A dynamic decision model for the optimal use of forest biomass for energy production

Abstract

The use of forest biomass for energy production requires a careful attention to the sustainable silvicultural practices. This is a complex task because of the different environmental and economic issues to be taken into account. To this aim, suitable tools must be used as regards the representation of the dynamics of forest biomass and the economic assessment. In this paper, a user-friendly optimization-based decision support system (DSS) that can help decision makers in the optimal management of forest biomass use for energy production is presented. Attention is focused on the forest system in order to take into account sustainable silvicultural practices and on the minimization of costs for the collection plans over years. Specifically, a non linear optimization model (that includes forest growth models) is formalized, aiming at determining, over a certain period, the optimal exploitation policy of forest biomass through a single plant whose location and size are assumed known, in order to minimize costs and to respect silvicultural constraints. The decision model is solved through a receding horizon approach and is applied to the case study of Val Bormida (Savona Province, Italy). Different tests and sensitivity analysis have been performed to validate the model and the approach. From an application point of view, observing the obtained results, it is evident that results are strongly influenced by the old average age of the vegetation in the specific case study. However, depending on the species, different trends for the results of annual mean increment and harvesting plans are observed.

Appendix

1.1 Nomenclature

1.1.1 Sets

• i, $i=1,\ldots ,N$: index for forest parcels;

• t, $t=0,\ldots , T-1$: index for time;

1.1.2 Variables

• $Age_{i,t}$ (years): the average forest age for each forest parcel;

• $I_{i,t}$ (m$^{3}$ ha$^{-1}$ year$^{-1}$): the mean (i.e., averaged over space) annual volume increment (per unit area) in the time interval (t,$t+1$);

• $u_{i,t}$ (m$^{3}$ year$^{-1}$): the volume of biomass harvested or thinned during the same time interval on the whole parcel I;

• $v_{i,t}$ (m$^{3}$): the whole volume of biomass in parcel i at time t;

• $C_{FP}$: the cost of forest biomass felling and processing;

• $C_{FT}$: the cost of forest biomass primary transportation;

• $C_T$: the transportation cost from the landing points to the plant;

1.1.3 Parameters

• $a_{i }$ (m$^{3}$ ha$^{-1}$ year$^{-3}$), $b_{i }$ (m$^{3}$ ha$^{-1}$ year$^{-2}$), $c_{i}$ (m$^{3}$ ha$^{-1}$ year$^{-1}$): site- and species-specific parameters;

• $\bar{I}_i$ (m$^{3}$ ha$^{-1}$ year$^{-1}$): the biomass increment per unit area of the new planted trees;

• $S_i$ (ha): the overall area of the biomass parcel;

• Age $_{max,i, }$ (years): the age at which the mean annual increment attains its maximum;

• $I_{\max ,i}$ (m$^{3}$ ha$^{-1}$ year$^{-1}$): maximum mean annual increment;

• $C_U^{FP}$ (€ m$^{-3}$): unit cost for the felling and processing phase;

• $\sigma _{Deb,i} ,\sigma _{Del,i} ,\sigma _{Cc,i}$: binary parameters (Deb for debarking, Del for delimbing, and Cc for cross cutting, respectively);

• $P_{Deb} ,P_{Del} ,P_{Cc}$: the percentage of cost [%] saved when the corresponding operation is not needed;

• $C_{z,i}^{FT}$ (€ m$^{-3}$): unit cost for each slope z;

• $d_i^{FL}$ (km): distance from the felling areas to the nearest landing point;

• $Acc_{z,i}$: the percentage of surface area of parcel i characterized by slope class z [%];

• $d_{SP_i }$ (km): distance from landing point to the plant location;

• $C_U^T$ (€ kg$^{-1}$ km$^{-1}$): unit cost for transport from landing point to the plant location;

• $VM_i$ (kg m$^{-3}$): biomass density;

• $\alpha _i$ (adim): parameter indicating the fraction of biomass that can be exploited (according to legislation);

• CAP (MW): the fixed plant capacity;

• $\eta _1 , \eta _2$: coefficients of suitable value for energy production bounds;

• f a conversion factor equal to the number of seconds in 1 year;

• LHV $_{i}$ (MJ/kg): the low heating value corresponding to the biomass in parcel i.