Dissolution and precipitation in subsurface reactive flow with common-ion effect
Ghaderi Zefreh, Masoud
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Simulation of multiphysics, multicomponent and multiphase ﬂow for oil reservoirs has become possible thanks to advances in computing technology. However, computational costs for simulating these strongly coupled processes in systems whose parameters are only known statistically remains a limiting factor. The coupling of the processes and the resulting systems of equations at the current computational power, however, only allows for resolutions of the order of tens to hundreds of metres. The course resolution hampers the understanding through numerical diffusion/dispersion that potentially leads to drastic under or overestimation of processes. Even at ﬁne resolutions, numerical solutions may not provide understanding about the nature of the processes unless an ensemble of solutions is obtained on the whole parameter space. In this dissertation, we aim to provide an understanding of a speciﬁc class of reactive ﬂow in the subsurface. The ultimate goal is to pave the way for a better intuition of reactive ﬂow relevant to precipitation of minerals around well-bore, known as scaling. This thesis presents the analytical solution for the reactive ﬂow of two dissolution/precipitation reactions. The two reactions are coupled through a common ion and therefore we have the co-ion effect. We account for the volume of precipitate and hence allow changes of the porosity during dissolution and precipitation. The solution is an extension to the one provided by Helfferich . An important ﬁnding here is the induced precipitation of one salt in the course of dissolution of another salt. Accounting for the volume of precipitates allows to analyse clogging of the medium using the ratio of molar densities and equilibrium constants for salts. Moreover, a streamline approach is discussed to extend the solution to multidimensional settings. In developing the streamline simulator, we account for the heterogeneity of the medium which creates a system of hyperbolic PDEs with discontinuous ﬂux function. It is shown that this speciﬁc problem can be solved following the minimum jump entropy condition. Hence, an analytical approach is provided which removes any numerical dispersion in transport of the ions. However, this imposes zero mixing at the well which requires another treatment. Mixing at the well, therefore, needs to be explicitly modelled. A such model is proposed and couplled with the transport similar to conventional streamline simulators. Finally, the problem is studied in the context of fractured networks. In fracture networks, mixing becomes more important because several locations exist at which different streams can mix. These locations are the intersection of the fractures which have tiny volumes comparing to the length of fractures. Hence, mixing and transport occur in scales that are different by several orders of magnitude. A novel algorithm is developed and studied for this type of problems. It is concluded that to effectively simulate the single phase transport of ions in networks of fractures, three time steps need to be identiﬁed. The ﬁrst is a time-step at which pressure of the system needs to be updated due to signiﬁcant changes in the intersections. This is similar to conventional streamline simulators. In addition, a list of times for arrival of fronts at mixers needs to be calculated. This is done via solving an equation of motion for each front. Finally, if a dissolution is happening, the time at which dissolution terminates needs to predicted. No other spatial information is required and hence the difﬁculty in the difference of scales is circumvented. The beneﬁt of this approach is the understanding it offers about the problem as well as the computational advantage over standard ﬁnite volume methods.