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\begin{document}

\title{Lattice Boltzmann simulations of viscous fingering: effect of wetting}



\author[1]{Peter Mora}%
\author[2]{Gabriele Morra}%
\author[3]{Dave Yuen}%
\affil[1]{College of Petroleum Engineering and Geosciences, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia}%
\affil[2]{Dept. of Physics and School of Geosciences University of Louisiana Louisana, USA}%
\affil[3]{Dept. of Applied Physics and Applied Mathematics, Columbia University, New York, , NY 10027, USA;  Dept. of Big Data, School of Computer Science, China University of Geosciences, Wuhan , China 430074}%


\vspace{-1em}



  
  \date{June 17, 2024}


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\begin{abstract}
The Lattice Boltzmann Method (LBM) is an elegant method to simulate
fluid dynamics based on modelling distributions of particles moving and
colliding on a lattice. We present examples of two phase flow using the
Rothman and Keller (RK) colour gradient Lattice Boltzmann model to study
phenomena associated with two phase immiscible fluid flow relevant to
water being injected into an oil saturated sandstone. The model involves
streaming and colliding two distribution functions (red and blue)
representing the number densities of two fluids, where the collision
step involves two terms which represents how particle distributions
change in each time step due to collision while encouraging colour
segregation. We conducted 2D numerical experiments to study the effect
of wetting angle on the morphology of flow of a lower viscosity fluid
being injected at the left of a simplified model rock matrix that was
filled with a higher viscosity fluid. The cases studied involved the
injected fluid being non-wetting (wetting angle = 180 degrees), neutral
wetting (wetting angle = 90 degrees) and wetting (wetting angle = 0
degrees). These three cases show viscous fingering behaviour with
different morphologies for the different wetting angles. For the case of
the non-wetting fluid injection, a series of narrow fingers are
observed. For the case of neutral wetting, broader and rounded fingers
are observed. And for the case of injecting a wetting fluid, a broad but
distorted front is observed approaching stable displacement. The results
show the importance of the wetting angle on the morphology of viscous
fingering. This study demonstrates that the multiphase Lattice Boltzmann
Method can simulate phenomenology relevant to studies of enhanced oil
recovery such as water injection, and hence, may lead to improved
estimates of oil recovery factors.%
\end{abstract}%



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