Hamidreza M. Nick

PoreFlow: A complex pore-network model for simulation of reactive transport in variably saturated porous media

This study introduces PoreFlow, a pore-network modeling tool capable of simulating fluid flow and multi-component reactive and adsorptive transport under saturated and variably saturated conditions. PoreFlow includes a variety of modules, such as: pore network generator, drainage simulator, calculation of pressure and velocity distributions, and modeling of reactive solute transport accounting for advection and diffusion. The pore space is represented using a multi-directional pore-network capable of capturing the random structure of a given porous media with user-defined directional connectivities for anisotropic pore structures. The chemical reactions can occur within the liquid phase, as well as between the liquid and solid phases which may result in an evolution of porosity and permeability. Under variably saturated conditions the area of interfaces changes with degree of the fluid saturation. PoreFlow uses complex formulations for more accurate modeling of transport problems in presence of the nonwetting phase. This is done by refining the discretization within drained pores. An implicit numerical scheme is used to solve the governing equations, and an efficient substitution method is applied to considerably minimize computational times. Several examples are provided, under saturated and variably saturated conditions, to demonstrate the model applicability in hydrogeology problems and petroleum fields. We show that PoreFlow is a powerful tool for upscaling of flow and transport in porous media, utilizing different pore scale information such as various interfaces, phase distributions and local fluxes and concentrations to determine macro scale properties such as average saturation, relative permeability, solute dispersivity, adsorption coefficients, effective diffusion and tortuosity. Such information can be used as constitutive relations within continuum scale governing equations to model physical and chemical processes more accurately at the larger scales.

Upscaling two-phase flow in naturally fractured reservoirs

Simulation grid blocks of naturally fractured reservoirs contain thousands of fractures with variable flow properties, dimensions, and orientations. This complexity precludes direct incorporation into field-scale models. Macroscopic laws capturing their integral effects on multiphase flow are required. Numerical discrete fracture and matrix simulations show that ensemble relative permeability as a function of water saturation (kri[Sw]), water breakthrough, and cut depend on the fraction of the cross-sectional flux that occurs through the fractures. This fracture-matrix flux ratio (qf/qm) can be quantified by steady-state computation. Here we present a new semianalytical model that uses qf/qm and the fracture-related porosity (f) to predict kri(Sw) capturing that, shortly after the first oil is recovered, the oil relative permeability (kro) becomes less that that of water (krw), and krw/kro approaches qf/qm as soon as the most conductive fractures become water saturated. To include a capillary-driven fracture-matrix transfer into our model, we introduce the nonconventional parameter Af,w(Sw), the fraction of the fracture-matrix interface area in contact with the injected water for any grid-block average saturation. The Af,w(Sw) is used to scale the capillary transfer modeled with conventional transfer functions and expressed in terms of a rate- and capillary-pressure-dependent kro. All predicted parameters can be entered into conventional reservoir simulators. We explain how this is accomplished in both, single- and dual-continua formulations. The predicted grid-block-scale fractional flow (fi[Sw]) is convex with a near-infinite slope at the initial saturation. The upscaled flow equation therefore does not contain an Sw shock but a long leading edge, capturing the progressively widening saturation fronts observed in numerical experiments published previously.

The impact of different aperture distribution models and critical stress criteria on equivalent permeability in fractured rocks

Predicting equivalent permeability in fractured reservoirs requires an understanding of the fracture network geometry and apertures. There are different methods for defining aperture, based on outcrop observations (power law scaling), fundamental mechanics (sublinear length-aperture scaling), and experiments (Barton-Bandis conductive shearing). Each method predicts heterogeneous apertures, even along single fractures (i.e., intrafracture variations), but most fractured reservoir models imply constant apertures for single fractures. We compare the relative differences in aperture and permeability predicted by three aperture methods, where permeability is modeled in explicit fracture networks with coupled fracture-matrix flow. Aperture varies along single fractures, and geomechanical relations are used to identify which fractures are critically stressed. The aperture models are applied to real-world large-scale fracture networks. (Sub)linear length scaling predicts the largest average aperture and equivalent permeability. Barton-Bandis aperture is smaller, predicting on average a sixfold increase compared to matrix permeability. Application of critical stress criteria results in a decrease in the fraction of open fractures. For the applied stress conditions, Coulomb predicts that 50% of the network is critically stressed, compared to 80% for Barton-Bandis peak shear. The impact of the fracture network on equivalent permeability depends on the matrix hydraulic properties, as in a low-permeable matrix, intrafracture connectivity, i.e., the opening along a single fracture, controls equivalent permeability, whereas for a more permeable matrix, absolute apertures have a larger impact. Quantification of fracture flow regimes using only the ratio of fracture versus matrix permeability is insufficient, as these regimes also depend on aperture variations within fractures.

A geometrically based method for predicting stress-induced fracture aperture and flow in discrete fracture networks

Modeling of fluid flow in naturally fractured reservoirs is often done through modeling and upscaling of discrete fracture networks (DFNs). The two-dimensional fracture geometry required for DFNs is obtained from subsurface and outcropping analog data. However, these data provide little information on subsurface fracture aperture, which is essential for quantifying porosity and permeability. Apertures are difficult to obtain from either outcropping or subsurface data and are therefore often based on fracture size or scaling relationships, but these do not consider the orientation and spatial distribution of fractures with respect to the in situ stress field. Using finite-element simulations, mechanical aperture can be modeled explicitly, but because changes in fracture geometry require renewed meshing and simulating, this approach is not easily integrated into subsurface DFN modeling workflows. We present a geometrically based method for calculating the shear-induced hydraulic aperture, that is, an aperture of up to 0.5 mm (0.02 in.) that can result from shear displacement along irregular fracture walls. The geometrically based method does not require numerical simulations, but it can instead be directly applied to DFNs using the fracture orientation and spacing distributions in combination with an estimate of the regional stress tensor and orientation. The frequency distribution of hydraulic aperture from the geometrically based method is compared with finite-element models constructed from five real fracture networks, digitized from outcropping pavements. These networks cover a wide range of possible geometries and spatial distributions. The geometrically based method predicts the average hydraulic aperture and equivalent permeability of fractured porous media with error margins of less than 5%.

An integrated workflow for stress and flow modelling using outcrop-derived discrete fracture networks

Fluid flow in naturally fractured reservoirs is often controlled by subseismic-scale fracture networks. Although the fracture network can be partly sampled in the direct vicinity of wells, the inter-well scale network is poorly constrained in fractured reservoir models. Outcrop analogues can provide data for populating domains of the reservoir model where no direct measurements are available. However, extracting relevant statistics from large outcrops representative of inter-well scale fracture networks remains challenging. Recent advances in outcrop imaging provide high-resolution datasets that can cover areas of several hundred by several hundred meters, i.e. the domain between adjacent wells, but even then, data from the high-resolution models is often upscaled to reservoir flow grids, resulting in loss of accuracy. We present a workflow that uses photorealistic georeferenced outcrop models to construct geomechanical and fluid flow models containing thousands of discrete fractures covering sufficiently large areas, that does not require upscaling to model permeability. This workflow seamlessly integrates geomechanical Finite Element models with flow models that take into account stress-sensitive fracture permeability and matrix flow to determine the full permeability tensor. The applicability of this workflow is illustrated using an outcropping carbonate pavement in the Potiguar basin in Brazil, from which 1082 fractures are digitised. The permeability tensor for a range of matrix permeabilities shows that conventional upscaling to effective grid properties leads to potential underestimation of the true permeability and the orientation of principal permeabilities. The presented workflow yields the full permeability tensor model of discrete fracture networks with stress-induced apertures, instead of relying on effective properties as most conventional flow models do. Display Omitted A new workflow for realistic discrete fracture-matrix flow models is proposed.Realistic fracture geometries are obtained from outcrops using photogrammetry.Aperture and permeability are calculated from geomechanical Finite Element models.The result is a permeability tensor for large-scale discrete fracture-matrix models.

Application of infrared thermography for temperature distributions in fluid-saturated porous media

Infrared thermography has increasingly gained importance because of environmental and technological advancements of this method and is applied in a variety of disciplines related to non-isothermal flow. However, it has not been used so far for quantitative thermal analysis in saturated porous media. This article suggests infrared thermographic approach to obtain the entire surface temperature distribution(s) in water-saturated porous media. For this purpose, infrared thermal analysis is applied with in situ calibration for a better understanding of the heat transfer processes in porous media. Calibration is achieved with a combination of invasive sensors which are inserted into the medium and non-invasive thermal sensors in which sensors are not inserted to measure temperatures but it works through the detection of infrared radiation emitted from the surface. Thermocouples of relatively thin diameter are used to minimize the disturbance for flow. Thermocouples give the temperature values at specified positions inside the porous medium, and these values are compared with the values suggested by the infrared thermographic device at the same positions, in the calibration exercise. The calibration process was repeated for different temperatures and flow rates to get the temperature distributions of the whole material inside the system. This technique enables us to measure accurate two-dimensional temperature distributions, which is not possible by using thermocouples only. Continuous point heat sources at different flow rates and temperatures are studied experimentally. Additionally, it offers numerical simulations of the experiments utilizing a finite element-based model. A two-dimensional density and viscosity-dependent flow and transport model accounting for thermal dispersion is utilized to simulate the experimental results. Possible small heat losses from the surface are incorporated in the model according to the properties and thickness of the Plexiglass material used for the construction of the experiment tank. The numerical results agree well with the experimental observations.