2005 SINTEF Energy Research. Reprinted with permission.

Transcription

1 Holmberg H, Ahtila P. Optimization of the bark dryg process combed heat and power production of pulp and paper mill. In: Odilio AF, Eikevik TM, Strommen I, editors. Proceedgs of the rd Nordic Dryg Conference, Karlstad, Sweden; 5 7 June, 5. 5 SINTEF Energy Research Reprted with permission.

2 OPTIMIZATION OF THE BARK DRYING PROCESS IN COMBINED HEAT AND POWER PRODUCTION OF PULP AND PAPER MILL Henrik Holmberg, Pekka Ahtila Helski University of Technology P.O.Box 44, 5 TKK, Fland henrik.holmberg@tkk.fi Keywords: contuous fixed bed dryg, biofuel, seconry heat, steam ABSTRACT Solid biofuels, such as bark, forest residues, sawdust, and wood chips are important mill fuels the forest dustry. They are combusted combed heat and power plants (CHP-plants) to generate heat and electricity for pulp and paper makg processes. Biofuels usually have high moisture content. The high moisture content decreases the effective heatg value of fuel and makes the operation of the boiler more difficult. Until now, biofuels have not been dried before combustion Fland; however, the forest dustry is currently highly terested biofuel dryg. The designer of the dryg process should be able to determe the fal fuel moisture, dryg temperature, and degree of energy efficiency of the dryer, thereby maximizg earngs from the dryg. This paper presents a calculation model for answerg these questions. Earngs are determed usg net present value. The calculation model is created for a contuous cross-flow dryer, which air is aspirated through a fixed bark bed. The highest possible dryg temperature depends on the heat source used for the heatg of the dryg air. The most suitable heat sources pulp and paper mills are seconry heat flows, backpressure steam, and extraction steam. Usg current energy prices, and the economic lifetime of years with an terest rate of 5%, the optimally designed dryer uses only seconry heat for the heatg of dryg air, consists of two dryg stages and dries the fuel/bark flow to fal moisture, which is the order of.kg/kg dm. INTRODUCTION The heat needed for the manufacturg processes of the mill is produced at the combed heat and power plant (CHP-plant) of the pulp and paper mill. Electricity is produced as a by-product for the mill or electricity markets. The most important mill fuels at dustrial CHP-plants are black liquor and solid biofuels, such as bark, forest residues, and sawdust. In addition to black liquor and solid biofuels, fossil fuels are usually needed as margal fuels to cover the heat production for all heat loads. Black liquor is burnt a recovery boiler. The recovery boiler generates high-pressure steam and regenerates used cookg chemicals []. Solid biofuels are usually combusted fluidized bed boilers. The most important solid biofuel is bark, which is obtaed as a by-product from a debarkg plant. Figure shows energy and material flows and of the control region at a typical dustrial CHP-plant.

3 Bark has a high moisture content, typically between % (water per total mass) []. The moisture content and its variation depend on weather, season, and type of bark (pe, spruce etc.). The high moisture content decreases considerably the effective heatg value of bark. The occasional variation of moisture content also makes the operation of the boiler more difficult. Bark and other biofuels are not dried before combustion toy despite clear disadvantages. The ma reasons for this are the negative experiences of flue gas dryg the 97 s and an tensive development of fluidized bed boiler technology. Fluidized boiler technology enables the combustion of moist biofuel. In spite of this development, biofuel dryg has been researched quite tensively at universities and research centers Fland. At the moment, the forest dustry is showg an creasg terest biofuel dryg. Pilot-dryer projects are planned and one mill has already decided to build a biofuel dryer. Seconry heat from mill Back pressure turbe G Electricity to mill Bark from mill Purchased biofuels (e.g. bark, forest residues,and saw dust ) Purchased fossile fuels (e.g. coal, oil, and peat) Bark dryer Fluidised bed boiler Steam to feed water pre-heater Steam to feed water tank Back pressure steam to mill Extraction steam to mill Energy and material losses Feed water tank Condensate from mill make-up water Figure. Energy and material flows and of control region at an dustrial CHP-plant The dryer type with great potential for biofuel/bark dryg is a contuous fixed bed dryer, which uses warm air as dryg gas. In cross-flow dryg, air is blown or aspirated through a fixed fuel bed that moves forward by means of a mechanical conveyor. Use of a counter- or co-current dryer is also possible. The energy flows with the greatest potential for the heatg of dryg air a pulp and paper mill are seconry heat flows (hot water the temperature range of 5-9 o C), backpressure steam (typical pressure level -5bar) and extraction steam (typical pressure level - bar). Seconry heat (also known as waste heat) is heat recovered to a heat recovery system from energy flows leavg the manufacturg processes. The recovered heat can be returned back to the CHP-plant from the mill. When a biofuel dryer is gog to be built at the CHP-plant of pulp and paper mill, the designer of dryg process should be able to answer the followg questions:. What is the fal fuel moisture that maximizes earngs of the dryg?. What heat sources should be used for the heatg of dryg air? Should we use only a low temperature seconry heat, or could it be more profitable to use both seconry heat and steam or only steam?. How energy-efficient a dryg system should we build? In other words, is it more profitable to build a less energy-efficient dryg system with low vestment costs (e.g. sgle-stage dryer with oncethrough air flow heatg) or more energy-efficient system with higher vestment costs (e.g. a multistage dryer or sgle-stage dryer with partial recycle of spent air)? The target of this paper is to present a calculation model for answerg questions - and apply it a case study. The calculation model is presented for a contuous fixed bed dryer which air is aspirated through a fixed fuel bed. The fuel to be dried is bark. The energy efficiency of the dryg system is taken to account by makg the calculation model for -, - and -stage dryg systems. Other ways to improve the energy efficiency are not discussed this paper.

4 DESCRIPTION OF DRYING SYSTEM Figure a shows a flow sheet for a -stage dryg system. Figure b illustrates the states of the dryg air on an enthalpy-humidity chart diagram. A dryg stage consists of the heatg and dryg period. The dryg air each dryg stage is heated usg first seconry heat, then backpressure steam, and fally extraction steam, if all heat sources are used for heatg. Addg dryg stages decreases heat consumption dryg, because the air temperature is clearly higher before the second than the first dryg stage (see Figure b) []. Addg the dryg stages also decreases the air demand dryg, if all dryg stages operate at the same temperature level. The reason for this is the higher let air moisture, which is achieved as a result of several dryg stages (see. Figure b). Although the air demand decreases, the dryer dimension do not become smaller because the dryg air must pass through several dryg stages. Heatg the dryg air successively three heat exchangers does not decrease the specific heat consumption but decreases the consumption of steam, which is more expensive energy than seconry heat flows. a) b) Air (t, x, m ) Φ Φ Φ Bark (t, u, M dm ) 4 Dryg stage Dryg stage Φ Seconry heat, typical temperature range 5-9 o C Φ Back pressure steam, typical temperature range -45 o C Φ Extraction steam, typical temperature range 8-9 o C Φ Φ Φ Air (t, x, m ) 9 Bark (t, u, M dm ) Heatg period Dryg period Heatg period Heatg period Moisture (kg/kg ) Heatg period Heat source Seconry heat Back pressure steam Extraction steam Saturation curve Enthalpy (kj/kgd.a) Temperature( o C) Figure. Two-stage dryg system a) Flow sheet b) The states of the dryg air on an enthalpy-humidity chart CALCULATION MODEL The efficiency of the CHP-plant is defed as follows: η = P + Φ Q f h () where P is the power generation, Φ h the generated process heat the form of steam, and Q f the fuel put to the fluidized bed boiler. An important term CHP-production is power-to-process heat ratio: P α = () Φ h The power-to-p rocess heat ratio and efficiency are known parameters for each CHP-plant. The ma target of the CHP-plant is to produce enough steam to cover the heat consumption at all times. This means that the fuel put must be balance with the heat consumption. The fuel consumption can easily be calculated from equations () and () as the heat consumption is known.

5 4 Dryg creases the effective heatg value of the biofuel. As a result of the improved heatg value, margal fuel can be replaced with biofuel. Savgs margal fuel consumption represent a positive cash flow for a company. If steam is used as dryg energy, primary heat consumption creases, and fuel put to the boiler may crease, too. This creases power production. If the dryer uses seconry heat, backpressure and extraction steam, the net come (NI) of dryg a time unit is calculated as follows: NI & bs bs bs = M dm (u u )l vb mf Φ shbsh b mf + α bsφ bsb e ( Φ es + α η es Φ es ) b mf + α es ( Φ Φ es b e + α η m& ρ Φ fan ) Δp b η e () The dryer heat consumption Φ for a certa heat source (e.g. seconry heat) is determed as follows: Φ = m& ( Δh + Δh +.. Δh ) = m& (c + xc )( Δt + Δt +.. Δt ) (4) n p where n is the number of dryg stages, Δh the enthalpy difference and Δt the temperature difference over the heat exchanger. The earngs of the dryg are calculated usg net present value (NPV), which takes to account all cash flows over the economic lifetime of the dryer. Takg vestment costs and matenance costs as negative cash flows, the net present value for the dryer becomes [4]: NPV = τ= = k τ (NIτ op C ( + i) ) pv ma t enance C τ vestment (5) db db dbn where k is the total number of years over which cash flows occur and τ op the annual operatg hours of the dryer. Investment costs are expressed as a function of suitable capacity factor. For a contuous cross flow dryer a suitable capacity factor is the air mass flow, which case IC = f (m& ). In some cases, the function describg the vestment costs may be only a rough estimate of actual vestment costs. If the dryg time for a certa fuel moisture decrease u -u is known, the air mass flow contuous crossflow dryg may be determed as follows [5]: v ρ M& a dm & = τ dry (6) Z( ε)ρdm m where τ dry is the dryg time from an itial fuel u moisture to a desired fal fuel moisture u. In the case of cross-flow dryg, the dryg time can be experimentally determed a small-scale batch- reactor (see Figure 4c). The measured dryg curve is analogous to a dryg curve of a contuous cross- dryer. Choices of optimal bed height and air velocity are discussed [5]. To take to account the flow effect of let air moisture on dryg time, we assume that dryg time is proportional to the temperature difference between dry-bulb and wet-bulb temperature. As a result of this assumption, we can determe experimentally dryg curves for various let air temperatures usg only one let air moisture. The dry bulb temperature as a function of wet-bulb temperature may be given approximately as follows [6]: t db x' (t wb ) x = t wb + l v (t wb ) (7a) c pa

6 x'(t wb p o.78(t wb 99.64) (t wb + ) 5 e.78(t wb 99.64) (t wb + ) 5 5 e ) =.6 (7b) l v(t wb ) = 5-4t wb (7c) The saturated air moisture x (t wb ) Equation (7b) is expressed usg a approximation correlation for saturated vapor pressure. By measurg dryg curves for several temperature differences (t db -t w b), a regression curve givg the correlation between dryg time and the temperature difference tdb-t wb can be determed. The correlation is determed for a certa fuel moisture decrease u -u, and is expressed as this paper follows: τ dry = Aln(t db -t wb ) + B (8) In - and -stage dryg, the fal fuel moisture u is achieved after the last dryg stage, and the fuel moisture after the previous dryg stages is somewhere between u -u (see Figure ). This means that the regression curve should tell how the let fuel moisture dependences on dryg time and the temperature difference tdb-t wb. To also use the correlation (8) -, and -stage-dryg, we share the fuel flow between each dryg stage as shown Figure. The moisture decrease for the shared flow each dryg stage is u -u, and correlation (8) can be used for -, and -stage-dryg, too. We emphasize that sharg the fuel flow is only a computational action, and there is no reason to share the fuel flow a real dryer. y M, u y M,u y M, u dm dm dm Dryg stage Dryg stage Dryg stage Δu = u -u y + y + y = y M dm, u y M dm,u y M dm, u M dm, u Figure. Sharg the fuel flow between dryg stages -stage dryg The let air moisture after the dryg chamber is obtaed from the mass balance of chamber [7]: x M & dm = x + (u u ) (9) m& The let air temperature after the dryg chamber is determed approximately by assumg that the enthalpy of the air remas constant the dryer (h =h ). In this case, the let air temperature becomes t c p t + x (c pvt + 5) 5x = () c + c x p pv The air density may be expressed usg perfect the gas equation

7 6 ρ = R(t p + M 7. 5) () All nec essary equations needed for the calculation of net present value are now determed. Substitutg Equations (-4) and (6-8) Equation (5), net present value is expressed as a function of t wbi and y j. If the number of dryg stages is higher than, the let air temperature and moisture of the previous dryg stage are new let values for the next stage. For n dryg stages, the number of t wbi is n and the number of y j is n. Now, we present bounry conditions for a -stage dryer. Numbers subscripts refer to Figure. Initial values: x, t, u, u, M dm, v a, Z, b sh, b e, b mf, i, k, Δp,τ op, α bs, α es, η,η fan Variables: t wb, t wb, t wb4, t wb6, t wb7, t wb8, y, y τ dry = Aln(t db -t wb + t db -t wb -t db + t wb + t db4 -t wb4 -t db + t wb ) + B (a) τ dry = Aln(t db6 -t wb6 + t db7 -t wb7 -t db6 + t wb6 + t db8 -t w b8-t db7 + t wb7 ) + B (b) t db t db, t db t db, t db4 t db, t db6 t db5, t db7 t db6, t db8 t db7 (c) t db t db,max, t db t db,max, t db4 t db4,max (d) t db6 t db6,max, t db7 t db7,max, t db8 t db8,max (e) t db5 t db5, t db9 t db9 (f) y v ρ M& M& a dm a dm τ dry = y τ dry Z( ε)ρdm Z( ε)ρ dm v ρ, y + y = (g) The mod el calculates the dryg temperature(s), heat consumptions, and air mass flow maximizg the NPV a case where the fal fuel moisture u and the number of dryg stages are given. To determe the fal fuel moisture maximizg the NPV, the calculation must be made for different values of u. On the basis of these values, NPV can be drawn as a function of u, and the optimal fal fuel moisture is found graphically (see Figure 5). RESULTS AND DISCUSSION The model is applied a case study to answer the questions - mentioned the troduction. The material to be dried is soft w ood bark. Dryg curves givg the correlation between the bark moisture and the temperature difference t db -t wb are shown Figure 4a. Dryg curves are measured a fixed-bed reactor shown figure 4c. Figure 4b shows a few examples of the regression curves determed on the basis of dryg curves. The dryg system is assumed to consist of conveyor, heat exchangers, air ducts, coverg, and fan. Cost functions as a function of air mass flow or cross-sectional area of the dryer, also dependent on air mass flow, are shown Table. Cost functions are taken from [5], which they are also explaed more detail. To take to account costs such as strumentation, laggg etc., the sum of the cost functions is multiplied by a factor of.6. The factor is also taken from [5] and is origally based on formation obtaed from [4]. We will first calculate the NPV as a function of fal bark moisture usg energy prices correspondg to present price levels Fland. The economic lifetime of the dryer is years and terest 5%. Matenance costs are assumed to be per cent of vestment costs. The itial bark moisture, bark flow and temperature levels of seconry heat, backpressure steam and extraction steam correspond roughly to a CHP-plant situated a Fnish pulp and paper mill. Power-to-heat ratios and

8 7 plant efficiency correspond to this CHP-plant, too. Table shows a summary of all itial values used the calculations. Figures 5 shows the calculation results for -, - and -stage dryg systems. Bark moisture [kg/kgdm] a) b) Bed height mm, air velocity per free-sectional area.65m/s.. C 95 C 78 C 6 C 46 C C Dryg time [s] tdb-twb C 46 C 6 C 78 C 95 C C c) Dry air m Evaporator Dryg time [s] x humidity transmitter m mass flow control t thermocouple Initial fuel moisture.5kg/kgdm, bed thickness mm, air velocity.65m/s Fal fuel moisture.4kg/kgdm y = -69.Ln(x) R =.9856 Fal fuel moisture.7kg/kgdm y = -5.Ln(x) R =.979 Fal fuel moisture kg/kgdm y = -7.Ln(x) + 7. R =.955 Fal fuel moisture.kg/kgdm y = -.75Ln(x) R = tdb-twb [ C] Reactor x Vapour Bark bed Pre heater Moist air x t By pass Figure 4. a) Experimentally determed dryg curves for various temperature differences t db -t wb b) Four examples of regression curves used the calculations c) Test rig used for the determation of dryg curves Table. Cost functions for ma components of the dryer [5] Equipment Relationship Capacity parameter Y Additional parameter Conveyor 7Y Cross-sectional area Air-water heat exchanger 9ΔtY.9 Air mass flow Δt is temperature crease heat exchanger Air-steam heat exchanger 8ΔtY. 9 Air mass flow Δt is temperature crease heat exchanger Air duct. 5 77Y Air mass flow Fan.9ΔpY.7 Air mass flow Δp is pressure drop of dryg stage Coverg.5 Y Cross-sectional area Table. Initial values for calculation cases. Temperatures parentheses refer to Figure a. Parameter Value Parameter Value Highest dryg temperature when seconry heat is used (t,t 6 ) o 7 C Initial bark moisture.5kg/kg dm Highest dryg temperature when backpressure steam is used (t, t 7 ) o C Bulk density of dry bark 85kg/m Highest dryg temperature when extraction steam is used (t 4, t8) o 5 C Dry mass flow of bark 4kg/s Annual operatg time of dryer 84h Price of electricity euro/mwh Air velocity per free-sectional area of dryer.65m/s Price of seconry heat.5euro/ MWh Power to heat ratio extraction steam production.7 Price of margal fuel 4euro/MWh Power to heat ratio backpressure steam production.6 Economic life of dryer years Efficiency of CHP-plant (equation ()).87 Interest rate 5% Pressure drop of each dryg stage (estimated) 4Pa Outdoor temperature (t ) o 5 C Bed thickness mm Outdoor moisture (x ).4kg/ kg Margal fuel is assumed to be peat and the price cludes cost of emission trade In the next cases, we assess how the length of the economic lifetime and prices of margal fuel, electricity and seconry heat affect the fal bark moisture, dryg temperatures, and number of dryg

9 ] 8 stages maximizg the NPV. In each case, one parameter (e.g. price of margal fuel) is changed and other parameters have the same value as table. The followg values are used the calculations: length of economic life - years, price of margal fuel 6-euro/MWh, price of electricity - 7euro/MWh and price of seconry heat -euro/mwh. Figures 7-8 show the results for these cases. Results are calculated a way similar to that shown Figure 6; only the best case is shown Figures 7-8. If the dryg temperature is higher than 7 o C, steam must be used for the heatg of dryg air addition to seconry heat. However, some cases, it may be more profitable to use only steam, not seconry heat, the dryer. These cases are marked separately Figures 6-7. NPV (keuro) stage dryg -stage dryg -stage dryg Fal bark moisture [kg/kgdm] Initial bark moisture.5kg/kgdm Price of seconry heat.5euro/mwh Price of margal fuel 4euro/MWh Price of electricity euro/mwh Economic lifetime of dryer years Interest 5% Calculation results at global optimum Number of dryg stages Optimal dryg temperature [ o C] Optimal fal bark moisture [kg/kg dm ] Specific heat consumption [kj/kg HO ] Investment costs Maximum net present value [keuro] [keuro] Figure 5. Net present values as a function of fal bark moisture and calculation results at global optimum maximizg the net present value Fal bark moisture [kg/kgdm].6 Initial bark moisture.5kg/kgdm Price of seconry heat.5euro/mwh.4 Price of margal fuel 4euro/MWh Price of electricity euro/mwh Interest 5%. 8 = optimal dryg temperature = optimal number of dryg stages C Economic lifetime of dryer [year] NPV [keuro].7 Initial bark moisture.5kg/kgdm C Price of seconry heat.5euro/mwh.6 Price of electricity euro/mwh Economic lifetime of dryer years Interest 5%.5 5 C = optimal dryg temperature = optimal number of dryg stages.4. 5 C Seconadry heat consumption is MW Price of margal fuel [euro/mwh] Fal bark moisture [kg/kgdm] NPV [keuro] Figure 6. Net present value and optimal fal bark moisture, dryg temperature and number of dryg stages as a function of economic lifetime and price of margal fuel. Columns show optimal fal bark moisture and le maximum net present value each case. Fal bark moisture [kg/kgdm] Initial bark moisture.5kg/kgdm Price of seconry heat.5euro/mwh Price of margal fuel 4euro/MWh Economic lifetime of dryer years Interest 5% 5 C = optimal dryg temperature = optimal number of dryg stages 5 C 5 C 5 C C NPV [keuro] Fal bark moisture [kg/kgdm Initial bark moisture.5kg/kgdm Price of margal fuel 4euro/MWh Price of electricity euro/mwh Economic lifetime of dryer years Interest 5% = optimal dryg temperature = optimal number of dryg stages NPV [keuro] Seconadry heat consumption is MW Price of electricity [euro/mwh] Price of seconry heat [euro/mwh]

10 Figure 7. Net present value and optimal fal bark moisture, dryg temperature and number of dryg stages as a function of price of electricity and price of seconry heat. Columns show optimal fal bark moisture and le maximum net present value each case. 9 Figures 6 and 7 show that the optimal dryg temperature is most cases either 7 o C or 5 o C. There are only two cases where the optimal temperature differs from these values. Results also show that optimal dryg temperatures are always similar each dryg stage the case of - and -stage dryg. The production cost of steam depends on the prices of margal fuel and electricity. If the economic lifetime or the price of seconry heat is changed, the production costs of backpressure and extraction steams become so expensive that it is never economical to produce them for the heatg of dryg air. In these cases, the optimal dryg temperature is always 7 o C, which is achieved usg only seconry heat dryg. If the price of margal fuel is 6euro/MWh or the price of electricity 65 or 7 euro/mwh, the production costs of steams are negative. The more steam produced the more money gaed; therefore, seconry heat is not used the dryer. However, these prices differ significantly from current prices and are therefore unrealistic cases. It is also important to remember that dryg is not the only way to crease the steam and electricity production. Alternative ways are, for example, an auxiliary condenser or condensate turbe. On the other hand, dryg is the only way to homogenize the fuel quality, which may be important some cases. If the price of margal fuel is 8- euro/mwh or the price of electricity 55-6 euro/mwh, the dryer uses both steams and seconry heat. In these cases, production costs of steams become so low that it is more profitable to build a small dryer with a high dryg temperature than a large dryer with low dryg temperature. The optimal fal bark moisture is most cases between. and.4kg/kg dm, which is fairly low. Bark has quite a small particle size as well as slightly different material properties (e.g., diffusion factors and density) from some other biofuels, which may expla the relatively low value for optimal fal moisture. It is probable that the optimal fal moisture is higher for biofuels with larger particle size and different material properties (e.g. forest residues). If the economic lifetime of the dryer is less than 4 years, the dryer vestment is unprofitable. Figure 5 shows that the heat consumption decreases considerably when the number of dryg stages is added from to. If the number of dryg stages is stead of, the heat consumption does not decrease as much. It is also important to notice that the number of dryg stages only has an fluence on seconry heat consumption, not steam consumption. The heatg system is built such a way that the dryg air can always be heated to 7 o C before the steam consumption begs (see Figure a). When the price of seconry heat is kept constant at.5euro/mwh, a -stgae dryer is a better choice than a - stage most cases. Compared to that of a -stage dryer, the seconry heat consumption of a -stgae dryer decreases so much that savgs cover the creased vestment costs. However, a -stage dryer is always the best choice if steam is used the dryer (dryg temperature is over 7 o C). This is an obvious result. Addg the dryg stages does not reduce the steam consumption cases, where seconry heat is used. On the other hand, as a -stage dryer always consumes more steam than - or -stage-dryer, it will always be more profitable to use only steam for the heatg of dryg air. A dryer with three dryg stages becomes competitive when the price of seconry heat is over.5 euro/mwh. The more expensive price of seconry heat also means a higher value for optimal fal moisture. However, seconry heat is usually not so expensive, which makes these cases less terestg. It is probable that fossil margal fuels particular will be expensive the future because of the emission trade, for example. Seconry heat will also have a certa price (probably quite low) the future. In Nordic Countries, the behavior of electricity price is strongly dependent on annual precipitation due to the large capacity of hydropower. In addition, wter temperatures affect the annual price level. Because of these factors, it is more difficult to estimate the behavior of the future electricity price. On the other hand, results show that the electricity price has not any fluence on optimal design parameters until the price exceeds 45euro/MWh. Durg the last four years, the annual average price of electricity has varied between and 6 euro/mwh Nordic electricity markets [8].

11 CONCLUSIONS Usg current energy prices, and the economic lifetime of years with an terest rate of 5%, the optimally designed dryer uses only seconry heat for the heatg of dryg air, consists of two dryg stages and dries the fuel/bark flow to fal moisture, which is the order of.kg/kg dm. If future energy prices behave, as we have speculated the discussion above, the optimal design parameters will be very similar to those calculated usg current price levels. NOTATION b Price of energy [euro/mwh] c p Specific heat capacity [kj/kgk] C Cost [euro] h Enthalpy [kj/kg] i Interest [%] k Economic lifetime [year] l v Vaporization heat of water [J/kg] m& Dry mass flow of air [kg/s] M & dm Dry mass flow of fuel [kg/s] M Molecule mass of dry air=.88kg/mol NI Net come [euro/h] NPV Net present value [euro] p pressure [Pa] P Power generation [W] Qf Fuel put [W] R Gas constant = 8.4 J/molK o t Temperature [ C] u Fuel moisture [kg HO /kg dm ] v Air velocity [m/s] x Air moisture [kg HO /kg ] Z Bed height [m] Greeks α Power to heat ratio [-] ε Volume fraction of air fuel bed [-] Φ Heat generation/consumption [W] η Efficiency ρ Density [kg/m ] τ dry Dryg time [s] τ op Annual operatg time of dryer [h] Subscripts a Air bs Backpressure steam Dry air db Dry bulb dm Dry mass e Electricity es Extraction steam Inlet mf Margal fuel Outlet sh Seconry heat v Vapor wb Wet bulb REFERENCES [] Vakkilaen E. Recover boiler. In: Gullichsen J, Fogelholm C-J, editors. Chemical Pulpg. Helski, Fland: Fapet Oy;. p [] Huhten M, Hotta A. Combustion of bark. In: Gullichsen J, Fogelholm C-J, editors. Chemical Pulpg. Helski, [] Fland: Fapet Oy;. p Spets J-P, A new multi-stage dryg system. In: Proceedg of st Nordic Dryg Conference, Paper No.. Trondheim, Norway 7 th -9 th June. [4] [5] Brennan D. Process Industry Economics. United Kgdom: Institution of Chemical Engeers Holmberg H, Ahtila P. Comparison of dryg costs biofuel dryg between multi-satge and sgle-stage dryg. Biomass&Bioenergy 6 (4) [6] Lampen M.J. Chemical Thermodynamics Energy Engeerg. Publications of laboratory of applied thermodynamics. Fland: Helski University of Technology [ Fnish]. [7] Pakowski Z, Mujumr A S. Basic Process Calculations Dryg. In: Mujumr AS. (Editor). Handbook of Industrial Dryg. New York, USA: Marcel Dekker p. 7- [8] www pages of Nord Pool,