Sharif Digital Repository

The petroleum industry tends to paint an optimistic picture with respect to future petroleum availability. In order to anticipate demand, the size of connected volume of hydrocarbon of fields needs to be known. During the early stage of life of a reservoir, due to the lake of certain data, connected volume of hydrocarbon is usually based on analogues or rules of thumb and not detailed reservoir modeling. Therefore, there is a great incentive to produce physically-based methodologies to make an estimation of connected volume of hydrocarbon. Percolation theory is used to estimate the connected volume of hydrocarbon very fast. Furthermore, the result has been validated against areal field... 

We investigate the effects of anisotropy on the finite-size scaling of connectivity and conductivity of continuum percolation in three dimensions. We consider a system of size X×Y×Z in which cubic bodies of size a×b×c are placed randomly. We define two aspect ratios to request anisotropy then we expect that the displacement of average connected fraction P (averaged over the realizations), about the isotropic universal curves will be a function of the two aspect ratios. This is accounted by considering an apparent percolation threshold in each direction which leads to 50% of realizations connecting in that direction. We find the aspect ratios' dependency of the apparent threshold and... 

The outcome of the classic percolation approach is several power-law curves with some universal (critical) exponents. Here, the universality means that these power laws as well as their critical exponents, which control the global properties of a system, are independent of its details. Classic percolation considers the connectivity between two lines and two faces at opposite sides of a system in 2- and 3D problems, respectively; whereas, in practice (e.g. hydrocarbon formations), production and injection wells are represented by points (in 2D areal models) and lines (in 3D models). This study presents the results of Monte Carlo simulations of a 2D percolation model wherein the connection... 

Simultaneous capillary dominated displacement of the wetting and non-wetting phases are processes of interest in many disciplines including modeling of the penetration of polluting liquids in hydrology or the secondary migration in petroleum reservoir engineering. Percolation models and in particular invasion percolation is well suited to characterize the slow immiscible displacement of two fluids when both the gravity and viscous effects are negligible. In particular, the characteristic of the percolating cluster and the other important percolation properties at the breakthrough can be inferred. However, with the inclusion of the gravity forces, the behavior may change. For example, as the... 

The standard percolation theory uses objects of the same size. Moreover, it has long been observed that the percolation properties of the systems with a finite distribution of sizes are controlled by an effective size and consequently, the universality of the percolation theory is still valid. In this study, the effect of power law size distribution on the critical exponents of the percolation theory of the two dimensional models is investigated. Two different object shapes i.e., stick-shaped and square are considered. These two shapes are the representative of the fractures in fracture reservoirs and the sandbodies in clastic reservoirs. The finite size scaling arguments are used for the... 

Simultaneous capillary dominated displacement of the wetting and non-wetting phases are processes of interest in many disciplines including modeling of the penetration of polluting liquids in hydrology or the secondary migration in petroleum reservoir engineering. Percolation models and in particular invasion percolation is well suited to characterize the slow immiscible displacement of two fluids when both the gravity and viscous effects are negligible. In particular, the characteristic of the percolating cluster and the other important percolation properties at the breakthrough can be inferred. However, with the inclusion of the gravity forces, the behavior may change. For example, as the... 

Correlations between electrical and thermal conduction in polymer composites are blurred due to the complex contribution of charge and heat carriers at the nanoscale junctions of filler particles. Conflicting reports on the lack or existence of thermal percolation in polymer composites have made it the subject of great controversy for decades. Here, we develop a generalized percolation framework that describes both electrical and thermal conductivity within a remarkably wide range of filler-to-matrix conductivity ratios (Y f / Y m), covering 20 orders of magnitude. Our unified theory provides a genuine classification of electrical conductivity with typical Y f / Y m ≥ 10 10 as... 

The connectivity of high conductivity pathways in geological formations depend on the spatial distribution of geological heterogeneities that may appear on various length scales. Appropriate modeling of this is crucial within in hydrology and petroleum systems. The approach taken in this study is to use percolation theory to quantify the connectivity, hydraulic conductivity, and breakthrough time behavior between an injector and a producer within such systems. In particular, a three-dimensional overlapping sandbody model is considered which assumes that the geological formation can be split into either conductive flow units (i. e., good sands) or non-conductive units (i. e., poor sands). The... 

The knowledge of the conductivity across the reservoir that is based on the swept fraction controls the recoverable rates of the hydrocarbon in the secondary displacement processes. Most of the time, we need a fast estimation of the conductivity for decision making during field development. Percolation theory is a very useful tool to get this goal. According to this fact that the results of this method are universal, they could be used widely. In this study connectivity and conductivity percolation models are developed and the universal exponents for connectivity and conductivity in fractured reservoir as well as their dependency on the correlation length are investigated. For L< ξ the... 

The knowledge of the conductivity across the reservoir that is based on the swept fraction controls the recoverable rates of the hydrocarbon in the secondary displacement processes. Most of the time, we need a fast estimation of the conductivity for decision making during field development. Percolation theory is a very useful tool to get this goal. According to this fact that the results of this method are universal, they could be used widely. In this study connectivity and conductivity percolation models are developed and the universal exponents for connectivity and conductivity in fractured reservoir as well as their dependency on the correlation length are investigated. For L< ξ the... 

We study loop-erased random walk (LERW) on the percolation cluster, with occupation probability p≥pc, in two and three dimensions. We find that the fractal dimensions of LERWp are close to normal LERW in a Euclidean lattice, for all p>pc. However, our results reveal that LERW on critical incipient percolation clusters is fractal with df=1.217±0.002 for d=2 and 1.43±0.02 for d=3, independent of the coordination number of the lattice. These values are consistent with the known values for optimal path exponents in strongly disordered media. We investigate how the behavior of the LERWp crosses over from Euclidean to fractal geometry by gradually decreasing the value of the parameter p from 1 to... 

We present a model of fractures based on the idea that the elastic free energy due to the fracture density follows a Boltzmann distribution. The resulting expression for the spatial correlation in the displacement of fractures is used as an objective function in a simulated annealing algorithm to generate realizations of correlated fracture networks. This approach determines the appropriate statistical distribution for the fractures (e.g., length distribution) rather than imposing them as is done conventionally. The model consists of two families of parallel fractures which are perpendicular under isotropic conditions. There also exists a positive correlation between the position of... 

The connectivity of high conductivity pathways in geological formations depend on the spatial distribution of geological heterogeneities that may appear on various length scales. Appropriate modeling of this is crucial within in hydrology and petroleum systems. The approach taken in this study is to use percolation theory to quantify the connectivity, hydraulic conductivity, and breakthrough time behavior between an injector and a producer within such systems. In particular, a three-dimensional overlapping sandbody model is considered which assumes that the geological formation can be split into either conductive flow units (i. e., good sands) or non-conductive units (i. e., poor sands). The... 

Complicated sedimentary processes control the spatial distribution of geological heterogeneities. This serves to make the nature of the fluid flow in the hydrocarbon reservoirs immensely complex. Proper modeling of these heterogeneities and evaluation of their connectivity are crucial and affects all aspects of fluid flow. Since the natural variability of heterogeneity occurs in a myriad of length scales, accurate modeling of the rock type connectivity requires a very fine scheme, which is computationally very expensive. Hence, this makes other alternative methods such as the percolation approach attractive and necessary. The percolation approach considers the hypothesis that a reservoir can... 

The connectivity between two points in porous media is important for evaluating hydrocarbon recovery in underground reservoirs or toxic migration in waste disposal. For example, the connectivity between a producer and an injector in a hydrocarbon reservoir impact the fluid dispersion throughout the system. The conventional approach, flow simulation, is computationally very expensive and time consuming. Alternative method employs percolation theory. Classical percolation approach investigates the connectivity between two lines (representing the wells) in 2D cross sectional models whereas we look for the connectivity between two points (representing the wells) in 2D aerial models. In this...