M2: Static MFA and quasi-stationary modelling Flashcards
What is a model?
A model is any goal satisfying (goal oriented) representation or description of a given entity , such as an object, system, process, or property
A model is a real or abstract system which is the carrier of a function or property of another pre selected system or process with requested or sufficient accuracy
Sloppy:
- A model is a simplified representation (real or abstract) of reality –> e.g., physical hydraulic model of a river, or mathematical model of a river
- A model is developed with a goal or purpose in mind –> e.g., impact of a storm flood, or long term sedimentary deposition
- A model needs to be accurate enough to satisfy the purpose –> e.g., properties of river bed need to be different based on model purpose.
What is a system?
A system is a set of interacting or interdependent elements (real or abstract , forming an integrated whole)
Examples:
• Solar system (real) or an abstraction there of e.g., with sun and planets as elements
• Cell (real) or an abstraction there of e.g., with nuclei, cytoplasm, and organelles as elements
• Sentence (spoken or written) e.g., with individual words as elements
A system is a holon ””*, which is i ) a whole consisting of parts, but simultaneously also (ii) a part of a larger system.
What is the difference on a MFA system and a mathematical model?
MFA system: Consist of a system boundary, elements (processes) and interactions (mass or energy flows).
Mathematical Model: model inputs (parameters and constants), model outputs (system variables).
What can models be used for?
- Understand a system
- -> system identification: analyze interrelations between elements of the system (what are the fundamental laws governing the system?)
- -> Sensitivity analysis: analyze the impact of changes in model inputs on outputs. (what are the key parameters determining the behavior of the system?)
- -> Uncertainty propagation / calculus of observation: analyze the role of errors (what is the impact of uncertainties in observations on the overall system? how can uncertainties be reduced?) - Predictions or forecasts
- -> Simulation modeling: If then calculations, scenarios (how is the system changing under given assumptions?)
- -> Optimization modeling: minimize or maximize an objective function (how is the system changing if it acts to maximize / minimize certain values without violating resource constraints?) - Data management and visualization
- -> Data structure: models help structuring data (orientation)
- -> Visualization: allows for fast access and improved control
–> Simulation models often complement field experiments (if they are very time consuming, expensive, or impossible)
Mention three basic types of models
- First principle (ab initio) models:
–> Rely exclusively on basic and established laws of nature without additional assumptions or special models.
Example: law of conservation of energy - Phenomenological models:
–> Combine basic laws with phenomenological approaches (phenomenological approaches are empirically tested
Example: process models (chemical engineering, ecology…) - Data based models:
–> Use exclusively empirical data from measurements in combination with statistics to describe input and/or output characteristics of a system.
Example: Dose response relationships in toxicology
A model improvement is usually a step towards type 1
- -> reduce hypotheses and assumptions
- -> increase knowledge about inner relationships
What type of model is MFA?
- Every MFA model need/has elements from first principle models. We need mass balances for every process in the model.
- MFA also has data based model elements. For instance recycling will need data based modelling because the recycling rate for materials are not the same.
- So in general MFA uses phenomenological models because it combines principles and data.
What type of model is LCA?
- The LCI in general uses the same as MFA (phenomenological models)
- LCIA uses data-based models (think about toxicology assessment)
What type of models are used in economics?
More towards data based models (need info about prices etc.)
How should the goodness of a model be?
A model should be as simple as possible and as complex as necessary.
In other words, a model should
- reflect reality as accurate as possible
- use as few parameters as possible
Mention three different kinds of koefficients
- Transfer coeffcients: You want to know how much of a particular inflow goes to a particular outflow. Fx 10% of A goes to R and 15% from B goes to R and 20% of C goes to R. (most commonly in MFA). A good example is recycling efficiency of materials
- Allocation coefficients: how much of a inflow A goes to the different outflows Q, R and S. fx use of scrap metal in different products.
- Selective coefficients: one-to-one ratio
Mention 4 types of mathematical models
Static models: All system variables are invariant under time reversal
Stationary models: All system variables are invariant under time shift
Quasi-stationary models:
- Flows are invariant under time shift.
- Stocks may change under time shift.
Dynamic models:
- Flows may change under time shift
- Stocks may change under time shift
List the approach for quasi-stationary models
- Define system
- List system variables, count unknowns
- Number of unknowns = number of equations!!! - Mass balance equations
- First principle part of MFA (no parameters!) - Model approach equations
- Empirical part of MFA (all the parameters) - Solve equation system for all system variables
a) algebraic (substitution of variables) approach
b) matrix inversion approach
System is defined (solvable) if:
- One equation exists for each unknown
- Equations are independent (e.g., if no equation can be expressed through the others)
(See slide in lecture for visual representation of the approach)
