__Non-linear least squares (NLLS) analysis of total production__

Figure 1 shows total petroleum production for 1965-2009 as reported in the BP statistical review:

The solid red line is the NLLS best fit to the full data set using the Hubbert equation with the parameters “a,” Qo and Q∞ allowed to vary to minimize the sum of the residual sums of squares (Srss). Because there is not enough sign of the production data reaching a plateau, the Hubbert equation “blows up” and gives an unrealistically high estimate for Q∞ (“a” = 0.0228; Qo = 19.27; Q∞ = 30015).

The solid pink line is the NLLS best fit to the full data set with Q∞ fixed equal to 178, the estimated proven reserves for Canada , as reported in the EIA country analysis brief. “Proven reserves,” however, have sometimes been notoriously underestimated (because trends for improvements in extraction technology may not be considered) or overestimated (to overcome OPEC production quotas in the Middle East ), so I am not too confident in such numbers.

The total production data for Canada showed a local peak in 1973, similar to the USA total production which peaked in 1970. However, whereas the Canadian production started to increase again after a minimum in 1976, the USA total production went into a steady decline. Overall, the trend in Canadian production is most like the trend seen in NGL production in the USA which had a local peak in 1972, a minimum in the late 70s and steady increase thereafter.

I adopted the same approach that I used to analyze the NGL production in the USA .

__Modified analysis of the production data from 1980-2009__I used the best fit values of “a”, Q

_{o}and Q∞ obtained from fitting the 1965-76 data using Hubbert’s equation also shown in Figure 1, as “fixed” parameters for a subsequent fit to the 1978-2009 data, using equation [9], derived in Part 7 of the “Refining the Peak Oil Rosy Scenario” series, with “a”, Qo and Q∞ fixed to their best fit values from the 1965-1976 analysis and one or both fca and fcq varied. The results are shown in Figure 2 below:The solid blue line in Figure 2 shows the best fit to the 1965-1976 data using the Hubbert equation (“a” = 0.0966; Qo = 1.26; Q∞ = 11.69). The solid green line shows the best fit obtained to the 1977-2009 data using equation [9] with fca = 0.0968 and fcq = 1.052.

The overall Srss obtained using the Hubbert equation to the full data set (1965-2009) equaled 0.2069. The sum of the Srss for the Hubbert equation fit to 1965-77 (Srss = 0.0233) plus the modified equation [9] best fit to 1978-2009 (Srss = 0.0932) with only fcq varied (best fit fcq=1.039) was significant less (F-test, p<0.0001).

However, the sum of the Srss for the Hubbert equation fit to 1965-77 (Srss = 0.0233) plus the modified equation [9] best fit to 1978-2009 (Srss = 0.0294) with

__both__fcq and fca varied gave a still better fit than the fit with only fcq varied (F-test, p<0.0001).These best fit parameters from fca and fcq imply that for the 1978-2009 there is a trend for the total extractable oil (Q∞) to increase 5.2 percent per year while the rate constant for production (“a”) is decreasing by 3.2 percent per year. The increase in Q∞ overcomes the decrease in “a” to give an overall increase in the production rate (dQ/dt) through the 1978-2009 time span.

The trend based on the modified equation [9] analysis predicts that the production rate will continue to increase over the next 20 years. In fact, the projection based on the modified analysis is nearly the same as that predicted from the Hubbert equation best fit that “blew up” (dashed red line in Figure 2) up until about 2020 but then shows signs of a declining rate of increase in production thereafter. The predicted production rate is substantially higher than what one might have expected assuming that in Q∞ equals 178 (dashed pink line in Figure 2).

__Non-linear least squares (NLLS) analysis of total consumption__

Despite being a net exporter, Canada is still a significant importer of petroleum (about 1.2 bbl/d of crude oil and refined products in 2008) apparently because its major eastern population centers are not connected to production facilities in the west. The EIA country analysis brief states that most of Canada ’s oil imports come from Algeria and Norway (crude oil) and the U.S. (refined products).

Figure 3 shows the best fit to Canadian petroleum consumption data (as reported in the BP statistical review).

Figure 3 shows the best fit to Canadian petroleum consumption data (as reported in the BP statistical review).

The short-dash red line in Figure 3 shows the best-fit of the Hubbert equation to the full data set 1965-2009 from the BP statistical review (“a” = 0.0206; Qo =28.60; Q∞ = 173). Similar to the USA consumption data, local peaks in consumption in 1979 and again in 1990 tend to skew the best fit to a shallower curve than suggested by the more recent data.

The long dashed red line in Figure 3 shows the best fit of the Hubbert equation to the more limited data set 1984-2009, which shows the more recent trend in consumption after the peak in consumption in 1979 and decline through 1983. Unfortunately, this best fit “blew up” resulting in an unrealistically high estimate of Q∞ (e.g., Q∞ = 5195) and low estimate of “a” (“a”=0.0167).

Finally, the solid red line shows the best fit to the last 18 years of data from 1991-2009 (“a” = 0.0445; Qo =16.54; Q∞ = 81.9), which I have take to be the most reasonable estimate of Canadian consumption of the three fits depicted in the figure. The predicted consumption curve from 2010 to 2030 is not all that different from that predicted from the best fit to the full data set. Although, the consumption max in 2021 of 0.91 bbs/yr would be years early than that predicted from the full data set.

It is interesting to note that the total predicted maximum petroleum consumed of about 82 bbs is about 11% percent of the total predicted maximum petroleum consumed (about 744 bbs) predicted for the USA . This is roughly proportional to the relative populations of the USA (307 million) and Canada (33 million), suggesting that over the long run, Canada ’s and the USA ’s utilization of petroleum would be about the same, if these consumption trends were to continue.

### --Updated Nov 28, 2010: as explained in Canada—Petroleum Superpower or Super-slave? --

__Comparing future trends in Canadian petroleum production and consumption__The extrapolated trend predicts Canada to continue to produce more than it consumes for at least the next 20 years. The net difference between the predicted production and consumption is shown as the dashed brown line and open symbols.

As discussed in the article Canada —Petroleum Superpower or Super-slave? The total net exports to the USA equals the 73 percent of total petroleum production send from Canada to the USA minus 12 percent of total petroleum consumption sent to Canada from the USA .

Net exports to the USA are predicted to increase about 42 percent from the present amount of about 0.8 bbs/yr to 1.14 bbs/yr in 2030. This is mainly because of the predicted increase in production as well as the plateau in domestic consumption. In about 2013 the net amount of petroleum exported to the USA is predicted to actually exceed domestic Canadian consumption.

__Impact on__USA

This is good news for the USA, since as indicted by the EIA country analysis brief, most of Canada’s petroleum production goes to the USA, and as discussed in Canada —Petroleum Superpower or Super-slave? The proportion to the available to USA can be decreased in accordance with the NAFTA proportionality clause.

Moreover, I would expect that this trend would continue going forward because the cost to export oil anywhere else would be more expensive than just pumping it through pipelines to the USA .

But just how much does of this bounty of Canadian oil mitigate the downward trend in USA production and the great disparity between USA production and consumption?

To answer this question, I prepared Figure 5, which reproduces the USA production and consumption trends shown in Figure 11 from the previous article, “Trends in USA petroleum production and consumption.” I further modified this graph to plot the predicted USA production plus Canadian exported petroleum from Figure 4 above.

The brown line, showing USA production plus Canadian exportable petroleum, illustrates that the Canadian petroleum alone will not do much to serve to predicted USA consumption for 2010-2030. The Canadian exports do tend to mitigate and then flatten out the decline in USA production from 2020-2030 but still, the sum of petroleum provided is far below what the USA is projected to consume. For instance, is the plateau region from 2020-2030 USA production plus Canadian exportable petroleum is predicted to provide the USA with about the same amount of petroleum that the USA consumed in 1955. But in 1955 the USA ’s population was 165 million http://www.census.gov/popest/archives/1980s/st5060ts.txt or about 54 percent of the present 307 million population.

Can the USA ’s other next door neighbor, Mexico , makeup for some of the shortfall to the USA ?

This is explored in the next post....

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