# Is LNQ friend or foe?

The BC government has recently reached an agreement to allow the construction of a liquefied natural gas processing and export facility in Kitmat.

The discussion about the project has been a bit similar to the site C discussion. Some mention the economic advantage, others mention local environmental risks. As with the site C, I think that is missing the point. I think we have to focus on the transition to renewable energy sources and the climate change impact.

The bc green party argument is at least focused on green house gasses emissions. But it doesn't look at what LNG might be used for.

According to the lngcanada's website, a target market is Asia, where the gas would be used as a replacement for coal. Since the gas production would be in BC and the coal power plants are not, I think it is important to look at the global balance, not just the BC emissions.

It is clear that LNG is not a renewable energy source. But if it is better than sources like coal, we should consider the possibility that it is a useful tool for the transition. Is it better to burn gas instead of coal while renewable sources come online?

Lets first look at the difference in emissions by burning gas instead of coal. Natural gas is mostly methane, which is the simplest hydrocarbon with a formula $CH_4$. The first thing to notice is that the atomic mass of carbon is 12, while that of hydrogen is 1. That means that even the simplest hydrocarbon is $12/16$ or $75\%$ carbon by mass.

As for $CO_2$, the atomic mass of oxygen is $16$, which means that the the mass of $CO_2$ is $2*16 + 12 = 44$. So $CO_2$ is $12/44$ or $27\%$ carbon by mass.

The available energy from burning methane is $50$ MJ/kg. Since we are interested about the produced CO2, the energy content is $50/0.75$ or $66$ MJ/kg of carbon. For high grade coal it is $32.50$ MJ/kg. This quick calculation matches the claim that per KWh natural gas produces half as much CO2 as coal.

So we have that each Kg of carbon from LNG used in electricity generation saves one Kg of carbon in the atmosphere. Given their atomic masses, a Kg of carbon is present in $16/12$ Kg of methane and $44/12$ Kg of $CO_2$. So it looks like burning 1 Kg of methane produces (and saves) $44/16 = 2.75$ Kg of $CO_2$.

The proposed Kitmat project is expected to produce $14$ mega tonnes ($1.4*10^{10}$ Kg) per year of LNG. The estimates on the green house emissions per year range from $3.4$ to $10$ mega tonnes of $CO_2$ equivalent. That is surprisingly inefficient. The reason for the inefficiency seems to be that methane is, over a $100$ years time frame, $20$ times worse than $CO_2$ for global warming. So a small leak ($5\%$ say) dwarfs other production problems.

Even taking the $10$ mega tonnes $CO_2$ equivalent number, it would seem that if the LNG is used to replace coal than the project would still save $14*2.75 - 10 = 28.5$ mega tonnes equivalent per year.

The total emissions from the project are $14*2.75 + 10$ mega tonnes of $CO_2$ equivalent. That is, $4.85 * 10^{10}$ Kg. Given the $50$ MJ/Kg heat of combustion and a $50\%$ efficient generator, the total electricity that can be generated per year is $1.4*10^{10} * 50*10^6/2 = 3.5*10^{17}J$ or $9.72 *10^{10}$ KWh. So the emissions are about $499$ g/KWh according to this estimate.

The above leaves out transportation inefficiency for gas, but coal mining has its own problems too.

A much more detailed paper using data from actual power plants when looking at whether the US should export LNG arrived at $655$ g/KWh $CO_2$ equivalent. That would still be saving $550$ g/KWh of electricity if replacing coal according to the same paper.

LNG is a much more complicated case than site C, but it seems that LNG can be an useful short/medium term tool for reducing emissions. It is just important be careful on how much methane is leaked.

This also creates an interesting accounting problem on the carbon market. BC should receive credit if it lowers emissions in Asia. The same authors seem to have a paper on the subject.

One last thing that I still agree with the greens is that the project should not be subsidized. If the above analysis is correct, there should be plenty of demand for LNG and a subsidy is just giving away free money.

# Site C and the BC Greens

I was disappointed when I first learned that the BC Green Party was against the constructions of the Site C hydroelectric dam. The only criticism of the project I saw at the time was about loss of land and harm to local communities and environments.

Those are the arguments I would expect from a "tree hugger", not a factual environmentalist. Looking into it I found out that the BC Greens actually have a good reason for opposing the project and I would like to share it.

I think the "tree hugger" arguments are weak because our fossil fuel dependency and global warming are critical problems. If those are not solved we risk far greater damage to our society and environment.

To solve these great problems we need renewable energy sources. Gains in efficiency will not be sufficient. In Canada the energy consumption per capita is about 9.6 $KW$. As we know from The Matrix (and from a 2 $KCal$ diet), a human body consumes about 100 $W$, so about 1% of what we use. We had horses and firewood before industrialization, but it should be clear that to depend on efficiency gains is suicidal.

Fortunately in BC most of the electricity is already renewable (hydroelectric), but electricity is just a part of our energy consumption. We have to replace our use of gasoline and diesel and natural gas. With the current technology electrifying transportation and heating seems the best alternative.

I first realized that the Greens must be thinking about this when I found that their platform lists electrification.

Lets see how much electricity we need. I got the energy content of the various fuels from Wikipedia and the efficiency is an educated guess.

5,770,067 cubic meters of gasoline with 32.18 $GJ/m^3$ thermal and an engine thermal efficiency of 30% gives 55.7 useful $PJ$ per year.

1,747,579 cubic meters of diesel with 35.86 $GJ/m^3$ thermal and an engine thermal efficiency of 40% gives 25.1 useful $PJ$ per year.

The natural gas table is already in energy units: 98.1 $PJ$. To replace that with heat pumps with a coefficient of performance of 4 we need 24.5 $PJ$ per year.

The total is 105 $PJ$ per year, which is 3.34 $GW$ or 29.25 $TWh$ per year.

Site C is 5.1 $TWh$ per year. We need 5.73 times what it would produce to replace our fossil fuel use.

So we need a lot of electricity, but is Site C the best way to get a part of it? In a reply to an email I sent about it to the Green Party I was pointed to a speech where Andrew Weaver mentions Oregon and Washington. I got curious as to what they are doing for electricity.

Oregon has a population a bit smaller than BC. In 7 years (2005-2012) Oregon added 5.6 $TWh$ per year of wind power.

It seems possible then for BC to get the equivalent of the Site C generation from wind in the time it would take to finish Site C. Wind can also be built incrementally, and Site C will produce nothing in the next 7 years.

Another advantage of wind is that there is a lot of it. According to BC Hydro itself there is a potential for 38.9 $TWh$ per year which is more than sufficient for replacing current fossil fuel use.

Which brings us to the real reason to oppose Site C: there are other ways to get our renewable energy and we should consider their cost. And the cost of wind is very competitive.

And since we are talking cost, why is BC Hydro the one that has to decide what gets built? Electricity generation is an area that allows for competition, now more than ever with wind going mainstream.

BC hydro could just buy renewable electricity and let the market figure out what is the cheapest option. It looks like it would be wind, but if in the end someone figures out a way to finish Site C at a lower cost, that would be great.

I was very happy to find out (in the same speech) that that is exactly the position Andrew is pushing for.

Long story short, my first impression of the party was wrong. I have decided to join the party and so far I am very happy with that decision.

# Canadians should not retire at 65

Or at least, they should not take the canadian pention plan (CPP) at 65.

The age one should claim a pension depends on the life expectancy, but also on objectives. In this post I look at a simple objective: maximizing payments. The post ignores things like reinvesting the payments or needing the money earlier for whatever reason.

The CPP rules say that you can claim it any time from 60 to 70, but 65 is the default, so why not?

To incentivize people to retire later, each month after 65 years increases the monthly payment by 0.7% (1.4% for two month, 2.1% for three, 42% at 70 years). In a similar way, each month before 65 reduces the monthly payment by 0.6% (1.2% for two months, 1.8% for three, 36% at 60 years).

The asymmetry (0.6% versus 0.7%) has in interesting impact. Lets first look at what would happent without the asymmetry.

Without it, given any retiment month $T$, the monthly payment would be

\begin{equation*} R(1 + K(T - 65*12)) \end{equation*}

where $R$ is the monthly payment you would get at 65 years, and $K$ is the relative gain or loss each month (the 0.7% or 0.6% in the case of the CPP).

Now lets consider when it makes sense to delay retirement from $T$ to $T+1$. If one dies at $D$ months, each of the remaining $D - (T + 1)$ payments will be $R*K$ bigger. On the other hand, one would miss out on the original first payment. So delaying retirement by one month from $T$ is worth it when

\begin{equation*} (D - (T + 1))R*K > R(1 + K(T - 65*12)) \end{equation*}

Which simplifies to

\begin{equation*} T < \frac{D - \frac{1}{K} - 1 + 12*65}{2} \end{equation*}

Since $T$ is an integer, and it profitable to go from $T$ to $T+1$ when $T$ is smaller than the right hand side, we conclude that the best $T$ to retire is

\begin{equation*} T = \left\lceil\frac{D - \frac{1}{K} - 1 + 12*65}{2}\right\rceil \end{equation*}

Note for every 2 months increase in the life expectancy $D$, $T$ goes up by 1. A change of $K$ is just an offset. Lets see what a plot looks like for a $K$ of 0.6% or 0.7%.

So if $K$ were always 0.6% or 0.7% (or any other value), it would be easy. Make a guess about the life expectancy and read the best retirement age in the graph.

Given that in the CPP $K$ changes at 65, what happens at the transition? When the best retirement age is above 65, we are in the 0.7% rule. When it is below, we are in the 0.6% rule. Let's take a look at just those data points

There is still an overlap around a life expectancy of 78 years. If $T$ were not required to be an integer, the difference in the best retiment age between two values for K would be

\begin{equation*} \Delta T = \frac{D - \frac{1}{K_1} - 1 + 12*65}{2} - \frac{D - \frac{1}{K_2} - 1 + 12*65}{2} = \frac{1}{2K_2} - \frac{1}{2K_1} \end{equation*}

For 0.6% and 0.7%, that is about 11.9 months. What we want to find is when is it worth to transition from

\begin{equation*} T_1 = \frac{D - \frac{1}{K_1} - 1 + 12*65}{2} \end{equation*}

to

\begin{equation*} T_2 = \frac{D - \frac{1}{K_2} - 1 + 12*65}{2} \end{equation*}

The logic is the same that we used for retiring from $T$ to $T+1$: the extra amount earned on the months that are left has to be larger than the lost payments

\begin{equation*} (D - T_2)((65*12 - T_1)K_1 + (T_2 - 65*12)K_2) > (T_2 - T_1)(1 - K_1(65*12 - T_1)) \end{equation*}

Doing the substitutions (I used GiNaC) we get

\begin{equation*} \frac{D^2}{4000} - \frac{39D}{100} + \frac{12276379}{84000} > 0 \end{equation*}

Which has a solution of a life expectancy just over 77 years and 10 months. For the discrete case we can just test the 0.6% and 0.7% solutions and pick the best. The combined result is on the last graph:

And indeed, with a life expectancy of 77 years and 10 months one should retire at 64 years and 6 months. But with a life expectancy just a month longer, the best retirement age is 65 years and 6 months.

When I first got curious about this I was lazy and just wrote a python script to try all the possible retirement ages. I was surprised to see the discontinuity in the graph and decided to do the math to see what was going on.

The program is available at gitlab in case anyone wants to try it.

# Airbnb crackdown in Victoria

The Victoria city council is trying to restrict short term rentals.

Ironically when we moved to Victoria airbnb made the move much easier than moving to Toronto a few years before. With airbnb it was possible to search for various options and find a convenient 1 month rent.

In my previous move there was no airbnb. Despite Toronto being much bigger, there were fewer choices. There were no reviews on the choices and paying for it from outside Canada was inconvenient.

The airbnb that we rented for the move is a small basement in a house. Not the kind of space that would normally be used as a regular rental or bnb. We had a similar experience in Stratford. The convenience of airbnb does seem to create options that would simply not exist otherwise.

Airbnb is criticized for increasing the cost of long term rentals, which is likely true, but it also creates interesting subletting possibilities. In trips to Montreal and Vancouver we stayed in units that were clearly sublet. By crashing at a friend's place for a weekend a tenant can offset a substantial part of their rent.

But yes, in another trip we have stayed in a pretty conventional apartment that could have been otherwise rented long term. Even here it is important to discount the fact that a higher return on investment for landlords incentivizes the construction of more units. In the current construction boom in Toronto some of the buildings are bought mostly for investment. Not as many would have been built otherwise.

There is a fairness issue too. If when traveling to, for example, Montreal we can stay in a airbnb, it feels wrong to deny the same to Montrealers visiting Victoria.

Overall increasing the utilization of a scarce resource like space seems like a good thing, even if renters like myself get the short end of the stick.

The higher housing prices will also generate higher property taxes. The surplus could be given back to the community as income, but that would be another post.