Wood Biomass Supply Model for Bioenergy Production in Northwestern Ontario

Md. Bedarul Alam1, Chander Shahi2, Reino Pulkki3 1Ph.D. Candidate, 2Assistant Professor, 3Professor

Faculty of Forestry and the Forest Environment, Lakehead University 955 Oliver Road, Thunder Bay, Ontario P7B 5E1

Abstract: Wood biomass procurement for bioenergy production in an economic and sustainable way is a complex problem as it involves conflicting objectives of minimizing cost and distance of procurement, and maximizing quality of biomass, which is measured in terms of its moisture content. The multi-objective optimization problem is solved through pre-emptive goal programming approach using LINGO 11 software, where the cost of procurement is given the first priority, distance of procurement the second priority, and quality of biomass the third priority. The use of the model is demonstrated using a realistic example for bioenergy production for the recently established Abitibi-Bowater Inc. power plant at Fort Frances in northwestern Ontario, Canada, which has a weekly demand of 13,000 green tonnes for 50 Megawatt power production. The model selects quantity of biomass to be procured from each of the three zones ranging from 0-50 km, 50-70 km, and 70-100 km to meet the weekly demand.

1. Introduction Canada is committed to reducing its Green House Gas (GHG) emissions to 6% below the 1990 level by 2012 under the Kyoto Protocol [1]. One of the ways to meet its commitment under the Protocol is to replace coal with biomass as feedstock, since coal fired power generating stations produce 18% of Canada's current emissions [2]. The provincial governments in Canada have chalked out plans to phase out coal fired power generating stations. For example, the Ontario Government has decided to phase out coal fired power generating stations by 2014. However, no studies have been done to ensure sustainable supply of biomass feedstock to the power generating stations in the most economic way.

To sustainably supply biomass feedstock in the most economic way from a given area around the power generating station, it is necessary to decide the quantity and quality of biomass to be procured over different distances from the power generating station [3]. The problem therefore, involves conflicting objectives of minimizing cost and distance of procurement, and maximizing the quality of biomass, which is measured in terms of its moisture content. In the multi-objective decision-making problem, it may not be possible to get an optimal value for all the objectives simultaneously [4]. Generally, due to the conflicting nature of the objectives, the solution to the problem that optimizes one objective cannot simultaneously optimize any other objective. Therefore, in multi-objective optimization problem, the

notion of optimality cannot be used in totality, as there could be an infinite number of efficient solutions for a multi-objective optimization problem, and the objective of the decision making problem is to find out the most efficient solution. However, the multi-objective optimization problem can be solved using pre-emptive goal programming technique, where the notion of optimality is replaced by the concept of non-inferiority, efficient and Pareto-optimality [4, 5]. In order to get the most efficient solution for the multi-objective optimization problem through pre-emptive goal programming, each objective is assigned a priority and the priorities are fulfilled serially rather than simultaneously.

The purpose of this paper is to develop a model to find out the most efficient way of maintaining a sustainable supply of wood biomass to the power generating stations. The specific objectives are: (i) to minimize the cost of procurement of the biomass feedstock, (ii) to minimize the distance of procurement of the biomass feedstock keeping the cost of procurement at the optimal level, and (iii) to maximize the quality (minimize the moisture content) of biomass procured at the optimal levels of cost and distance of procurements.

The pre-emptive goal programming model is applied to the biomass based power plant established in Fort Frances, northwestern Ontario by Abitibi-Bowater Inc. The power plant has a capacity of 50 MWh and it requires about 13,000 green tonnes of biomass per week (Gt/wk) as feedstock [6]. The power plant uses two types of biomass as feedstock: (i) forest harvest residues from the major harvestable species such as spruce, pine and fire, and (ii) unutilized wood species such as poplar and other hardwood species [7]. The forest harvest residues constitute leftover of the tops, branches and other parts of the trees in the forest after harvesting trees from the forest mainly for lumber, pulp and paper industries. The unutilized wood supplies constitute trees species with no economic value for the forest industries. Abitibi-Bowater Inc. has three Forest Management Units (FMUs) within a radius of 100 kms around the power generating station with about 73,500 green metric tonnes of biomass annually available to supply both types of biomass to the power generating station [8,9]. The model is solved using the LINGO 11 software to find out the quantity of biomass procured from each of the three zones within 50

kms, 50-70 kms, and 70-100 kms from the power plant respectively.

2. Methodology The order in which priorities have been assigned to the objectives in the pre-emptive goal programming optimization problem include: (i) to minimize the cost ($/Gt) of biomass feedstock procurement, (ii) to minimize the distance (Km/Gt) of biomass procurement, and (iii) to minimize the percentage of moisture content (maximize quality). The mathematical form of the objectives can be described in the following way:

(1) First priority objective: Cost (Z1)

Total procurement cost (TPC) is defined as:

TPC = FC + VC where, FC is the fixed cost and VC is the total variable cost associated with procuring the biomass feedstock from each of the three zones. These costs are defined as:

kk

k ZFFC .∑=

ijki j k

ijk XPVC .∑∑∑=

where, i = 1,2 stands for two types of biomass, j = 1 stands for the power plant to which the biomass is supplied, and k = 1, 2, 3 stands for three zones from which the biomass is being supplied.

Pijk = Cost of a unit of biomass i for power plant j procured from zone k

Fk = Fixed cost associated with procuring biomass from zone k

Xijk = Number of units of biomass i for power plant j procured from zone k

Zk = A binary variable which takes on value 1 if the biomass is procured from zone k and value 0 otherwise

(2) Second priority objective: Distance (Z2) The total distance involved for procuring biomass feedstock is defined as

ijki j k

ijk XLZ .2 ∑∑∑=

Lijk = Distance from which a unit of biomass i for power plant j procured from zone k

(3) Third priority objective: Quality (Z3) The quality (overall moisture content) is calculated by summing over all types of wood biomass and quantity procured

ijki j k

ijk XQZ .3 ∑∑∑=

Qijk = Quality of a unit of biomass i for power plant j procured from zone k which is measured as a percentage of moisture content available in the biomass feedstock

In addition, the following variables are used in this model:

Ck = Capacity of zone k to supply biomass feedstock

Dij = Demand of biomass i by industry j

The pre-emptive goal programming model is specified as:

Min Z = P1d1+ + P2d2

+ + P3d3+

subject to the following constraints

)1(,.. 11 jiGoalCostddZFXPi j k

kkijkk

ijk ∀=−+⎟⎟⎠

⎞⎜⎜⎝

⎛+ +−∑∑ ∑∑

)2(,tan. 22 jiGoalceDisddXL ijkk

ijk ∀=−+ +−∑)3(,. 33 jiGoalQualityddXQ ijk

kijk ∀=−+ +−∑

)4(,. kiZCX kkj

ijk ∀≤∑)5(, jidX

kijijk ∀=∑

)6(}1,0{ kZk ∀=)7(,,0 kjiXijk ∀≥

where, P1, P2, and P3 are pre-emptive weights assigned to priorities d1

+, d2+, and d3

+ respectively. The goal constraint used in the model is defined by the following equation:

fi(x) + d−i − d+i = bi

where, fi is the objective to be achieved with a target value of bi, d−i is under-achievement of the goal, and d+i is over-achievement of the goal.

The wood biomass feedstock for Abitibi-Bowater Inc. Fort Frances power plant is procured from three forest zones, which lie within 100 km radius of the power generating station, in the Forest Management Units. These zones include: (i) Zone 1, which is within 50 km distance from the power plant, (ii) Zone 2, which is within 50-70 km distance from the power plant, and (ii) Zone 3, which is within 70-100 km from the power plant.

The data used in this model for Abitibi-Bowater Inc. Fort Frances power plant has been collected from the local contractors and is described as follows: Pijk: Cost ($/Gt) of a unit of biomass i for power plant j

procured from zone k is 30, 33, 37, 29, 32, and 35 respectively.

Fk: Fixed cost ($/week) associated with procuring biomass from zone k is 9000, 8000 and 8000 respectively.

Dij: Demand (Gt/wk) of biomass i by industry j is 8000 and 5000 respectively.

Lijk: Average distance (kms/Gt) from which a unit of biomass i for power plant j procured from zone k is 25, 60, 85, 25, 60, and 85 respectively.

Qik: Quality (% of moisture content) of a unit of biomass i for power plant j procured from zone k is 0.35, 0.3, 0.3, 0.4, 0.45, and 0.4 respectively.

Ck: Procurement capacity (Gt/wk) of zone k to supply each biomass type is 3434, 4134 and 6494 respectively.

3. Results and Discussions The optimal solution for the preemptive goal programming model with three consecutive priorities defined by the minimization function Z, subject to constraints defined by equations (1) to (7), is run using LINGO 11 software. The model found the following optimal solution for cost, distance, and quality goals for supplying wood biomass feedstock to the Abitibi-Bowater Inc. Fort Frances wood biomass based power generating plant:

1. Cost goal: $430,124 2. Distance goal: 55.04 km 3. Quality goal: 4.77%

The model also found the optimum quantities (Gt/week) of two types of wood biomass to be collected from each of the three selected forest zones. The optimum quantities of forest harvest residue and unutilized wood species are presented in Table 1. Table 1: Quantities of forest harvest residue and unutilized wood species to be collected from each zone

Wood Biomass Forest Zones Quantity (Gt/wk)

Forest harvest residue Zone 1 3434

Forest harvest residue Zone 2 4134

Forest harvest residue Zone 3 432

Unutilized wood supply Zone 1 3434

Unutilized wood supply Zone 2 1566

Unutilized wood supply Zone 3 0

The results show that in order to satisfy the multi-objective optimization function, Abitibi-Bowater Inc., Fort Frances power generating station should collect the entire available forest harvest residue from zone 1 and zone 2, and only 6.6% of available forest harvest residue from zone 3. In order to meet the weekly demand of unutilized wood species biomass, it should collect the entire available unutilized wood supply from zone 1, 37.8% of the available unutilized wood supply from zone 2, and none from zone 3.

4. Conclusions The procurement of wood biomass feedstock for generating power in a sustainable and economically feasible way is one of the most critical aspects in bioenergy production. In this paper, the wood biomass procurement problem has been modeled as a multi-objective pre-emptive goal programming model by giving first priority to the cost of wood biomass procurement,

second priority to the distance of the wood biomass procurement zone from the power plant, and third priority to the quality of wood biomass. An important characteristic of pre-emptive goal programming is that it solves the first priority goal before the successive priority goals are even considered. When lower priority goals are taken into consideration, the solutions of higher priority goals are sustained. By using pre-emptive goal programming the industry can procure wood biomass using more than one criterion. Normally, the multi-objective problems are solved by assigning weights to each of the objectives, which depends on the discretion of the decision maker. However, in pre-emptive goal programming, the decision maker has only to specify the rank ordering of the priorities of the objective functions. Moreover, the utility function of the decision maker need not be linear and it is also not necessary to scale the criteria value in the pre-emptive method. LINGO 11 software was used to find an efficient solution to the multi-objective pre-emptive goal programming model to supply wood biomass for bioenergy production in Abitibi-Bowater Inc., Fort Frances power generating station in northwestern Ontario. The results suggest that the demand of forest harvest residues and unutilized species wood biomass for the Fort Frances bioenergy power plant could be fulfilled optimally by collecting the entire available wood biomass from zone 1 and part of the available biomass from zone 2 and zone 3. The pre-emptive goal programming model for procurement of wood biomass for bioenergy production developed in this paper can be applied elsewhere in Canada and other countries.

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