Appendix B - Monte carlo model and scenario submodule descriptions

This appendix provides the technical description of the Carbon Capture and Sequestration Monte Carlo model of damages presented in this report. It is intended that the following mathematical description of the Monte Carlo model provide, in combination with the tables of discrete probability distributions for random variables listed in the main text, the blueprint necessary to understand the calculations underlying results and conclusions herein.

Event scenarios

The full plant damage model is composed of multiple sub-modules of independently modeled damage-producing event scenarios. The events are modeled as either 50-year or 100-year time series based on whether the specific event is solely related to active operation of the plant or, otherwise, continues after the 50-year lifespan of active operations. There is an independent annual probability of each event. A full list of the six event scenarios appears below.

Event Scenarios Modeled for 50 Years of Active Plant Operations

1. Pipeline Puncture
2. Pipeline Rupture
3. Aboveground Wellhead Release
4. Plant Site Event

Event Scenarios Modeled for 100 Years of Active and Post-Closure Plant Operations

5. Injection Well Leakage
6. Other Well Leakage

Components of damage

Each scenario includes sub-modules independently calculating the various components of total scenario damages. As detailed in the scenario-specific descriptions below, total event scenario damages consist of either all or a subset of the following components.

1. Health Damages

a. By chemical

i. H₂S

ii. CO₂

b. By severity

i. Temporary

ii. Irreversible

iii. Fatal

2. Ecological damages

3. Release Stoppage Costs

4. Carbon Offset Costs

5. Groundwater Damages

Carbon price calculation

As part of the Carbon Offset Costs sub-modules, the carbon price is the lone random variable shared between the various event scenarios. All other random variables, regardless of being drawn from identical probability distributions (e.g., health damage values, environmental damage vales, etc.), are selected separately for each event scenario and sub-module. Because the carbon price would be identical for events occurring in a given year, it is an input into all Carbon Offset-containing scenarios.

The carbon price in dollars per tonne p_t in year t is a random variable selected from the uniform probability distribution U(min_pt, max_pt) with minimum price in year t of min_pt and maximum price in year t of max_pt. The table of annual carbon price minimum and maximum values is provided in the report text.

Pipeline puncture scenario

The total Pipeline Puncture damages D_p are calculated as,

For:

Health effect category values m = {temporary, irreversible, fatal}

Chemical categories c = {CO₂, H₂S}.

Where:

E_p,t is the random variable signifying the occurrence of a pipeline puncture event in year t with a value taken from the Bernoulli distribution such that Pr(E_p,t = 1) = 1 − Pr(E_p,t = 0) e_p = 0.01 and e_p is the annual probability of a pipeline puncture event;

V_p,t is the random variable totaling the dollar value of ecological damages for a pipeline puncture event in year t with a value taken from the ecological damages discrete probability distribution table;

p_t is the random variable signifying the dollars per tonne of carbon released in year t (as described above);

N_p,c,m,t is the random variable counting the number of pipeline puncture health effects due to chemical c in health effect category m in year t with a value taken from the discrete probability distribution table;

H_p,c,m,t is the random variable representing the dollar value of each pipeline puncture health effect due to chemical c in health effect category m in year t with a value taken from the discrete probability distribution table.

Pipeline rupture scenario

The total Pipeline Rupture damages D_r are calculated as,

For:

Health effect category values m = {temporary, irreversible, fatal}

Chemical categories c = {CO₂, H₂S}.

Where:

E_r,t is the random variable signifying the occurrence of a pipeline rupture event in year t with a value taken from the Bernoulli distribution such that Pr(E_r,t = 1) = 1 − Pr(E_r,t = 0) = e_r = 0.005 and e_r is the annual probability of a pipeline rupture event;

V_r,t is the random variable totaling the dollar value of ecological damages for a pipeline rupture event in year t with a value taken from the discrete probability distribution table;

p_t is the random variable signifying the dollars per tonne of carbon released in year t (as described above);

N _r,c,m,t is the random variable counting the number of pipeline rupture health effects due to chemical c in health effect category m in year t with a value taken from the discrete probability distribution table;

H _r,c,m,t is the random variable representing the dollar value of each pipeline rupture health effect due to chemical c in health effect category m in year t with a value taken from the discrete probability distribution table.

Aboveground wellhead release scenario

The total Aboveground Wellhead Release damages D_a are calculated as,

For health effect category values m = {temporary, irreversible, fatal},

Where:

E_a,t is the random variable signifying the occurrence of an aboveground wellhead release event in year t with a value taken from the Bernoulli distribution such that Pr(E_a,t =1) = 1 − Pr(E_a,t =0) = e_a = 0. 0000606 and e_a is the annual probability of an aboveground wellhead event;

N _a,m,t is the random variable counting the number of aboveground wellhead release health effects due to H₂S in health effect category m in year t with a value taken from the discrete probability distribution table;

H _a,m,t is the random variable representing the the dollar value of each aboveground wellhead release health effect due to H₂S in health effect category m in year t with a value taken from the discrete probability distribution table

Plant site event scenario

The total Plant Site Event damages D_s are calculated as,

Where:

E_s,t is the random variable signifying the occurrence of a plant site event in year t with a value taken from the Bernoulli distribution such that Pr(E_s,t =1) = 1 − Pr(E_s,t =0) = e_s = 0. 000055 and e_s is the annual probability of a pipeline puncture event;

N_s,t is the random variable counting the number of plant site temporary health effects due to H₂S in health effect category m in year t with a value taken from the discrete probability distribution table;

H_s,t is the random variable representing the dollar value of each plant site temporary health effect due to H₂S in health effect category m in year t with a value taken from the discrete probability distribution table.

Injection well leakage scenario

The total Injection Well Leakage damages D_i are calculated as,

Where:

E_i,t is the random variable signifying the occurrence of an injection well leakage event in year t with a value taken from the Bernoulli distribution such that Pr(E_i,t =1) = 1 − Pr(E_i,t = 0) = e_i = 0. 00003 and e_s is the annual probability of an injection well leakage event;

V_i,t is the random variable totaling the dollar value of ecological damages for an injection well leakage event in year t with a value taken from the discrete probability distribution table;

C_i,t is a random variable totaling the volume in tonnes of carbon released by the injection well leakage event in year t selected from the uniform probability distribution

with minimum volume of either 0.1 or 0.6 tonnes depending on the value of year t, and maximum volume of either 16.5 or 99 tonnes depending on the value of in year t;

p_t is the random variable signifying the dollars per tonne of carbon released in year t (as described above);

N_i,t is the random variable counting the number of injection well leakage temporary health effects due to H₂S in year t with a value taken from the discrete probability distribution table;

H_i,t is the random variable representing the dollar value of each injection well leakage temporary health effect due to H₂S in year t with a value taken from the discrete probability distribution table.

Other well leakage scenario

The total Other Well Leakage damages D_o are calculated as,

Where:

E_o,t is the random variable signifying the occurrence of an other well leakage event in year t with a value taken from the Bernoulli distribution such that Pr(E_o,t = 1) = 1 − Pr(E_o,t = 0) = e_o = 0.07 and e_o is the annual probability of an other well leakage event;

V_o,t is the random variable totaling the dollar value of ecological damages for an other well leakage event in year t with a value taken from the discrete probability distribution table;

C_o,t is a random variable totaling the volume in tonnes of carbon released by the other well leakage event in year t selected uniform probability distribution U(99, 5400) with minimum volume of 99 tonnes and maximum volume of 5,400 tonnes;

p_t is the random variable signifying the dollars per tonne of carbon released in year t (as described above);

S_o,t is the random variable signifying the leakage stoppage costs in dollars in year t selected from the nested Bernoulli and uniform probability distributions

Pr (U_So,t = U(50000, 50000))= 1 − Pr(U_So,t = U(2000000, 3650000))=0.9 where U_So,t is the uniform probability distribution of S_o,t.

N_o,t is the random variable counting the number of other well leakage temporary health effects due to H₂S in year t with a value taken from the discrete probability distribution table;

H_o,t is the random variable representing the dollar value of each other well leakage temporary health effect due to H₂S in year t with a value taken from the discrete probability distribution table.