Unlike the traditional two-stage methods, a conditional and inverse-conditional simulation approach may directly generate independent, identically distributed realizations to honor both static data and state data in one step. The Markov chain Monte Carlo (McMC) method was proved a powerful tool to perform such type of stochastic simulation. One of the main advantages of the McMC over the traditional sensitivity-based optimization methods to inverse problems is its power, flexibility and well-posedness in incorporating observation data from different sources. In this work, an improved version of the McMC method is presented to perform the stochastic simulation of reservoirs and aquifers in the framework of multi-Gaussian geostatistics. First, a blocking scheme is proposed to overcome the limitations of the classic single-component Metropolis-Hastings-type McMC. One of the main characteristics of the blocking McMC (BMcMC) scheme is that, depending on the inconsistence between the prior model and the reality, it can preserve the prior spatial structure and statistics as users specified. At the same time, it improves the mixing of the Markov chain and hence enhances the computational efficiency of the McMC. Furthermore, the exploration ability and the mixing speed of McMC are efficiently improved by coupling the multiscale proposals, i.e., the coupled multiscale McMC method. In order to make the BMcMC method capable of dealing with the high-dimensional cases, a multi-scale scheme is introduced to accelerate the computation of the likelihood which greatly improves the computational efficiency of the McMC due to the fact that most of the computational efforts are spent on the forward simulations. To this end, a flexible-grid full-tensor finite-difference simulator, which is widely compatible with the outputs from various upscaling subroutines, is developed to solve the flow equations and a constant-displacement random-walk particle-tracking method, which enhances the com / Fu, J. (2008). A markov chain monte carlo method for inverse stochastic modeling and uncertainty assessment [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/1969

This thesis focuses on solute transport upscaling. Upscaling of solute transport is usually required to obtain computationally efficient numerical models in many field applications such as, remediation of aquifers, environmental risk to groundwater resources or the design of underground repositories of nuclear waste. The non-Fickian behavior observed in the field, and manifested by peaked concentration profiles with pronounced tailing, has questioned the use of the classical advection-dispersion equation to simulate solute transport at field scale using numerical models with discretizations that cannot capture the field heterogeneity. In this context, we have investigated the use of the advection-dispersion equation with mass transfer as a tool for upscaling solute transport in a general numerical modeling framework. Solute transport by groundwater is very much affected by the presence of high and low water velocity zones, where the contaminant can be channelized or stagnant. These contrasting water velocity zones disappear in the upscaled model as soon as the scale of discretization is larger that the size of these zones. We propose, for the modeling solute transport at large scales, a phenomenological model based on the concept of memory functions, which are used to represent the unresolved processes taking place within each homogenized block in the numerical models. We propose a new method to estimate equivalent blocks, for which transport and mass transfer parameters have to be provided. The new upscaling technique consists in replacing each heterogeneous block by a homogeneous one in which the parameters associated to a memory functions are used to represent the unresolved mass exchange between highly mobile and less mobile zones occurring within the block. Flow upscaling is based on the Simple Laplacian with skin, whereas transport upscaling is based in the estimation of macrodispersion and mass transfer parameters as a result of the interpretation of the r / Llerar Meza, G. (2009). Upscaling nonreactive solute transport [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/5848