New mathematical models were introduced for RAM optimisation in waste management.
They cover some specific WMS parts and consider all the features that affect availability, reliability and maintainability. The following ones were considered in each model in addition to the specific statements and assumptions described along with the definitions:
• Consider repairable and non-repairable system components
• Distinguish series and parallel subsystems
• Consider the changes of unit failure rates according to age and replacement
• Differentiate operating classes
• Handle independent, mutually exclusive and conditional probability of failure
• Identify units in partial operation 5.1.1 Solid waste combustion models
Two solid waste combustion models were introduced by the Author, namely the reliability model for waste drying and that of energy conservation, respectively. The models were prepared for a two-stage reciprocating waste incinerator where the waste undergoes drying, pyrolysis, and combustion along the grate after entering the incinerator.
The distributions of temperature, wastes and mass flowrate of gas are non-uniform. The temperature of the gas from the drying and pyrolysis sectors is lower, and contains lots of oxygen and unburned hydrocarbon. The gas from the combustion zone is hotter and scarce in
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oxygen. These gases will then mix with the secondary air and burn in the combustion chamber above the waste bed, while exchanging heat with the waste bed and furnace walls.
Both models apply assumptions. The initial assumptions are used to form the basic (ideal) case. Later, these models will be extended in order to meet all criteria. The solid waste entering the process is homogenous. The operation of the thermal treatment plant is stable. This assumption can be avoided by perturbating the process with reliability. Additionally, it is assumed that the waste moves continuously with contstant speed in the direction of the grate.
Again, this should not be included if availability and reliability are taken into account. The height and width of waste are within the allowable constraints. The treatment of bulk wastes can be considered for more realistic modelling. For the basic models, the heat exchange between the furnace wall and the surrounding areas was not included. The distributions of temperature and species, used as the boundary conditions of gas phase combustion above the bed, are determined by the numerical simulation of solid waste burning.
5.1.1.1 Availability model for waste drying
Due to the variety of waste management equipment units and technologies it is hard to set general models. Thus the system type should be well defined. The mathematical model of the Author was developed for two-stage reciprocating waste incinerators where solid waste reaches the drying process after entering the plant. Heat and water mass transfers are simultaneous and are in opposite directions. Furthermore, there are some assumptions for which the definitions held. Most important of all, it is assumed that all units should be available in order to achieve overall availability. The operation of the thermal treatment plant is stable. The solid waste that enters the incinerator is originally homogenous. Waste velocity should be constant.
The availability of air transfer for such cases can be defined as
( )
where i represents all combustor units to consider. Typically they are the following units:
inlet fan, decoupling chamber, mixing chamber, membrane valve for inlet air, pressure transducer, pipe to dryer, anti-explosion valves, nozzle, drying chamber. The list of units depends on the type of the dryer and can be customized according to it.
j represents measuring apparatus including
• Temperature sensors for measuring air temperature t [°C]
• Air density measurement equipment for measuring air densityρa [kg/m3]
• Air velocity meter for measuring velocity va [m/s]
• Humidity meters for measuring the difference between absolute outlet and inlet air humidity, i.e. Hao and Hai [kg/kg]
Note that the main assumption can be missed and Eq. 5.1 altered for more specific definitions. Thus the equation can be customized.
5.1.1.2 Reliability model for thermal treatment
The probability of failure occurrence of equipment units in two-stage reciprocating incinerators can be described as
(
P P1∩ 2)
⋅(
P3∪ ∪P4 P5) (
⋅ P6∪ ∪P7 P P P P P8)
⋅ ⋅ ⋅ ⋅P S T(
9∪P10∪P11)
(5.2)where the numbers denote the probability of failure occurrence in the following equipment units:
Proposed methods in WMS analyses 8) Refractory wall (combustion chamber) 9) Ports
10) Temperature sensors 11)Sampling tubes or LASER
P represents the magnetic, S the non-ferrous and T the pneumatic separators, respectively.
Since P9, P10 and P11 are, in contrast with P3, P4, P5 and P6, P7, P8, mutually exclusive, the probability of separator failures should be calculated differently as described in probability theory.
The reliability of solid waste combustion in thermal treatment plants described above can be defined as
The model was developed with focus on units that are required for burner processes. It can be extended with the number of sensors, other equipment units and further subsystems of treatment plants.
5.1.2. Optimisation model for reliability of waste recycling
Waste recycling can be performed in various ways. The model introduced by the Author considers the reliability of equipment units from collection and transportation through material recycling andreprocessing. It includes the separation of materials into their constituent parts. The reliability of recycling for such systems, in general, can be defined as
1 1 RC is the reliability of separate waste collection facilities for recycling paper, heavy plastic, plastic bags, plastic bottles, glass, organic material, wood, metals, textiles etc. Such values can be used for decision variables in optimisation. RM is the reliability of material recycling facilities such as conveyor belt, magnets, and screening devices. RS is the reliability of equal spares. RR is the reliability of reprocessors that handle the various materials including heater for metal and glass, coverters for plastic to produce granulate or pellet, the pulper and shredder facilities for paper and so on. Their reliability factors are therefore mutually exclusive. The small letters represent the following:
• n is the number of separate waste collection facilities
• m is the number of material recycling facilities
• p is the number of reprocessing facilities
• q is the number of equal spares
Scraps, residues and inert matters sent to recycling can be considered as well upon request (not included in the basic model).
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If the component groups in parallel contain partial redundancy with individually duplicated components, the following definition can be derived from Eq. 5.4:
where n is the number of waste collection units in parallel with b individually duplicated components. Analogically, c is the number of material recycling equipment units in parallel with d duplicated components while f is the number of reprocessor units and g represents the number of duplicated units.
If u unequal components are considered in parallel, RCu represents the probability that all u waste collection components will survive time t.
u 1
C C
uR Q− is the probability that u−1will survive and one will fail while uR QC Cu−1represents the case when one component will survive and u−1 will fail.
Cu
Q means that all u waste collection equipment units will fail in time t.
Similar probabilities can be described for the material recycling facilities and reprocessors.
The optimisation of waste recycling with the structure decribed above is the maximisation of the value of the reliability function:
maxRWR (5.6)
subject to
a, b, c, d, f, g ≥ 1,
n, m, p ≥ 1 and are integers, q, s ≥ 0 and are integers.
RAMS software packages solve such problems in addition to reliability estimation and calculations.