World oil production/consumption

gistfile1.r

# oil production per day by country
production = read.csv("production.csv", header = T)
# proven oil reserves by country
reserves = read.csv("reserves.csv", header = T)
# oil consumption by country
consumption = read.csv("consumption.csv", header = T)

# the total amount of oil production per year
total_production = sum(production$Production) * 365

# total world proven reserves
total_reserves   = sum(reserves$Reserves)

# total world consumption per year
total_consumption = sum(consumption$Consumption) * 365

# derivation of time formula
#
# Take the simple exponential growth function
# q is initial quantity, r is growth rate, t is time
#
# f(t) = q * exp(r * t)
#
# Total usage over time is the integral of f(t):
#
# V(T) = int(f(t), 0, T)
#      = int(q * exp(r * t), 0, T)
#      = q / r * (exp(r * T) - 1)
#
# See when this hits some limit L
#
# L = V(T)
#   = q / r * (exp(r * T) - 1)
#
# Solve for T
#
# T = ln(L * r / q + 1) / r

# initial quantity is current production
q = total_production

# set growth rate to 1.18%
r = 0.0118

# set limit equal to current proved reserves
L = total_reserves

print(sprintf("Current reserves are %e, current consumption is %e, current production is %e.", total_reserves, total_consumption, total_production))

# this is when we will hit that limit
t = log(L * r / q + 1) / r
print(sprintf("Assuming no production growth, we will hit L in %f years.", total_reserves / total_production))
print(sprintf("Assuming a growth rate of %f%% per year, we will hit L in %f years.", round(r * 100, 2), t))

# now for consumption
q = total_consumption
t = log(L * r / q + 1) / r
print(sprintf("Assuming no consumption growth, we will hit L in %f years.", total_reserves / total_consumption))
print(sprintf("Assuming a growth rate of %f%% per year, we will hit L in %f years.", round(r * 100, 2), t))