Maša Prodanović

Multiscale, Multiphysics Network Modeling of Shale Matrix Gas Flows

We present a pore network model to determine the permeability of shale gas matrix. Contrary to the conventional reservoirs, where permeability is only a function of topology and morphology of the pores, the permeability in shale depends on pressure as well. In addition to traditional viscous flow of Hagen–Poiseuille or Darcy type, we included slip flow and Knudsen diffusion in our network model to simulate gas flow in shale systems that contain pores on both micrometer and nanometer scales. This is the first network model in 3D that combines pores with nanometer and micrometer sizes with different flow physics mechanisms on both scales. Our results showed that estimated apparent permeability is significantly higher when the additional physical phenomena are considered, especially at lower pressures and in networks where nanopores dominate. We performed sensitivity analyses on three different network models with equal porosity; constant cross-section model (CCM), enlarged cross-section model (ECM) and shrunk length model (SLM). For the porous systems with variable pore sizes, the apparent permeability is highly dependent on the fraction of nanopores and the pores’ connectivity. The overall permeability in each model decreased as the fraction of nanopores increased.

Imaged-based multiscale network modelling of microporosity in carbonates

Abstract Diagenetic changes such as cementation or dissolution have a strong control on carbonate pore structure, and often disconnect the original intergranular pore space. Spatial distribution of submicron porosity (microporosity) that develops in the process, as well as its influence on flow properties, is difficult to image and characterize. Yet, a petrophysically rigorous pore-scale model that accounts for submicron porosity interconnectivity would help in the understanding and development of carbonate reservoirs dominated by microporosity. We present algorithms to geometrically match pore–throat networks from two separate length scales that can be extracted directly from three-dimensional (3D) rock images, or be constructed to match the relevant measured properties. We evaluate the combined influence of cementation and dissolution using a Bentheimer Sandstone sample, as well as image-identified microporosity on flow transport properties in an Estaillades Limestone sample.

Effects of Magnetic Field on the Motion of Multiphase Fluids Containing Paramagnetic Nanoparticles in Porous Media

When paramagnetic nanoparticles are adsorbed at the oil-water interface or dispersed in one of the fluid phases in reservoir rock pores, then exposed to an external magnetic field, the resultant particle movements displace the interface. Interfacial tension acts as a restoring force, leading to interfacial fluctuation and a pressure (sound) wave. Here we focus on the interface motion. We apply the theory of ferrofluids to the case of an interface in a cylindrical pore. The predictions are consistent with experiments with an aqueous suspension of iron oxide nanorods in which the interface motion is measured by optical coherence tomography. The relative densities of the fluid phases (air/aqueous and dodecane/aqueous in our case) strongly affect the displacement of the interface. Application of a magnetic field introduces pressure-like terms into the equation of fluid phase motion. We then recast the problem in terms of interface motion, extending a numerical interface-tracking model based on the level-set method to account for capillarity and magnetic pressures simultaneously. We use the model to illustrate the motion of an interface between inviscid fluids at the pore scale when magnetic forces are imposed on one fluid phase.

Numerical Algorithms for Network Modeling of Yield Stress and other Non-Newtonian Fluids in Porous Media

Many applications involve the flow of non-Newtonian fluids in porous, subsurface media including polymer flooding in enhanced oil recovery, proppant suspension in hydraulic fracturing, and the recovery of heavy oils. Network modeling of these flows has become the popular pore-scale approach for understanding first-principles flow behavior, but strong nonlinearities have prevented larger-scale modeling and more time-dependent simulations. We investigate numerical approaches to solving these nonlinear problems and show that the method of fixed-point iteration may diverge for shear-thinning fluids unless sufficient relaxation is used. It is also found that the optimal relaxation factor is exactly equal to the shear-thinning index for power-law fluids. When the optimal relaxation factor is employed it slightly outperforms Newton’s method for power-law fluids. Newton-Raphson is a more efficient choice (than the commonly used fixed-point iteration) for solving the systems of equations associated with a yield stress. It is shown that iterative improvement of the guess values can improve convergence and speed of the solution. We also develop a new Newton algorithm (Variable Jacobian Method) for yield-stress flow which is orders of magnitude faster than either fixed-point iteration or the traditional Newton’s method. Recent publications have suggested that minimum-path search algorithms for determining the threshold pressure gradient (e.g., invasion percolation with memory) greatly underestimate the true threshold gradient when compared to numerical solution of the flow equations. We compare the two approaches and reach the conclusion that this is incorrect; the threshold gradient obtained numerically is exactly the same as that found through a search of the minimum path of throat mobilization pressure drops. This fact can be proven mathematically; mass conservation is only preserved if the true threshold gradient is equal to that found by search algorithms.

A Multiscale Method Coupling Network and Continuum Models in Porous Media I: Steady-State Single Phase Flow

We propose a numerical multiscale method for coupling a conservation law for mass at the continuum scale with a discrete network model that describes the microscale flow in a porous medium. In this work we focus on coupling pressure equations. Evaluating pressure from a detailed network model over a large physical domain is typically computationally very expensive. We assume that over the same physical domain there exists an effective mass conservation equation at the continuum scale which could have been solved efficiently if the equation had been explicitly given. Our coupling method uses local simulations on sampled microscale domains to evaluate the continuum equation and thus solve for the pressure in the full domain. We allow nonlinearity in the network model as well as in the mass conservation equation. Convergence of the coupling method is analyzed. In the case where classical homogenization applies, we prove convergence of the proposed multiscale solutions to the homogenized equations. Numerical ...

Numerical Simulation of Diagenetic Alteration and Its Effect on Residual Gas in Tight Gas Sandstones

In this study, we numerically cemented a segmented X-ray microtomography image of a sandstone to understand changes to pore space connectivity, capillary control on gas, and water distributions, and ultimately production behavior in tight gas sandstone reservoirs. Level set method-based progressive quasi-static algorithm (a state-of-the-art direct simulation of capillarity-dominated fluid displacement) was used to find the gas/water configurations during drainage and imbibition cycles. Further, we account for gas–water interfacial tension changes using 1D burial history model based on available geologic data. We have found the displacement simulation method robust, and that diagenetic changes impart a significantly larger effect on gas trapping compared with interfacial tension changes.

Deformation-assisted fluid percolation in rock salt

Salted away no longer? Rock salt deposits are thought to be impermeable to fluid flow and so are candidates for nuclear waste repositories. Ghanbarzadeh et al. found that some salt deposits in the Gulf of Mexico are infiltrated by oil and other hydrocarbons. If these salt domes are not completely isolated from the surrounding environment, they will not be suitable for deep geological waste storage sites. Science, this issue p. 1069 Salt deposits in the Gulf of Mexico show evidence of deformation-driven fluid percolation. Deep geological storage sites for nuclear waste are commonly located in rock salt to ensure hydrological isolation from groundwater. The low permeability of static rock salt is due to a percolation threshold. However, deformation may be able to overcome this threshold and allow fluid flow. We confirm the percolation threshold in static experiments on synthetic salt samples with x-ray microtomography. We then analyze wells penetrating salt deposits in the Gulf of Mexico. The observed hydrocarbon distributions in rock salt require that percolation occurred at porosities considerably below the static threshold due to deformation-assisted percolation. Therefore, the design of nuclear waste repositories in salt should guard against deformation-driven fluid percolation. In general, static percolation thresholds may not always limit fluid flow in deforming environments.

Correlating Gas Transport Parameters and X-Ray Computed Tomography Measurements in Porous Media

Abstract Gas transport parameters and X-ray computed tomography (CT) measurements in porous medium under controlled and identical conditions provide a useful methodology for studying the relationships among them, ultimately leading to a better understanding of subsurface gaseous transport and other soil physical processes. The objective of this study was to characterize the relationships between gas transport parameters and soil-pore geometry revealed by X-ray CT. Sands of different shapes with a mean particle diameter (d50) ranging from 0.19 to 1.51 mm were used as porous media under both air-dried and partially saturated conditions. Gas transport parameters including gas dispersivity (&agr;), diffusivity (DP/D0), and permeability (ka) were measured using a unified measurement system (UMS). The 3DMA-Rock computational package was used for analysis of three-dimensional CT data. A strong linear relationship was found between &agr; and tortuosity calculated from gas transport parameters ( ), indicating that gas dispersivity has a linear and inverse relationship with gas diffusivity. A linear relationship was also found between ka and d50/TUMS2, indicating a strong dependency of ka on mean particle size and direct correlation with gas diffusivity. Tortuosity (TMFX) and equivalent pore diameter (deq.MFX) analyzed from microfocus X-ray CT increased linearly with increasing d50 for both Granusil and Accusand and further showing no effect of particle shape. The TUMS values showed reasonably good agreement with TMFX values. The ka showed a strong relationship when plotted against deq.MFX/TMFX2, indicating its strong dependency on pore size distribution and tortuosity of pore space.

Investigating Matrix/Fracture Transfer via a Level Set Method for Drainage and Imbibition

Multiphase flow and transport phenomena within fractures are important because fractures often represent primary flow conduits in otherwise low permeability rock. Flows within the fracture, between the fracture and the adjacent matrix, and through the pore space within the matrix typically happen on different length and time scales. Capturing these scales experimentally is difficult. It is therefore useful to have a computational tool that establishes the exact position and shape of fluid/fluid interfaces in realistic fracture geometries. The level set method is such a tool. Our progressive quasistatic (PQS) algorithm based on the level set method finds detailed, pore-level fluid configurations satisfying the Young-Laplace equation at a series of prescribed capillary pressures. The fluid volumes, contact areas and interface curvatures are readily extracted from the configurations. The method automatically handles topological changes of the fluid volumes as capillary pressure varies. It also accommodates arbitrarily complicated shapes of solid confining surfaces. Here we apply the PQS method to analytically defined fracture faces and aperture distributions, to geometries of fractures obtained from high-resolution images of real rocks, and to idealized fractures connected to a porous matrix. We also explicitly model a fracture filled with proppant, using a cooperative rearrangement algorithm to construct the proppant bed and the surrounding matrix. We focus on interface movement between matrix and fracture, and snap-off of non-wetting phase into the fracture during imbibition in particular. The configuration of fluids is strongly affected by asperities in unpropped fractures and by the locally open regions at the proppant/matrix interface. The area of phase in contact with the matrix is nonlinear with phase saturation and strongly hysteretic, and thus transfer functions based on saturations should be used with caution. The effect of coupling fracture capillarity and matrix capillarity on multiphase flow properties depends on the relative sizes of typical pore throats in the matrix and typical aperture in the fracture. The simulations agree with direct obsevations of fluid configurations in fractures.

High temperature ultralow water content carbon dioxide-in-water foam stabilized with viscoelastic zwitterionic surfactants

Ultralow water content carbon dioxide-in-water (C/W) foams with gas phase volume fractions (ϕ) above 0.95 (that is <0.05 water) tend to be inherently unstable given that the large capillary pressures that cause the lamellar films to thin. Herein, we demonstrate that these C/W foams may be stabilized with viscoelastic aqueous phases formed with a single zwitterionic surfactant at a concentration of only 1% (w/v) in DI water and over a wide range of salinity. Moreover, they are stable with a foam quality ϕ up to 0.98 even for temperatures up to 120°C. The properties of aqueous viscoelastic solutions and foams containing these solutions are examined for a series of zwitterionic amidopropylcarbobetaines, R-ONHC3H6N(CH3)2CH2CO2, where R is varied from C12-14 (coco) to C18 (oleyl) to C22 (erucyl). For the surfactants with long C18 and C22 tails, the relaxation times from complex rheology indicate the presence of viscoelastic wormlike micelles over a wide range in salinity and pH, given the high surfactant packing fraction. The apparent viscosities of these ultralow water content foams reached more than 120cP with stabilities more than 30-fold over those for foams formed with the non-viscoelastic C12-14 surfactant. At 90°C, the foam morphology was composed of ∼35μm diameter bubbles with a polyhedral texture. The apparent foam viscosity typically increased with ϕ and then dropped at ϕ values higher than 0.95-0.98. The Ostwald ripening rate was slower for foams with viscoelastic versus non-viscoelastic lamellae as shown by optical microscopy, as a consequence of slower lamellar drainage rates. The ability to achieve high stabilities for ultralow water content C/W foams over a wide temperature range is of interest in various technologies including polymer and materials science, CO2 enhanced oil recovery, CO2 sequestration (by greater control of the CO2 flow patterns), and possibly even hydraulic fracturing with minimal use of water to reduce the requirements for wastewater disposal.