Steady-state Pressure Gradients Research Articles

Mechanistic foam flow model with variable flowing foam fraction and its implementation using automatic differentiation

Foam injection is an effective method for modifying gas mobility in subsurface flow applications making it ideal for environmental remediation applications. Remediation of contaminated soils/aquifers of nonaqueous phase liquids using foamed surfactant solutions is a viable option but a predictive foam model is needed that is flexible to the addition of more accurate physical descriptions. Such a model is essential to ensure successful operations in soil remediation applications. The objective of this paper is to develop a full-physics, mechanistic transient foam flow model and integrate it into the multiphysics, modular AD-GPRS framework (Automatic Differentiation–General Purpose Research Simulator). We chose AD-GPRS because it allows rapid prototyping and addition of complex physics and modeling strategies. We develop the model ground-up from pore-scale observations and implement a new flowing foam fraction constitutive relation that depends on the local pressure gradient, local permeability, and flowing bubble density. Our model predicts the two flow regimes commonly observed in steady-state pressure gradient measurements: the low-quality regime and the high-quality regime. Additionally, the model is used to match transient experimental results of homogeneous and slightly heterogeneous cores with a wide range of permeability values. The implementation of this model within AD-GPRS allows testing of ideas and modeling strategies as well as inclusion of more complex physics or foam generation kinetics.

Static and stability analysis of partial slip texture multi-lobe journal bearings

This paper presents one-dimensional analysis of modified dynamic Reynolds equation derived for partial slip texture multi-lobe journal bearings. The novelty included in this study is the configuration of partial slip texture region on the bottom bearing lobe surface of a multi-lobe journal bearing under a constant vertical load. The nondimensional pressure and shear stress for steady-state and nondimensional pressure gradients for dynamic coefficients for each lobe with partial slip texture configuration are derived based on narrow groove theory. Linearized stability analysis is evaluated using infinitesimal perturbation method. Results of static and stability characteristics of partial slip texture multi-lobe (two-axial groove, elliptical, three-lobe and offset) journal bearings are presented. Partial slip texture configuration significantly enhances load capacity, coefficient of friction, and stability of two-lobe journal bearing.

Modeling Steady-State Foam Flow: Hysteresis and Backward Front Movement

Foaming gaseous injectants is an attractive option because of the much lower gas mobility achieved in porous media. This paper reports an experimental and numerical investigation to improve our understanding of aqueous foam flow in heterogeneous sandstone. Our experimental program reveals two interesting behaviors: hysteresis in the steady-state pressure gradient and movement of a foam front opposite the direction of flow. Steady-state pressure gradient measurements across a sandstone core demonstrate the absence of a critical velocity requirement for foam generation, support the possibility of foam propagation away from the injection well, and exhibit hysteresis in the pressure gradient upon decreasing the injection gas velocity. Quasi-steady pressure drop profiles show that the pressure gradient increases against the direction of flow in what we coin the ”backward front movement”. This paper models experimental observations of steady-state pressure-drop hysteresis as well as quasi-steady backward front movement. Specifically, a steady-state population balance model that is based on pore-scale observations is developed. The model is verified against experimental data to confirm the steady-state predictions of the pressure, the flowing bubble density, and the flowing foam fraction (Tang and Kovscek, Transport in Porous Media 2006, 65, 287–307; Chen et al. SPE J. 2010, 15, 171–183). The model is then used to predict the experimental behavior. The flowing foam fraction (i.e., the fraction of the gas saturation that flows) is a key parameter in interpreting both hysteresis and backward propagation of the pressure gradient. Our findings highlight the importance of the flowing foam fraction to predicting various foam behavior.

A Macroscale Hydrogeological Numerical Model of the Suio Hydrothermal System (Central Italy)

The complex behaviour of the Suio hydrothermal system (central Italy) and its potential exploitation as a renewable energy source are still unclear. To quantitatively evaluate the geothermal resource, the Suio hydrothermal system has been investigated with a hydrogeological numerical model that couples fluid flow, thermal convection, and transport of diluted species inside a hybrid continuum-discrete medium. The numerical model, calibrated and validated with available and new experimental data, unveiled the complex behaviour of the hydrothermal system. The normal tectonic displacements, the fracturing of the karst hydrostructure, and the aquitard distribution strongly influence the hydrothermal basin. In particular, a dual fluid circulation, sustained by steady-state thermal and pressure gradients, modulates the hydrothermalism at the several springs and wells. The presence of a medium to a low-temperature reservoir allows for potential exploitation of the geothermal resource.

Low-Dimensional Modeling of Transient Two-Phase Flow in Pipelines

Presented are reduced-order models of one-dimensional transient two-phase gas–liquid flow in pipelines. The proposed model is comprised of a steady-state multiphase flow mechanistic model in series with a transient single-phase flow model in transmission lines. The steady-state model used in our formulation is a multiphase flow mechanistic model. This model captures the steady-state pressure drop and liquid holdup estimation for all pipe inclinations. Our implementation of this model will be validated against the Stanford University multiphase flow database. The transient portion of our model is based on a transmission line modal model. The model parameters are realized by developing equivalent fluid properties that are a function of the steady-state pressure gradient and liquid holdup identified through the mechanistic model. The model ability to reproduce the dynamics of multiphase flow in pipes is evaluated upon comparison to olga, a commercial multiphase flow dynamic code, using different gas volume fractions (GVF). The two models show a good agreement of the steady-state response and the frequency of oscillation indicating a similar estimation of the transmission line natural frequency. However, they present a discrepancy in the overshoot values and the settling time due to a difference in the calculated damping ratio. The utility of the developed low-dimensional model is the reduced computational burden of estimating transient multiphase flow in transmission lines, thereby enabling real-time estimation of pressure and flow rate.

Aspect ratio effects on limited scrape-off layer plasma turbulence

The drift-reduced Braginskii model describing turbulence in the tokamak scrape-off layer is written for a general magnetic configuration with a limiter. The equilibrium is then specified for a circular concentric magnetic geometry retaining aspect ratio effects. Simulations are then carried out with the help of the global, flux-driven fluid three-dimensional code GBS [Ricci et al., Plasma Phys. Controlled Fusion 54, 124047 (2012)]. Linearly, both simulations and simplified analytical models reveal a stabilization of ballooning modes. Nonlinearly, flux-driven nonlinear simulations give a pressure characteristic length whose trends are correctly captured by the gradient removal theory [Ricci and Rogers, Phys. Plasmas 20, 010702 (2013)], that assumes the profile flattening from the linear modes as the saturation mechanism. More specifically, the linear stabilization of ballooning modes is reflected by a 15% increase in the steady-state pressure gradient obtained from GBS nonlinear simulations when going from an infinite to a realistic aspect ratio.

Long-term impact of temperature on the hydraulic permeability of bentonite

Abstract In a Swedish repository for the disposal of heat-emitting waste, the long-term thermal stability of the bentonite engineered barrier forms a key component of the safety case. Central to such consideration is the evolution of hydraulic permeability and a potential degradation of hydraulic properties, in response to prolonged thermal exposure of the clay. To address this issue, a detailed programme of laboratory-based experiments has been undertaken at both the British Geological Survey and Studiecentrum voor Kernenergie/Centre d'Etude de L'Energie Nucleaire, in order to examine the hydraulic behaviour of bentonite that had previously been exposed to elevated temperatures. Hydraulic properties were calculated from both steady-state pressure gradients and from analysis of the pressure transients. Inspection of the data found no significant difference in hydraulic behaviour between the virgin material and clay samples taken from the Canister Retrieval Test. Based on these observations, the authors find no evidence for an adverse increase in hydraulic conductivity of bentonite as a result of prolonged thermal exposure to temperatures of 80 °C.

An improved simplified analytical model for CO2 plume movement and pressure buildup in deep saline formations

This study presents an evaluation of the three-region simplified analytical model of Burton et al. (2008) based on fractional flow and steady-state pressure gradient considerations for predicting CO2 plume movement and pressure buildup in deep saline formations. The saturation and pressure profiles as well as injection-well pressure buildup predicted by the analytical model are benchmarked against those from the numerical simulator STOMP to suggest improvements as needed for the simplified modeling approach. Good agreement is observed between the two approaches for predicting CO2 saturations. However, using a two-phase mobility based on average saturations as proposed by Burton et al. results in under-prediction of the pressure buildup. An improved method is presented for calculating a representative two-phase mobility based on the actual mobility profile in the two-phase region. This leads to a much better match between predictions of STOMP and the three-region model for both formation pressure profile and injection-well pressure buildup.

Steady-state nonequilibrium temperature gradients in hydrogen gas–metal systems: challenging the second law of thermodynamics

Differences in gas reaction rates between disparate surfaces have been proposed as a means to achieve steady-state pressure and temperature gradients within a single blackbody cavity, thereby challenging the second law of thermodynamics (Sheehan 1998 Phys. Rev. E 57 6660; Sheehan 2001 Phys. Lett. A 280 185; Capek and Sheehan 2005 Challenges to the Second Law of Thermodynamics (Theory and Experiment) (Fundamental Theories of Physics Series vol 146) (Dordrecht: Springer)). This paper reports on laboratory tests of this hypothesis; specifically, molecular hydrogen is found to dissociate preferentially on rhenium surfaces versus tungsten at identical elevated temperatures and reduced pressures (T ⩽ 2100 K; ). Steady-state nonequilibrium H/H2 ratios over the surfaces suggest that temperature gradients could be maintained under blackbody cavity conditions. Preliminary results from bimetallic blackbody cavity experiments are discussed.

Plasma pressure generated auroral current system: A case study

An anti‐sunward directed azimuthal pressure gradient drives meridional currents perpendicular to the magnetic field in the dusk and dawn closed field line regions. These currents are closed through the auroral ionosphere consisting of a pair of upward and downward sheet field aligned currents cross connected in the ionosphere. Using a conjunction of FAST and Polar the intensity of the up‐down sheet FAC pair was measured in the dusk sector in typical auroral conditions. The T96 field model was used to define the geometry and it predicted that field lines at the satellites were stretched to 15 RE. The steady state pressure gradient current was calculated through a surface in the magnetosphere separating the upward and downward going FAC. With the field stretching predicted by the model a typical quiet time azimuthal pressure gradient of 0.01 nPa/Re generated sufficient current to be the source of the observed auroral current loops.

Experimental study of high-temperature foam for acid diversion

Foam treatments are used worldwide for acid diversion in matrix acid well stimulation. Many field treatments require foam effectiveness at elevated temperature in the presence of both acid and corrosion inhibitor. This study examines four surfactant formulations at room temperature, 104 °C (220 °F) and 204 °C (400 °F), with and without acid and corrosion inhibitor. The surfactants included amphoteric as well as nonionic foaming agents. The acid formulation was a mixture of chelating agent and HCl, with pH about 4. Formulations were tested at all three temperatures for foaming with N 2 gas (80% quality) at back-pressure of 600 psi (4.1 MPa) in sandpacks and for bulk-foam stability in a pressure cell. Foam was created in most cases at 24 °C (75 °F) without acid or corrosion inhibitor. Creating foam with acid and corrosion inhibitor at 204 °C was more difficult, requiring higher injection rates and lower foam quality. Once formed, strong foam had higher mobility at elevated temperatures than at room temperature. Addition of corrosion inhibitor was more adverse to foaming than acid itself. At 204 °C foam propagation was slower, and steady-state pressure gradient was lower, than at 24 °C. The two steady-state strong-foam regimes reported elsewhere were present at 104 °C and in the presence of acid. Pressure gradient at 104 °C was lower in both high-quality and low-quality foam regimes. The bulk-foam stability results agree qualitatively with the sandpack results, but quantitative relationships between the two tests are hard to draw. These results also suggest that these surfactants may degrade over a period of time, for example, a couple of hours at 204 °C. Residence time in the heated sandpack therefore should be properly accounted for in design of experiments. These results are consistent with decreasing foam stability at higher temperature; adverse interactions between foaming surfactant and inhibitor; easier foam generation and propagation at higher velocity and lower foam quality; and greater difficulty in creating foam under conditions that reduce steady-state foam strength. These results can aid design of high-temperature foam-acid diversion treatments.

Swelling and osmotic flow in a potential host rock

Measurements of osmotic and hydraulic permeability are reported for a series of tests conducted on Opalinus Clay samples from the Mt. Terri underground research laboratory in the Jura Mountains of NE Switzerland. Osmotic flow was observed across discs of this clayshale separating 0.245 M NaCl solution from distilled water. Pressure transients monitored during constant flow rate testing were analysed to give permeability and specific storage values. The mean permeability normal to bedding of the two Opalinus Clay specimens was 7.9 × 10 −21 m 2. The mean specific storage based on all reliable determinations was 4.1 × 10 −4 m −1. Values calculated from the steady-state pressure gradients established during constant flow rate testing were very close to those obtained by mathematical analysis of pressure transients. The calculation of the transients was carried out using a new model of flow and solute transport which included terms for the osmotic coupling. The form of the pressure transients and the magnitude of the strain seen during the tests lead to a revision to the definition of solid phase compressibility to incorporate a term dependent upon the osmotic coupling coefficient. Steady-state osmotic flow rates were in the range 0.1–0.6 μL h −1 when the specimens were placed between a sodium chloride solution with a theoretical osmotic pressure of 1.19 MPa and distilled water. Transient flow rates were substantially larger. Membrane efficiencies were found to be relatively low, ranging from 1% to 6% (mean around 4%). The mean osmotic permeability normal to bedding was 3.5 × 10 −22 m 2. Specific storage and pore compressibility values were substantially larger than anticipated, suggesting that the volumetric strain of the clayshale under the conditions of laboratory testing must be largely determined by quasi-elastic deformation processes such as swelling and crack dilation. To test this hypothesis, a 3-D swelling test was performed on a cubic specimen of the same material. When immersed in distilled water, the cube swelled preferentially in a direction normal to bedding. Swelling was accompanied by visible opening of cracks. Volumetric strains of the clayshale during the swelling test were of the same order of magnitude as those during permeability testing. The presence of dilated cracks could explain the low membrane efficiency, since the dissociated ions of the salt would be able to diffuse through the crack network relatively unimpeded by electrostatic interactions with the clay mineral surfaces. The high compressibility and low membrane efficiency revealed by these experiments may be a consequence of fabric damage during sampling and specimen preparation or may actually be representative of the rock characteristics within the engineering disturbed zone (EDZ) of the tunnel niches. It is entirely possible that undisturbed rock remote from the excavations displays significantly lower compressibility and higher membrane efficiency. Even though the clayshale membrane in these experiments is inefficient, the results clearly demonstrate that Opalinus Clay is capable of supporting an osmotic flow of water. This has important implications in the specification, operation and interpretation of borehole tests aimed at the hydrogeological characterisation of this potential host rock. In addition the osmotic coupling term modifies the effective diffusion coefficient which should be accounted for when undertaking safety assessments.

Role of nitrogen in transmucosal gas exchange rate in the rat middle ear

This study investigates the role of nitrogen (N2) in transmucosal gas exchange of the middle ear (ME). We used an experimental rat model to measure gas volume variations in the ME cavity at constant pressure. We disturbed the steady-state gas composition with either air or N2 to measure resulting changes in volume at ambient pressure. Changes in gas volume over time could be characterized by three phases: a primary transient increase with time (phase I), followed by a linear decrease (phase II), and then a gradual decrease (phase III). The mean slope of phase II was -0.128 microl/min (SD 0.023) in the air group (n = 10) and -0.105 microl/min (SD 0.032) in the N2 group (n = 10), but the difference was not significant (P = 0.13), which suggests that the rate of gas loss can be attributed mainly to the same steady-state partial pressure gradient of N2 reached in this phase. Furthermore, a mathematical model was developed analyzing the transmucosal N2 exchange in phase II. The model takes gas diffusion into account, predicting that, in the absence of change in mucosal blood flow rate, gas volume in the ME should show a linear decrease with time after steady-state conditions and gas composition are established. In accordance with the experimental results, the mathematical model also suggested that transmucosal gas absorption of the rat ME during steady-state conditions is governed mainly by diffusive N2 exchange between the ME gas and its mucosal blood circulation.

Centrifugal Separation for Cleaning Well Gas Streams

An examination of centrifugal gas separation applied to natural gas wells shows that it has some technical advantages for bulk removal of souring components in highly contaminated streams. Different criteria from those used in traditional UF6 processing apply, and we develop and describe these. In particular, the distribution of components means that enrichment occurs much closer to the center, which would imply easier separation. Symmetry considerations during analysis of a binary system show that the previous implicit assumption of steady-state pressure gradient requiring zero component convection during the setting up of the concentration gradient is incorrect, although the correction for our case is relatively small. Analysis of times for batch spin-up as well as radial pressure distributions indicate that high throughput operation at elevated pressures may be an option.

Phase Space Analysis of a Gravitationally-Induced, Steady-State Nonequilibrium

Recently a new type of pressure gradient was introduced, a gravitationally-induced, dynamically-maintained, steady-state pressure gradient (GDSPG) (D P Sheehan and J Glick 2000 Physica Scripta 61 635). In this paper, three dimensional numerical test particle simulations detail its phase space structure. These verify the underlying physical mechanism originally hypothesized for its operation and support key assumptions upon which it is based. The GDSPG appears to be a member of a more general class of steady-state nonequilibrium systems that arise under extreme thermodynamic conditions (D P Sheehan 1998 Phys. Rev. E 57 6660).

Unified Model for Steady-State Foam Behavior at High and Low Foam Qualities

SummaryFoams are routinely used worldwide to divert acid in well-stimulation treatments, and to divert gas flow in improved oil recovery (IOR) projects on a pilot basis. The complexity of foam behavior and the apparent contradictions among foam studies have bedeviled attempts to understand foams and to design effective field treatments.In 1992, Osterloh and Jante1 identified two distinct foam-flow regimes: a high-quality (dry) regime, in which the steady-state pressure gradient is independent of the gas flow rate, and a low-quality (wet) regime, in which the pressure gradient is independent of the liquid flow rate. New data for strong foams in a variety of porous media, with various surfactant formulations, and over a range of flow rates, show this behavior to be general. In each regime, foam behavior is dominated by a single mechanism: at high qualities by capillary pressure and coalescence, and at low qualities by bubble trapping and mobilization. Based on these insights, a new, unified model unites foam behavior in acid-well stimulation and gasdiversion IOR and reconciles apparently contradictory data. This model correlates the effects of parameters, such as rock permeability and surfactant formulation, on foam behavior in the two flow regimes and on the transition between the two regimes. A variety of laboratory data supports the model's assumptions.The implications of these results for designing foam processes for IOR and acid diversion are discussed. These insights can guide the selection of foam formulation and injection quality for foam applications.

High CO 2 emissions through porous media: transport mechanisms and implications for flux measurement and fractionation

Diffuse emissions of CO 2 are known to be large around some volcanoes and hydrothermal areas. Accumulation-chamber measurements of CO 2 flux are increasingly used to estimate the total magmatic or metamorphic CO 2 released from such areas. To assess the performance of accumulation chamber systems at fluxes one to three orders of magnitude higher than normally encountered in soil respiration studies, a test system was constructed in the laboratory where known fluxes could be maintained through dry sand. Steady-state gas concentration profiles and fractionation effects observed in the 30-cm sand column nearly match those predicted by the Stefan-Maxwell equations, indicating that the test system was functioning successfully as a uniform porous medium. Eight groups of investigators tested their accumulation chamber equipment, all configured with continuous infrared gas analyzers (IRGA), in this system. Over a flux range of ∼200–12,000 g m −2 day −1, 90% of their 203 flux measurements were 0–25% lower than the imposed flux with a mean difference of −12.5%. Although this difference would seem to be within the range of acceptability for many geologic investigations, some potential sources for larger errors were discovered. A steady-state pressure gradient of −20 Pa/m was measured in the sand column at a flux of 11,200 g m −2 day −1. The derived permeability (50 darcies) was used in the dusty-gas model (DGM) of transport to quantify various diffusive and viscous flux components. These calculations were used to demonstrate that accumulation chambers, in addition to reducing the underlying diffusive gradient, severely disrupt the steady-state pressure gradient. The resultant diversion of the net gas flow is probably responsible for the systematically low flux measurements. It was also shown that the fractionating effects of a viscous CO 2 efflux against a diffusive influx of air will have a major impact on some important geochemical indicators, such as N 2/Ar, δ 15N–N 2, and 4He/ 22Ne.

The second law and chemically-induced, steady-state pressure gradients: controversy, corroboration and caveats

Experimental results are reported supporting key aspects of a recently proposed chemical pressure gradient (D.P. Sheehan, Phys. Rev. E 57 (1998) 6660). This pressure gradient has been invoked in a paradox involving the second law of thermodynamics (T.L. Duncan, Phys. Rev. E 61 (2000) 4661).

Gravitationally-Induced, Dynamically-Maintained, Steady-State Pressure Gradients

Under sealed blackbody cavity conditions, pressure gradients typically take three forms: (a) statistical fluctuations, (b) transients associated with the system relaxing toward equilibrium, and (c) equilibrium pressure gradients, such as those associated with static gravitational potentials. In this paper a new type of pressure gradient is introduced, one which arises if a gravitator has surfaces with different trapping probabilities for suprathermal gas collisions. Three-dimensional test particle simulations of this system using realistic physical parameters support this hypothesis. This gas phase is inherently nonequilibrium in character and represents an unstudied thermodynamic regime involving low-density gas-surface interactions. This is the gravitational analog of a previously studied, chemically-induced pressure gradient (D P Sheehan 1998 Phys. Rev. E 57 6660).

Reply to "Comment on 'Dynamically maintained steady-state pressure gradients' "

A reply is made to Duncan's Comment [T. L. Duncan, Phys. Rev. E 61, 4661 (2000)] on my earlier paper [D. P. Sheehan, Phys. Rev. E 57, 6660 (1998)] in which he raises an apparent second-law paradox arising from dynamically maintained, steady-state pressure gradients. Resolutions to this paradox are considered in light of current theoretical and experimental understanding.