MATHEMATICAL MODELING OF SURFACTANT EFFECT ON THE DYNAMICS OF A VISCOUS DROPLET AND THE ALTERATION OF ITS WETTABILITY ON A SOLID SURFACE

• Main Author: YULIANTI (NIM: 30111018), KARTIKA
• Format: Dissertations
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/28400
• Institution: Institut Teknologi Bandung

Chemical injection is one of the techniques to remove or drain more oil from a reservoir, which is known as Enhanced Oil Recovery (EOR). This technique is an <br /> <br /> extension of the water-flooding method, which is done by adding chemicals concentrates such as surfactants (surface active agents) into water injection. The role of surfactant in that technique are to reduce the interfacial tension between oil and water, and to alternate the wettability of oil to becomes preferentially non-wetting <br /> <br /> fluid. As a result, oil might be detached easily or imbibed spontaneously from the porous of rocks. <br /> <br /> In this dissertation, we construct some mathematical models to study effects of an insoluble surfactant on the behavior of a viscous droplet for two phenomena, i.e. <br /> <br /> its wettability alteration, and its movement towards a solid surface. For the first phenomenon we use three different approaches. In the first approach, we solve <br /> <br /> the Navier-Stokes equations to simulate the dynamics of the contact point of the oil droplet immersed in surfactant solution. In constructing numerical schemes for <br /> <br /> equations of the surfactant dynamics, we propose a new method that ensures the surfactant mass conservation. In the second approach, we propose a new method for the contact-point dynamic, involving forces acting on the droplet motion such as the friction force from the wall and the mechanical force balance from the threephase <br /> <br /> contact point. The droplet shape formula is then determined through the surface energy minimization, subjected to mass conservation. In the third approach, <br /> <br /> we investigate the influence of the surfactant concentration to the alteration of the contact angle of a steady sessile droplet. We construct a model for the distribution of the surfactant at the interface and an equation for the shape of droplet. Assuming that the surfactant effect is dominant than the gravity force, the equations are then solved both numerically and asymptotically for a small surfactant concentration. By <br /> <br /> this study, the factors that affect the detachment of the droplet from the substrate are investigated. From the models, it is also found that the surfactant causes the value of the droplet's contact angle is bigger than the free surfactant one. The present result was consistent with some experimental results, which stated that the wettability of an oil drop can be altered to be non-wetting by the surfactant solution. For the second phenomenon, i.e. the influence surfactant to the position changes of an oil droplet moving toward a solid surface, we use two different approaches; the thin film and the fully Navier-Stokes equations. In the first approach, we assume that the fluid between the oil droplet and the substrate can be considered as thin film. In this model, we propose a formulae for the drop's velocity moving downward to the substrate. This formulae reduces the thin fluid two-layers problem into the one layer problem. The effect of the surfactant on the dynamics of the thin film is then investigated. We also examine the case when a little surfactant concentration is added into the system. To the best of our knowledge, the study that involves the <br /> <br /> additional surfactant concentration parameter is still limited. To justify our simulations, the steady state solution is also presented by using the asymptotic expansion method. In the second approach, (fully Navier-Stokes equations), we modify the method we have made to simulate the dynamics of the contact point, in the case of <br /> <br /> droplet moving toward the solid surface, by setting up suitable boundary condition. This model indicates that the presence of the surfactant in the interface only affects <br /> <br /> to slow the movement of the droplet. This is accordance to the result of the thin film approach.