One-dimensional Laboratory Experiments Research Articles

The inverse problem of determining the filtration function and permeability reduction in flow of water with particles in porous media

Deep bed filtration of particle suspensions in porous media occurs during water injection into oil reservoirs, drilling fluid invasion of reservoir production zones, fines migration in oil fields, industrial filtering, bacteria, viruses or contaminants transport in groundwater etc. The basic features of the process are particle capture by the porous medium and consequent permeability reduction. Models for deep bed filtration contain two quantities that represent rock and fluid properties: the filtration function, which is the fraction of particles captured per unit particle path length, and formation damage function, which is the ratio between reduced and initial permeabilities. These quantities cannot be measured directly in the laboratory or in the field; therefore, they must be calculated indirectly by solving inverse problems. The practical petroleum and environmental engineering purpose is to predict injectivity loss and particle penetration depth around wells. Reliable prediction requires precise knowledge of these two coefficients. In this work we determine these quantities from pressure drop and effluent concentration histories measured in one-dimensional laboratory experiments. The recovery method consists of optimizing deviation functionals in appropriate subdomains; if necessary, a Tikhonov regularization term is added to the functional. The filtration function is recovered by optimizing a non-linear functional with box constraints; this functional involves the effluent concentration history. The permeability reduction is recovered likewise, taking into account the filtration function already found, and the functional involves the pressure drop history. In both cases, the functionals are derived from least square formulations of the deviation between experimental data and quantities predicted by the model.

Real‐scale miscible grout injection experiment and performance of advection–dispersion–filtration model

AbstractA model was developed, to describe miscible grout propagation in a saturated deformable porous medium, based on Bear's statistical model with spatial volume averaging. In a previous paper, the model was first successfully confronted to one‐dimensional laboratory experiments.In the present paper, the numerical model is used to simulate practical grouting operation in a cylindrical injection model. The cylindrical injection model lends itself to study main flow and propagation character istics for a dispersed suspension‐type grout, under axisymmetric conditions close to real scale conditions.Comparison between numerical solutions and experimental results is essential to confirm the validity and accuracy of the proposed model from a phenomenological standpoint. The numerical model performances show that the underlying mathematical model constitutes a realistic predictive model reproducing most prominent features during injection of a suspension‐type grout into a deformable porous medium. The basic mechanism by which injected miscible grout permeates a soil mass is discussed in detail. Such a tool leads to quality control criteria for grouting on a theoretical basis, which complements existing criteria acquired through engineering practice. Copyright © 2001 John Wiley & Sons, Ltd.

Oblique evaporation waves

Evaporation waves are processes that may occur under certain conditions in which a metastable or superheated liquid undergoes a sudden phase transition in a narrow and observable region, which resembles a shock wave. It is inferred from photographic documentation that in certain liquid jet flashing regimes the phenomenon is present. The evaporation wave discontinuity has been successfully modeled in a similar way as a deflagration wave in a combusting gas. One-dimensional laboratory experiments have demonstrated the existence of the (lower) Chapman-Jouguet solution for the cases where the liquid were at a high degree of metastability. Subsonic solutions were also observed for less pronounced degree of metastability (Hill 1991, Sim oes-Moreira 1994). In this paper, the fundamental theory is briefly revised and compared with some of the experimental results obtained for the cases operating at the C-J condition. Next, the paper presents the extension of the one-dimensional theory to include the oblique evaporation wave geometry. Relationships between upstream and downstream flow properties are discussed ant further consequences of these relationships are analyzed.

Empirical Theory of Vacuum-Assisted Steam Stripping of Organic Pollutants from Contaminated Soils

Abstract A theoretical model was developed for the removal of organic chemicals from soil via vacuum-assisted steam stripping. The model considers a homogeneous, isotropic soil described by a single steam permeability coefficient. (The author realizes that this is an idealization of most field situations.) It is assumed that the entire soil mass has been steam heated to 100°C (or slightly above), so the temperature can be considered a constant for the entire decontamination process. The steady-state steam pressure and velocities are determined by solving Laplace's equation for two geometries: a circular symmetry model and a point source model (results for the latter are available upon request). One-dimensional laboratory experiments were conducted to determine the needed steam permeability and decontamination rate of a particular pollutant during steady-state steam flow. The rate of decontamination was determined over a range of steam velocities. The soils used in this particular study were 100% sand, 75% sand/25% Delaware River silt, and 50% sand/50% Delaware River silt. The “pollutant” was commercially available kerosene at a level of 5% by weight in the soil. The soil was initially moisture-free. Results are presented as the time needed to produce either 80 or 100% decontamination. These times depend on the position in the soil—the higher the steam-flow velocity, the shorter the times to decontaminate. Drawing on previous work, the times to reach steady state are also presented. For contaminated regions as large as 10 m in diameter for these three soil types, the times to decontaminate to at least 98% appear reasonable.

Water Exchange in Two-Layer Stratified Waters

A mathematical model of two-layer stratified flow is presented. One-dimensional and radial flows are considered. The numerical solution is based on the method of characteristics. The reliability of the mathematical model is investigated with the help of one-dimensional laboratory experiments and a hydraulic model of a real bay. Agreement between calculations and experiments is achieved but since the numerical method of solution does not allow Courant numbers exceeding one the calculations are time consuming.