Technology Model Example

Here is a very simple model for electrolysis of water. We just have water, electricity, a catalyst, and some lab space. We choose the fundamental unit of operation to be moles of H₂:

H₂O → H₂ + ½ O₂

For this example, we treat the catalyst as the capital that we use to transform inputs into outputs. Our inputs are water and electricity, and our outputs are oxygen and hydrogen. Our only fixed cost is the rent on the lab space at $1000/year. Using our past experience with electrolysis technology as well as some historical data, we estimate that we’ll be able to produce 6650 mol/year of hydrogen and at this scale, our catalyst has a lifetime of about 3 years. The metrics we’d like to calculate for our electrolysis technology are cost, greenhouse gas (GHG) emissions, and jobs created. Based on this information, the designs dataset for the base case electrolysis technology is as shown in Table 10.

Table 10 designs dataset for the base case (without any R&D) of the simple electrolysis example technology.

Technology	Tranche	Variable	Index	Value	Units	Notes
Simple electrolysis	Base Electrolysis	Input	Water	19.04	g/mole
Simple electrolysis	Base Electrolysis	Input efficiency	Water	0.95	1	Due to mass transport loss on input.
Simple electrolysis	Base Electrolysis	Input	Electricity	279	kJ/mole
Simple electrolysis	Base Electrolysis	Input efficiency	Electricity	0.85	l	Due to ohmic losses on input.
Simple electrolysis	Base Electrolysis	Output efficiency	Oxygen	0.9	1	Due to mass transport loss on output.
Simple electrolysis	Base Electrolysis	Output efficiency	Hydrogen	0.9	1	Due to mass transport loss on output.
Simple electrolysis	Base Electrolysis	Lifetime	Catalyst	3	yr	Effective lifetime of Al-Ni catalyst.
Simple electrolysis	Base Electrolysis	Scale	n/a	6650	mole/yr	Rough estimate for a 50W setup.
Simple electrolysis	Base Electrolysis	Input price	Water	4.80E-03	USD/mole
Simple electrolysis	Base Electrolysis	Input price	Electricity	3.33E-05	USD/kJ
Simple electrolysis	Base Electrolysis	Output price	Oxygen	3.00E-03	USD/g
Simple electrolysis	Base Electrolysis	Output price	Hydrogen	1.00E-02	USD/g

Note that this is not the only way to model the electrolysis technology. We could choose to purchase lab space and equipment instead of renting, in which case we would have more types of capital, each with a particular lifetime. We could treat the oxygen output from our technology as waste instead of a coproduct and remove it from the model entirely. We could operate at a different scale and perhaps change our fixed or capital costs by doing so. Depending on where we operate this technology, our input and output prices will likely change. The Tyche framework offers great flexibility in representing technologies and technology systems; it is unlikely that there will only be a single correct way to model a decision context.

A key quantity that is not included in the designs dataset is our fixed cost, rent for the lab space. This quantity is included in the parameters dataset in Table 11, along with the necessary data to calculate our metrics of interest (cost, GHG, jobs).

Table 11 parameters dataset for the base case (without any R&D) of the simple electrolysis example technology.

Technology	Tranche	Parameter	Offset	Value	Units	Notes
Simple electrolysis	Base Electrolysis	Oxygen production	0	16	g
Simple electrolysis	Base Electrolysis	Hydrogen production	1	2	g
Simple electrolysis	Base Electrolysis	Water consumption	2	18.08	g
Simple electrolysis	Base Electrolysis	Electricity consumption	3	237	kJ
Simple electrolysis	Base Electrolysis	Jobs	4	1.50E-04	job/mole
Simple electrolysis	Base Electrolysis	Reference scale	5	6650	mole/yr
Simple electrolysis	Base Electrolysis	Reference capital cost for catalyst	6	0.63	USD
Simple electrolysis	Base Electrolysis	Reference fixed cost for rent	7	1000	USD/yr
Simple electrolysis	Base Electrolysis	GHG factor for water	8	0.00108	gCO2e/g	based on 244,956 gallons = 1 Mg CO2e
Simple electrolysis	Base Electrolysis	GHG factor for electricity	9	0.138	gCO2e/kJ	based on 1 kWh = 0.5 kg CO2e

Within our R&D decision context, we’re interested in increasing the input and output efficiencies of this process so we can produce hydrogen as cheaply as possible. Experts could assess how much R&D to increase the various efficiencies \(\eta\) would cost. They could also suggest different catalysts, adding alkali, or replacing the process with PEM.

The indices table (see Table 12) simply describes the various indices available for the variables. The Offset column specifies the memory location in the argument for the production and metric functions.

Table 12 Example of the indices table.

Technology	Type	Index	Offset	Description	Notes
Simple electrolysis	Capital	Catalyst	0	Catalyst
Simple electrolysis	Fixed	Rent	0	Rent
Simple electrolysis	Input	Water	0	Water
Simple electrolysis	Input	Electricity	1	Electricity
Simple electrolysis	Output	Oxygen	0	Oxygen
Simple electrolysis	Output	Hydrogen	1	Hydrogen
Simple electrolysis	Metric	Cost	0	Cost
Simple electrolysis	Metric	Jobs	1	Jobs
Simple electrolysis	Metric	GHG	2	GHGs

Production function (à la Leontief)

\(P_\mathrm{oxygen} = \left( 16.00~\mathrm{g} \right) \cdot \min \left\{ \frac{I^*_\mathrm{water}}{18.08~\mathrm{g}}, \frac{I^*_\mathrm{electricity}}{237~\mathrm{kJ}} \right\}\)

\(P_\mathrm{hydrogen} = \left( 2.00~\mathrm{g} \right) \cdot \min \left\{ \frac{I^*_\mathrm{water}}{18.08~\mathrm{g}}, \frac{I^*_\mathrm{electricity}}{237~\mathrm{kJ}} \right\}\)

Metric functions

\(M_\mathrm{cost} = K / O_\mathrm{hydrogen}\)

\(M_\mathrm{GHG} = \left( \left( 0.00108~\mathrm{gCO2e/gH20} \right) I_\mathrm{water} + \left( 0.138~\mathrm{gCO2e/kJ} \right) I_\mathrm{electricity} \right) / O_\mathrm{hydrogen}\)

\(M_\mathrm{jobs} = \left( 0.00015~\mathrm{job/mole} \right) / O_\mathrm{hydrogen}\)

Performance of current design.

\(K = 0.18~\mathrm{USD/mole}\) (i.e., not profitable since it is positive)

\(O_\mathrm{oxygen} = 14~\mathrm{g/mole}\)

\(O_\mathrm{hydrogen} = 1.8~\mathrm{g/mole}\)

\(\mu_\mathrm{cost} = 0.102~\mathrm{USD/gH2}\)

\(\mu_\mathrm{GHG} = 21.4~\mathrm{gCO2e/gH2}\)

\(\mu_\mathrm{jobs} = 0.000083~\mathrm{job/gH2}\)

Technology Model

Each technology design requires a Python file with a capital cost, a fixed cost, a production, and a metrics function. Listing 1 shows these functions for the simple electrolysis example.

Listing 1 Example technology-defining functions.

# Simple electrolysis.


# All of the computations must be vectorized, so use `numpy`.
import numpy as np


# Capital-cost function.
def capital_cost(
  scale,
  parameter
):

  # Scale the reference values.
  return np.stack([np.multiply(
    parameter[6], np.divide(scale, parameter[5])
  )])


# Fixed-cost function.
def fixed_cost(
  scale,
  parameter
):

  # Scale the reference values.
  return np.stack([np.multiply(
    parameter[7],
    np.divide(scale, parameter[5])
  )])


# Production function.
def production(
  capital,
  fixed,
  input,
  parameter
):

  # Moles of input.
  water       = np.divide(input[0], parameter[2])
  electricity = np.divide(input[1], parameter[3])

  # Moles of output.
  output = np.minimum(water, electricity)

  # Grams of output.
  oxygen   = np.multiply(output, parameter[0])
  hydrogen = np.multiply(output, parameter[1])

  # Package results.
  return np.stack([oxygen, hydrogen])


# Metrics function.
def metrics(
  capital,
  fixed,
  input_raw,
  input,
  img/output_raw,
  output,
  cost,
  parameter
):

  # Hydrogen output.
  hydrogen = output[1]

  # Cost of hydrogen.
  cost1 = np.divide(cost, hydrogen)

  # Jobs normalized to hydrogen.
  jobs = np.divide(parameter[4], hydrogen)

  # GHGs associated with water and electricity.
  water       = np.multiply(input_raw[0], parameter[8])
  electricity = np.multiply(input_raw[1], parameter[9])
  co2e = np.divide(np.add(water, electricity), hydrogen)

  # Package results.
  return np.stack([cost1, jobs, co2e])