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ECO-BOND GRAPHS An Energy-Based Modeling and Simulation Framework
for Complex Dynamic Systems with a focus on Sustainability and Embodied Energy Flows
Dr. Rodrigo Castro ETH Zürich, Switzerland.
University of Buenos Aires & CIFASIS-CONICET, Argentina.
The 10th International Multidisciplinary Modelling & Simulation Multiconference
The 1st Int’l. Workshop on Simulation for Energy, Sustainable
Development & Environment
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 2
• Problem formulation – Emergy tracking & Complex Dynamics Systems
• Possible approaches • Our approach
– Networked Complex Processes – 3-faceted representation of energy flows
• The Bond Graph formalism • The new Eco Bond Graphs
– Definition – Examples – Simulation results
• Conclusions
Agenda
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 3
System Theoretic Approach
• Complex Dynamics Systems – Global scale socio-natural processes
• We live in a nonlinear world, mostly away from equilibrium
Problem formulation
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 4
System Theoretic Approach
• Complex Dynamics Systems – Global scale socio-natural processes
• We live in a nonlinear world, mostly away from equilibrium
Problem formulation
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 5
System Theoretic Approach
• Complex Dynamics Systems – Global scale socio-natural processes
• We live in a nonlinear world, mostly away from equilibrium
Problem formulation
×
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 6
System Theoretic Approach
• Complex Dynamics Systems – Global scale socio-natural processes
• We live in a nonlinear world, mostly away from equilibrium
Problem formulation
×
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 7
Storages and Processes Problem formulation
• Flows of Mass and Energy – Each process can abstract several internal sub processes
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 8
Storages and Processes Problem formulation
• Flows of Mass and Energy – Each process can abstract several internal sub processes
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 9
Storages and Processes Problem formulation
• Flows of Mass and Energy – Each process can abstract several internal sub processes
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 10
Storages and Processes Problem formulation
• Flows of Mass and Energy – Each process can abstract several internal sub processes
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 11
Storages and Processes Problem formulation
“Grey Energy”
• Flows of Mass and Energy – Each process can abstract several internal sub processes
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 12
Storages and Processes Problem formulation
“Grey Energy”
• Flows of Mass and Energy – Each process can abstract several internal sub processes
– We want to model systematically this type of systems – Structural approach Sustainability properties
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 13
• Sankey Diagrams – Static (snapshot-like) World Energy Flow.
Considering energy losses Possible approaches
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 14
• Sankey Diagrams – Static (snapshot-like) World Energy Flow.
Considering energy losses Possible approaches
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 15
Considering energy losses
• Energy System Language (H.T. Odum) – Account for dynamics Differential Eqns.
Possible approaches
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 16
Considering energy losses
• Energy System Language (H.T. Odum) – Account for dynamics Differential Eqns.
Possible approaches
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 17
Considering energy losses
• Energy System Language (H.T. Odum) – Account for dynamics Differential Eqns.
Possible approaches
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 18
Considering energy losses
• Energy System Language (H.T. Odum) – Account for dynamics Differential Eqns.
Possible approaches
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 19
Networked processes
• Multi Input/Multi Output Processes – Including recycling paths
Our approach
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 20
Networked processes
• Multi Input/Multi Output Processes – Including recycling paths
Our approach
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 21
Networked processes
• Multi Input/Multi Output Processes – Including recycling paths
Our approach
P3
P5
P1
P2
P4P6
RB
RC
RA
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 22
Focus on mass flows
• 3-Faceted representation
Our approach
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 23
Focus on mass flows
• 3-Faceted representation
Our approach
Balance: Mass and Energy
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 24
Focus on mass flows
• 3-Faceted representation
Our approach
Balance: Mass and Energy
321 EEEME ++=
1E
2E
3E Tracking: Emergy
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 25
Focus on mass flows
• 3-Faceted representation
Our approach
Balance: Mass and Energy
321 EEEME ++=
1E
2E
3E Tracking: Emergy
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 26
• Minimum required formulation – To achieve the modeling
goal systematically
• How do we formalize and generalize this structure ?
Basic formulation Our approach
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 27
• Bondgraph is a graphical modeling technique – Rooted in the tracking of power [Joules/sec=Watt] – Represented by effort variables (e) and flow variables (f)
Bondgraphic approach The Bond Graph Formalism
e f
Power = e · f e: Effort f: Flow
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 28
• Bondgraph is a graphical modeling technique – Rooted in the tracking of power [Joules/sec=Watt] – Represented by effort variables (e) and flow variables (f)
• Goal: – Sound physical modeling of generalized flows of energy – Self checking capabilities for thermodynamic feasibility
• Strategy: – Bondgraphic modeling of phenomenological processes – Including emergy tracking capabilities
Bondgraphic approach The Bond Graph Formalism
e f
Power = e · f e: Effort f: Flow
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 29
Energy domains
• Bondgraph is multi-energy domain
The Bond Graph Formalism
e f
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 30
Energy Domain
e Effort variable
f Flow variable
Mechanical, translation Force Linear velocity
Mechanical, rotation Torque Angular velocity
Electrical Electromotive force Current
Magnetic Magnetomotive force Flux rate
Hydraulic Pressure Volumetric flow rate
Thermal temperature entropy flow rate
Energy domains
• Bondgraph is multi-energy domain
The Bond Graph Formalism
e f
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 31
• As every bond defines two separate variables – The effort e and the flow f – We need two equations to compute values for these two
variables • It is always possible to compute one of the two
variables at each side of the bond.
Causal Bonds The Bond Graph Formalism
e f
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 32
• As every bond defines two separate variables – The effort e and the flow f – We need two equations to compute values for these two
variables • It is always possible to compute one of the two
variables at each side of the bond. • A vertical bar symbolizes the side where the flow is
being computed.
Causal Bonds The Bond Graph Formalism
e f
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 33
• Local balances of energy
Junctions The Bond Graph Formalism
0 e1
e2
e3 f1
f2
f3
e2 = e1 e3 = e1 f1 = f2 + f3
⇔
1 e1
e2
e3 f1
f2
f3
f2 = f1 f3 = f1 e1 = e2+ e3
⇔
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 34
• Local balances of energy
Junctions The Bond Graph Formalism
0 e1
e2
e3 f1
f2
f3
e2 = e1 e3 = e1 f1 = f2 + f3
⇔
1 e1
e2
e3 f1
f2
f3
f2 = f1 f3 = f1 e1 = e2+ e3
⇔
Junctions of type 0 have only one flow equation, and therefore, they must have exactly one causality bar.
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 35
• Local balances of energy
Junctions The Bond Graph Formalism
0 e1
e2
e3 f1
f2
f3
e2 = e1 e3 = e1 f1 = f2 + f3
⇔
1 e1
e2
e3 f1
f2
f3
f2 = f1 f3 = f1 e1 = e2+ e3
⇔
Junctions of type 0 have only one flow equation, and therefore, they must have exactly one causality bar.
Junctions of type 1 have only one effort equation, and therefore, they must have exactly (n-1) causality bars.
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 36
• An electrical energy domain model
Example I The Bond Graph Formalism
Electrical Circuit
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 37
• An electrical energy domain model
Example I The Bond Graph Formalism
Electrical Circuit
Voltage Source
Capacitor
Resistor
Inductor
Resistor
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 38
• An electrical energy domain model
Example I The Bond Graph Formalism
U0.e
U0.
eU
0.e
C1.e C1.e
C1.e
R1.e
U0.
fL1
.f
R1.f
R1.f R1.f R2.f
C1.f
Bondgraphic equivalent Electrical Circuit
Voltage Source
Capacitor
Resistor
Inductor
Resistor
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 39
Example I
The Bond Graph Formalism
U0.e
U0.
e U
0.e
C1.e C1.e
C1.e
R1.e
U0.
f L1
.f
R1.f
R1.f R1.f R2.f
C1.f
Bondgraphic model
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 40
Example I
The Bond Graph Formalism
U0.e
U0.
e U
0.e
C1.e C1.e
C1.e
R1.e
U0.
f L1
.f
R1.f
R1.f R1.f R2.f
C1.f
Bondgraphic model
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 41
Example I
The Bond Graph Formalism
U0.e
U0.
e U
0.e
C1.e C1.e
C1.e
R1.e
U0.
f L1
.f
R1.f
R1.f R1.f R2.f
C1.f
Systematic derivation of equations Bondgraphic model
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 42
Example I
The Bond Graph Formalism
U0.e
U0.
e U
0.e
C1.e C1.e
C1.e
R1.e
U0.
f L1
.f
R1.f
R1.f R1.f R2.f
C1.f
Systematic derivation of equations
U0 .e = f(t) Bondgraphic model
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 43
Example I
The Bond Graph Formalism
U0.e
U0.
e U
0.e
C1.e C1.e
C1.e
R1.e
U0.
f L1
.f
R1.f
R1.f R1.f R2.f
C1.f
Systematic derivation of equations
U0 .e = f(t) U0 .f = L1 .f + R1 .f
Bondgraphic model
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 44
Example I
The Bond Graph Formalism
U0.e
U0.
e U
0.e
C1.e C1.e
C1.e
R1.e
U0.
f L1
.f
R1.f
R1.f R1.f R2.f
C1.f
Systematic derivation of equations
U0 .e = f(t) U0 .f = L1 .f + R1 .f
d/dt L1.f = U0 .e / L1
Bondgraphic model
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 45
Example I
The Bond Graph Formalism
U0.e
U0.
e U
0.e
C1.e C1.e
C1.e
R1.e
U0.
f L1
.f
R1.f
R1.f R1.f R2.f
C1.f
Systematic derivation of equations
U0 .e = f(t) U0 .f = L1 .f + R1 .f
d/dt L1.f = U0 .e / L1 R1 .e = U0 .e – C1 .e
Bondgraphic model
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 46
Example I
The Bond Graph Formalism
U0.e
U0.
e U
0.e
C1.e C1.e
C1.e
R1.e
U0.
f L1
.f
R1.f
R1.f R1.f R2.f
C1.f
Systematic derivation of equations
U0 .e = f(t) U0 .f = L1 .f + R1 .f
d/dt L1.f = U0 .e / L1 R1 .e = U0 .e – C1 .e R1 .f = R1 .e / R1
Bondgraphic model
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 47
Example I
The Bond Graph Formalism
U0.e
U0.
e U
0.e
C1.e C1.e
C1.e
R1.e
U0.
f L1
.f
R1.f
R1.f R1.f R2.f
C1.f
Systematic derivation of equations
U0 .e = f(t) U0 .f = L1 .f + R1 .f
d/dt L1.f = U0 .e / L1 R1 .e = U0 .e – C1 .e R1 .f = R1 .e / R1 C1 .f = R1 .f – R2 .f
Bondgraphic model
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 48
Example I
The Bond Graph Formalism
U0.e
U0.
e U
0.e
C1.e C1.e
C1.e
R1.e
U0.
f L1
.f
R1.f
R1.f R1.f R2.f
C1.f
Systematic derivation of equations
U0 .e = f(t) U0 .f = L1 .f + R1 .f
d/dt L1.f = U0 .e / L1 R1 .e = U0 .e – C1 .e R1 .f = R1 .e / R1 C1 .f = R1 .f – R2 .f
d/dt C1.e = C1 .f / C1
Bondgraphic model
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 49
Example I
The Bond Graph Formalism
U0.e
U0.
e U
0.e
C1.e C1.e
C1.e
R1.e
U0.
f L1
.f
R1.f
R1.f R1.f R2.f
C1.f
Systematic derivation of equations
U0 .e = f(t) U0 .f = L1 .f + R1 .f
d/dt L1.f = U0 .e / L1 R1 .e = U0 .e – C1 .e R1 .f = R1 .e / R1 C1 .f = R1 .f – R2 .f
d/dt C1.e = C1 .f / C1 R2 .f = C1 .e / R2
Bondgraphic model
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 50
Example I
The Bond Graph Formalism
U0.e
U0.
e U
0.e
C1.e C1.e
C1.e
R1.e
U0.
f L1
.f
R1.f
R1.f R1.f R2.f
C1.f
Systematic derivation of equations
U0 .e = f(t) U0 .f = L1 .f + R1 .f
d/dt L1.f = U0 .e / L1 R1 .e = U0 .e – C1 .e R1 .f = R1 .e / R1 C1 .f = R1 .f – R2 .f
d/dt C1.e = C1 .f / C1 R2 .f = C1 .e / R2
Bondgraphic model
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 51
Example I
The Bond Graph Formalism
U0.e
U0.
e U
0.e
C1.e C1.e
C1.e
R1.e
U0.
f L1
.f
R1.f
R1.f R1.f R2.f
C1.f
Systematic derivation of equations
U0 .e = f(t) U0 .f = L1 .f + R1 .f
d/dt L1.f = U0 .e / L1 R1 .e = U0 .e – C1 .e R1 .f = R1 .e / R1 C1 .f = R1 .f – R2 .f
d/dt C1.e = C1 .f / C1 R2 .f = C1 .e / R2
Bondgraphic model
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 52
• A multi-energy domain model – Electricity – Mechanical rotational – Mechanical translational
Example II The Bond Graph Formalism
Special elements such as Gyrator and Transformer convert energy flows across diff. physical domains
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 53
• A multi-energy domain model – Electricity – Mechanical rotational – Mechanical translational
Example II The Bond Graph Formalism
Special elements such as Gyrator and Transformer convert energy flows across diff. physical domains
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 54
• A multi-energy domain model – Electricity – Mechanical rotational – Mechanical translational
Example II The Bond Graph Formalism
ua ia
ia
ia
ia
uRa
uLa
ui τ ω1
ω1
ω1
ω1
τB3
τB1
τB1
τB1
τJ1
ω2
ω12
ω2
ω2
ω2
τk1
τG FG
v
v
v v
v
FB2 Fk2
Fm -m·g τJ2
Special elements such as Gyrator and Transformer convert energy flows across diff. physical domains
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 55
Facets and Bonds
• Bond Graph variables for Complex Systems – Facets 1 and 2
• Power variables: – Specific Enthalpy [J/kg] (an effort variable) – Mass Flow [kg/sec] (a flow variable). [J/sec] = [J/kg] · [kg/sec] represents power
• Information variable – Mass [Kg] (a state variable)
– Facet 3 (the emergy facet) • Information variable
– Specific Emergy [J/kg] (a structural variable) – [J/sec] = [J/kg] · [kg/sec] also denotes power
Eco Bond Graphs
EcoBG
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 56
Facets and Bonds
• Bond Graph variables for Complex Systems – Facets 1 and 2
• Power variables: – Specific Enthalpy [J/kg] (an effort variable) – Mass Flow [kg/sec] (a flow variable). [J/sec] = [J/kg] · [kg/sec] represents power
• Information variable – Mass [Kg] (a state variable)
– Facet 3 (the emergy facet) • Information variable
– Specific Emergy [J/kg] (a structural variable) – [J/sec] = [J/kg] · [kg/sec] also denotes power
Eco Bond Graphs
EcoBG
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 57
Facets and Bonds
• Bond Graph variables for Complex Systems – Facets 1 and 2
• Power variables: – Specific Enthalpy [J/kg] (an effort variable) – Mass Flow [kg/sec] (a flow variable). [J/sec] = [J/kg] · [kg/sec] represents power
• Information variable – Mass [Kg] (a state variable)
– Facet 3 (the emergy facet) • Information variable
– Specific Emergy [J/kg] (a structural variable) – [J/sec] = [J/kg] · [kg/sec] also denotes power
Eco Bond Graphs
EcoBG
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 58
Facets and Bonds
• Bond Graph variables for Complex Systems – Facets 1 and 2
• Power variables: – Specific Enthalpy [J/kg] (an effort variable) – Mass Flow [kg/sec] (a flow variable). [J/sec] = [J/kg] · [kg/sec] represents power
• Information variable – Mass [Kg] (a state variable)
– Facet 3 (the emergy facet) • Information variable
– Specific Emergy [J/kg] (a structural variable) – [J/sec] = [J/kg] · [kg/sec] also denotes power
Eco Bond Graphs
EcoBG
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 59
Facets and Bonds
• Bond Graph variables for Complex Systems – Facets 1 and 2
• Power variables: – Specific Enthalpy [J/kg] (an effort variable) – Mass Flow [kg/sec] (a flow variable). [J/sec] = [J/kg] · [kg/sec] represents power
• Information variable – Mass [Kg] (a state variable)
– Facet 3 (the emergy facet) • Information variable
– Specific Emergy [J/kg] (a structural variable) – [J/sec] = [J/kg] · [kg/sec] also denotes power
Eco Bond Graphs
EcoBG
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 60
Accumulators
• The EcoBG Storage element – A Capacitive Field (CF) accumulates more than one
quantity: Enthalpy, Mass and Emergy
Eco Bond Graphs
The specific enthalpy is a property of the accumulated mass
Known in advance -> A parameter
q
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 61
Junctions
• The EcoBG 0-Junction
Eco Bond Graphs
M1
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 62
Reusable structures
• Basic unit based on EcoBG elements – An important “building block”
• Storage of mass and energy adhering to the proposed 3-Faceted approach:
Eco Bond Graphs
M1 M2
M3
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 63
Modeling processes
• EcoBG Process elements
Eco Bond Graphs
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 64
Modeling processes
• EcoBG Process elements
Eco Bond Graphs
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 65
Modeling processes
• EcoBG Process elements
Eco Bond Graphs
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 66
Example
• Extraction of renewable resources for consumption
Eco Bond Graphs
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 67
Example
• Extraction of renewable resources for consumption
Eco Bond Graphs
Natural Renewable Primary
Reservoir
Consumption Secondary Reservoir Supply
Process
Demand
Process
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 68
Software tools
• EcoBG library implemented in the Dymola® tool.
Eco Bond Graphs
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 69
Software tools
• EcoBG library implemented in the Dymola® tool.
Eco Bond Graphs
Natural Renewable Primary
Reservoir
Consumption Secondary Reservoir
Supply Process
Demand
Process
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 70
The Mass Layer Eco Bond Graphs
Rain
Accumulated Deposit (Ma)
Consumption Reservoir (Mc)
Human Demand
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 71
The Mass Layer Eco Bond Graphs
Rain
Accumulated Deposit (Ma)
Consumption Reservoir (Mc)
Human Demand
dcirrscasc
casra
MMKMMKMMMKMM
−−=
−=
..
..
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 72
The Mass Layer Eco Bond Graphs
Rain
Accumulated Deposit (Ma)
Consumption Reservoir (Mc)
Human Demand
dcirrscasc
casra
MMKMMKMMMKMM
−−=
−=
..
..
ra MM +=
dcirrdc MMKM −−=
cirrscasc
casa
MKMMKMMMKM
−=
=
..
..
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 73
The Mass Layer Eco Bond Graphs
Rain
Accumulated Deposit (Ma)
Consumption Reservoir (Mc)
Human Demand
dcirrscasc
casra
MMKMMKMMMKMM
−−=
−=
..
..
ra MM +=
dcirrdc MMKM −−=
cirrscasc
casa
MKMMKMMMKM
−=
=
..
..
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 74
The Mass Layer Eco Bond Graphs
Rain
Accumulated Deposit (Ma)
Consumption Reservoir (Mc)
Human Demand
dcirrscasc
casra
MMKMMKMMMKMM
−−=
−=
..
..
sKgM r 2=
KgM a 1500, = KgM c 10, =
1.0
001.0
=
=irrs
s
KK
sKgM d 05.0=
0=dirrK
ra MM +=
dcirrdc MMKM −−=
cirrscasc
casa
MKMMKMMMKM
−=
=
..
..
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 75
Energy and Emergy Layers Eco Bond Graphs
Rain
Accumulated Deposit (Ma)
Consumption Reservoir (Mc)
Human Demand
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 76
Energy and Emergy Layers Eco Bond Graphs
Rain
Accumulated Deposit (Ma)
Consumption Reservoir (Mc)
Human Demand
).(.)...(.
)...(.).(.
dcccascac
casaarrra
MhTrMMKhTrMEMMKhTrMhTrME
−=
−=
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 77
Energy and Emergy Layers Eco Bond Graphs
Rain
Accumulated Deposit (Ma)
Consumption Reservoir (Mc)
Human Demand
).(.)...(.
)...(.).(.
dcccascac
casaarrra
MhTrMMKhTrMEMMKhTrMhTrME
−=
−=
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 78
Energy and Emergy Layers Eco Bond Graphs
Rain
Accumulated Deposit (Ma)
Consumption Reservoir (Mc)
Human Demand
).(.)...(.
)...(.).(.
dcccascac
casaarrra
MhTrMMKhTrMEMMKhTrMhTrME
−=
−=
).(. rrra MhTrME +=
).(. dccc MhTrME −=
)...(.
)...(.
cascac
casaaa
MMKhTrMEMMKhTrME
+=
−=
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 79
Energy and Emergy Layers Eco Bond Graphs
Rain
Accumulated Deposit (Ma)
Consumption Reservoir (Mc)
Human Demand
).(.)...(.
)...(.).(.
dcccascac
casaarrra
MhTrMMKhTrMEMMKhTrMhTrME
−=
−=
).(. rrra MhTrME +=
).(. dccc MhTrME −=
)...(.
)...(.
cascac
casaaa
MMKhTrMEMMKhTrME
+=
−=
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 80
Energy and Emergy Layers Eco Bond Graphs
Rain
Accumulated Deposit (Ma)
Consumption Reservoir (Mc)
Human Demand
1
1
1
==
=
=
r
rr
r
r
hemTr
kgJem
kgJh
kgJha 1=
kgJhc 1=
001.0=sK
).(.)...(.
)...(.).(.
dcccascac
casaarrra
MhTrMMKhTrMEMMKhTrMhTrME
−=
−=
).(. rrra MhTrME +=
).(. dccc MhTrME −=
)...(.
)...(.
cascac
casaaa
MMKhTrMEMMKhTrME
+=
−=
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 81
• Accumulated quantities (Deposit and Reservoir)
Simulation results Eco Bond Graphs
eq.
Energy Emergy
Transformity
eq.
eq.
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 82
• Experiment: Rain flow reduced 4x. Results for Reservoir.
Simulation results Eco Bond Graphs
Mass
Energy Emergy
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 83
• Eco Bond Graphs – A new “Plumbing Technology” for modeling Complex Dynamics Systems – A low-level tool to equip other higher-level modeling formalisms
• with the ability to track emergy flows
• Hierarchical interconnection of EcoBG subsystems – Automatic and systematic evaluation of sustainability:
• global tracking of emergy and • local checking of energy balances
• M&S practice – The laws of thermodynamics are not an opinable subject
• Every sustainability-oriented effort should -at some point- consider emergy
• We should become able to inform both: • decision makers (experts, politicians, corporations) and • people who express their wishes (democratic societies)
– about which are the feasible physical boundaries • within which their -largely opinable- desires and/or plans can
be possibly implemented in a sustainable fashion.
Conclusions
Dr. Rodrigo Castro I3M–SESDE 2013. Athens, Greece . September 27, 2013. 84
Q&A
rodrigo.castro@usys.ethz.ch rodrigo.castro@cifasis-conicet.gov.ar rcastro@dc.uba.ar
Thanks for your attention !
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