Wind and solar energy consumption have grown quickly from 1994 to 2014 based on data from BP’s Statistical Review of World Energy 2015 at a rate of 25% per year combined. Historical data on oil consumption from 1900 to 1975 shows that oil use grew by about 7% per year over that period. Note that this rate of growth was constrained by demand for energy as evidenced by very low oil prices from 1950 to 1972 and the high rates of oil consumption growth from 1960 to 1970. World GDP and population grew rapidly over that period before supply constraints became apparent and rates of oil consumption growth slowed markedly after 1979.
The scenarios above cover a range of possibilities with the lowest representing growth in Wind and solar output at 7%/year from 2016 to 2070, the middle scenario was chosen to end at about midway between the low and high scenarios in 2070 with a simple exponential increase of 8.4% per year.
The high scenario uses separate scenarios for wind and solar over the 2015 to 2030 period which are then added together. Wind grew at an annual rate of 22% from 2001 to 2013 and solar grew by 45%/year from 2004 to 2014.
The high scenario assumes that wind grows by 10%/year from 2015 to 2030 and that solar grows at a variable annual rate starting at 36%/year in 2015 and decreasing in rate each year by 2% until 2027, then growth continues at 12%/year until 2030.
The combined rate of growth of wind and solar is 11% from 2029 to 2030. I assume this growth rate continues for a decade, then the annual growth rate falls to 10%/year in 2041 and to 9%/year in 2051. In 2056 the rate of growth begins to slow as most energy is provided by wind and solar at that point, it is assumed that demand becomes a constraint on further wind and solar consumption.
I believe the low scenario is too pessimistic because there will be plenty of demand for wind and solar as costs fall, while the cost of fossil fuels rises so that switching will be economically attractive. The high scenario is likely too optimistic, as there will be technical barriers which may prove difficult to overcome and there may be efficiency gains that I have not accounted for, which may result in lower demand growth. I have assumed 1.4% per year growth in primary energy demand from 2015 to 2070 (the 2005 to 2014 rate of growth) which would lead to energy consumption of 28,000 Mtoe/year in 2070.
Bottom line, reality will fall somewhere between the low and high scenarios, if there is not a World economic collapse (equal to or worse than the Great Depression) between 2015 and 2070. Note that a Global Financial Crisis(GFC) similar to 2008 to 2010 is certainly possible, if not likely, but wise economic policy using Keynesian principles can stabilize the World economy.