Reservoir Engineering: Are we strictly following continuum hypothesis in a petroleum reservoir?
1. With the possibility of multiple (tortuous) pathways, which pathway remains the fastest (or the least resistive pathway); and how fast oil and water travel along the principal direction of the reservoir towards production well (or during injection of alkaline or surfactants or polymers from an injection well)?
If there is uncertainty not only in identifying the fastest path from the limited reservoir data but also in travel time owing to the uncertainty in path length as well as in data or approaches used to compute the travel times of the injected chemicals (in chemical EOR), then, should we seek help from ML/AI in order to deduce the fastest path of likely surfactant (or alkali or polymer) transport?
2. Reservoir heterogeneity being a continuous phenomenon (as it exists at all scales); even, if we treat reservoir heterogeneity to be homogenous @ Darcy’s scale, then, won’t the reservoir would remain to be heterogeneous @ pore-scale and @ field-scale?
In chemical EOR applications, if we apply Darcian approach for deducing the resulting oil flow rates, then, does it directly mean that ‘we are supposed to ignore/neglect phenomena at scales lesser than Darcy’s scale’?
For example, the concept of IFT and contact angle – which remain associated with sub-pore-scale (that remains much lesser than Darcy’s scale);
not play a vital role in enhancing the resulting oil production rate?
If so, how could the parameters contact-angle and IFT be related with macroscopic Darcian approach?
In case, if both IFT and Darcian approaches are taken into consideration simultaneously, then, do we really have more than one REV for a petroleum reservoir?
If yes, then, are we no more following continuum hypothesis (where, the concerned fluid is supposed to behave as if it remained to be continuous in space @ macroscopic-scale, say over 10 mm)?
By considering contact angle and IFT into picture, how could we claim that the fluid flow through a petroleum reservoir remains represented macroscopically?
If so, then, how could we treat the flow of oil and water to remain to be treated as a continuum in space?
If heterogeneity is just a relative phenomenon, which essentially depends on the scale of the observation, then, how exactly, are we directly relating the reservoir heterogeneity to the scale of the problem in a petroleum reservoir?
3. In essence, what exactly is the scale @ which petroleum reservoir properties remain varying smoothly as well as continuously?
In a petroleum reservoir, when we treat the fluid as a continuum, what exactly we mean by ‘the measured fluid property remains as a constant for volumes which are smaller on the macroscopic-scale but remain larger on the microscopic-scale’?