Numerical studies of reactive polymer flows in porous materials

This dissertation presents a new numerical model of reactive polymer flow in heterogeneous porous media. A moment representation of the log-normal polymer molecular weight distribution is used to model polymer as a multi-component species. Three leading moments are used to simulate the polymer transport and reaction processes in a two-dimensional porous medium. A new operator splitting technique that allows the moment equations for polymerization to be incorporated into a finite-difference transport model is developed. The novelty of this approach is the use of two different dependent variables (for the transport versus reaction parts of the problem). It is significant from a physical standpoint because previous techniques did not allow us to observe the full evolution of polymer molecular weights in space and time. In this dissertation, two types of flows are examined. The first is the injection of a polymerizing fluid into a heterogeneous material containing low viscosity fluid (e.g., air or water). Simulations show that, depending on the Damkohler number, preferential loss of material permeability can occur in either low or high permeability regions. Because this effect dictates subsequent flow patterns, this result suggests that front stability can be controlled through proper design of the flow dynamics versus reaction dynamics. The formation of steady viscous fingers was observed, which is a fundamentally different phenomenon than previously observed transient viscous fingering formed during displacements. It is affected by the competition between reaction and convection, which allows the behavior to be correlated with the Damkohler number. A critical Damkohler number exists, above which steady-state conditions are not observed. The critical Damkohler number is affected by the Peclet number and permeability field. The second type of simulation is the injection of polymerizing fluids under conditions that lead to viscous instabilities. Results show the Damkohler number again to be a critical parameter. In both cases, the scale and structure of the material heterogeneities have a significant effect on the resulting flow. These research results provide important information for various polymer processing applications

Modélisation et simulation de la stimulation acide des puits carbonatés

L'injection d'acide dans un puits au sein de roches carbonatées permet l'amélioration de sa productivité, en particulier si celui-ci est endommagé. Cette opération s'appuie sur un mécanisme instable qui sous certaines conditions produit de longues percées appelées "wormholes". L'objectif pour l'opérateur est d'utiliser cette instabilité afin de reconnecter le puits au réservoir en minimisant le temps du traitement et la quantité d'acide nécessaire. Les travaux présentés dans cette thèse ont pour objectif d'améliorer la compréhension des mécanismes de l'instabilité et optimiser le traitement acide. Dans une première partie nous réalisons une série d'études de stabilité linéaire du front de dissolution d'un milieu poreux. Les résultats expliquent les rôles des nombres adimensionnels dans les transitions entre les différents régimes de dissolution et permettent de prédire ces transitions. Nous utilisons ensuite des simulations d'acidification de carottes pour étudier la densité de wormholes, les mécanismes de la compétition entre wormholes ainsi que l'effet du confinement des carottes sur les figures de dissolution dans des géométries 2D et 3D, cartésiennes et radiales. Dans une dernière partie nous proposons une modélisation à grande échelle de la dissolution basée sur une approche double milieux. Ce modèle est présenté avec un exemple de simulation de traitement acide d'un puits. Enfin, ce simulateur est inclus dans une boucle d'inversion permettant d'optimiser les paramètres du traitement en fonction de la production d'huile du puits.ABSTRACT : Matrix acidizing of a well in a carbonate reservoir improves its productivity, especially when the well is damaged. This stimulation technique relies on an unstable process which creates, under specific conditions, empty channels called “wormholes”. The objective of the operator is to use this instability to reconnect the well to the reservoir while minimizing the duration of the treatment and the volume of acid injected. The aim of the present thesis is to improve the understanding of the mechanisms of instability and to optimize the acid treatment. In the first part we present a series of linear stability analysis of the dissolution front in a porous media. Results explain the role of dimensionless numbers in transitions between the different dissolution regimes and serve to predict these transitions. We also use simulations of core acidizing to study the wormhole density, the mechanism of wormhole competition and the effect of confinement induced by the core boundaries on dissolution patterns in 2D and 3D, in linear and radial geometries. Then, in the second part, we propose a large scale model to simulate full acid treatments, based on a dual porosity approach. An example of simulation of a full acid treatment illustrates the model. Finally, we link this acidizing simulator to a reservoir simulator and an inversion software in order to optimise the treatment parameters, as a function of the oil productio