Natural hydraulic fractures (NHFs) are fractures whose growths are driven by fluid loading. The fluid flow properties of the host rock have a primary, but hitherto little appreciated control on the NHF propagation rates. This study focuses on investigating the impacts of host rock fluid flow on the propagation and pattern development of multiple NHF in a poroelastic media. A realistic geomechanical model is developed to combine both the fluid flow and mechanical interactions between multiple fractures. The natural hydraulic fracture propagation is observed to consist of a series of crack-seal processes indicating incremental stop-start growth. Growth timing is on the scale of millions of years based on recent natural fracture growth reconstructions. These time scales are compatible with some model scenarios. My newly developed numerical model captures the crack-seal process for multiple NHF propagation. A sensitivity study conducted to investigate the impacts of different fluid flow properties on NHF propagation shows that permeability is a predominate influence on the timescale of NHF development. In low-permeability rocks, fractures have more stable initiation and much longer propagation timing compared to those in high-permeability rocks. Another aspect of great interest is the influence of fluid flow on fracture spacing and pattern development for multiple NHFs propagation in a poroelastic environment. My new poroelastic geomechanial model combines the natural hydraulic fracturing mechanism with the mechanical interactions between fractures. The numerical results show that as host rock permeability decreases, more fractures can propagate and a much smaller spacing is reached for a given fracture set. The low permeability slows down the propagation of long fractures and prevents them from dominating the fracture pattern. As a result, more fractures are able to grow at a similar speed and a more closely spaced fracture pattern is achieved for either regularly spaced or randomly distributed multiple fractures in low-permeability rocks. Investigation is also conducted in analyzing the distributions of fracture attributes (length, aperture and spacing) in low- and high-permeability rocks. For shales with high subcritical index, low permeability helps the fractures propagate more closely spaced instead of clustering. Meanwhile, in low-permeability rocks, factures have relatively smaller apertures, which lead to a slower fracture opening rate. The competition between the slow fracture opening rate and quartz precipitation rate will affect the effective permeability and porosity of the naturally fractured reservoir. However, the competition is trivial in high-permeability rocks. Other factors, such as reservoir boundary condition, layer thickness, subcritical index and pattern development stage, all have considerable impact on fracture pattern development and attribute distribution in a poroelastic media. / text

Spatial variability of porous media often prevents precise physical characterization of the system. In order to model moisture and solute transport through this media, certain sacrifices in precision must be made. Physical characteristics of the system must be averaged over large scales, lumping the small scale variability into the large scale characterization. Although this precludes a precise definition of the small scale flow characteristics, parameterization is much more attainable. This study addresses methods for determining effective hydraulic conductivity of unsaturated porous media. Effective conductivity is used to describe the large scale behavior of the system. Different methods for calculating the effective conductivity are presented and compared. Results indicate that the unit mean gradient method produces good estimates of the effective conductivity and can be applied using limited field data. The zone of correlation of the hydraulic parameters can be used in experimental design to minimize the errors associated with estimation of the mean pressure. An inverse method for evaluating the optimum effective hydraulic parameters is presented. Results indicate the optimization procedure is more sensitive to wetting than to drying conditions. Because of interaction between the hydraulic parameters, concurrent optimization of more than two of the parameters based on soil pressure data alone is not advised. Anisotropy in an unsaturated soil was found to be a function of the profile mean soil pressure. Results indicate the effective conductivity for flow parallel to soil layering can be estimated from the arithmetic mean of the unsaturated conductivity values for each of the layers and is between the harmonic and geometric means of these data for flow perpendicular to the layering. Estimates of the effective unsaturated hydraulic conductivity obtained through stochastic analysis agreed well with simulation results. Deviations between the stochastic predictions and simulation results are larger when the variability of the soil profile is greater and begin to deviate significantly when the variance of ln K(ψ₀) exceeds 5.0 and the variance of a exceeds 0.02 1/cm².

It has been shown by Neuman [1990], Di Federico and Neuman [1997, 1998a,b] and Di Federico et al. [1999] that observed multiscale behaviors of subsurface fluid flow and transport variables can be explained within the context of a unified stochastic framework, which views hydraulic conductivity as a random fractal characterized by a power variogram. Any such random fractal field is statistically nonhomogeneous but possesses homogeneous spatial increments. When the field is statistically isotropic, it is associated with a power variogram γ(s) = Cs²ᴴ where C is a constant, s is separation distance, and If is a Hurst coefficient (0 < H< 1). If the field is Gaussian it constitutes fractional Brownian motion (fBm). The authors have shown that the power variogram of a statistically isotropic or anisotropic fractal field can be constructed as a weighted integral from zero to infinity of exponential or Gaussian vario grams of overlapping, homogeneous random fields (modes) having mutually uncorrelated increments and variance proportional to a power 2H of the integral (spatial correlation) scale. Low- and high-frequency cutoffs are related to length scales of the sampling window (domain) and data support (sample volume), respectively. Intermediate cutoffs account for lacunarity due to gaps in the multiscale hierarchy, created by a hiatus of modes associated with discrete ranges of scales. In this dissertation, I investigate the effects of domain and support scales on the multiscale properties of random fractal fields characterized by a power variogram using real and synthetic data. Neuman [1994] and Di Federico and Neuman [1997] have concluded empirically, on the basis of hydraulic conductivity data from many sites, that a finite window of length-scale L filters out (truncates) all modes having integral scales λ larger than λ = μL where μ ≃ 1/3. I confii in their finding computationally by generating truncated fBm realizations on a large grid, using various initial values of μ, and demonstrating that μ ≃ 1/3 for windows smaller than the original grid. My synthetic experiments also show that generating an fl3m realization on a finite grid using a truncated power variogram yields sample variograms that are more consistent with theory than those obtained when the realization is generated using a power variogram. Interpreting sample data from such a realization using wavelet analysis yields more reliable estimates of the Hurst coefficient than those obtained when one employs variogram analysis. Di Federico et al. [1997] developed expressions for the equivalent hydraulic conductivity of a box-shaped support volume, embedded in a log-hydraulic conductivity field characterized by a power variogram, under the action of a mean uniform hydraulic gradient. I demonstrate that their expression and empirically derived value of μ ≃ 1/3 are consistent with a pronounced permeability scale effect observed in unsaturated fractured tuff at the Apache Leap Research Site (ALRS) near Superior, Arizona. I then investigate the compatibility of single-hole air permeability data, obtained at the ALRS on a nominal support scale of about 1 m, with various scaling models including fBm, fGn (fractional Gaussian noise), fLm (fractional Lévy motion), bfLm (bounded fractional Lévy motion) and UM (Universal Multifractals). I find that the data have a Lévy-like distribution at small lags but become Gaussian as the lag increases (corresponding to bfLm). Though this implies multiple scaling, it is not consistent with the UM model, which considers a unique distribution. If one nevertheless applies a UM model to the data, one obtains a very small codimension which suggests that multiple scaling is of minor consequence (applying the UM model to permeability rather than log-permeability data yields a larger codimension but is otherwise not consistent with these data). Variogram and resealed range analyses of the log-permeability data yield comparable estimates of the Hurst coefficient. Resealed range analysis shows that the data are not compatible with an fGn model. I conclude that the data are represented most closely by a truncated fBm model.

When CO₂ is injected in deep saline aquifers on the scale of gigatonnes, pressure buildup in the aquifer during injection will be a critical issue. Because fracturing, fault activation and leakage of brine along pathways such as abandoned wells all require a threshold pressure (Nicot et al., 2009); operators and regulators will be concerned with the spatial extent of the pressure buildup. Thus a critical contour of overpressure is a convenient proxy for risk. The location of this contour varies depending on the target aquifer properties (porosity, permeability etc.), the geology (presence of faults, abandoned wells etc.), and boundary conditions. Importantly, the extent also depends on relative permeability (Burton et al., 2008). First we describe ways of quantifying the risk due to pressure buildup in an aquifer with a constant pressure boundary, using the three-region injection model to derive analytical expressions for a specific contour of overpressure at any given time. All else being the same, the two-phase-region mobilities (and hence relative permeability characteristics) provide a basis for the ranking of storage formations based on risk associated with pressure elevation during injection. The pressure buildup during CO₂ injection will depend strongly upon the boundary conditions at the boundary of the storage formation. An analytical model for pressure profile in the infinite-acting aquifer is developed by combining existing water influx models in traditional reservoir engineering (Van-Everdingen and Hurst model, Carter-Tracy model) to the current problem for describing brine efflux from the storage aquifer when CO₂ injection creates a "three-region" saturation distribution. We determine evolution of overpressure with time for constant pressure, no-flow and infinite-acting boundary conditions, and conclude that constant pressure and no-flow boundary conditions give the most optimistic and pessimistic estimates of risk respectively. Compositional reservoir simulation results, using CMG-GEM simulator are presented, to show the effect of an isolated no-flow boundary on pressure buildup and injectivity in saline aquifers. We investigate the effect of multiple injection wells on single-phase fluid flow on aquifer pressure buildup, and demonstrate the use of an equivalent injection well concept to approximate the aquifer pressure profile. We show a relatively inexpensive method of predicting the presence of unanticipated heterogeneities in the formation, by employing routine measurements such as injection rate and injection pressure to track deviation in the plume path. This idea is implemented by combining Pro-HMS (probabilistic history matching software, that carries out geologically consistent parameter estimation), and a CMG-GEM model which has been tuned to the physics of the CO₂-brine system. / text

Altering the wettability of reservoir rock using fluoro-chemical treatments has proved to be a viable solution to the condensate blocking problem in gas wells. Alteration of rock wettability to neutral-wet is the primary reason for improvement in gas and condensate relative permeabilities. Stability/compatibility test, drop tests and X-ray photoelectron spectroscopy (XPS) analysis along with core flood results were used to characterize wettability changes. XPS tests, drop tests, and relative permeability measurements were conducted and correlated with each other. It is shown that XPS analysis and imbibition tests provide a quantitative measure of chemical adsorption and surface modification, but only a qualitative measure of the possible change in relative permeability. As such these simple analytical tools may be used as a screening tool. A positive but imperfect empirical correlation was obtained with results from core flood experiments. The varying concentration of fluorine observed on the rock surface was found to be directly correlated to the wettability change in the rock, which in turn is responsible for improving the deliverability of wells in gas condensate/volatile oil reservoirs. The method discussed in this thesis can be used to identify chemical treatments to change rock wettability and, therefore, relative permeability. This provides a simple, quick and inexpensive way to screen chemicals as wettability altering agents and relative permeability modifiers which saves time, cost and effort. / text

No description available.

Researchers using Darcy's law to model flow in porous media must satisfy the requirement for sufficient scale separation between the pore scale and the model scale. This requirement is analogous to that for any continuum model, where application is restricted to scales larger than the underlying discrete structure. In the case of Darcy's law when the model scale becomes too small, the measurement of the permeability - the material property required to close the relationship - becomes polluted by the boundary conditions, either physical or numerical. The requirements for adequate scale separation to obtain permeability measurements (also known as satisfying the conditions for a representative elementary volume, or REV, for permeability) have not been previously reported. Likewise, the behavior of Darcy models when applied at sub-REV length scales has not been reported. Here, the results of Stokes simulations of transverse flow in 90,000 sequential random packings of monodisperse cylinders at a variety of liquid fractions and averaging-volume sizes show that approximately 200 cylinders must be present in an averaging volume before the effects of periodic boundary conditions on the Stokes simulations (the conventional choice for permeability measurements using Stokes flow) are no longer evident in the measured permeability. Direct comparisons between flow predictions from a two-dimensional, tensor-based Darcy model and a Stokes model for additional 10,000 domains show that the Darcy model is an unbiased predictor of the flow distribution in the system, even when the permeability is expected to contain boundary-condition artifacts. Though unbiased, the Darcy models do show considerable reduction in accuracy as the model scale shrinks toward the pore scale, with significant declines observed after the side length of a square averaging volume reaches 10 times the cylinder diameter. Finally, a novel approach for visualizing flows using the linear properties of the Stokes equations shows how the periodic boundary conditions affect the flow, and motivates the development of a generalized approach for obtaining permeability that does not require periodic boundary conditions. Modest improvements in the Darcy model relative to the actual Stokes flow result when the new approach is used to obtain permeability at small averaging volumes.

No description available.

Thermosolutal fluid flow has a strong influence on the evolution of solidification microstructures. While porous media theory and volume-averaged permeability relations give a basis to quantify these phenomena, traditional methods of permeability estimation used for random porous media fail to adequately characterize the full relation of microstructural morphology to volume-average permeability. Most significantly, the link between microstructural parameters and permeability is treated as a deterministic function at all scales, ignoring the variability inherent in porous media.The variation in permeability inherent to random porous media is investigated by the numerical solution of Stokes equations on an ensemble of porous media, which represent of many scales of sampling and morphological character. Based on volume-averaging and statistical treatment, the stochastic character of tensoral permeability in porous media is numerically investigated. Quantification of permeability variation and autocorrelation structure are presented as conditions, which future realistic stochastic permeability fields must respect.

No description available.