Analytical modelling of fines migration in porous media

Abstract

Hereby I present a PhD thesis by publications. Altogether, the thesis includes: a) five journal papers, b) one book chapter, and one c) SPE conference paper. Five journal papers have already been published. The journal publication list includes high-impact- factor academic journals: International Journal of Coal Geology, Geothermics, Journal of Natural Gas Science and Engineering. The list also includes Journal of Petroleum Science and Engineering, which is a major academic journal in petroleum industry. I have also submitted one book chapter to be edited by Springer. Besides, the content of this thesis is published in six full-volume SPE technical papers of Society of Petroleum Engineering. The thesis presents new analytical models for fines migration in porous media. The novelty of this work is the new governing equation system accounting for two effects during fines migration in rocks: slow drift of mobilised fines along rock surface, and the delayed release of fine particles (non-equilibrium effect). Migration of fine particles in natural reservoirs is one of the main causes for formation damage in oil and gas fields. Numerous laboratory observations show that permeability stabilisation time is much longer than one pore volume injected. However, the existing mathematical models for fines migration, which are widely used in petroleum reservoir simulation, cannot predict the long-term stabilisation phenomenon. The new analytical solutions derived in this thesis successfully model the physical mechanisms of the permeability stabilisation delay and match well with laboratory data. Long permeability stabilisation period during coreflood tests exhibiting fines migration is explained by slow fines rolling and sliding, and also by the diffusive delay in particle mobilisation. The analytical models have been derived for both slow fines migration and delayed mobilisation. Laboratory coreflood tests to observe the effects of flow velocity and salinity on fines migration and consequent permeability decline have been carried out, with the measurements of breakthrough fines concentration and pressure drop along the whole core and its sections. Matching of the experimental data, along with the analysis of the tuned coefficients shows that the slow-particle model exhibits higher accuracy of matching and more typical strained-concentration dependency of the tuning parameters than the delay-release model. The effect of temperature on fines migration is analysed systematically, which can be applied to geothermal reservoir conditions. In this thesis, a new analytical solution is derived for the simultaneous processes of deep bed filtration and cake build-up during injection of two-sized particles. Formation of low permeable external filter cake during drilling and water injection has been intensively studied in the literature. The external cake may significantly reduce the well index. There are no existing mathematical models accounting for simultaneous particle filtration through external cake and in the core. The proposed model in this work fills the gap. Two scenarios of cake formation are identified, corresponding to the high and low fractions of small particles injected, respectively. Laboratory coreflooding tests with injection of two-sized particles have been performed, from which the rate and pressure drop data are collected. The data treatment shows excellent agreement between the measured pressure drop history and the modelled result. The derived mathematical models and their analytical solutions in this thesis are applicable to the prediction of the extent of formation damage and the well behaviour in different types of reservoirs, including oil/gas, geothermal and coal bed methane reservoirs. Also, these models can be applied to numerous environmental and chemical engineering processes, including the disposal of industrial wastes into aquifers, propagation of contaminants and pollutants in vadose zone, and industrial water treatment.