size of reactor is small scale, heat recovery to feed biomass and/or to air is needed. Slim reactor is recommended to achieve good heat recovery. Heat balance is adjusted by insulation thickness and un-insulated surface.

Air nozzles are split into n numbers.

Gas cooler shall be big enough to cool down gas near ambient temperature and condensate shall be removed. The size of the cooler will be determined for start up operation which generate much of the water. Condensate accumulation capacity will be provided in condensate separator for accumulating all water generated during start up operation. If engine is started before water level becomes low, engine oil might be fouled by condensate.

<Engine Generator Specifications>

Design of reactor will be made to meet commercially available gasoline fueled engine generator specifications.

Engine Generator Specification

When you input certain biomass feed rate, the program answer back needed cylinder volumes. You can then adjust feed rate to meet available engine size.

<Reactor Specifications>

After once though simulation you can adjust equipment size.

As FAO manual shows two different figures of Hearth Load, intermediate figures of both was taken as the basis of throat diameter.

Input Equipment Data

<Operational Procedure>

Operation start by putting ignited charcoal into the hearth. Start up induced fan keeps necessary air flows during biomass charge into biomass container. Start up air nozzle keeps necessary flow velocity to burning spot. After hatch of biomass charge mouth is closed, Start up air is throttled. Adequate burnable gas quality is checked by igniting gas coming from induced fan. After engine is started, start up induced fan is stopped and start up air valve could be throttled.

2. Chemical Equilibrium  (Free Energy Sheet)

There are two ways of calculating chemical equilibrium. One way is a method via chemical equilibrium constants K_p as described in Appendix. And second is minimizing Gibbs free energy of the entire system. In any case, every thing starts from calculating free energy of formation.

Biomass is a complex material described generally as(C_aH_bO_c)n+H₂O_m and it is difficult to establish chemical reaction equation. Therefore, only viable method is minimizing free energy.

In this model, I have assumed that free energy of formation of biomass is a molar average of the constituting element. This means that heat of formation of dry biomass DH⁰_fdry is zero. But when you have a data of actual heat of combustion of the biomass, then you can calculate.

DH⁰_fdry=(heat of combustion calculated from elements) - (measured heat of combustion of the biomass)

As

Heat of combustion calculated from elements=0

Then

DH⁰_fdry= - measured heat of combustion of the biomass

You can use this for Gibbs Free Energy calculation and for heat balance. Here I assumed

DH⁰_fdry=0

Generally, standard free energy of formation at T is defined by Gibbs-Helmholtz as

 T

DG⁰_{f t}= - T∫DH⁰_f/T² dt
25

Integrating it, you can obtain

DG⁰_ft = DH⁰_f -DH_t -TDS⁰ (kcal/kgmol)

The value of  DH⁰_f is published in Thermodynamics by Kojima 1969

3. Enthalpy Calculation (Enthalpy Sheet)

Enthalpy of the gas could be calculated from specific heat at constant pressure Cp. Cp is a function of temperature T. Enthalpy could be calculated from an equation, having a integral form of Cp as follows.

 _T

DH_t = ∫C_pdT

  25

Integral form of above equation for each substance are tabulated in the following table. Where H^* is an integral constant.

Individual enthalpy sheet were prepared for reaction temperature, reactor inlet and outlet temperature, cooler outlet etc.

4. Entropy Calculation　(TS Sheet)

TDS⁰ could be calculated by integration Gibbs-Helmholtz equations.

TS^* is integral constants.

5. Standard free energy of formation at T (Free Energy Sheet)

By following equation

DG⁰_ft =DH⁰_f -DH_t -TDS⁰ (kcal/kgmol)

We get following diagram.

Standard Free Energy of Formation

6. Gas Composition  (Gibbs Sheet)

Chemical equilibrium achieves minimum Gibbs free energy. Gibbs reactor module of process simulator PRO/II use this method. Standard Gibbs free energy DG_if0 of formation of each substance i  is described by following equation.

DG⁰_fi =  DH⁰_fi - T DS⁰_fi

Free energy change of the reaction is

DG⁰=(SX_iDG⁰_fi)_prod - (SX_iDG⁰_fi)_feed

Here,

Objective Function=DG⁰

Using Solver of EXCEL you can find  X_i  of product gas which will give minimum value of above equation with the constraint of X_i>0

Ｘ_C、Ｘ_O2、Ｘ_Ｈ2、X_N2 in product gas could be directly calculated by following material balanace.

Regarding carbon element,

(Ｘ_C+X_CO2+X_CO+X_CH4)_prod=(C_dry)_feed

When unburned carbon Ｘ_C was found, increase air injection rate Ｘ_O2 and consume all biomass.

Regarding  oxygen element,

(2Ｘ_O2 + 2X_CO2 + X_CO + X_H2O)_prod=(O_dry+X_H2O+2Ｘ_O2)_feed

Regarding hydrogen element,

(2Ｘ_Ｈ2 + 2X_H2O + 4X_CH4)_prod=(H_dry+2X_H2O)_feed

Regarding nitrogen element,

(X_N2)_prod=(X_N2)_feed

Thus unknown variables of the objective function becomes 4 i.e. X_CO2、X_CO、X_H2O、X_CH4.

Initial estimate of the X_i is important. I have used a set of values calculated by PRO/II on the same condition.

When wet biomass feed rate is CHO+Water=1.7kg/h and air feed rate is 1.923kg/h, the composition of the generated gas in mol. % at each reaction temperature are shown in the following chart. Some unburned carbon is generated at the temperature from 500 to 600^oC.

Gas Composition

Flue gas composition during start up operation was calculated from stoichiometric calculation, assuming that only CO₂ and H₂O are generated.

7. Heat Balance Calculation (Balance Sheet)

Based on calculated mol. flow of gas and enthalpy of each component, total gas enthalpy was calculated.

<Gassificaton Operation>

Heat balance of the gasification operation is described like;

DH_out = -DH⁰ + DH_t - DH_loss+ DH_in

DH_out is an enthalpy of product gas leaving the reactor at temperature of T_out. From those, you can calculate gas temperature leaving the reactor T_out by Goal Seek method of EXCEL.

       T_out

DH_out =  ∫SX_iC_pi dT

        25

DH⁰  is standard heat of reaction. Value having minus figures are exothermic reactions. plus figures are endothermic reactions.

DH_t is an enthalpy of gas at reaction temp. T

DH_loss is a heat loss from the wall of reactor and could be calculated by engineering calculation.

DH_in  is  incoming enthalpy of biomass. As air flow is normally zero for wood.  Some air might be needed for char coal but heat is recycled internally. Air for startup operation also recycles heat internally. Therefore it has no influence on overall heat balance. Biomass is charged batch wise near standard condition and heated up to stabilizing temperature during start up operation. Therefore,

 DH_in= DH_biomass

Here, DH_biomass is an enthalpy of  feed biomass

DH_biomass=  DH_dry+ DH_water

DH_water = X_{moisture in biomass}(-10,514kcal/kgmol)

DH_dry is an enthalpy of dry biomass, DH_water is an  evaporation of moisture contained in the biomass. Latent heat = -10,514 kacal/kgmol).

<Startup Operation>

During startup, DH_in= 0 and container heating up to stable temperature would behave like heat loss. Therefore,

DH_out = -DH⁰ + DH_t - DH_loss+ DH_in - DH_biomass

Heat balance shall be within the equipment size of gasification operation. Burning temperature shall be 900oC which is maximum allowable temperature for thermal resistance metal.

<Cooler>

Heat balance around gas cooler is

DH_duty = DH_out - DH_cool

Outlet enthalpy of gas cooler DH_cool is

T_cool

DH_cool = ∫SX_iC_pi dT

25

Find T_cool by goal seek。

Heat balance calculation was conducted for temperature of 400^oC、600^oC、700^oC、800^oC、900^oC and for start up operation. Engine calculation was conducted for 400^oC、600^oC、700^oC (Design Case).

<Others>

Combustion heat (LHV) of biomass dry basis and wet basis and gas were calculated from standard heat of formation. Estimated figures well meet the published heating value of biomass. This means that assumption made at the beginning is almost true. The assumption made was that free energy of formation of biomass is a molar average of the constituting element.

Pressure profile is adjustable reflecting pressure drop calculation conducted in engineering calculation by direct replacement.

Volumetric flow and gas density of various position were calculated here.

Results of Heat Balance

Heat of reaction in above graph means standard heat of reaction -DH⁰ at 25^oC

8. Engineering Calculation (Engineering Sheet)

Using all information made available, following items were calculated.

(1) Stoichiometric air to fuel ratio (air/gas) ; Stoichiometric calculation of gas combustion.

(2) Lower Flammability Limit of the Gas ; Data source is Reference 4.

(3) Upper Flammability Limit of the Gas ; Data source is Reference 4.

(4) Water Dew Point of the Gas ; Data source is Reference 4.

(5)Energy Conversion Efficiency of the Gasifier (Ratio of total energy contained in the gas and that contained in the biomass.

(6) Upward gas velocity in the annular space shall be lower than the terminal velocity of 160 micron ash particulate calculated by Stokes' Law taken from Reference 6.

(7) A container is required to house enough feed biomass. Input value of  Sp. Gr. of biomass and average void e were used for calculation of batch wise operation duration.

(8) Diameter of the throat was selected to ensure uniform contact of gas and charcoal based on FAO manual.

(9) Pressure drop of the air nozzle was calculated from orifice calculation equation of Reference (9)

(10) Pressure drop of the throat was calculated by Carman's equation of  Reference (9)

(11) Pressure drop of the gas cooler was calculated by Hagen-Poiseuille equation of  Reference (9)

(12) Pressure drop of the engine choke to match with total system pressure profile was calculated by orifice calculation of  Reference (9)

(13) Head requirements of startup induction fan could be determined similarly.

(14) Gasificaion air preheating was calculated from assumed heat transfer coefficient of 10kcal/m² h C.

(15) Biomass preheating would be completed during start up operation. Once certain temperature is achieved no further heating would occur. Heat transfer would be through container wall. Input  heat transfer coefficient of natural convection was used. This is sufficient to vaporize all water content in biomass.

(16) Heat loss of the reactor is calculated for insulated portion and bare portion separately. Insulated portion considers insulation thickness, thermal conductivity of rock wool and film coefficient of natural convection.  Bare portion does not consider insulation.

(17) Overall heat transfer coefficient of gas cooler was calculated from gas side and water side film coefficient. Goal Seek of water rate is possible for better water side film coefficient estimation.

(18) Cooling water flow rate is determined by duty and outlet temperature specified by input sheet.

(19) Maximum condensate height is estimated.

9. Docking with Engine Analysis Program (Engine Sheet)

Normally, commercially available gasoline engine is converted to gas fuel. Reciprocating Engine Analysis Program will calculate intake gas volume and thermal efficiency form gasoline engine performance data. In this case, theoretical thermal efficiency is calculated assuming polytropic efficiency is 100%. Then acutual/theoretical ratio is calculated. It was assumed that the same ratio could be applied to gas.

Gas composition at 700^oC was selected as design feed gas composition. Combustion Sheet will calculate gas combustion stoichiometry and generate flue gas composition.

Cp Sheet calculate Cp for air gas mixture compression and Cp for exhaust gas expansion.

Finally, Engine Sheet make whole reciprocating engine cycle calculation. Goal Seek calculation is needed for convergence of various temperature.

In the case of power generation, normally speed is kept constant and throttle valve reduce suction pressure low.

10. Calculation Procedure

The calculation procedures are illustrated in the following chart.

Calculation Flow Chart

Solver of Gibbs Sheet only need to use once when biomass composition is changed.

Balance Sheet has 19 Goal Seek calculations. Macro program was developed to do many Solver calculations automatically. Goal Seek for pressure profile is not needed as it does not affect entire systems.

Goal Seek for water forced flow film coefficient has small impact on cooler design.

Please read  "User Manual for Design Program for Power Generation by Biomass Gasification Version 3"

11. Calculation Results (Output Sheet)

Following table show the summary of the design calculation.

Output Data

Acknowledgements

Author wishes special thanks to Mr. Tetsuo Maejima for his contribution to analytical solution, to Mr. Ron Cooper for his sharp question raised during my preliminary calculations, to Mr. Akamatsu pointing bugs in Eq. No. 11 and to Dr. Dietinberger of USDA Forest Service giving me an incentive to improve my simulator up to version-3.

References

1. Science Dictionary Japan 1953

2. Chemical Process Principles by Hougen and Watson, 1954

3. Mathematics I, 1956

4. Chemical Hand Book, Japan 1960

5. John H. Perry's Chemical Engineers' Handbook 1963

6. Ernest E. Ludwig, Applied Process Design for Chemical and Petrochemical Plants Vol.1

7. Thermodynamics by Kazuo Kojima 1968

8. Data Book on Hydrocarbons by J.B.Maxwell, Sixth Edition, 1950

9. Chemical Engineering Hand Book, Japan 1968 was not used. Because it was lost during this work.

10. Chemical Engineering Lecture Note by Tesuo Maejima for 2003 Faculty of Science, Tokyo University of Science.

11. Design Manual by Forestry Department of FAO (Food Agricultural Organization)

March 31, 2003

Rev. January 27, 2009