DARCY'S LAW AND FUTURE FLOW OF CRUDE OIL

Most people know of Einstein’s formula E=mc²“Energy is the mass times the square of the speed of light”. Some know the first law of thermodynamics: “Energy cannot be created but only converted from one form to another”. However, few people known of Darcy’s Law despite the fact that it is this law that delimits historical, current and future oil production. Darcy’s Law, a little more complicated than Einstein’s, determines the flow rate of oil from an oilfield and this is its formula:

q = - A k / µ ∙ ∂P/∂L

At first glance this law can seem difficult to understand but its logic is actually quite simple. The flow rate, q, is directly proportional to the cross-sectional area through which the flow occurs, A, and to k that is a measure of how porous the field is. The viscosity of oil is given as µ so that a thick oil with high viscosity flows more slowly than a thin oil. The term ∂P/∂L is a measure of the pressure in the field and the larger that is the larger the flow. When the oil industry discusses new technology it is one of the above parameters that they are trying to manipulate. Horizontal drilling involves increasing the cross-sectional area A while fracking can increase the porosity k. The pressure in the field can be increased by pumping in water and new technology in which solvents are pumped into the field can change the viscosity.

Historically we have never seen global economic growth without increased global oil production. During the post-war period until 1973 oil flow increased by around 8% annually. In the following ten years we saw a transition to a new relationship between increase of oil production and economic growth. From 1983 the oil flow increased by about 1.5% annually related to a GDP increased with about 3%. We now know that this trend was broken in 2005 and since when we have seen a plateau in the production of oil. At the moment it seems that production of “tight oil” may allow a small increase in global production annually and it is unclear if this is sufficient to, once again, grow the global economy. Darcy’s law limits the production.

In contrast, what is completely clear is that future oil production cannot generate the carbon dioxide emissions foreseen in the scenarios described by the IPCC in 2000. However, having said this I would note that CO₂ emissions may, nevertheless, be too high to reverse the trend that we see of increasing atmospheric CO₂.