Stochastic Structural Modeling

A consistent stochastic model for faults and horizons is described. The faults are represented as a parametric invertible deformation operator. The faults may truncate each other. The horizons are modeled as correlated Gaussian fields and are represented in a grid. Petrophysical variables may be modeled in a reservoir before faulting in order to describe the juxtaposition effect of the faulting. It is possible to condition the realization on petrophysics, horizons, and fault plane observations in wells in addition to seismic data. The transmissibility in the fault plane may also be included in the model. Four different methods to integrate the fault and horizon models in a common model is described. The method is illustrated on an example from a real petroleum field with 18 interpreted faults that are handled stochastically.     

Irreversible thermodynamic treatment of frost heave

The coupled transport of mass and heat which occurs in frost heave, is described by irreversible thermodynamics. The approach is macroscopic phenomenological and thus it correlated macroscopic measurable parameters. It avoids as far as possible details about mechanism and is therefore complementary to derivations by, e.g., Everett (1961) based on microscopic models. A new derivation is given for the coupling between the transport of liquid water and the transport of heat from 0°C to the ice lens. Assumption of local equilibrium in this region is not necessary. The temperature difference over the region causes a water flux, which in turn causes a build-up of pressure gradients.     

Vadose zone-attenuated artificial recharge for input to a ground water model

Accurate representation of artificial recharge is requisite to calibration of a ground water model of an unconfined aquifer for a semiarid or arid site with a vadose zone that imparts significant attenuation of liquid transmission and substantial anthropogenic liquid discharges. Under such circumstances, artificial recharge occurs in response to liquid disposal to the vadose zone in areas that are small relative to the ground water model domain. Natural recharge, in contrast, is spatially variable and occurs over the entire upper boundary of a typical unconfined ground water model. An improved technique for partitioning artificial recharge from simulated total recharge for inclusion in a ground water model is presented. The improved technique is applied using data from the semiarid Hanford Site. From 1944 until the late 1980s, when Hanford's mission was the production of nuclear materials, the quantities of liquid discharged from production facilities to the ground vastly exceeded natural recharge. Nearly all hydraulic head data available for use in calibrating a ground water model at this site were collected during this period or later, when the aquifer was under the diminishing influence of the massive water disposals. The vadose zone is typically 80 to 90 m thick at the Central Plateau where most production facilities were located at this semiarid site, and its attenuation of liquid transmission to the aquifer can be significant. The new technique is shown to improve the representation of artificial recharge and thereby contribute to improvement in the calibration of a site-wide ground water model.     

Formation and growth of multiple,distinct ice lenses in frost heave

This paper presents a fully coupled thermo-hydro-mechanical (THM) model which simulates frost heave in fully saturated soils. The model is able to simulate the formation and growth of multiple distinct ice lenses. The basic equations of the system were derived using the continuum theory of mixtures, nonequilibrium thermodynamics, and fracture mechanics, considering skeleton deformation, water flow and heat transport. Central to this model is the coupled transport of mass due to the temperature gradient across the frozen fringe, which acts as the main driving force of the phenomenon. The model is formulated in terms of measurable physical properties and thus no ad hoc parametrization is required. In an ice-lens-free state, the system is solved as a continuum using the finite element method (FEM). It is then locally treated as a discontinuous system upon the formation of ice lens, by enriching the elements carrying the embedded ice lens(es) using the extended finite element method (X-FEM). The accuracy and efficiency of the proposed model has been verified using several laboratory tests on Devon silt samples at different overburden pressures and thermal boundary conditions. Shut-off pressures have been also estimated and compared with the experimental results.