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An optimization model for the utilization of wood residues as an energy source
Resources
and Energy
IO (1988) 79--94. North-Holland
AN OPTIMIZATION MODEL FOR THE UTILIZATION RESIDUES AS AN ENERGY SOURCE
OF WOOD
Abdulaziz S. ALIDI King Fahd Uniwrs~ty of Petroleum and Minerals, Dhahran 31261, Saudi Arabia Received November
1987
The use of wood residues as an energy source is limited by two major problems. (a) the high cost of transportation due to their high volume with respect to their energy content, and (b) the stochastic generation of these materials. A dynamic mixed-integer linear programming distribution model has been developed. The model has been tested and the results obtained show a conslderable amount of savings m transportatton costs.
1. Introduction
Most of the wood energy produced in the United States is generated by co-generation facilities. The term co-generation implies that at least two different forms of useful energy are being produced. The most common example of two systems that can be linked in co-generation is the production of electricity and process steam at the same time. Many large wood products companies which produce considerable amounts of wood residues have their own co-generation facilities. But most of the wood products industry in the United States is represented by many small sawmills scattered all over the country. They are too small to use their wood waste as an energy source, but the waste represents a huge amount of material and a severe problem. The problems arise from the danger of fires in the stockpiles, and the large amount of land required for disposal. A major problem which is limiting the use of these wood residues at these sawmills is that their generation depends on the demand for wood products which in turn depends on the general status of the economy. Therefore, the owners of these sawmills are not certain that they will produce enough wood wastes to be used for energy production. The logistical di~culties in gathering and bringing wood residues from wood products mills to the site of a wood-fired power generation plant frequently make them more expensive than coal. Additionally, their lowdensity, high-moisture nature generally makes it uneconomical to transport beyond about 40-80 kilometers. In a study prepared for the United States 0165-0572/88/$3.50
0
1988. Elsevier Science Publishers
B.V. (North-Holland)
80
A.S. Alidi, Utilization
of wood residues
Environmental Protection Agency (1980) it was reported that transportation of green wood chips by truck for 160 kilometers at 0.03 U.S. dollars per ton/kilometer would add about 0.42 U.S. dollars per 1.06 x 10’ joule to the fuel cost. Burlington Electric Department (1982) reported that the cost of wood fuel (with 1.05 x lo7 joule per kilogram) for its 50MW (mega watts) power plant including the cost of chipping and transportation was estimated at 19.0 U.S. dollars per ton. Based on the department report this compares with existing coal (with 2.94 x lo7 joule per kilogram) cost of about 60.0 U.S. dollars per ton. The department also reported that off-highway trucking of wood chips costs about 0.05 U.S. dollars per ton/kilometer and to truck the fuel 80.0 kilometers would cost 4.0 U.S. dollars per ton or about 20 percent of the average price of the fuel at the power plant (which is 19.0 U.S. dollars per ton). Officials at Lake Superior District Power Company (1982) pointed out that one of the major suppliers of wood residues for their 30MW power generation plant is Louisiana-Pacific Corporation whose mill is located only 4 kilometers from the power plant. In 1979 the company signed a live-year contract to take all of this mills’ residues (20,000 tons per year plus its 40,000 ton stockpile) for 1.0 U.S. dollars per ton with transportation cost of about 2.0 U.S. dollars per ton. Transportation of low bulk density materials such as wood residues is usually limited by volume rather than the weight load. In summary, the unsteady generation of wood residues and the cost of transportation are the major obstacles which limit the use of wood residues as an energy source on a large scale. In this paper the possibility of installing regional wood residues densitication and quality upgrading stations between wood residues suppliers and a wood-tired power generation plant in order to reduce the transportation cost is studied, A mathematical model which simulates the stochastic nature and transportation aspects of wood residues is developed. The development of this model is based on Alidi’s work (1985). The model has been tested and the obtained results show a considerable amount of savings in wood residues transportation. The model can be used by management to facilitate the utilization of wood residues as an energy source.
2. Literature review In a report prepared for the United States Department of Energy, Inaba and Eakin (1981) gave an overview on the collection, transportation, and storage of biomass residues in the Pacific Northwest of the United States. They pointed out that some of the factors that should be considered when assessing the transportation of forestry residues are bulk density of the material, material size range, length of haul, access and road conditions, and space and facilities available for the loading and unloading processes. Adler et al. (1978) have indicated that truck transportation seems to be the most
A.S. Altdt. Utilization of wood restdues
81
economic mode of transportation for harvested wood chips. They considered the indirect (or social) cost of wood chips transportation systems which included traffic congestion, noise, air pollution, and highway deterioration. Their analysis concludes that the specific wood-fired power generation plant site has a strong influence on the costs, direct and indirect, of the various possible transportation systems and they recommended a complete cost analysis for each site. Resource Management Services (1981) conducted a study to investigate the possibility of installing a wood-fired power generation plant at Wendel, California. Based on the study’s findings it was concluded that intermediate storage and transfer at satellite locations have disadvantages such as cost of additional equipment, facilities, and handling, as well as introducing the possibility of transportation difficulties due to extreme weather or labor problems. The above three studies in addition to other similar studies were prepared to investigate the best way to bring wood fuel to the sites of power generation plants. These studies are based not on a specific mathematical programming technique but on economic evaluation of the situation under consideration. In addition to that the concept of installing intermediate wood residues densification stations and the stochastic nature of wood residues generation at the different suppliers were not considered. The concept of locating intermediate stations between suppliers of materials and/or services and demand centers has been analyzed by many investigators. Harvey and O’Flaherty (1973) formulated the problem of solid waste collection, transportation and disposal as a mixed-integer linear programming model. The objective of their research is to identify from among several alternatives which sanitary land-fill site or sites should be seriously considered for disposal. Costs for collection vehicles, transfer stations, large road carriers, and land-fill sites were considered on present worth basis over the time period specified. A facility location model has been developed and used by Marks and Liebman (1974) to screen preliminary data in order to learn something about the issues of whether and where to locate solid waste transfer stations in the city of Baltimore, Maryland. A linear programming model used to determine the alternative distribution of coal from producers to consumers by available transportation modes and routes was developed by Chang et al. (1981). They pointed out that since there are two options available for coal-users in choosing coal, i.e., to use low-sulfur compliance coal or to use scrubbers to clean high-sulfur coal before burning, the objective for the entire system minimizes the sum of the respective costs from the two different decisions. Although all the above models considered the concept of using transfer stations as a means of reducing the total transportation costs, each lacks the inclusion of several important features such as the stochastic generation of materials at suppliers and the different modes and operational policies of
82
A.S. Alidi, Uthzat~on of wood residues
transportation systems which should be considered in any distribution network. A comprehensive mathematical distribution model incorporating the concept of processing stations was developed by Alidi (1985). The stochastic nature of materials generation was included in Alidi’s model (1985) utilizing the methodology of ReVelle and Gundelach (1975) who addressed the stochastic nature of rainfall. In the process of developing Alidi’s model (1985) only one location for the primary demand center is considered and the fixed cost of building processing stations at the different possible sites was not explicit in the objective function of the model. The current research is based on the extension of Alidi’s model (1985) to accommodate more than one location for the primary demand center and the inclusion of the fixed cost of building processing stations since it is a major cost which will have a major impact on the station selection.
3. Model development As stated previously, unutilizable variable quantities of wood residues which are generated at different wood products mills, scattered throughout a specific region, can be collected and transported to a central wood fuel power generation plant. The plan proposed and studied in this paper suggests a method for reducing the cost of transporting these wood residues by installing regional densitication stations between wood products mills and a wood-fired power generation plant. At these stations wood residues are dried and compressed so that they have a higher energy density than unprocessed wood residues. The process of densification will provide a dry, uniform, easily stored, and conveniently shipped fuel from the wide variety of residues product in the wood products industry. Due to the stochastic nature of wood residues generation and specific needs dictated by owners of wood products mills, the quantities of wood residues which may be made available for the wood fuel power plant will vary from one period to another. This variation will make the locations of the densification stations and the site of the proposed wood fuel power generation plant to be not the best on the long range in terms of minimizing the total cost of wood residues transportation and utilization. The above problem is simulated by a three-stage mathematical model as described below.
3.1. Determination supplier As proposed will be willing
of the quantities
of wood residues obtainable from each
by Alidi (1985) the owner (supplier) of a wood products mill to sell wood residues if certain conditions are met. These
AS. Alidl, Utilization of wood residues
83
conditions can be summarized as follows: (a) the storage area of wood residues at his mill should be as small as possible, (b) a specific area within the storage area has to be available at the beginning of each period of a cycle (such as a month within a year) for storing wood residues in case there is a sudden increase in their generation, (c) a specific quantity of wood residues has to be available at the storage area at the beginning of each period of a cycle in case there is a sudden need for it by the supplier for his own internal use, and (d) a specific quantity of wood residues has to be purchased from the supplier at the beginning of each period of a cycle to insure him of a minimal income from selling these residues. As stated previously, in order to keep regional densification stations between suppliers of wood residues and the proposed wood-fired power generation plant operating over several future cycles, the variations between the quantity of wood residues obtained from a particular supplier at the beginning of a period of a cycle and the quantity obtained from the same supplier at the beginning of the same period in the following cycles have to be as small as possible. This optimization problem has to be addressed, taking into consideration the above four conditions imposed by the supplier. The Linear Decision Rule which was developed by ReVelle and Gundelach (1975) addresses a similar optimization problem and it may be utilized for the solution of this problem. This mathematical tool is introduced and explained in full detail in Alidi (1985). Based on the Linear Decision Rule of ReVelle and Gundelach (1975) the following equation is used to predict the quantity of wood residues which can be obtained from each supplier at the beginning of each period (month) without violating his needs and interests: X,,i=(l-B,_~)R,_~+B,_~R,_~-b,_~+b,...,
(1)
where = the amount of wood residues to be obtained from supplier i during month t, R,_ l,i = the amount of wood residues generated at supplier i during the previous month, B,_ l,i = a coefficient for the previous month for supplier i obtained by solving a system of linear equations as described in Alidi (1985), and =a decision constant for month t for supplier i. b,, i x,, I
Values for b,,, can be obtained min C,. i, subject
to C,,,+b,,iZ(VJC)!!“i+
I/;,i,
by solving
the following
linear program:
84
A S. Alldi, Utilization of wood residues
b,, i 2 ( VJC)f, ; bf,*.-b,_, and the feasibility NI
N
wz- Sm,,
izq f.1 -(vKC)‘-W3 f,L
condition NI
)
is
N
where =storage area of wood residues at supplier i, to be minimized, =a specific portion of the storage area of wood residues to be made available at the beginning of each month for a sudden increase in the generation of wood residues, to be specified by the supplier, =a specific amount of wood residues to be available at the beginning of each month for the unexpected need of these residues by supplier i for his internal use, to be specified by the supplier, =a minimum amount of wood residues to be purchased from supplier i at month t to insure him with a minimum income form selling these residues, = the value of (VJC),,i which is exceeded w1 percent of the time
cZ, i "t,i
Sm,
41,i
(VJW (VJC):;
w
C(VJC),,i=R,.i+B,-1,,R,-,,il,
= the value
of (VJC),
(VKC);,;“3
time, = t h e value
i which
is exceeded
I-
w2 percent
of the
of ( VKQi
which
is exceeded
1- wa percent
of the
N NI
time C(VKC),,i=(l-B,~,,i)Rt-1,,+Bt-2.iRt-2,rl, =number of periods in a cycle such as months in a year, and = number of suppliers.
Utilizing projected data of quantities of wood residues to be generated at each supplier during each month of several future years, estimates of the amounts of wood residues obtainable from each supplier during each month of the forecasted years can be calculated using eq. (1). The detailed procedure of this calculation is provided by Alidi (1985). 3.2. Second stage: Distribution network configuration A dynamic mixed-integer linear programming model is developed to help in the determination of the wood residues distribution network. Fig. 1 depicts the distribution network to be determined. The model requires that the possible locations of the required densification
85
AS. Alidl, Utilization of wood residues
Suppliers of Wood residues _____________
LEGEND
i S r
j
Note:
Proposed Sites for Densification Stations _______________
Locations of Markets __________
Proposed Sites for Wood-Fired Power Plant __________
Suppliers of Wood residues (i=1,2,...,NI) Proposed Sites for Densification Stations (s 2, . . . . NS) Location of Possible Markets for Processed residues (r = 1, 2, . . . . NR) Proposed Sites for the Wood-Fired Power Plant 1, 2, . . . . NJ) Movement of Wood residues and Processed residues
different possible For all the routes, transportation (trucks, railcars, etc.) sidered under different types of operational (purchasing, renting, etc.) Fig. 1. A wood residues
distribution
= 1, Wood (j = Wood
modes of are conpolicies
network.
stations and the possible sites of the wood-tired power generation plant to be determined before solution of the model takes place. The solution of the model will point out the number of regional densification stations, their sites, and the site of the wood-fired power generation plant, which will result in the minimization of the distribution cost of the network during the forecasted years. The transportation of wood residues and densified wood residues is
AS. Alidi. Utilization of wood residues
86
assumed to be accomplished by different modes of transportation (such as trucks, railcars, and/or other modes). These different modes can be operated with different operational policies (such as purchasing, leasing, contracting and/or other operational policies). Again, these modes and operational policies will be chosen so as to result in the lowest total distribution cost. The following is a list of constants, variables, and subscripts used in the development of the model.
Constants
c D
E VN BM BN V W WN P AN SN
QS QP
=unit transportation cost of wood residues (WR) from a supplier to a densitication station, in U.S. dollars per ton, =unit transportation cost of processed wood residues (PWR) from a densification station to a proposed site of the wood tired power plant (WFPP), in U.S. dollars per ton, =unit transportation cost of WR from a supplier to a proposed site of the WFPP, in U.S. dollars per ton, =unit transportation cost of PWR from a densification station to a market, in U.S. dollars per ton. =unit purchasing cost of WR to be transported from a supplier to a densification station, in U.S. dollars per ton, = unit purchasing cost of WR to be transported to a possible site of the WFPP, in U.S. dollars per ton, =unit production cost of PWR to be transported to a possible site of the WFPP, in US. dollars per ton, =unit handling cost of PWR at a possible site of the WFPP, in U.S. dollars per ton, =unit handling cost of WR at a possible site of the WFPP, in US. dollars per ton, =unit selling price of PWR to be sold to a market, in U.S. dollars per ton, =a fixed cost for the construction of the WFPP at a particular site, in U.S. dollars per number of projected cycles (years), =a fixed cost for the construction of a densification station at a particular site, =capacity of the WFPP, in tons per number of projected cycles, =maximum amount of WR allowable by environmental and community regulations to be transported from a supplier to a densification station, in tons per cycle, =maximum amount of PWR allowable by environmental and community regulations to be transported to a possible site of the WFPP, in tons per cycle, =maximum amount of WR allowable by environmental and commun-
AS. Alidi, Utilization of wood resrdues
87
ity regulations to be transported from a supplier to a possible site of the WFPP, in tons per cycle, QM =maximum amount of PWR allowable by environmental and community regulations to be transported from a densitication station to a market, in tons per cycle, HS =fraction of utilizable PWR per unit total weight of PWR to be transported from a densification station to a possible site of the WFPP, EF =efticiency at which a piece of equipment utilizes PWR at the WFPP, in percentage (e.g., efficiency of a boiler burning processed WR at a power generation plant), LNO = the unit capacity of a densification station plus one, in tons per number of projected cycles, HR =fraction of utilizable PWR per total weight of PWR to be transported from a densification station to a market, H =fraction of utilizable WR per unit total weight of WR to be transported from a supplier to a densification station, HN =fraction of utilizable WR per unit total weight of WR to be transported from a supplier to a possible site of the WFPP, C’S =designed capacity of a densification station, in tons per cycle. Variables X
=amount of WR to be transported from a supplier to a densitication station, in tons per cycle, Z =amount of PWR to be transported from a densification station to a possible site of the WFPP, in tons per cycle, Y =amount of WR to be transported from a supplier to a possible site of the WFPP, in tons per cycle, MN =amount of PWR to be transported from a densification station to a market, in tons per cycle, F =a O-1 integer variable representing a proposed site of a densitication station (0: station will not be installed at the proposed site, 1: station will be installed at the proposed site), G =a &l integer variable representing a proposed site of the WFPP (0: WFPP will not be built at the proposed site, 1: WFPP will be built at the proposed site), XS =total amount of WR arriving at a densitication station, in tons per cycle.
Subscripts i
= a supplier
s
= a possible
of WR (15 i 5 NZ), site of a densitication
station
(15 s 5 NS),
88
m
4 t
j r
NI NS NM NQ NT
NJ NR
AS. Alidi, Utilization qf wood residues
= a mode of transportation (I 5 m $ NM), = a type of an operational policy ( 15 q 5 NQ), =a cycle (lstgi;NT), = a possibie site of the WFPP (1 sj 5 NJ). =a market (tgrzNR), = total number of suppliers, = total number of possible sites of densification stations, = total number of modes of transportation, = total number of types of operational policies, = total number of cycles, =total number of possible sites of the WFPP, = total number of markets.
Based on the constants, variables, and subscripts defined above, the dynamic mixed-integer linear program can be described with the following objective function: Minimize: NT
NQ
NM NS Nf
NT
NQ
NM
NS NJ
+ f (AN)jGj j
NT +_C
?iQ
MN
NJ
NI
C
C
Z:
~[I~~,j.~,~,~+~~~~~,j.~.q,t+~~~~~,j,~,q.~l~,j,m,q,t
NQ
NM
NS
NR
f q m j I
NT
subject to the following constraints: (1) supply constraints,
AS. Alidi, Utilization
bt-l%i+bt,i
~(1-B,-1,i)R,-l.i+B,-z,iRf-2.,-
N7;
t=l,2,..., (2) continuity
constraints
89
of wood residues
i=l,2,...,NI; at densification
stations,
-rCWR)
1
,.,,,,q,,)((~N),,,,,,q,,)l =O;
(3) constraints for determination arriving at each station, NQ
NM
NI
T
T
CXi,,,,,,.,-(XS),,=O,
(4) stations
capacity
(XS),, t 5 (5) selection
of the total
t=lv&-..,NT
(W,
NT
t
(6) selection
NT,
t=1,2,...,
f?
NQ
NM
NI
C
1
CXi,s,m,q,tZO,
4
s=l,2,...,NS;
s =
1,2,. . . , NS;
m i
+~Hi.j.n.q.*~,j.n,q.r (7) community
s=l,2y...,NS;
stations,
of the site for the wood-fired
I
of wood
constraints,
of sites for densification
(‘NOIs’s-1
quantities
power generation
-(CP)jGj>=O, II
and environmental
constraints,
j=1,2
plant,
, . . . , NJ;
residues
90
AS
Alldi, Utilization of wood restdues
NQ
7 Z,,,,,,,,,~(QS)j.s,m,t
for eachj,s.m,t,
7 ~,j.,,,.,~(Qp)l,j,m,t
for eachi,j,m,t,
(8) limited
number
of sites for the wood-tired
(9) limited
number
of sites for densification
power generation
plant,
stations,
$F,,NS;
(10)
one site for the wood-fired
(11) O-l integer
variables
F,=O
or
1,
G,=O
or
1,
3.3. Third stage: Periodical
power generation
plant must be selected,
constraints,
s=l,2,...,
distribution
NS,
j=1,2
,..., NJ.
analysis
The distribution analysis is concerned with the determination of the periodical (monthly) flow of wood residues and densitied wood residues throughout the distribution network. This flow can be determined by using a standard linear program similar in structure to the above dynamic mixedinteger linear program, except in the right-hand side of the supply constraints the actual amounts of wood residues generated in the last two periods (months) are used to estimate the amount of wood residues to be obtained from each supplier. Additionally, only the sites of the densification stations and the location of the wood-tire power generation plant selected by the solution of the above dynamic mixed-integer linear program should be considered when determining the distribution analysis.
AS. Alidr. Utilization
oj” wood residues
91
4. An application example To illustrate the application of the developed model it is assumed that there are three suppliers of wood residues, two possible locations for wood residues densilication stations, two possible sites for the wood-fired power generation plant and one market for excess densified wood residues. It is also assumed that there are two possible modes of transportation governed by two operational policies. To run the dynamic mixed-integer linear program, two forecasted years are considered. Data obtained from Alidi (1983, Banta (1979) Reed (1981) and Bungay (1981) were used in the model as feed data. The computer package LINDO (Linear, Interactive, aNd Discrete Optimizer) is used to determine the distribution network configuration and a typical periodical (monthly) distribution analysis. Results of the analysis are presented in tables 14. 5. Conclusions
and recommendations
Wood residues which are produced as by-products mills scattered all over the United States represent Table
at many small saw a huge amount of
1
Results of the dtstribution network configuration of the model applied to the case of the wood residues’ distributton system of the Umversity of Kansas at Lawrence. Proposed sites for the densificatton stations
Proposed sites for the wood-fired power generation plant
Decision
1
2
1
2
Install
Yes
No
Yes
No
Table 2 Typical
actual output for distribution analysis Kansas) when no excess densified
covering one month (the case of the Umversity wood residues are sold to the market.
of
Vartable
Quantity
Descriptton
x21221
808
Tons of wood restdues to be transported from supplier by the purchased (2) 45-foot trailers (2) in month (1)
Zll221
897
Tons of densified wood residues to be transported from station (1) to the wood-fired power plant (WFPP) (1) of the University of Kansas at Lawrence by the purchased (2) 45-foot trailers (2) m month (1)
XSll
808
Tons of wood residues
Total cost of the system is 12.689 U.S. dollars
to be densified for month
(1)
at station
(2) to station
(1) in month
(1)
(1)
AS. Ahdi, Utilization of wood residues
92
Table 3 Typical
actual
output for distrtbution analysis covermg one month (the case of the University Kansas) when excess densdied wood residues are sold to the market.
of
Variable
Quantity
Description
Xlllll
442
Tons of wood residues to be transported from suppher by the rented (1) 20-foot dump trucks (1) m month (1)
(1) to station
(1)
x21221
1441
Tons of wood residues to be transported from supplier by the purchased (2) 45foot trailers (2) in month (1)
(2) to station
(I)
211221
897
Tons of denstfied wood residues to be transported from station (1) to the wood-tired power plant (WFPP) (1) of the Universtty of Kansas at Lawrence by the purchased (2) 45-foot trailers (2) m month (1)
MN11221
993
Tons of densified wood residues to be transported sold to the market (1) by the purchased (2) 45foot (1)
XSll
1922
Tons of wood residues
Total cost of the system is 821 U.S. dollars
to be densilied
for month
from station (1) and trawlers (2) in month
(1) in month (1)
at station
(1)
Table 4 A detailed developed
calculation of the annual amount of savings resultmg from the application of the model to the case of the wood residues tired steam plant of the University of Kansas. U.S. dollars per year
Explanation Total cost of the wood-fired power plant (WFPP) of the Universtty of Kansas at Lawrence during the next two years based on the results of the dtstribution network configuration of the model
611.000
Annual cost of the WFPP based on the results of the drstribution contiguratton of the model
306,000
Annual
operatmg
cost of the WFPP
as reported
by Banta (1979)
Total annual cost of the WFPP of the Universrty results of the developed model Total annual cost of purchasing reported by Banta (1979)
and operating
network
of Kansas
500.000
based on the 806,000
the transportatton
facilities as 209,000
Total annual cost of purchasing and handling wood residues, the cost of the boner and other related costs as estimated by Banta (1979)
600,000
Annual
500,000
operating
cost of the WFPP
Total annual cost of the WFPP Banta (1979)
as reported
of the University
by Banta (1979) of Kansas
as calculated
by 1,309,OcM
Annual amount of savings resultmg from the application of the developed model to the case of the WFPP of the University of Kansas Annual amount of savmgs in percentage compared the WFPP calculated by Banta (1979)
to the total annual
503.ooo
cost of 38
AS. Altdi, Utilization of wood residues
93
material. The danger of fire in the stockpiles, and the large amount of land required for disposal are two major environmental concerns. There are two major obstacles which limit the use of wood residues for the production of energy at wood-fired power generation plants: (a) the unsteady generation of wood residues at sawmills makes them an unreliable source for energy production, and (b) their low-density, high-moisture nature generally makes the transportation and collection of these residues costly. A three-stage simulation model taking into consideration the above two problems is developed. The model has been tested utilizing data obtained from literature. The obtained results show a 38 percent savings in wood residues transportation compared to the cost of the existing system. The model can be used to find answers for such questions as: From which suppliers can wood residues be obtained? What is the excess quantity of densified wood residues to be sold to markets? How much is the cost of distribution of wood residues and densified wood residues? How much income can be obtained from selling the excess quantity of densified wood residues? What is the quantity of wood residues to be processed by each processing station? What is the type of transportation mode to be used to transport wood residues or densified wood residues on a specific route? And what is the type of operational policy to undertake to transport wood residues or densified wood residues on a specific route. The developed model is general in structure and can be used in other situations such as municipal solid waste collection and disposal, hazardous waste management and other compatible situations. Due to the limited computational capabilities of the software package, LINDO, which was used for the solution of the model, a small-scale problem was considered for the model testing. Therefore, it is recommended that other software packages with more computational capabilities be used in the case of a large-scale problem.
References Adler, T.J., M. Blackey and T. Meyer, 1978, The direct and indirect costs of transporting wood chips to supply a wood-fired power plant (U.S. Department of Energy, Washington, DC). Alidi, AS., 1985, A stochasttc dynamtc mixed-integer linear programming distribution model, Doctor of Engineering dissertation (Tulane University of Louisiana, New Orleans, LA). Banta, A.R., 1979, Wood as a supplement fuel to solid waste at a university of Kansas steam plant, Doctor of Engineering dissertation (University of Kansas, Lawrence, KS). Bungay, H.R., 1981, Energy. Thebiomass options (Wiley, New York). Charm. C.J.. R.D. Miles and K.C. Sinha, 1981. Transportation Research 15-B. 227-238. Harvey, D.J. and T.G. O’Flaherty, 1973. Canadian Journal of Operations Research and Information Processmg 17, 187-200. Inaba, L.K. and D.E. Eakin, 1981. Collection, transportatron, and storage of biomass restdues in the Pacific Northwest (U.S. Department of Energy, Washington, DC).
94
AS
Ahdl, Utilization
of wood residues
Marks. D.H. and J.C. Ltebman, 1974, A solid waste collection example, in: R. De Neufville and D.H. Marks, eds., Systems planning and design (Prentice-Hall, Englewood Cliffs, NJ) 202218. Reason, J., 1982, Power 127, 55-58. Reed, T.B. (ed.), 1981, Biomass gastftcation: Princtples and technology (Noyes Data Corportion). Resource Management Services, 1981. Wood fuel for power generation at Wendel, California (National Technical lnformatton Service, Birmingham, AL). ReVelle, C. and J Gundelach, 1975, Water Resources Research 11, 1977203. U.S. Environmental Protection Agency, 1980, Environmental and technologtcal analysis of the use of surplus wood as an mdustrial fuel (U.S. Envtronmental Protection Agency, Cincmnatt, OH).
and Energy
IO (1988) 79--94. North-Holland
AN OPTIMIZATION MODEL FOR THE UTILIZATION RESIDUES AS AN ENERGY SOURCE
OF WOOD
Abdulaziz S. ALIDI King Fahd Uniwrs~ty of Petroleum and Minerals, Dhahran 31261, Saudi Arabia Received November
1987
The use of wood residues as an energy source is limited by two major problems. (a) the high cost of transportation due to their high volume with respect to their energy content, and (b) the stochastic generation of these materials. A dynamic mixed-integer linear programming distribution model has been developed. The model has been tested and the results obtained show a conslderable amount of savings m transportatton costs.
1. Introduction
Most of the wood energy produced in the United States is generated by co-generation facilities. The term co-generation implies that at least two different forms of useful energy are being produced. The most common example of two systems that can be linked in co-generation is the production of electricity and process steam at the same time. Many large wood products companies which produce considerable amounts of wood residues have their own co-generation facilities. But most of the wood products industry in the United States is represented by many small sawmills scattered all over the country. They are too small to use their wood waste as an energy source, but the waste represents a huge amount of material and a severe problem. The problems arise from the danger of fires in the stockpiles, and the large amount of land required for disposal. A major problem which is limiting the use of these wood residues at these sawmills is that their generation depends on the demand for wood products which in turn depends on the general status of the economy. Therefore, the owners of these sawmills are not certain that they will produce enough wood wastes to be used for energy production. The logistical di~culties in gathering and bringing wood residues from wood products mills to the site of a wood-fired power generation plant frequently make them more expensive than coal. Additionally, their lowdensity, high-moisture nature generally makes it uneconomical to transport beyond about 40-80 kilometers. In a study prepared for the United States 0165-0572/88/$3.50
0
1988. Elsevier Science Publishers
B.V. (North-Holland)
80
A.S. Alidi, Utilization
of wood residues
Environmental Protection Agency (1980) it was reported that transportation of green wood chips by truck for 160 kilometers at 0.03 U.S. dollars per ton/kilometer would add about 0.42 U.S. dollars per 1.06 x 10’ joule to the fuel cost. Burlington Electric Department (1982) reported that the cost of wood fuel (with 1.05 x lo7 joule per kilogram) for its 50MW (mega watts) power plant including the cost of chipping and transportation was estimated at 19.0 U.S. dollars per ton. Based on the department report this compares with existing coal (with 2.94 x lo7 joule per kilogram) cost of about 60.0 U.S. dollars per ton. The department also reported that off-highway trucking of wood chips costs about 0.05 U.S. dollars per ton/kilometer and to truck the fuel 80.0 kilometers would cost 4.0 U.S. dollars per ton or about 20 percent of the average price of the fuel at the power plant (which is 19.0 U.S. dollars per ton). Officials at Lake Superior District Power Company (1982) pointed out that one of the major suppliers of wood residues for their 30MW power generation plant is Louisiana-Pacific Corporation whose mill is located only 4 kilometers from the power plant. In 1979 the company signed a live-year contract to take all of this mills’ residues (20,000 tons per year plus its 40,000 ton stockpile) for 1.0 U.S. dollars per ton with transportation cost of about 2.0 U.S. dollars per ton. Transportation of low bulk density materials such as wood residues is usually limited by volume rather than the weight load. In summary, the unsteady generation of wood residues and the cost of transportation are the major obstacles which limit the use of wood residues as an energy source on a large scale. In this paper the possibility of installing regional wood residues densitication and quality upgrading stations between wood residues suppliers and a wood-tired power generation plant in order to reduce the transportation cost is studied, A mathematical model which simulates the stochastic nature and transportation aspects of wood residues is developed. The development of this model is based on Alidi’s work (1985). The model has been tested and the obtained results show a considerable amount of savings in wood residues transportation. The model can be used by management to facilitate the utilization of wood residues as an energy source.
2. Literature review In a report prepared for the United States Department of Energy, Inaba and Eakin (1981) gave an overview on the collection, transportation, and storage of biomass residues in the Pacific Northwest of the United States. They pointed out that some of the factors that should be considered when assessing the transportation of forestry residues are bulk density of the material, material size range, length of haul, access and road conditions, and space and facilities available for the loading and unloading processes. Adler et al. (1978) have indicated that truck transportation seems to be the most
A.S. Altdt. Utilization of wood restdues
81
economic mode of transportation for harvested wood chips. They considered the indirect (or social) cost of wood chips transportation systems which included traffic congestion, noise, air pollution, and highway deterioration. Their analysis concludes that the specific wood-fired power generation plant site has a strong influence on the costs, direct and indirect, of the various possible transportation systems and they recommended a complete cost analysis for each site. Resource Management Services (1981) conducted a study to investigate the possibility of installing a wood-fired power generation plant at Wendel, California. Based on the study’s findings it was concluded that intermediate storage and transfer at satellite locations have disadvantages such as cost of additional equipment, facilities, and handling, as well as introducing the possibility of transportation difficulties due to extreme weather or labor problems. The above three studies in addition to other similar studies were prepared to investigate the best way to bring wood fuel to the sites of power generation plants. These studies are based not on a specific mathematical programming technique but on economic evaluation of the situation under consideration. In addition to that the concept of installing intermediate wood residues densification stations and the stochastic nature of wood residues generation at the different suppliers were not considered. The concept of locating intermediate stations between suppliers of materials and/or services and demand centers has been analyzed by many investigators. Harvey and O’Flaherty (1973) formulated the problem of solid waste collection, transportation and disposal as a mixed-integer linear programming model. The objective of their research is to identify from among several alternatives which sanitary land-fill site or sites should be seriously considered for disposal. Costs for collection vehicles, transfer stations, large road carriers, and land-fill sites were considered on present worth basis over the time period specified. A facility location model has been developed and used by Marks and Liebman (1974) to screen preliminary data in order to learn something about the issues of whether and where to locate solid waste transfer stations in the city of Baltimore, Maryland. A linear programming model used to determine the alternative distribution of coal from producers to consumers by available transportation modes and routes was developed by Chang et al. (1981). They pointed out that since there are two options available for coal-users in choosing coal, i.e., to use low-sulfur compliance coal or to use scrubbers to clean high-sulfur coal before burning, the objective for the entire system minimizes the sum of the respective costs from the two different decisions. Although all the above models considered the concept of using transfer stations as a means of reducing the total transportation costs, each lacks the inclusion of several important features such as the stochastic generation of materials at suppliers and the different modes and operational policies of
82
A.S. Alidi, Uthzat~on of wood residues
transportation systems which should be considered in any distribution network. A comprehensive mathematical distribution model incorporating the concept of processing stations was developed by Alidi (1985). The stochastic nature of materials generation was included in Alidi’s model (1985) utilizing the methodology of ReVelle and Gundelach (1975) who addressed the stochastic nature of rainfall. In the process of developing Alidi’s model (1985) only one location for the primary demand center is considered and the fixed cost of building processing stations at the different possible sites was not explicit in the objective function of the model. The current research is based on the extension of Alidi’s model (1985) to accommodate more than one location for the primary demand center and the inclusion of the fixed cost of building processing stations since it is a major cost which will have a major impact on the station selection.
3. Model development As stated previously, unutilizable variable quantities of wood residues which are generated at different wood products mills, scattered throughout a specific region, can be collected and transported to a central wood fuel power generation plant. The plan proposed and studied in this paper suggests a method for reducing the cost of transporting these wood residues by installing regional densitication stations between wood products mills and a wood-fired power generation plant. At these stations wood residues are dried and compressed so that they have a higher energy density than unprocessed wood residues. The process of densification will provide a dry, uniform, easily stored, and conveniently shipped fuel from the wide variety of residues product in the wood products industry. Due to the stochastic nature of wood residues generation and specific needs dictated by owners of wood products mills, the quantities of wood residues which may be made available for the wood fuel power plant will vary from one period to another. This variation will make the locations of the densification stations and the site of the proposed wood fuel power generation plant to be not the best on the long range in terms of minimizing the total cost of wood residues transportation and utilization. The above problem is simulated by a three-stage mathematical model as described below.
3.1. Determination supplier As proposed will be willing
of the quantities
of wood residues obtainable from each
by Alidi (1985) the owner (supplier) of a wood products mill to sell wood residues if certain conditions are met. These
AS. Alidl, Utilization of wood residues
83
conditions can be summarized as follows: (a) the storage area of wood residues at his mill should be as small as possible, (b) a specific area within the storage area has to be available at the beginning of each period of a cycle (such as a month within a year) for storing wood residues in case there is a sudden increase in their generation, (c) a specific quantity of wood residues has to be available at the storage area at the beginning of each period of a cycle in case there is a sudden need for it by the supplier for his own internal use, and (d) a specific quantity of wood residues has to be purchased from the supplier at the beginning of each period of a cycle to insure him of a minimal income from selling these residues. As stated previously, in order to keep regional densification stations between suppliers of wood residues and the proposed wood-fired power generation plant operating over several future cycles, the variations between the quantity of wood residues obtained from a particular supplier at the beginning of a period of a cycle and the quantity obtained from the same supplier at the beginning of the same period in the following cycles have to be as small as possible. This optimization problem has to be addressed, taking into consideration the above four conditions imposed by the supplier. The Linear Decision Rule which was developed by ReVelle and Gundelach (1975) addresses a similar optimization problem and it may be utilized for the solution of this problem. This mathematical tool is introduced and explained in full detail in Alidi (1985). Based on the Linear Decision Rule of ReVelle and Gundelach (1975) the following equation is used to predict the quantity of wood residues which can be obtained from each supplier at the beginning of each period (month) without violating his needs and interests: X,,i=(l-B,_~)R,_~+B,_~R,_~-b,_~+b,...,
(1)
where = the amount of wood residues to be obtained from supplier i during month t, R,_ l,i = the amount of wood residues generated at supplier i during the previous month, B,_ l,i = a coefficient for the previous month for supplier i obtained by solving a system of linear equations as described in Alidi (1985), and =a decision constant for month t for supplier i. b,, i x,, I
Values for b,,, can be obtained min C,. i, subject
to C,,,+b,,iZ(VJC)!!“i+
I/;,i,
by solving
the following
linear program:
84
A S. Alldi, Utilization of wood residues
b,, i 2 ( VJC)f, ; bf,*.-b,_, and the feasibility NI
N
wz- Sm,,
izq f.1 -(vKC)‘-W3 f,L
condition NI
)
is
N
where =storage area of wood residues at supplier i, to be minimized, =a specific portion of the storage area of wood residues to be made available at the beginning of each month for a sudden increase in the generation of wood residues, to be specified by the supplier, =a specific amount of wood residues to be available at the beginning of each month for the unexpected need of these residues by supplier i for his internal use, to be specified by the supplier, =a minimum amount of wood residues to be purchased from supplier i at month t to insure him with a minimum income form selling these residues, = the value of (VJC),,i which is exceeded w1 percent of the time
cZ, i "t,i
Sm,
41,i
(VJW (VJC):;
w
C(VJC),,i=R,.i+B,-1,,R,-,,il,
= the value
of (VJC),
(VKC);,;“3
time, = t h e value
i which
is exceeded
I-
w2 percent
of the
of ( VKQi
which
is exceeded
1- wa percent
of the
N NI
time C(VKC),,i=(l-B,~,,i)Rt-1,,+Bt-2.iRt-2,rl, =number of periods in a cycle such as months in a year, and = number of suppliers.
Utilizing projected data of quantities of wood residues to be generated at each supplier during each month of several future years, estimates of the amounts of wood residues obtainable from each supplier during each month of the forecasted years can be calculated using eq. (1). The detailed procedure of this calculation is provided by Alidi (1985). 3.2. Second stage: Distribution network configuration A dynamic mixed-integer linear programming model is developed to help in the determination of the wood residues distribution network. Fig. 1 depicts the distribution network to be determined. The model requires that the possible locations of the required densification
85
AS. Alidl, Utilization of wood residues
Suppliers of Wood residues _____________
LEGEND
i S r
j
Note:
Proposed Sites for Densification Stations _______________
Locations of Markets __________
Proposed Sites for Wood-Fired Power Plant __________
Suppliers of Wood residues (i=1,2,...,NI) Proposed Sites for Densification Stations (s 2, . . . . NS) Location of Possible Markets for Processed residues (r = 1, 2, . . . . NR) Proposed Sites for the Wood-Fired Power Plant 1, 2, . . . . NJ) Movement of Wood residues and Processed residues
different possible For all the routes, transportation (trucks, railcars, etc.) sidered under different types of operational (purchasing, renting, etc.) Fig. 1. A wood residues
distribution
= 1, Wood (j = Wood
modes of are conpolicies
network.
stations and the possible sites of the wood-tired power generation plant to be determined before solution of the model takes place. The solution of the model will point out the number of regional densification stations, their sites, and the site of the wood-fired power generation plant, which will result in the minimization of the distribution cost of the network during the forecasted years. The transportation of wood residues and densified wood residues is
AS. Alidi. Utilization of wood residues
86
assumed to be accomplished by different modes of transportation (such as trucks, railcars, and/or other modes). These different modes can be operated with different operational policies (such as purchasing, leasing, contracting and/or other operational policies). Again, these modes and operational policies will be chosen so as to result in the lowest total distribution cost. The following is a list of constants, variables, and subscripts used in the development of the model.
Constants
c D
E VN BM BN V W WN P AN SN
QS QP
=unit transportation cost of wood residues (WR) from a supplier to a densitication station, in U.S. dollars per ton, =unit transportation cost of processed wood residues (PWR) from a densification station to a proposed site of the wood tired power plant (WFPP), in U.S. dollars per ton, =unit transportation cost of WR from a supplier to a proposed site of the WFPP, in U.S. dollars per ton, =unit transportation cost of PWR from a densification station to a market, in U.S. dollars per ton. =unit purchasing cost of WR to be transported from a supplier to a densification station, in U.S. dollars per ton, = unit purchasing cost of WR to be transported to a possible site of the WFPP, in U.S. dollars per ton, =unit production cost of PWR to be transported to a possible site of the WFPP, in US. dollars per ton, =unit handling cost of PWR at a possible site of the WFPP, in U.S. dollars per ton, =unit handling cost of WR at a possible site of the WFPP, in US. dollars per ton, =unit selling price of PWR to be sold to a market, in U.S. dollars per ton, =a fixed cost for the construction of the WFPP at a particular site, in U.S. dollars per number of projected cycles (years), =a fixed cost for the construction of a densification station at a particular site, =capacity of the WFPP, in tons per number of projected cycles, =maximum amount of WR allowable by environmental and community regulations to be transported from a supplier to a densification station, in tons per cycle, =maximum amount of PWR allowable by environmental and community regulations to be transported to a possible site of the WFPP, in tons per cycle, =maximum amount of WR allowable by environmental and commun-
AS. Alidi, Utilization of wood resrdues
87
ity regulations to be transported from a supplier to a possible site of the WFPP, in tons per cycle, QM =maximum amount of PWR allowable by environmental and community regulations to be transported from a densitication station to a market, in tons per cycle, HS =fraction of utilizable PWR per unit total weight of PWR to be transported from a densification station to a possible site of the WFPP, EF =efticiency at which a piece of equipment utilizes PWR at the WFPP, in percentage (e.g., efficiency of a boiler burning processed WR at a power generation plant), LNO = the unit capacity of a densification station plus one, in tons per number of projected cycles, HR =fraction of utilizable PWR per total weight of PWR to be transported from a densification station to a market, H =fraction of utilizable WR per unit total weight of WR to be transported from a supplier to a densification station, HN =fraction of utilizable WR per unit total weight of WR to be transported from a supplier to a possible site of the WFPP, C’S =designed capacity of a densification station, in tons per cycle. Variables X
=amount of WR to be transported from a supplier to a densitication station, in tons per cycle, Z =amount of PWR to be transported from a densification station to a possible site of the WFPP, in tons per cycle, Y =amount of WR to be transported from a supplier to a possible site of the WFPP, in tons per cycle, MN =amount of PWR to be transported from a densification station to a market, in tons per cycle, F =a O-1 integer variable representing a proposed site of a densitication station (0: station will not be installed at the proposed site, 1: station will be installed at the proposed site), G =a &l integer variable representing a proposed site of the WFPP (0: WFPP will not be built at the proposed site, 1: WFPP will be built at the proposed site), XS =total amount of WR arriving at a densitication station, in tons per cycle.
Subscripts i
= a supplier
s
= a possible
of WR (15 i 5 NZ), site of a densitication
station
(15 s 5 NS),
88
m
4 t
j r
NI NS NM NQ NT
NJ NR
AS. Alidi, Utilization qf wood residues
= a mode of transportation (I 5 m $ NM), = a type of an operational policy ( 15 q 5 NQ), =a cycle (lstgi;NT), = a possibie site of the WFPP (1 sj 5 NJ). =a market (tgrzNR), = total number of suppliers, = total number of possible sites of densification stations, = total number of modes of transportation, = total number of types of operational policies, = total number of cycles, =total number of possible sites of the WFPP, = total number of markets.
Based on the constants, variables, and subscripts defined above, the dynamic mixed-integer linear program can be described with the following objective function: Minimize: NT
NQ
NM NS Nf
NT
NQ
NM
NS NJ
+ f (AN)jGj j
NT +_C
?iQ
MN
NJ
NI
C
C
Z:
~[I~~,j.~,~,~+~~~~~,j.~.q,t+~~~~~,j,~,q.~l~,j,m,q,t
NQ
NM
NS
NR
f q m j I
NT
subject to the following constraints: (1) supply constraints,
AS. Alidi, Utilization
bt-l%i+bt,i
~(1-B,-1,i)R,-l.i+B,-z,iRf-2.,-
N7;
t=l,2,..., (2) continuity
constraints
89
of wood residues
i=l,2,...,NI; at densification
stations,
-rCWR)
1
,.,,,,q,,)((~N),,,,,,q,,)l =O;
(3) constraints for determination arriving at each station, NQ
NM
NI
T
T
CXi,,,,,,.,-(XS),,=O,
(4) stations
capacity
(XS),, t 5 (5) selection
of the total
t=lv&-..,NT
(W,
NT
t
(6) selection
NT,
t=1,2,...,
f?
NQ
NM
NI
C
1
CXi,s,m,q,tZO,
4
s=l,2,...,NS;
s =
1,2,. . . , NS;
m i
+~Hi.j.n.q.*~,j.n,q.r (7) community
s=l,2y...,NS;
stations,
of the site for the wood-fired
I
of wood
constraints,
of sites for densification
(‘NOIs’s-1
quantities
power generation
-(CP)jGj>=O, II
and environmental
constraints,
j=1,2
plant,
, . . . , NJ;
residues
90
AS
Alldi, Utilization of wood restdues
NQ
7 Z,,,,,,,,,~(QS)j.s,m,t
for eachj,s.m,t,
7 ~,j.,,,.,~(Qp)l,j,m,t
for eachi,j,m,t,
(8) limited
number
of sites for the wood-tired
(9) limited
number
of sites for densification
power generation
plant,
stations,
$F,,NS;
(10)
one site for the wood-fired
(11) O-l integer
variables
F,=O
or
1,
G,=O
or
1,
3.3. Third stage: Periodical
power generation
plant must be selected,
constraints,
s=l,2,...,
distribution
NS,
j=1,2
,..., NJ.
analysis
The distribution analysis is concerned with the determination of the periodical (monthly) flow of wood residues and densitied wood residues throughout the distribution network. This flow can be determined by using a standard linear program similar in structure to the above dynamic mixedinteger linear program, except in the right-hand side of the supply constraints the actual amounts of wood residues generated in the last two periods (months) are used to estimate the amount of wood residues to be obtained from each supplier. Additionally, only the sites of the densification stations and the location of the wood-tire power generation plant selected by the solution of the above dynamic mixed-integer linear program should be considered when determining the distribution analysis.
AS. Alidr. Utilization
oj” wood residues
91
4. An application example To illustrate the application of the developed model it is assumed that there are three suppliers of wood residues, two possible locations for wood residues densilication stations, two possible sites for the wood-fired power generation plant and one market for excess densified wood residues. It is also assumed that there are two possible modes of transportation governed by two operational policies. To run the dynamic mixed-integer linear program, two forecasted years are considered. Data obtained from Alidi (1983, Banta (1979) Reed (1981) and Bungay (1981) were used in the model as feed data. The computer package LINDO (Linear, Interactive, aNd Discrete Optimizer) is used to determine the distribution network configuration and a typical periodical (monthly) distribution analysis. Results of the analysis are presented in tables 14. 5. Conclusions
and recommendations
Wood residues which are produced as by-products mills scattered all over the United States represent Table
at many small saw a huge amount of
1
Results of the dtstribution network configuration of the model applied to the case of the wood residues’ distributton system of the Umversity of Kansas at Lawrence. Proposed sites for the densificatton stations
Proposed sites for the wood-fired power generation plant
Decision
1
2
1
2
Install
Yes
No
Yes
No
Table 2 Typical
actual output for distribution analysis Kansas) when no excess densified
covering one month (the case of the Umversity wood residues are sold to the market.
of
Vartable
Quantity
Descriptton
x21221
808
Tons of wood restdues to be transported from supplier by the purchased (2) 45-foot trailers (2) in month (1)
Zll221
897
Tons of densified wood residues to be transported from station (1) to the wood-fired power plant (WFPP) (1) of the University of Kansas at Lawrence by the purchased (2) 45-foot trailers (2) m month (1)
XSll
808
Tons of wood residues
Total cost of the system is 12.689 U.S. dollars
to be densified for month
(1)
at station
(2) to station
(1) in month
(1)
(1)
AS. Ahdi, Utilization of wood residues
92
Table 3 Typical
actual
output for distrtbution analysis covermg one month (the case of the University Kansas) when excess densdied wood residues are sold to the market.
of
Variable
Quantity
Description
Xlllll
442
Tons of wood residues to be transported from suppher by the rented (1) 20-foot dump trucks (1) m month (1)
(1) to station
(1)
x21221
1441
Tons of wood residues to be transported from supplier by the purchased (2) 45foot trailers (2) in month (1)
(2) to station
(I)
211221
897
Tons of denstfied wood residues to be transported from station (1) to the wood-tired power plant (WFPP) (1) of the Universtty of Kansas at Lawrence by the purchased (2) 45-foot trailers (2) m month (1)
MN11221
993
Tons of densified wood residues to be transported sold to the market (1) by the purchased (2) 45foot (1)
XSll
1922
Tons of wood residues
Total cost of the system is 821 U.S. dollars
to be densilied
for month
from station (1) and trawlers (2) in month
(1) in month (1)
at station
(1)
Table 4 A detailed developed
calculation of the annual amount of savings resultmg from the application of the model to the case of the wood residues tired steam plant of the University of Kansas. U.S. dollars per year
Explanation Total cost of the wood-fired power plant (WFPP) of the Universtty of Kansas at Lawrence during the next two years based on the results of the dtstribution network configuration of the model
611.000
Annual cost of the WFPP based on the results of the drstribution contiguratton of the model
306,000
Annual
operatmg
cost of the WFPP
as reported
by Banta (1979)
Total annual cost of the WFPP of the Universrty results of the developed model Total annual cost of purchasing reported by Banta (1979)
and operating
network
of Kansas
500.000
based on the 806,000
the transportatton
facilities as 209,000
Total annual cost of purchasing and handling wood residues, the cost of the boner and other related costs as estimated by Banta (1979)
600,000
Annual
500,000
operating
cost of the WFPP
Total annual cost of the WFPP Banta (1979)
as reported
of the University
by Banta (1979) of Kansas
as calculated
by 1,309,OcM
Annual amount of savings resultmg from the application of the developed model to the case of the WFPP of the University of Kansas Annual amount of savmgs in percentage compared the WFPP calculated by Banta (1979)
to the total annual
503.ooo
cost of 38
AS. Altdi, Utilization of wood residues
93
material. The danger of fire in the stockpiles, and the large amount of land required for disposal are two major environmental concerns. There are two major obstacles which limit the use of wood residues for the production of energy at wood-fired power generation plants: (a) the unsteady generation of wood residues at sawmills makes them an unreliable source for energy production, and (b) their low-density, high-moisture nature generally makes the transportation and collection of these residues costly. A three-stage simulation model taking into consideration the above two problems is developed. The model has been tested utilizing data obtained from literature. The obtained results show a 38 percent savings in wood residues transportation compared to the cost of the existing system. The model can be used to find answers for such questions as: From which suppliers can wood residues be obtained? What is the excess quantity of densified wood residues to be sold to markets? How much is the cost of distribution of wood residues and densified wood residues? How much income can be obtained from selling the excess quantity of densified wood residues? What is the quantity of wood residues to be processed by each processing station? What is the type of transportation mode to be used to transport wood residues or densified wood residues on a specific route? And what is the type of operational policy to undertake to transport wood residues or densified wood residues on a specific route. The developed model is general in structure and can be used in other situations such as municipal solid waste collection and disposal, hazardous waste management and other compatible situations. Due to the limited computational capabilities of the software package, LINDO, which was used for the solution of the model, a small-scale problem was considered for the model testing. Therefore, it is recommended that other software packages with more computational capabilities be used in the case of a large-scale problem.
References Adler, T.J., M. Blackey and T. Meyer, 1978, The direct and indirect costs of transporting wood chips to supply a wood-fired power plant (U.S. Department of Energy, Washington, DC). Alidi, AS., 1985, A stochasttc dynamtc mixed-integer linear programming distribution model, Doctor of Engineering dissertation (Tulane University of Louisiana, New Orleans, LA). Banta, A.R., 1979, Wood as a supplement fuel to solid waste at a university of Kansas steam plant, Doctor of Engineering dissertation (University of Kansas, Lawrence, KS). Bungay, H.R., 1981, Energy. Thebiomass options (Wiley, New York). Charm. C.J.. R.D. Miles and K.C. Sinha, 1981. Transportation Research 15-B. 227-238. Harvey, D.J. and T.G. O’Flaherty, 1973. Canadian Journal of Operations Research and Information Processmg 17, 187-200. Inaba, L.K. and D.E. Eakin, 1981. Collection, transportatron, and storage of biomass restdues in the Pacific Northwest (U.S. Department of Energy, Washington, DC).
94
AS
Ahdl, Utilization
of wood residues
Marks. D.H. and J.C. Ltebman, 1974, A solid waste collection example, in: R. De Neufville and D.H. Marks, eds., Systems planning and design (Prentice-Hall, Englewood Cliffs, NJ) 202218. Reason, J., 1982, Power 127, 55-58. Reed, T.B. (ed.), 1981, Biomass gastftcation: Princtples and technology (Noyes Data Corportion). Resource Management Services, 1981. Wood fuel for power generation at Wendel, California (National Technical lnformatton Service, Birmingham, AL). ReVelle, C. and J Gundelach, 1975, Water Resources Research 11, 1977203. U.S. Environmental Protection Agency, 1980, Environmental and technologtcal analysis of the use of surplus wood as an mdustrial fuel (U.S. Envtronmental Protection Agency, Cincmnatt, OH).