• Introduction
• Modelling the materials/product life cycle
• Temporal system boundary treatment
• MARKAL datasheets
• Data collection method
• Conversion of literature data into MARKAL input
• Example poplar

The energy system can be modelled as a set of linked chains from recovery of natural energy resources to the final energy use. The materials system is more complex because materials and products can be recycled. This makes an important difference for the model structure (Figure 1).

Figure 1: The life cycle structure in the materials system model

ll other processes are defined as "black boxes" with a fixed ratio of annual inputs and outputs of energy carriers, materials, products, waste products and waste materials. Apart from inputs and outputs, processes are characterised by investment costs, annual fixed costs, and variable costs that are proportional to the production. The technical life of the installation is also considered. The existing capacities at the beginning of the model period can be defined. Bounds for capacities or bounds for annual production can be added to represent barriers for capacity expansion or barriers for capacity reduction.

It is possible to add for example an additional flow variable of "product parts" and a process "product part manufacturing" between materials and products, or to add a flow that represents the reuse of waste products. Such additions do not fundamentally change the model structure, and can be incorporated into the MARKAL framework. Too much detail can however deteriorate the insight into the analysis results. Because the bulk of the GHG emissions in the product life cycle is concentrated in materials production, product use and waste handling, the model structure in Figure 1 includes the key processes from a GHG point of view.

The model structure is generic: the subdivision into materials and products can be chosen by the model user. The model can be used to assess the impact of the aggregated materials consumption. The choice of a region, technologies, the demand for products and the time horizon can be set by the model user.

Temporal system boundary treatment

The time horizon in this analysis will be approximately half a century (2040-2050). This long term is necessary because a much shorter time horizon will only show small emission reduction potentials because of the slow replacement rate of the capital equipment. Major technological change takes generally decades. Moreover, current materials consumption will affect the waste release in a period of decades. In order to study this interaction, a time horizon of decades is required. A much broader time horizon makes little sense because the scope of system configurations and the uncertainty in technological development precludes sensible scenario building. Moreover, a time horizon of more than 50 years has generally little relevance for policy making. For a practical reason, the calculations will be extended to the year 2070. The model results for the last decades can be influenced by boundary conditions. Therefore, model calculation results for the period beyond 2050 are not reported because of potential effects of the system boundary on the system configuration in these periods.

For example waste materials that are released beyond the time horizon may affect the modelling results in the last two decades; the trade-off between direct emissions (during product use) and indirect emissions (during product manufacturing) may change. For example, it is not attractive to invest in a building with a low heating energy demand but with higher initial costs for insulation, if the life span extends far beyond the model time horizon. This problem is to some extent tackled by a salvage value (that reflects the residual value beyond the time horizon), but the determination of a correct salvage value is problematic for products that result in waste materials beyond their product life. For a period of more than two decades (2050-2070), the cost discounting effect ensures that costs or benefits beyond the product life are of minor importance for the modelling results for earlier decades. This is reflected in the modelling results where sudden changes in investment decisions and energy and material flows are limited to the period beyond 2050: this is a strong indication that this approach works.

Western Europe, the system that is studied with MARKAL, represents to a large extent a closed system. The allocation of resources that can be produced through different production processes, or the allocation of the environmental impacts of different waste treatment processes that are applied for one material, is problematic in chain analysis. A closed systems approach prevents allocation problems.

Costs are discounted in MARKAL. Because environmental impacts are endogenised in the costs, they are also discounted. All costs for the period 1990-2050 are translated into ECU for the base year 1990.

The dynamic approach allows the analysis of the relation between materials consumption and product demand in one year and waste release in the following years. This is a major difference with the static analysis approaches such as LCA and MFA (see Figure 2). The long time horizon allows identification of more substantial environmental improvement potentials. It can provide new insights regarding the complex relation between current materials consumption and future recycling and energy recovery possibilities.

Figure 2: Temporal system boundaries for the dynamic MARKAL approach compared to the static LCA and MFA approaches

Data input into and output from MARKAL is handled by the MARKAL User Support System (MUSS). Processes are characterised by two ‘datasheets’. One sheet describes the physical inputs and outputs (of energy and materials). The other sheet characterises the economic data and the other process data. The input data structure depends to some extent on the process that is characterised. Data for different types of power plants, for conversion processes, and for end-use technologies are characterised in different ways for a data structure description for energy technologies). For the modelling of processes in the materials system, two process types are relevant: conversion processes (materials production, product assembly, waste handling: processes no. 1,2,3,5,6, and 7 in the materials/product life cycle Figure 1) and product use processes (no. 4 in Figure 1). A schematic example of the input for conversion processes is shown in Table 1. The modelling is identical to the modelling of energy conversion processes. The data input is split into nine time periods (columns dubbed 1..9). The length of a time period is set by the model user (5 or 10 years). One column is reserved for time independent variables (TID). The physical data do not represent the total mass- and energy balance where input equals output (because of flows that are not accounted). The cost characteristics of the processes are split into investment costs (that are proportional to the installed capacity), fixed annual costs (proportional to the installed capacity) and variable costs (proportional to the production volume). The use of processes can be bounded by the model user, based on policy plans and other long term constraints. However such bounds must be applied with care in order to allow a sufficiently broad ‘window of feasible system configurations’.

Increasing process efficiency is modelled by decreasing inputs per unit of output (such as for energy carrier A and material A in Table 1). In a similar way, decreasing costs or changing bounds can be modelled.

Table 1: MARKAL model data structure for a conversion process

Sheet 1: Physical flows	Period	Unit	TID	1	2	3	4	5	6	7	8	9
Inputs	Energy carrier A	[GJ/unit]		2.0	1.9	1.8	1.7	1.7	1.7	1.7	1.7	1.7
	Energy carrier B	[GJ/unit]		1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0
	Material A	[t/unit]		5.0	4.5	4.2	4.0	4.0	4.0	4.0	4.0	4.0
Outputs	Energy carrier C	[GJ/unit]		0.1	0.1	0.1	0.1	0.1	0.1	0.1	0.1	0.1
	Product A	[unit]		1	1	1	1	1	1	1	1	1
Sheet 2: Other data
	Investments	[ECU/unit cap]		100	100	120	120	120	120	120	120	120
	Fixed annual costs	[ECU/unit cap./yr.]		5	5	5	5	5	5	5	5	5
	Variable costs	[ECU/unit]		2	2	2	2	2	2	2	2	2
	Delivery costs	[ECU/t A]		1	1	1	1	1	1	1	1	1
	Availability factor	[unit/unit cap]		0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9
	Life	[periods]	2
	Start	[period]	1
	Residual capacity	[unit cap]		2	0	0	0	0	0	0	0	0
	Maximum capacity	[unit cap]		5	10	50	50	50	50	50	50	50
	Minimum capacity	[unit cap]		0	0	0	0	0	0	0	0	0

The model input for a product use process is shown in Table 2. This type of processes has been developed especially for materials modelling in order to account for materials storage in products. The major difference compared to other processes is the modelling of the acquisition of one unit of product when the investment is made and the release of a unit of waste product beyond the product life. Both flows are shown in the column TID. In this case, the product life span is 2 periods (equal to 20 years). The model accounts for the waste material release 20 years after the product acquisition. The annual flows in columns 1-9 represent the average annual inputs and outputs related to the product use and the product maintenance.

Table 2: MARKAL model data structure for a product use process

Sheet 1: Physical flows	Period	Unit	TID	1	2	3	4	5	6	7	8	9
Inputs	Product A	[unit]	1.0
	Energy carrier a	[GJ/unit]		1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0	1.0
	Material A	[t/unit]		5.0	4.5	4.2	4.0	4.0	4.0	4.0	4.0	4.0
Outputs	Waste product A	[unit]	1.0
	Product service A	[unit]		1	1	1	1	1	1	1	1	1
Sheet 2: Other data
	Investments	[ECU/unit cap]		-	-	-	-	-	-	-	-	-
	Fixed annual costs	[ECU/unit cap./yr.]		-	-	-	-	-	-	-	-	-
	Variable costs	[ECU/unit]		2	2	2	2	2	2	2	2	2
	Delivery costs	[ECU/t A]		1	1	1	1	1	1	1	1	1
	Availability factor	[unit/unit cap]		0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9	0.9
	Life	[periods]	2
	Start	[period]	1
	Residual capacity	[unit cap]		5	0	0	0	0	0	0	0	0
	Maximum capacity	[unit cap]		10	100	100	100	100	100	100	100	100
	Minimum capacity	[unit cap]		0	0	0	0	0	0	0	0	0

Data collection method

The data compilation is based on literature sources. It can be split into six steps:

1. Process definition (process boundaries, process goal)
2. Identification of inputs and outputs
3. Data compilation for the current average process
4. Data compilation for current best available technology (BAT)
5. Estimation of future process data on the basis of literature study, BAT, extrapolation of historical trends, and thermodynamic considerations
6. Data quality estimates on the basis of uncertainty estimates