Fluid Flow through Petroleum Reservoirs: Role of Reservoir Engineers in the last couple of centuries (1827 - present)
From Navier-Stokes Equation in 1846 (derived by Navier, Poisson, Saint-Venant & Stokes between 1827 and 1845), it nearly took a decade to deduce an explicit momentum conservation equation that addresses single-phase incompressible fluid flow through a saturated homogeneous and isotropic porous medium under steady-state conditions namely Darcy’s law in 1856.
The extension of Darcy’s law for transient, compressible, multi-phase fluid flow with gravity and capillary effects remained “nearly” feasible using Muskat’s formulation in 1937 - despite - using the concept of ‘pressure gradient’ as against ‘hydraulic gradient’; and using the concept of ‘permeability’ as against ‘hydraulic conductivity’, although it did not remain as an analytical solution of the NSE but rather, it reflected the macroscopic resultant of solutions in which, the Darcy-flux (volumetric fluid flux per unit macroscopic area of the porous medium) and the fluid pressure are to be considered as statistical averages over a REV.
Even with the introduction of ‘fluid potential theory’ by Hubbert in 1953, we still cannot simply add all the numerical values of different potential energy to estimate the fluid potential because the scales and magnitudes of potential energy defined by different forces remain too different (for example, quite often, the interfacial potential energy arising from the capillary pressure remains orders of magnitude lower than that of the fluid potential that reflects only the macro migration of hydrocarbons); and in essence, the absolute values of the fluid potential are no more comparable.
And, the exploration of mathematical models is still going on at its own pace.
If so, will it remain so easy to give up the very idea of ‘fossil fuels’, which has not even begun its journey in full swing? On the other hand, on a lighter note, whether all the trees are not storing solar energy (naturally) in the form of ‘carbon’ – which, after ‘some’ great geological times become fossil fuels??
Predicting the future with absolute certainty is impossible, but I can provide some insights based on the information available up until my knowledge cutoff in September 2021. The transition away from fossil fuels is a complex and multifaceted process that involves technological advancements, policy changes, economic considerations, and public attitudes.
While the world has been making progress in reducing reliance on fossil fuels and shifting towards renewable energy sources, such as solar, wind, and hydropower, the complete phase-out of fossil fuels is likely to take time. Fossil fuels have been a dominant energy source for many decades, and their infrastructure and economic systems are deeply ingrained in our societies.
However, there are several factors that are contributing to the increasing momentum for the transition away from fossil fuels. These include concerns about climate change and the need to reduce greenhouse gas emissions, improvements in renewable energy technologies, declining costs of renewables, and increased public awareness and support for sustainable energy solutions.
Governments, businesses, and international organizations around the world are setting targets and implementing policies to accelerate the adoption of renewable energy and decrease reliance on fossil fuels. This includes incentives for renewable energy production, investments in research and development, and the implementation of stricter environmental regulations.
Technological advancements, such as improved battery storage systems, more efficient solar panels, and advancements in electric vehicle technology, are also helping to facilitate the transition away from fossil fuels. As these technologies continue to evolve and become more affordable, they are likely to play a significant role in reducing our dependence on fossil fuels.
That being said, the full-scale transition away from fossil fuels will still face challenges. The fossil fuel industry has significant political and economic influence, and there may be resistance to change from certain sectors. Additionally, the development of infrastructure for renewable energy, such as grid upgrades and energy storage systems, will require time and investment.
In conclusion, while the transition away from fossil fuels is underway and gaining momentum, it is unlikely to happen overnight. The process will take time, but with the increasing urgency to address climate change and the advancements in renewable energy technologies, it is possible that the shift will continue to progress in the coming years and decades.
"... on a lighter note, whether all the trees are not storing solar energy (naturally) in the form of ‘carbon’ – which, after ‘some’ great geological times become fossil fuels??". Very nice schematization of the transformation cycle of solar radiative energy into green energy (wood) and fossil energy (oil, Natural Gas ...). To go further, this schematization should enter into the equation, the radiative balance of the Earth, which involves various geological phenomena (geothermal activities, etc.), the various transfers associated with the dynamics of geofluids and the various cycles of water, carbon, etc. as well as to the various biotic and abiotic phenomena of transfer and transformation.
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