Assessing the value of a diversified by-product portfolio to allow for increased production flexibility in pulp mills

The steam utility system

A simplified flow sheet of the mill’s steam utility system is illustrated in Figure 1. The recovery boiler is the primary steam production unit. The steam production in the recovery boiler varies over time depending on variations in flow and heating value of the black liquor (see also Process data and capacity constraints for the pulp mill section). During most operating conditions, the steam production from the recovery boiler would be sufficient for covering the process steam demand. However, to manage the steam balances of the mill in the presence of variations in steam supply from the recovery boiler as well as variations in process steam demand, a supplementary boiler fired with bark is also constantly in operation.

Lignin extraction

This study includes the possibility for the mill to invest in a lignin extraction plant. The extraction of lignin enables conversion of surplus energy from the wood raw material into a value-added product by removal of lignin from the black liquor in the evaporation plant via acid precipitation. Extracting lignin would provide the pulp mill with an opportunity to generate a new by-product that could potentially be used for various applications (Gellerstedt et al. 2013, Téguia et al. 2017). Previous work has also shown that lignin extraction may provide a great opportunity for indirectly increasing the flexibility of the pulp mill’s utility system in response to steam demand variations (Svensson 2014, 2015). It does so by providing a way to adjust the load of the recovery boiler, thereby achieving a larger operating range for steam production that does not rely only on the limited capacity range of the bark boiler. Lignin extraction has also been shown to be of interest for debottlenecking the recovery boiler in case of a pulp production increase (Axelsson et al. 2006, Laaksometsä et al. 2009, Wallmo et al. 2009, Välimäki et al. 2010, Périn-Levasseur et al. 2011).

Production increase

The pulp mill company is investigating the opportunities for a strategic investment in a new production line, which would significantly increase the pulp production capacity. Different options for the pulp product of the new line are being investigated. We consider one of these options, where the new line extends the production capacity of one of the pulp products currently produced in the mill. However, all options are based on approximately the same increase in pulp production (about 80 %). The decision about the production increase is based on a number of criteria, most of which are beyond the scope of this study. The design of the new production line, and the resulting mass and energy balances based on spreadsheet calculations made by a consultancy company, were therefore used as input to this study. With regards to the steam system, the new production line will affect mainly the amount of black liquor being processed and the demand for steam at 4 and 12 bar(a) (all of which will increase by approximately 80 % on average). In addition, a change is planned to replace the current use of high-pressure steam (61 bar(a)) for soot blowing by 27 bar(a) steam. When the black liquor heat flow increases as a result of the pulp production increase, the existing recovery boiler becomes a bottleneck. However, an older recovery boiler, that is currently not in operation, is still available at the mill, and is planned to be started up again in connection with the production increase. However, the two recovery boilers together are nevertheless insufficient to handle the entire black liquor flow during high production after the production increase. Therefore, a lignin extraction plant is planned as a debottlenecking option.

In this work, an optimization model is used to determine the optimal capacity of the lignin extraction plant, and the best investment in new turbine capacity given predefined changes of black liquor heat availability and process steam demands. It is assumed that the pulp production increase is given, and not affected by changes in the lignin extraction rate above that required for debottlenecking the recovery boiler. This is a reasonable assumption if, when increasing the lignin extraction so that the recovery boiler is no longer a bottleneck, other parts of the process such as the digester, evaporation or bleaching plants, also have limited capacity for further production increase. It is further assumed that if debottlenecking of the steam main pipelines is required, this is included in the given pulp production investment plan, and no further optimization is considered.

Investment costs

The total investment costs InvCost may include investments in new turbines and a lignin extraction plant (Equation 2). The cost function Costx(Yx) for investment in equipment x is expressed by a piecewise linear function (in n linearization intervals) of the capacity, Yx, of the equipment (Equation 3). Cinv,x(i) is the investment cost at the i^th breakpoint, of the piecewise linear function, Y‾x(i), is the equipment capacity at that breakpoint, and kx(i) is the linear slope between Y‾x(i) and Y‾x(i+1). The binary variable zx is 1 if investment is made in technology x, and 0 otherwise. If investment is made in technology x, the equipment capacity Yx must be within the valid linearization range of the investment cost function, i. e. between starting point of the first linearization interval Y‾x(1) and the end point of the last Y‾x(n+1). This is given by Equation (4).

Operational costs and revenues

The year is divided into time periods t, of duration dt, which represent the total annual operating time of the mill.

BarkCost is the annual bark cost as a function of the bark price, pbark,t, and use of bark as fuel in the bark boiler, QBark,t, both of which may vary between the time periods t (Equation 5). Similarly, the annual lignin revenues, LigRev, associated with lignin extraction, QLig,t, are a function of the lignin price plig,t in different time periods (Equation 6).

ElecRev represents the annual revenues from electricity production, Eprod,t (Equation 7). Electricity produced in the steam turbines, Eprod,t can either be used at the mill, thus leading to reduced purchase of electricity from the grid, or be sold to the grid. Variations in own consumption of electricity due to variations in boiler and turbine loads, e. g. air fans and steam condenser pumps, have been neglected. The same electricity price, pel,t, is assumed for selling and purchasing electricity. The model could easily be adapted for differentiated purchase/sales prices if the mill electricity consumption is available with the time resolution of the model, by including an additional constraint for the electricity balances of the mill.

A share of the total electricity production is eligible for so-called green electricity certificates, which can be sold to generate additional revenues. However, the price for electricity certificates is assumed to drop significantly in the near future, and this revenue is therefore neglected in the base case. Appendix C describes the modelling of electricity certificates for an alternative scenario that assumes high prices of certificates.

The total electric power produced in the mill in a given time period, Eprod,t, is given as the sum of electric power outputs, ET,t, of all turbines T (Equation 8).

Boiler operation, bark use and extraction of lignin

Part-load operation of boilers is represented by the use of marginal efficiencies that are estimated to be valid as long as the boiler load is kept above the minimum load limits set in the model. While boiler efficiencies typically decrease at part-load conditions, the marginal efficiencies (i. e. the change in steam production divided by the change in fuel input) are almost constant. However, the use of constant marginal boiler efficiencies is based on the assumptions that the minimum load of the bark boiler has been set to have an acceptable efficiency over its full range of operating conditions.

The bark use, QBark,t, is consequently given by the steam production in the bark boiler MBB,tprod, the marginal boiler efficiency ηBB and the enthalpies of HP steam and feed water, h1 and hfw (Equation 9). (The steam headers are numbered j=1,2,…, starting from the highest pressure.) Lignin extraction reduces the steam production in the recovery boiler, MRB,tprod, from the reference steam production MRB,tref, which also varies between time periods, mainly due to variations in the flow and heating value of the black liquor fuelling the boiler. The lignin extraction QLig,t is therefore a function of the resulting steam production reduction, the enthalpy increase over the boiler and the recovery boiler’s marginal lignin efficiency, ηRB−LIG (Equation 10). Part-load efficiency effects of the lignin extraction plant are assumed to be negligible.

Previous model versions have included an opportunity to start and stop the bark boiler depending on the steam demand. However, according to mill personnel, the bark boiler is always required to be in operation for safety reasons. Consequently, both the recovery boiler and the bark boiler must always operate within the minimum and maximum load limits, here defined by the minimum and maximum steam production Mbmin and Mbmax (Equation 11).

The lignin extraction, QLig,t, is, furthermore, limited by the available heat content of the black liquor, which is directly proportional to the reference steam production in the recovery boiler. The maximum lignin extraction can therefore be expressed as ρMRB,tref, where ρ is a constant parameter (Equation 12). The lignin extraction is also limited by the capacity invested in the lignin extraction plant, YLIG (Equation 13).

Turbine models

The turbine models are linear functions relating the power output ET,t of a turbine T in time period t to the steam flow MT,s,tturb through the turbine stages s (Equation 14). The power output is a function also of the maximum inlet steam flow to the turbine. For existing turbines, this maximum inlet flow, MTmax, has a known value and can therefore be incorporated in a generic constant, bT,0(MTmax). However, for new turbines, the maximum inlet flow is a variable to be optimized, MTcap.

The estimation of parameters aT,s, bT,0, bT,1 and bT,2 is described in Appendix A, which also discusses the validation of the turbine model for existing turbines.

After discussion with mill staff, it was considered unrealistic to allow for turbines to be taken on and off operation in different time periods. However, the opportunity to replace existing turbines with new, more efficient ones, should be considered. Therefore, the model includes a variable γT representing the option to permanently turn off existing turbines. If investments are made in new turbine capacity, these new turbines are assumed to always be in operation. If an existing turbine is kept in operation, the binary variable γT takes the value one. Equation (15) then ensures that the inlet steam flow is kept between minimum and maximum flow limits, where the parameter μTmin defines the minimum inlet flow to a turbine as a fraction of the maximum inlet flow. A corresponding constraint for new turbines is given by Equation (16). If, instead, an existing turbine is taken off operation, the variable γT takes a zero value, which sets the inlet steam flow to zero according to Equation (15), and thereby the power output of the turbine is also zero as given by Equation (14).

Finally, some constraints are added to represent maximum turbine extraction flows and maximum power output. The extraction steam flow after turbine stage s(T) of turbine T, MT,s,text is given by Equation (17). For existing turbines, the steam extraction is limited by a maximum extraction flow, MT,smaxext according to Equation (18). Corresponding constraints for maximum extraction flows of new turbines are not included. Since the maximum extraction flow should depend on the size of the installed turbine capacity, it cannot be a fixed parameter. However, to include it as a variable would not make any sense as long as there is not any cost associated with increasing its value. Instead, for new turbines, the maximum power output, ET,t, is limited by a design capacity, ETmax (Equation 19), which in turn is used to determine the turbine capacity used in the investment cost function, see further below.

In order for the linear formulation of the turbine model (Equation 14) to hold with fixed coefficients, a turbine T should be either a back-pressure extraction turbine or a low-pressure condensing turbine. In principle, a wide variety of different combinations of back-pressure and condensing turbines, which inlets and extractions connected to different headers can be considered. While the above turbine constraints are generic, some more specific constraints are needed to describe the investment opportunities for specific new turbines in the mill. For the case study three main alternatives for new turbine investments were considered, namely:

1. TURB1: A back-pressure extraction turbine (BPETa) with extractions at header 27, 12 and 4 bar(a).

2. TURB2: A low-pressure condensing turbine (LPCTa)

3. TURB3: A combined turbine with inlet at the high-pressure steam header (header 1), extractions at header 27, 12 and 4 bar(a), and a condensing tail. This is modelled as a combination of a 3-stage back-pressure extraction turbine (BPETb) and a low-pressure condensing turbine (LPCTb).

Mass and energy balances

The steam header data are assumed to be constant and not optimized by the model. The steam headers are numbered j=1,2,…, starting from the highest pressure. Mass balances for steam pressure headers j are formulated in Equations (24)–(26). MT,s,tturb, Mv,tvlv and Mtvent denote the steam flows through the turbine stages s(T), expansion valves v and atmospheric vent, respectively; the notation in() and out(), refers to the inlet and outlet headers of turbines, turbine stages and valves, as relevant, and is used to mark subsets of turbines, turbine stages and valves, for which the steam flows should be included in the mass balances for a certain header. Mj,tproc denotes the process steam demands and Mj,tqw denotes quench water added for saturation purposes to steam header j.

The mass balances, as formulated in Equations (24–25), are not mill-specific, but still not fully generic. In particular, it is assumed that turbines may only have inlets at the highest-pressure steam header or the lowest-pressure steam header, and the atmospheric vents are only placed at the lowest pressure header. However, the mass balances can be used to represent any number of steam headers, valves and turbines, with inlets and outlets of valves and outlets of turbines at any header.

The process steam demands, Mj,tproc, are calculated according to Equation (26). The reference steam demand, Mj,tproc,ref, represents the steam demands of the mill if no lignin extraction or new condensing turbine is implemented, i. e. the reference demands that are not affected by investments or operating changes in the steam utility system as optimized by the model. For the production increase scenario, this reference steam demand is given by the estimated future process steam demand. If lignin is extracted, washing water used in the lignin extraction process is returned to the evaporation plant, causing an increased steam demand there to evaporate the added water. Therefore, in the model, a low-pressure steam demand is added to the reference steam demand if lignin is extracted, which depends on the lignin extraction rate QtLig and the specific increase in low-pressure steam flow per MW lignin extracted, σ. The potential effect of increased condensate flows to the feedwater system due to this steam demand increase is neglected. However, there will also be an increase in steam demand for condensate heating if the steam flow through condensing turbines, MT,s,tturb, is increased compared to the reference turbine condensate flow, Mtrefcond. The enthalpies, hfw, hcw, hj, refer to the enthalpies of feed water, condensate water and steam at header j.

Some process steam demands, such as steam used for feed water pre-heating, vary with boiler load. This boiler load-dependency has been neglected in the model (see Model simplifications and development needs section for a discussion about this simplification).

Energy balances for steam headers are given by Equation (27), where hT,sext represents the estimated enthalpy of the extraction flow from a turbine stage. In reality, this will vary with the steam flow through the turbine stage, but to keep the linearity of the model, a constant estimated value is applied.

Process data and capacity constraints for the pulp mill

Data for steam production and consumption at the mill was collected from the mill’s data information system. However, not all steam flows are measured and, consequently, some steam demands were calculated from mass and energy balances.

The heat content of black liquor fuelling the recovery boiler varies over time. The main causes of this variation are the different raw material campaigns, which lead to different compositions of the black liquor, and variations in the pulp production rate. The operation of the recovery boiler is determined by the need to process black liquor for regeneration of cooking chemicals. The steam production therefore varies according to the variations in flow and heating value of the black liquor (see Figure 2).

Figure 2

Reference steam production in the recovery boiler (RB) and process steam consumption at different pressure levels. Daily averages according to measurements 2017. Days which deviate significantly from normal operation are excluded.

Figure 2 also illustrates the variations in steam demand. For the low-pressure (4 bar(a)) steam demand a slight seasonal variation can be noticed in addition to the day-to-day variations. The demand as well as magnitude of variations are much lower for other steam pressures.

As a source of data for the prospective new mill with the new pulp production line, mass and energy balances were available for four different operating scenarios. However, data for day-to-day variations were not available. Since current variations in steam production and consumption are due to a large extent to changes between hardwood and softwood campaigns, and the new production line will operate only on softwood, it is not reasonable to scale up current variations to the new production level. Instead, and partly due to lack of other information, we chose to neglect any potential new variations in operation above those already occurring at the mill. Consequently, the production increase was modelled by adding a constant demand of steam at the steam pressures needed for the new production line and a constant increase in black liquor heat flow to the recovery boilers (see Production increase section).

More input data for the pulp mill is presented in the Appendix section. This includes, e. g., performance data for turbines (Appendix A) and boilers etc. (Appendix B).

Investment costs

The investment cost data used in the model is presented in Appendix B, Table B.1. This includes the investment costs for turbines and the investment cost for the lignin extraction plant. Cost functions for turbine investments are based on literature (Axelsson et al. 2006) and updated using the Chemical Engineering Plant Cost Index (CEPCI). However, the investment cost function for lignin extraction from the same literature source is more uncertain, since it was estimated at an early stage of technology development before the first actual commercial-scale investments were made. In this analysis, the cost function based on Axelsson et al. (2006) was therefore updated using CEPCI and thereafter adopted using a cost-correction multiplication factor of three. This was based on more recent indications from industry, ongoing research projects and press releases from the first commercial plants (Stora Enso 2013), all of which indicate that there are reasons to expect the investment cost to be substantially higher than suggested by the early estimations.

Energy market data

It was assumed in this study that the mill will continue to have a positive bark balance in all scenarios studied. This means that the mill will continue to export bark, and not have to purchase any additional wood fuel for operation of the bark boiler. We assumed a sales price of bark that is about 20 % lower than the market price of wood by-products in Sweden during 2018 (16 €/MWh (Swedish Energy Agency 2019a)). In practice, the price for selling bark varies over the year, mainly due to variations in the demand for solid biofuels for heating purposes in Sweden. The price can be as low as 10 % of the market price of higher quality wood by-products during extreme periods. However, it is possible to store bark for short periods of a few weeks. It was therefore assumed that during periods of low market demands, the bark storage is filled, to allow for selling the bark at a higher price once the demand increases again (see also Uncertainty in market parameters and costs section).

Lignin was considered to be valued higher than wood fuels, due to its potentially more valuable uses, for example as a raw material for production of biofuels, materials and chemicals (Gellerstedt et al. 2013, Téguia et al. 2017). Instead of explicitly modelling the direct operating costs for chemicals and electricity consumption in the lignin extraction plant, a net operating margin (= lignin price – operating costs for electricity, CO₂ and chemicals) was used. As a reference case, this operating margin was assumed to be 20 €/MWh, implying that the lignin needs to be sold for a somewhat higher price to be able to cover operating expenditures and still make the operating margin of 20 €/MWh. For comparison, the assumed lignin operating margin of 20 €/MWh is about 25 % higher than prices for wood fuels in Sweden 2019 (Swedish Energy Agency 2019a) and in the lower range of estimated future willingness-to-pay for biomass (Pettersson et al. 2020). Note that changes in steam and power production due to lignin extraction are explicitly included in the model and therefore not reflected in the lignin value. Neither is the value of the potential for pulp production increase captured in this value. This follows from the assumption that the pulp production is given, and not affected by variations of the lignin extraction rate.

For electricity prices, the reference price variation profile was determined based on daily average prices from the NordPool spot market (price area SE4) for the year 2017. However, the spot prices were relatively low during 2017. To construct alternative price profiles, new electricity generation capacity at the mill was assumed to be eligible for green electricity certificates (Swedish Energy Agency 2019b) (see Appendix C for more information) and the higher electricity spot prices and certificate prices from 2018 were applied. Note that the price of green electricity certificates is expected to drop significantly in the near future (Energimyndigheten 2018) which is why revenues from sales of certificates were not included in the standard model and base case price profile. The different price profiles considered are shown in Figure 3.

Figure 3

Daily electricity prices during 2017 and 2018. Prices from the NordPool spot market (SE4). In one series, the monthly spot close price for green electricity certificates is added to the electricity spot price. Sources: (Nord Pool 2017, 2018, Swedish Energy Agency 2018).

Figure 4

Model validation. Calculated and measured total electric power generation.

Model validation

The model was validated for current operating conditions by running the optimization with data for 2017, a constraint that sets all investments to zero, and constraints that fix the bark boiler steam production to the measured values for the same year. Since the recovery boiler steam production is fixed by default, the total steam production and process steam demands are then given, implying that the electricity production calculated by the model can be expected to be close to the measured electricity production. Figure 4 shows the calculated and measured electricity production.

The small deviations that are shown between measured and calculated electricity production can be explained by the following arguments:

1. The model optimizes the distribution of steam between the different turbines and assumes no unnecessary steam flow through let-down valves. In reality, the turbines might not be operated optimally, and some let-down valves might be open.

2. The model uses daily average values for the steam flows. In reality, the steam flows might vary significantly during a day. The non-linear relation between turbine efficiencies and steam flow might then cause a different average efficiency compared to what is estimated in the model.

3. Measurement errors could be an additional source of deviations.

Figure 5

Optimized electric power generation in existing turbines. Current operation of the mill.

Figure 6

Comparison between optimized and measured steam production in the bark boiler for the reference case representing current operation of the mill.

Optimal investments for current pulp production

First, the model was run with data representing pulp production levels and market prices of 2017. For this case, the investment cost for lignin extraction is too high in relation to the value of lignin and no investment is proposed by the model. Furthermore, the relatively low electricity prices in 2017 favours a reduced use of bark over electricity production, which causes the model to set the bark boiler operation at minimum load for most of the time, providing no incentives for investments in new turbines. When the bark boiler is at minimum load, the large variations in steam production from the recovery boiler due to shifting wood campaigns end up in the existing condensing turbine (T6), see Figure 5.

Figure 7

Optimized electricity generation, lignin extraction and bark use for the mill after the production increase and optimized investment in lignin extraction.

In reality, the bark boiler was operated well above the minimum load from March to August, as seen in Figure 6, while the model suggests minimizing the bark use during those months. Currently, no optimization-based decision support system is used at the mill for operating decisions in the steam boiler and turbine system. However, fuel and electricity prices are monitored continuously, and general relations between bark boiler and turbine loads are used together with rules-of-thumb to guide operational planning. According to mill personnel, the actual operation of the bark boiler (and condensing turbine) is at least partly explained by a low demand for bark on the biofuel market during the summer period, which together with difficulties associated with storing bark makes it better to combust the bark on-site (see also discussion in Uncertainty in market parameters and costs section).

Production capacity increase

Production increase – Reference case

This case applies the same basic assumptions as for the case of current pulp production, but adds increases in steam demands and black liquor heat representing the operation of a new production line (see Production increase section). Mill operating conditions were assumed to vary according to data from 2017, and market prices for 2017 were assumed.

Figure 7 shows the optimized lignin extraction, electricity generation and bark use over the year. Due to low electricity prices, relatively high lignin prices, and the requirement to invest in at least a small lignin extraction plant, this scenario strongly favours the investment in lignin extraction. This results in a solution with investment in a 209 MW lignin extraction plant, corresponding to a lignin extraction capacity of approximately 258 000 tonnes/year. This is more than four times the prospected capacity of 60 000 tonnes/year. Investment is also made in a new 37.5 MW back-pressure turbine.

With this huge capacity of the lignin extraction plant, the extraction rates become limited by the available black liquor flow and the assumed maximum lignin removal from black liquor as specified by Equation (12). This means that care must be taken about the uncertainty in this limit to ensure that stable recovery boiler operation can be maintained. Nevertheless, according to the model, most days of the year, the lignin extraction is maximized, either against the capacity of the lignin extraction plant (Equation 13) or against the available black liquor flow (Equation 12). Similarly, the bark boiler load is also typically minimized. This means that the total steam production is minimized, which leaves very little or no excess of steam for condensing power production. As a result, the model shuts down the existing condensing turbine in order to maintain the high lignin extraction rates while avoiding operating the turbine at too low loads. Note that the model does not allow for on/off operation of the turbines, i. e., the turbine must either always be on, or always off.

As a consequence of shutting down the condensing turbine, there will be significant amounts of steam vented to atmosphere during certain periods (see Figure 8). However, in some periods, depending on the operating conditions, the minimum steam production is not sufficient for covering the process steam demands. In these periods, the load of the bark boiler is increased, and if this is not sufficient, the lignin extraction rate must be reduced to allow for more steam production in the recovery boiler.

Figure 8

Optimized operation of new back-pressure turbine and steam vent resulting from shutting down the condensing turbine. Production increase scenario with investment in a huge lignin extraction plant.

Production increase – Higher electricity prices

The results above indicate that with the applied assumptions there is little value in generating electric power in a condensing steam turbine considering that not even the existing condensing turbine is utilized. However, electricity prices were low during 2017. To analyze the effect of the electricity price the model was run with electricity prices from 2018. Here, we also included the 2018 prices of tradable green electricity certificates for any electricity generation above the currently established normal year production (see Appendix C). Note that the price level for certificates observed in 2018 are not expected to be representative of future values. Nevertheless, these were included to simulate a price scenario with significantly larger price variations over the year.

In this case, electricity production is strongly favoured over lignin extraction. The optimal investment in lignin extraction is at the minimum capacity required for debottlenecking the recovery boilers (39.2 MW) and investment are made in both a new back-pressure turbine (50.9 MW) and in a new low-pressure condensing turbine (16.5 MW). A clear trend can be seen over the year with increasing electricity production and decreasing lignin extraction rates due to increasing electricity prices (see Figure 9). In particular, the price of tradable green certificates increased substantially during the second half of the year (see Figure 4). Lignin extraction even goes down to zero in periods when no debottlenecking is required, typically, during hardwood campaigns when the black liquor heating value is lower.

Figure 9

Optimized electricity generation, lignin extraction and bark use for the mill after the production increase and optimized investment in lignin extraction plant assuming a low investment cost for lignin extraction and electricity prices from 2018.

These results represent an especially interesting case for two reasons. Firstly, during the second half of the year, operation of the lignin extraction plant contributes to adapting the mill electricity production to electricity price variations. The variations in lignin extraction are not explained directly by electricity price variations, but above a certain electricity price, lignin extraction is no longer kept constant at maximum rate. In fact, the lignin extraction rate is reduced at high electricity prices, either until the point where no more steam can be accommodated by the condensing turbines, or until the minimum needed for debottlenecking the recovery boiler is reached. Secondly, since the optimal operation varies over the year, the investment decision needs to be optimized to obtain the flexibility to respond to market variations. Therefore, the capacity of 39.2 MW for lignin extraction is required even if the annual production of lignin reaches only 28.5 MW. This scenario is therefore a good example of when a simpler model assuming annual averages would not have been able to predict the value of investing in larger new steam turbines in combination with the investment in lignin extraction.

Power generation flexibility to varying electricity prices

The results presented above (for the scenario with production increase and 2018 prices) indicates that under certain conditions it could be profitable for a mill to invest in steam turbines for condensing power generation even if also investing in the lignin extraction plant. This way the mill gets increased flexibility to steer energy production towards either biofuels or electricity, depending on the market prices. It should be recognized that these operational adjustments are likely to be slow, and that this flexibility is probably only obtained for variations on hourly to daily scale.

Some of the variations in electricity generation given by the model are due to variations in electricity prices, but the variations in electricity generation are also a result of varying process conditions. To estimate the magnitude of the power generation flexibility for the mill if it invests in a lignin extraction plant and a new low-pressure condensing turbine, the model was solved with fixed investments according to the solution presented in Production increase – higher electricity prices section, i. e., investment in a 39.2 MW lignin extraction plant, a 50.9 MW back-pressure turbine and a 16.5 MW low-pressure condensing turbine. The model was then solved once with a constant high electricity price, and once with a constant low electricity price. This way, two distinct operating modes were simulated, one in which fuel use is minimized given the investments made (by maximizing lignin extraction and minimizing the load of bark boiler), and one in which electricity generation is maximized. The resulting electric power generation over the year is shown in Figure 10.

Figure 10

Resulting optimized electric power generation for a given investment (39.2 MW lignin extraction capacity, 50.9 MW back-pressure turbine, 16.5 MW low-pressure condensing turbine) assuming a constant, high electricity price (max electric power generation) or a constant, low electricity price (max lignin extraction).

The difference in electric power generation between the two operating modes in Figure 10 would be the potential production flexibility given this investment package. To highlight the distance between the two curves, the difference in electric power generation is plotted and sorted according to magnitude in a load-duration curve, see Figure 11. Figure 11 shows that the potential power generation varies between approximately 15 and 30 MW, and that it is above 20 MW for about 3/4 of the year.

Figure 11

Load-duration curve of potential power generation flexibility for a given investment (39.2 MW lignin extraction capacity, 50.9 MW back-pressure turbine, 16.5 MW low-pressure condensing turbine), calculated as the difference in electric power generation between an operating mode with maximized electricity production and an operating mode with maximized lignin extraction and minimized load of the bark boiler.

Influence of variations on optimal solution

Could the results presented above have been obtained by a simpler investment model accounting only for annual average process conditions and market prices? For some of the scenarios this is likely. However, whether the variations influence the results or not depends on a number of different parameters and assumptions and it is difficult to predict a-priori if the more advanced model proposed in this paper will give a different result than a single-period model.

To illustrate the differences that can result from using this model compared to a single-period model, a few scenarios with different combinations of lignin and electricity prices were investigated in some more detail. For every such scenario, the multi-period model was solved, as well as the corresponding single-period model using annual average process data. The solutions obtained were compared with regards to optimized lignin extraction capacity, optimized new turbine capacity, and annual bark use, lignin extraction and electricity generation. The results are shown in Table 1.

Table 1

Comparison of optimization results for multi-period and single-period models under different price scenarios.

In the price scenarios with higher lignin prices and electricity prices from 2017, the annual-average model identifies a lignin extraction capacity and an annual electricity production that are similar to the results from the multi-period model. The single-period model does slightly underestimate the new turbine capacity required to reach this annual electricity production. However, the most notable difference between the single-period and multi-period model results in these two scenarios is that the bark use is significantly underestimated. In the multi-period model, the bark boiler load is used to cover steam deficits in time periods when the recovery boiler steam production is low compared to the steam demand while in other time periods, steam is produced in excess and vented. In the single-period annual average model, on the other hand, the bark boiler operation can be exactly matched to balance the constant recovery boiler steam production and process steam demands and no heat is lost for venting.

Table 1 also shows that the single-period model fails to capture the required capacity for lignin extraction for off-loading the recovery boiler. By averaging the heat flow to the recovery boilers over softwood and hardwood campaigns, the available recovery boiler capacity is falsely determined to be sufficient. Consequently, the optimum lignin extraction capacity is determined to be 0 MW for several scenarios using the single-period model. To improve the quality of the solution from the single-period model, it was also solved with an additional constraint requiring that the capacity of the lignin extraction plant should be greater than or equal to 39.2 MW. The resulting solutions are shown in Table 1. However, with this constraint, the single-period model instead underestimates the turbine capacity required to reach a certain annual electricity production. Note especially that the condensing turbine investment is overlooked in the 2018 scenario with 20 EUR/MWh lignin price. Furthermore, this model cannot reliably predict the annual lignin extraction given a certain lignin extraction capacity, which is particularly apparent in the 2018 scenario with 15 EUR/MWh lignin price, where the annual lignin extraction is zero despite the forced investment.

Figure 12

Electricity price duration curves for current (solid line) and possible future conditions in 2030, 2040 and 2050 (dashed lines). Current electricity prices refer to spot prices for Swedish price area SE4 for year 2018. Future prices represent modelled scenarios for the short-term marginal electricity generation cost for the same price area in different years assuming strategic collaboration between sectors. Data is extracted from results generated using the model presented in Göransson et al. (2019).

Uncertainty in market parameters and costs

No detailed assessment of the bark balances was made in this study. The use of bark as fuel in the bark boiler was simply associated with an alternative cost representing the lost sales of bark on the fuel market. After optimization, we checked that the resulting bark use can be covered by the bark available (roughly estimated) at the mill. As mentioned in Energy market data section, the price for selling bark is characterized by significant seasonal variations, since the bark is mainly used for heating purposes, and the demand therefore varies significantly with the outdoor temperature. In our model it is assumed that bark can be stored at the mill site, to allow for sales at a higher price level. However, while bark can be stored for short periods of up to a few weeks, there are challenges associated with longer storage such as risk of self-ignition. In reality, there might therefore be incentives for burning bark at the mill instead of storing it when the demand is low. This could, for example, be part of the explanation for the results shown in Figure 6. Currently, effects related to varying bark demand, bark balances and storage are not captured in the model. Possible developments could be explicit modelling of bark generation and storage capacity, or a price model representing the seasonal demand variations, or a constraint representing different maximum bark exports during different time periods.

The market for lignin is also highly uncertain. The value of lignin could range from its fuel value to significantly higher values, especially in potential future applications. However, the latter might also require additional investments at the mill for further processing of the lignin. Depending on the application considered, and the corresponding assumed value of lignin, the market demand will also be different. In our model runs, we have tried different values of lignin, but in this article, we have not shown any results from these sensitivity analyses. The assumed lignin value is quite high for a wood fuel, but not very much higher. However, even with this modest lignin value, a very large lignin extraction capacity (209 MW), which corresponds closely with the assumed maximum lignin removal from black liquor, is identified as the optimal solution for the production increase (see Production increase – Reference case section). A more important uncertainty with regards to the lignin extraction investment is the capital cost, which has a strong influence on the optimal solution. In our model, an increase of this investment cost would quickly lead to results where the lignin extraction capacity is simply minimized.

It should be noted that without investment in a low-pressure condensing steam turbine, the possibility for flexible electricity production is drastically reduced. The electricity production in the back-pressure turbines is closely connected to the process steam demand and not flexible in the same way. With the electricity prices assumed in this work, investment in a low-pressure condensing turbine is, however, only favourable if rather high prices are assumed for green electricity certificates. Considering that prices of such certificates are expected to drop significantly in the near future, the power generation flexibility of pulp mills might not become very pronounced after all. Nevertheless, the mill is considering investment in a condensing turbine. Such a decision could be explained by the large uncertainties related to investment in lignin extraction, in combination with the above discussed difficulties to sell excess bark. The investment cost assumed for the condensing turbine in the model may also differ from the costs assumed by the pulping company.

The spot price for electricity can also be expected to change in the future. In Figure 12, the daily average electricity spot prices from 2018 are plotted as a price duration curve, which is compared to examples of possible future scenarios for short-term marginal electricity generation costs based on models developed by Göransson et al. (2019) with a 3 hour resolution. In the future scenarios, the shares of intermittent electric power generation from solar and wind increase due to successively more stringent targets on greenhouse gas emissions as well as an assumed cost reduction for wind and solar power plants. This leads to more hours with low prices (when it is windy and/or sunny), but also to higher prices when the capacity is limited. For these particular scenarios, it was assumed that there will be strategic collaboration between the electric power generation sector, an electrified steel plant, the electrified transport sector in the form of passenger electric vehicles, and residential heat supply, which enables severe price peaks to be avoided.

Based on our results, the pulp mill will only exploit operational flexibility towards the electricity market if the prices are high enough during a sufficient length of time to motivate investment in a condensing turbine and also low enough during a sufficient length of time to not simply maximize the utilization of that turbine capacity throughout the year. Figure 12 indicates that in 2030, the price between approximately 1000 and 4000 hours is estimated to be at a similar level to the prices of 2018, which were used in our model. However, for about half of the hours of the year (4000 hours and above), the prices are estimated to be notably lower, which means that it will be less attractive for the mill to invest in a condensing turbine. Admittedly, the price peaks are also higher in the 2030 scenario, but only during a limited number of time periods, and are therefore not expected to significantly increase the willingness to invest in electric power generation capacity in the mill. The scenarios for 2040 and especially 2050, involve many hours (>3000) of prices that are significantly higher than the prices of today, while also showing many hours of low (and very low) prices. Under such conditions, the high price periods might motivate investment in a condensing turbine, while the low price periods would favour lignin extraction.

No optimization runs were performed for the future price scenarios. Such a long-term perspective would require reconsidering a number of other assumptions in the model, e. g. future development of bark and lignin prices, future investment costs, and future financial incentives. Because of this uncertainty, and the large number of possible future scenarios, it was determined that such simulations would not add a significant value to the current study.

Model simplifications and development needs

Our previous models (Svensson 2014, 2015) allowed for starting and shutting down boilers and turbines as a response to daily variations in steam demand. However, potential costs or difficulties associated with starting and stopping equipment were not considered, and even if the steam demands and energy prices fluctuate significantly between days, it will not be technically or economically feasible to frequently start-up and shut down boilers, turbines and lignin extraction equipment. For this work it was therefore decided to not allow for any on/off operation of equipment. Further work could be motivated to include the costs and time required for start-ups and shut-downs in the model, to enable on/off operation for more long-term operating scenarios, such as seasonal variations. It could, for example, be motivated to have a boiler in operation during winter, but shut it down during summer.

The models of turbines and boilers could potentially be further developed also in other respects. Examples include how to constrain the steam flows through individual turbine stages and extractions. For example, a minimum extraction flow might be as relevant as the maximum extraction flow used for existing turbines. Similar constraints for new turbines should also be considered, but need to be associated with some cost function to be relevant. The effect of variations in cooling water temperature on the power output of condensing turbines should also be included in future models. Other examples of potential future developments include a more detailed modelling of steam condensates and boiler feed water preparation systems, as well as internal steam demands of the boilers and own electricity consumption that depends on turbine and boiler loads.

As described in Model input data for the case study section, the model was solved for 352 days of one year. Some of the other 13 days were excluded because of a maintenance stop at the mill, where the entire production was stopped. The remaining days were excluded because measurement data deviated too much from normal operation for different reasons, which lead to violations of constraints in the model. For example, days were excluded for which the daily average of a boiler or turbine load was less than the minimum load limit set in the model. In reality, the load has probably not been constantly below the minimum load, but for example, a boiler may have been out of operation during part of the day, and at part-load during the rest of the day, which leads to the observed constraint violations when averaging the measurement values. Better model accuracy could be obtained by dividing these days (and other days with big changes in operating conditions) into shorter periods. However, this improvement in accuracy was considered to be negligible in comparison to other large uncertainties affecting the model results, e. g. prices and investment costs.

The current version of the model has a time resolution of one day, and process data as well as prices are averaged over these time periods. While this approach leads to some problems since conditions may change significantly during a day, there are other challenges associated with using shorter time periods. One challenge is related to the computational effort required if solving the model with significantly higher number of time steps, especially since some model instances are already cumbersome to solve on a standard desktop computer. However, this could be handled by modelling time slices as, e. g., representative hours. Since no storage is considered in the model, this would be rather straightforward modelling-wise. However, identifying the representative time slices could be difficult due to the large number of varying parameters, with different and sometimes uncertain degrees of correlations. Furthermore, while it would be beneficial to use a higher time resolution to capture, for example, hourly electricity spot price variations, this is not necessarily advantageous for capturing different process conditions. Changes in the process, such as a change in production campaign to another type of raw material, may take several hours to propagate through the different process units. For a single hour during such a transition, it is likely that steady-state balances do not accurately represent the system. While it may be motivated to put large efforts into identifying representative time slices (of various duration) for an energy systems model used, e. g., in regional energy policy planning or scenario analysis (see e. g. Poncelet et al. 2017, Reichenberg et al. 2018), this is more doubtful for investment optimization in an individual mill where other uncertainties (such as investment costs) are likely to be more important for the investment decisions.