Dissertation

2019

#### Degree Name

Doctor of Philosophy

#### Department

Aerospace Engineering

#### Major

Engineering Mechanics

Thomas Ward

#### Abstract

Immiscible and miscible two-phase fluid flow in a porous media are important problems encountered in petroleum, manufacturing, pharmaceutical, and food industries. Enhanced oil recovery process used in the petroleum industry involves driving the viscous crude oil trapped in porous reservoir rocks using low-cost fluid cocktails of surfactants-chemicals-polymers that modify the surface tension and create a favorable viscosity profile, thereby increasing the production efficiency. Such flows in porous media can be studied in laboratory conditions by considering the porous media as a bundle of interconnected capillaries which can be further simplified by modeling them in a single capillary tube.\\

In the first problem, experiments were performed to study the immiscible displacement of a more viscous fluid using a less viscous one with mean velocity $U_m$ in a capillary tube. One set of experiments were performed where surfactant was introduced into the aqueous phase liquid at concentrations below the critical micellar concentration (CMC) and either mineral or silicone oil was used as the continuous phase. In second set of experiments surfactant formed at the interface via a saponification chemical reaction by introducing sodium hydroxide into the aqueous phase, and using corn oil that contains triglycerides as the continuous one. For both experiment conditions we measured surface tension using the pendant drop method, and that data were used to estimate adsorption and desorption Biot numbers $Bi_{\beta}$ and $Bi_{\alpha}$, respectively, whereas for surfactant produced via chemical reaction these curves provide an estimate for rate of change for surface tension that were used to estimate a Damk\"{o}hler number $Da$. We used equilibrium surface tension values, $\gamma_{eq}$, displaced fluid viscosity and displacing fluid tip velocity $U_t$ to estimate a capillary number $Ca$ and also estimated the fraction of residual film $m = 1-U_m/U_t$ left inside the capillary tube after displacement. The non-reactive surfactant case followed trends seen in homogeneous fluid displacement cases. For the reactive case, trends for $m$ are similar to the non-reactive one for $Da \to 1$; for values lower than this there is a local minimum in $Da$ and an asymptotic value of $m\approx 0.45$ as $Da \to 0$. This seems to suggest that the products created via saponification reaction tend to have an effect on the interface and film thickness that is entirely absent in non-reactive immiscible displacement experiments.\\

In the second problem, we examine the stability of an evaporating-unbounded axisymmetric liquid bridge confined between parallel-planar similar or chemically different substrates using both theory and experiments. With a quasistatic assumption we use hydrostatics to estimate the minimum stable volume $V_{min}$ via the Young-Laplace equation for Bond numbers 0$\leq Bo \leq$1, and top/bottom wall contact angles 5$^{\circ}\leq \theta \leq$175$^{\circ}$ although the primary focus is on wetting and partial wetting fluids. Solving the Young-Laplace equation requires knowledge of appropriate capillary pressure values, which appear as a constant, and may not provide unique solution. To examine uniqueness of numerical solutions and volume minima determined from the Young-Laplace equation for unbounded-axisymmetric liquid bridges we analyzed capillary pressure for large and small liquid volume-asymptotic limits at zero Bond number. Experiments were performed to compare with the volume minima calculations for Bond numbers 0.04$\leq Bo \leq$0.65. Three substrates of varying surface energy were used, with purified water as the primary liquid. Volume estimates and contact angle data were extracted via image analysis and evaporation rates measured from this data are reported. Volume minima were in the range 0.1$\leq V_{min} \leq$20 $\mu$l depending on Bond number. There was good agreement when comparing predicted volume minima and those determined from experiments for the range of parameters studied.\\

In the third problem, we experimentally study the miscible displacement of an aqueous low-concentration polymer solution that initially fills a capillary tube (diameter $< 1$ mm), using water. Aqueous carboxymethyl-cellulose (CMC) polymer solutions were prepared at initial concentration $0.5 < c_0 < 0.75$ (w/w). Polymer concentrations are low such that the displaced fluids may be considered shear-thinning. We measured shear viscosity of the aqueous polymer solutions and obtained values for Carreau shear-thinning fluid model parameters at each polymer concentration. Separately, we measured the average bulk diffusivity for each solution. Estimates of the residual film using penetrating fluid tip and mean velocities were measured as a function of Peclet ($Pe$), Reynolds ($Re$), Carreau ($Cu_0$) and a viscous Atwood number based on zero shear-rate viscosity ($At_0$) where the latter two were computed using $c_0$. For $Cu_0 > 1$ we observe a corkscrew type instability where the wavelength increases as diffusion is diminished, but requires a finite amount of diffusion to appear.\\

Tejaswi Soori

en

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131 pages

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