Doctor of Philosophy (PhD)


Petroleum Engineering

Document Type



This study derives from observations made in petroleum research and practices of chemical industry that efficient mixing takes place in segregated immiscible fluid flow in granular packs and static mixers. A hypothesis was formulated that transverse mixing (TM) across oil-water interface may occur in segregated inflow to wells resulting in progressive transition zone, more water production, and reduced oil productivity. “Mixing” is broadly interpreted here to address the entire range of stirring, splitting, dispersion and diffusion processes between two fluids.

Initial study showed that a commercial reservoir simulator would not model any transition zone in segregated oil-water flow at high pressure gradient as it lacks a mathematical description of the phenomenon. Initial analysis identified two major effects contributing to transverse mixing: shear mixing due to velocity contrast and momentum transfer due to tortuosity and streams’ collisions.

The shear mixing effect was studied in the Hele-Shaw (H-S) flow cell, and TM of oil and water above unstable interface were observed. However, considering wavelength reduction caused by H-S model gap size corresponding to rock’s pore size, the mixing zone appeared to be negligible.

The momentum transfer (collision) effect has been studied by considering ratio of size of pore and throat. TM criterion was developed using modified Richardson number.

Only early TM has been confirmed with granular-pack flow cell experiments due to dimensional restrictions. The results showed only water invading oil layer above the initial water/oil interface. Also, TM increased for higher pressure gradients and larger grain sizes, and reduced for more viscous oil.

A mathematical model of early TM has been derived by solving a diffusion equation with constant flow velocity and water saturation at the initial W/O interface. The model reasonably matches experimental results thus enabling determination of the transverse dispersion coefficient, similar to miscible dispersion.

The TM effect in wells was qualified by converting the linear TM model to radial flow model and integrating within the well’s inflow zone. The results showed TM would increase water production by 2.5%, and reduce oil rate by 8.3% thus reducing well’s productivity.

Limitations and shortcoming of the study are discussed together with recommendations.



Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Andrew K. Wojtanowicz