Analytical Modelling of Formation Damage in One-phase and Two-phase Flows: Applications for Laboratory Experiments

Abstract

I hereby present a Ph.D. thesis by publication. This thesis includes six journal publications, four of which have been published and two have been submitted for publication. This thesis is focussed on the application of analytical modelling in laboratory experiments of formation damage in one-phase and two-phase flows in porous media. It targets formation damage with chemical reactions, fines migration, as well as onedimensional (1D) and two-dimensional (2D) two-phase flows accounting for capillary end effects. The thesis develops a novel system of fundamental equations for reactive flows with large deposition of solid reaction products. A new class of exact analytical solutions has been derived for reactive flows with any arbitrary stoichiometric coefficients. The analytical solution yields breakthrough concentration and pressure drop type curves, significantly facilitating the interpretation of the laboratory data. The developed system of governing equations has been validated by laboratory modelling and can be used for the prediction of mineral precipitation chemical reactive flows in porous media. In addition, the three-point pressure method for large scale deposits has been investigated for the first time and the results show that the inclusion of outlet concentration data significantly decreases parameter uncertainty. The large parameter uncertainties without using outlet concentration arise due to the inability for the model to distinguish between a set of deposit profiles. Laboratory studies applying the three-point pressure method have also been conducted for fines migration in porous media to predict formation damage in a hydraulically fractured well. The results show that while pressure measurements alone can predict formation damage due to fracture fluid leak-off, breakthrough fines concentration is able to fully predict model functions and coefficients to characterise the system. The two-phase flow in porous media investigated in this thesis comprises steady-state and transient 1D flow with capillary end effects, and steady-state 2D flow with capillary end effects near a hydraulically fractured production well. Steady-state analytical solutions, along with transient numerical solutions, have been applied in the so-called steady-state-transient test (SSTT). It includes a three-dimensional (3D) modelling of the SSTT with the treatment of the simulated data by a 1D inverse solver. The main result shows a significant reduction in the 3D flow effects when using an inlet distributor with spiral (or concentric-circle) grooves rather than one with halfmoon grooves. Following this result, two SSTTs were carried out in the laboratory. In the concentriccircle SSTT, a weighting method for water cut measurements at the effluent was used, while in the half-moon SSTT, a visualisation method was used. Based on the results, the use of a concentric-circle distributor and the weighting method in SSTTs is recommended. Lastly, the exact solution to the steady-state 2D flow towards a fractured well was derived and applied to predict formation damage due to capillary-trapped water, known as water blocking. The results show water blocking is likely to be a significant factor in the productivity decline for the case study conducted.