Numerical Modeling of Polyvinyl Alcohol (PVA) Swelling and Dissolution in Water

This study investigates the numerical models for polymer dissolution, with a long-term goal of developing high performance dissolvable elastomer from Polyvinyl Alcohol (PVA) replacing current not dissolvable rubber based materials. With fast development of hydraulic-fracturing in past 15 years, the oil and gas industry is in great need of dissolvable materials to fabricate certain temporary downhole tools in replacing traditional metals/rubbers/composite parts. Such dissolvable tools can eliminate the current downhole milling and back-flush operations to meet the high pressure (>70MPa) and high temperature (>100oC) working environment, most of current “dissolvable” elastomers are mixtures of rubber and dissolvable polymers (such as Polylactic acid and poly(glycolic acid)) to achieve high ductility. These mixtures are only degradable and will break into small pieces after reactions. Starting from 2016, our group has been developing PVA based elastomer that will have comparable properties as acrylonitrile butadiene rubber (NBR). PVA is a known biocompatible and water dissolvable plastic material. What make it interesting is that water can act as a very effective plasticizer and alter its mechanical properties. PVA shows glassy mechanical behavior at nominal conditions, but becomes rubbery-like from water addition. With enough water, PVA molecules will disperse in water and form a solution. This study looks at the numerical solution of the PVA swelling and dissolving process in water. Our polymer dissolution model uses thermodynamics and kinematics. Thermodynamics explains why dissolution happens in the PVA/water looking at free energy differences for the initial and end states of polymer solvent system. Kinematics gives an insight to the process of polymer dissolution. At first the polymer only swells as small amount of solvent penetrates it and no dissolution occurs. Local solvent concentration is low and water molecules within the polymer act as a plasticizer. Accompany the increasing water concentration, there is a corresponding minimum time called de Genne’s reptation time, after which individual polymer chains is considered to disentangle from the bulk polymer. This moment defines the time after which the polymer dissolution begins. Here proposed our own numerical polymer dissolution model building on the kinematic models from literature. In solving the double moving boundary problems of swelling and dissolution, Landau transform is introduced to deal with the changing domains. An iterative scheme to track the location of the moving boundary demarking the polymer-solvent intersection at every time step has been developed to solve the problem. Therefore, our own methods and algorithms are introduced. The model’s results showed good qualitative agreement with published experimental results from others. A quantitative analysis showed that total polymer amount is not conserved through time initially. Conservation was obtained by modifying the governing equation of the moving boundary. Our model is a good foundation, but potential enhancements such non-linearization and expansion two dimensions are good opportunities for further work.