Transient-state Model Research Articles

Modelling the multiphase flow of an oil–gas–condensate system in porous media

The “Black oil” model is extended to describe the four-phase flow of the oil-gas–condensate systems in porous media, by considering the solubilities of gas in the condensate, water, and oil phases and condensate evaporation into the gas phase. The three-dimensional transient-state model equations are reduced to one-dimensional transient-state forms by the partial integration method. The finite-difference method is used for solution of this model. The calculations of the hydrodynamical parameters of an oil–gas–condensate reservoir element are carried out for several cases, involving a water table in its natural state of the development, water flooding under water–oil contact, combined state of water flooding under water–oil contact and gas pumping into gas zone of the reservoir. This study provides a comparison of the effect of the different exploitation methods of the reservoir fluids production. The present simulation studies indicate that the combined flooding method yields faster recovery.

Effect of optical saturation on pulsed photothermal deflection signals in flowing media

A two-level transient-state model has been developed which describes the effect of optical saturation on the photothermal signals, valid for conditions where a steady state may not exist. The theory is quite general, as it considers arbitrary pulse shapes, homogeneously and inhomogeneously broadened lines, and arbitrary spectral profile of the excitation. Equations for the temporally and spatially dependent absorption coefficient are derived, and, for generality, time-dependent photothermal deflection signals in a flowing medium are calculated (stationary medium being just a special case). The saturation behaviors of the photothermal signals obtained by monochromatic rectangular and Q-switched pulse excitations for homogeneously and inhomogeneously broadened lines are evaluated and compared. Differences between the predictions of the steady-state and transient-state models are discussed. Experiments have been performed using NO2 as a sample gas in a flowing medium. The experimental results are in agreement with the predictions of the transient state model.

EVALUATION OF A FUNCTIONAL MODEL FOR SIMULATING BORON TRANSPORT IN SOIL

There has been renewed interest in the application of functional models to the transport of nonpoint source pollutants at polypedon (i.e., farm) and watershed scales because of the ease of their coupling to a geographic information system and to the accepted organizational hierarchy of pedogenetic modeling approaches. However, very little work has been done to evaluate the performance of a functional transient-state model for the transport of a reactive solute over an extensive study period. Subsequently, the functional model TETrans (Trace Element Transport) was evaluated for model performance with boron (B) transport data collected from a meso-scale soil lysimeter column over a 1000-day study period (i.e., 40 irrigations). Because the ability to simulate water flow has been evaluated previously for TETrans, the focus of this evaluation centered around the performance of various functional models of B adsorption used as subroutines within the TETrans model, including the (1) Freundlich, (2) kinetic Freundlich, (3) Langmuir, (4) temperature-dependent Langmuir, and (5) pH-dependent Keren adsorption isotherm equations. Model performance was evaluated with statistical functions, specifically the Average Absolute Prediction Error, the Root Mean Square Error, the Reduced Error Estimate and the Coefficient of Residual Mass, and graphic displays of observed and predicted B concentration profiles. Even though no single adsorption isotherm equation, when coupled to TETrans, could be considered poor in its performance, results indicated that the order of model performance was the pH-dependent Keren equation first, followed by the temperature-dependent Langmuir and kinetic Freundlich equations, the Freundlich equation, and, finally, the Langmuir equation. Overall, the TETrans model was able to simulate the transport of B with deviations because no functional adsorption equation incorporated all the influences of pH, ionic strength, temperature, and kinetic effects into a single equation. The inability to correctly predict one of the measured peaks in B concentration near the soil surface suggests that problems with the timing of the sample collection may have occurred for the shallowest sampling depth.

Modelling and experimental study of the transient behaviour of plant tissue sensors in sensing dopamine

A chemical sensor is a device for measuring low concentrations of chemical solutes in a solution. Four different plant tissue sensors were used to measure the concentration of dopamine in aqueous solution. A mathematical model describing their transient characteristics was developed and experimentally verified. The rate parameters of the sensing process were determined by combining the present transient-state model with the analytical solution of a previously reported steady-state model. This combined approach simplified significantly the numerical solution of the transient-state model from a five to a two unknown parameters problem. A total of 285 transient response-time curves containing 34,911 data points were obtained experimentally with four different tissue powder dopamine sensors over a wide range of operating conditions. One hundred and ninety of them containing 18,573 data points were used for the numerical regression analysis and evaluation of the rate parameters. The remaining 95 sets were compared with the results predicted by the model using the regressed rate parameters. Good correlation and prediction were obtained confirming the adequacy of the model in describing the transient behavior of the biosensors and also the effectiveness of the combined models approach in the computation. The results facilitate the optimum design and fabrication of such sensors.

Modelling and experimental study of the transient behaviour of plant tissue sensors in sensing dopamine

A chemical sensor is a device for measuring low concentrations of chemical solutes in a solution. Four different plant tissue sensors were used to measure the concentration of dopamine in aqueous solution. A mathematical model describing their transient characteristics was developed and experimentally verified. The rate parameters of the sensing process were determined by combining the present transient-state model with the analytical solution of a previously reported steady-state model. This combined approach simplified significantly the numerical solution of the transient-state model from a five to a two unknown parameters problem. A total of 285 transient response-time curves containing 34,911 data points were obtained experimentally with four different tissue powder dopamine sensors over a wide range of operating conditions. One hundred and ninety of them containing 18,573 data points were used for the numerical regression analysis and evaluation of the rate parameters. The remaining 95 sets were compared with the results predicted by the model using the regressed rate parameters. Good correlation and prediction were obtained confirming the adequacy of the model in describing the transient behavior of the biosensors and also the effectiveness of the combined models approach in the computation. The results facilitate the optimum design and fabrication of such sensors.

Carbon cycling in mesohaline Chesapeake Bay sediments 2: Kinetics of particulate and dissolved organic carbon turnover

Temporal and depth variations in benthic carbon metabolism rates were examined in relation to particulate organic carbon (POC) deposition rates and particulate and dissolved organic carbon degradation kinetics in two sediments from the mesohaline region of Chesapeake Bay. The depth distribution of a single pool of metabolizable POC (MPOC) in mid-Bay sediments was estimated by curve-fitting of dry weight POC profiles (1-G approach). Estimated MPOC pools accounted for 3-4% of total POC content in the upper 10 cm of sediment. First-order MPOC decay constants of 10 yr -1 during the warm season were estimated from the ratio of MPOC pool size to weighted-average MPOC deposition rate derived from mid-water column sediment trap deployments. These results indicated that the MPOC pool defined by the 1-G approach corresponded to the most readily degradable component of coastal marine phytoplankton detritus. Transient-state kinetic models of MPOC turnover, based on observed MPOC deposition rates and temperature-dependent mineralization, predicted MPOC accumulation in sediments during the spring followed by depletion during the summer. The models also predicted an early summer maximum in MPOC mineralization rate associated with the degradation of MPOC accumulated during the spring, in agreement with the seasonal pattern of sulfate reduction rates in mid-Bay sediments. Model results suggested that MPOC deposition during the summer is important in maintaining high rates of benthic carbon metabolism throughout the warm season. Steady-state and transient-state models of depth-dependent POC degradation suggested that particle mixing influences the depth distribution of MPOC concentration and turnover rate within the upper 4-6 cm of mid-Bay sediments. However, because of the rapid rate of MPOC decay, random particle mixing is unlikely to transport significant quantities of MPOC below 4-6 cm. A steady-state diagenetic model was used to test the hypothesis that downward diffusion of acetate produced by anaerobic decomposition of MPOC in the upper 4-6 cm fuels sulfate reduction deeper in the sediment. The results suggest that because of the very rapid turnover of acetate pools (≥ 2 hr -1 ), acetate diffusion does not influence the depth distribution of carbon metabolism in the sediment. Therefore, sulfate reduction occurring at depths below 4-6 cm must be fueled by decomposition of some portion of the large pool of relatively refractory sediment POC. Degradation of this material is likely responsible for =1/3 of total warm season benthic carbon metabolism.

Measuring the flux of oxygen to a muddy sediment with a cylindrical microcosm

We have examined the effects of changing the flow velocity and the oxygen concentratin in the water overlying a muddy sediment on the flux of oxygen across the sediment-water interface and on the distribution of oxygen within the pore water. The experiment was carried out on an intertidal sediment from the western Wadden Sea, using a cylindrical microcosm with a calibrated flow regime. Steady-state and transient-state models were used to estimate the values of the effective diffusion coefficient for oxygen in the pore water. Increasing the flow velocity caused a significant though small increase in the oxygen concentration in the pore water, but had little effect on the concentration gradient at the sediment-water interface. The concentration gradient in the boundary layer was too small at any of the flow velocities to account for the oxygen flux into the sediment via molecular diffusion. This is ascribed to a pressure gradient which exists in rotating flows, disrupting the diffusive boundary layer and augmenting the flux via advection. Model calculations indicate that about 25% of the flux can be attributed to irrigation by burrowing organisms, but in contrast to previous results with sandy sediments, irrigation of the pore water caused by the radial pressure gradient can be considered to be negligible. The effective diffusion coefficient ranged from 4·10 −9 m 2·s −1 at a depth of 1 mm below the sediment-water interface to 1·10 −9 m 2·s −1 deeper in the sediment. These estimates are within a factor of 1 to 3 of the modelular diffusion coefficient for oxygen, which is suprisingly close in view of the high numerical densities of meiofauna and macrofauna in this sediment.

Conjunctive use of saline and non-saline waters. III. Validation and applications of a transient model for wheat

A transient state model for numerical simulations of water and solute transport and plant water uptake (V-H model) was modified and applied to develop saline irrigation strategies for wheat grown in Northern parts of India. Three modifications made in the sink term were: (1) allowing for increased tolerances to salinity stress at progressive growth stages of wheat; (2) time and depth patterns of root distribution as fitted to experimental data, i.e. a logistic function for rooting depth with time and an exponential function to define root distribution; and (3) reductions in osmotic stress due to ion pair formations on concentration of soil solutions with water uptake. With these modifications, the V-H model allowed for good agreement between observed and predicted wheat yields under various conjunctive use modes of saline and non-saline water (mean square error, MSE = 0.0027) as well as quantities and salinities of irrigation water over the years varying in rainfall (MSE = 0.0074). Production functions for different salinity waters and their quantities are also presented. Simulations indicated higher benefits of increasing frequency with saline irrigations when the quantity of water applied for each irrigation is simultaneously reduced. Otherwise, such a practice was predicted to increase salt load in soils, thus negating the benefits through aggrevated salinity. Potentialities of using higher salinity waters for wheat production increased when such waters were introduced late in the season.

Cyclic and blending strategies for using nonsaline and saline waters for irrigation

Large quantities of saline water frequently exist in irrigated areas of the world. Various strategies have been proposed to use these saline waters. Blending involves mixing saline water with good quality water to an acceptable salinity and then using this water to irrigate crops. The cyclic strategy uses waters of various salinities separately either during one season or in a crop rotation as a function of the crop's salt tolerance. A multi-seasonal transient state model, known as the modified van Genuchten-Hanks model, was used to investigate the effects of cyclic or blending application of irrigation waters of two salinity levels on alfalfa (Medicago sativa L.), and on a corn (Zea mays L.) and cotton (Gossypium hirsutum L.) crop rotation. Simulated alfalfa yields were similar for the cyclic and blending strategies that applied the same amount of salt and water. The cyclic strategy produced higher simulated yields of salt-sensitive corn than the blending strategy, whereas the simulated salt-tolerant cotton yield was not affected by the two strategies. The beneficial effects of the cyclic strategy on corn production decreased under deficit irrigation.

Simulated effects of water table and irrigation scheduling as factors in cotton production

Irrigation is essential for economic production of some crops in semiarid climates. Benefits from irrigation may be partially offset by detrimental effects of rising water tables and salinization. Drainage systems are usually installed when the water table rises to the root zone, but installation of a drainage system and safe disposal of drainage water are expensive. The long-term consequences of a high saline water table on crop production, particularly as related to irrigation scheduling, has not been firmly established. A multiseasonal transient state model, known as the modified van Genuchten-Hanks model, was used to simulate cotton (Gossypium hirsutum L.) production using a three or four in-season irrigation schedule (3irr or 4irr) under both free drainage and water table conditions. Under drainage conditions, irrigation scheduling to avoid applying more water than the soil water-holding capacity during any irrigation event is important, whereas this factor is less important under water table conditions. “Excess” water during an irrigation causes a rise in the water table, but this water remains available for later crop use which lowers the water table. In the presence of a water table the simulations indicate, (1) higher yields are achieved by applying less irrigation during the crop season and more during the preirrigation for salt leaching purposes, (2) annual applied water must equal evapotranspiration to avoid long-term water table rise or depletion, and (3) high cotton yields can be achieved for several years even if the water table is saline and no drainage occurs if the irrigation water is low in salinity.

Effect of media pore size distribution on deep-bed filtration

One important parameter of filtration, the media pore size distribution, has not been explicitly considered in modeling deep-bed filtration models by previous investigators. In this study, we propose, based on the hypothesis of O'Melia-Ali and the use of the effective medium approximation theory, a new transient-state model and examine the effect of the media pore size distribution on filter performance. From the simulation results based on six different pore size distribution functions, it is clear that the pore size distribution plays an important role in determining the removal efficiency as well as headloss development.

Simulated crop production under saline high water table conditions

Many irrigated lands in semi-arid regions of the world are underlain with saline high water tables. Water management is critical to maintain crop productivity under these conditions. A multi-seasonal, transient state model was used to simulate cotton and alfalfa production under various irrigation management regimes. The variables included in-season water application of 1.0 or 0.6 potential evapotranspiration (PET), and 18 or 33 cm pre-irrigation amounts for cotton. The water table was initially at a 1.5m depth and a 9 dS/m salinity. A impermeable lower boundary at 2.5 m depth was imposed. Irrigation water salinity was 0.4 dS/m. Climatic conditions typical to the San Joaquin Valley of California were used for PET and precipitation values. The simulations were for no-lateral flow and also lateral flow whereby the water table was raised to its initial level prior to each irrigation event. Uniform application of 1.0 PET provided for relative cotton lint yields and alfalfa yields of 95% or more for at least 4 years. In-season irrigation of cotton with 0.6 PET had higher yields when associated with a 33 cm rather than an 18 cm pre-irrigation. Lateral flow provided for higher cotton lint yields production than the no-lateral flow case for each pre-irrigation treatment. The beneficial effects of lateral flow diminished with time because of the additional salt which accumulated and became detrimental to crop production. Substantial alfalfa yield reductions occurred after the first year when irrigation was set at 0.6 PET regardless of other conditions. Evaporation losses from the soil during the cotton fallow season were higher when the soil water content entering the fallow season were higher.

Optimization of isotachophoretic analysis: use of the charge-based transient-state model

A charged-based transient-state model of the isotachophoretic separation of a multi-component mixture is described. The model enables both the column hold-up required for the full separation of a multi-component sample and the analysis time to be calculated. The optimum pH of the leading electrolyte can be found by plotting the analysis time vs. the pH of leading electrolyte. The method was applied to the separation of a three-component mixture (acetate, lactate, butyrate) and the theoretical values of the required column hold-up were compared with those obtained experimentally. Good agreement between the theoretical and experimental values was found.

Separation process in isotachophoresis : III. Transient state models for a three-component system

The separation of a three-component mixture (4,5-dihydroxy-3-( p-sulphophenylazo)-2,7-naphthalenedisulphonic acid, monochloracetic acid and picric acid) was measured by the use of a multichannel ultraviolet-photometric zone detector. Two theoretical models which previously applied to binary systems were extended to treat the transient state of a three-component system. The formulation and the computational procedure are described in detail. Good agreement was obtained between the observed and simulated boundary velocities and resolution time, confirming the validity of the models used. Especially, the slight sample pH dependence of the resolution time was successfully simulated by one of the models (modified sample property reflecting model). The decrease in the separation capacity in the three-component system in comparison with that in the binary system was explained by the difference in the boundary velocities caused by the different potential gradients of the mixed zones.

Very fast linear and non-linear observers Part 2. Application to a power system

A new approach to the very fast state estimation of a synchronous generator is presented. The transient-state models of a generator are represented by a set of non-linear equations for three synchronous generator models. Digital computer simulation for a generator of Sn = 432 M V A is presented.

A transient state model for predicting maintenance requirements

A microcomputer-based model is used to predict the life cycle maintenance requirements of a population of repairable items. By recognizing the variability of maintenance requirements over the life cycle and the heterogeneity of age and deployment environment of units in the population, the model produces estimates of overall population requirements. The uses of the model are demonstrated in the context of a case study.

A transient state model for predicting maintenance requirements

A microcomputer-based model is used to predict the life cycle maintenance requirements of a population of repairable items. By recognizing the variability of maintenance requirements over the life cycle and the heterogeneity of age and deployment environment of units in the population, the model produces estimates of overall population requirements. The uses of the model are demonstrated in the context of a case study.

Observing the state of a synchronous generator Part 2. Applications

New portional and proportional-integral observers that estimate the transient state of a synchronous generator are presented. The transient-state model of a generator is represented by a set of non-linear differential equations. Observers for four synchronous generators are given. Digital computer simulation for three types of generators S = 3125 MVA, 432 MVA and 555 MVA confirms that the non-linear observers estimate the state correctly not only in a local region of the equilibrium point but also in a large area which includes the typical regime of generator transient processes.

Transient three phase, three component, nonequilibrium inhomogeneous flow

Transient and steady state, nonequilibrium, two-fluid and drift flux models have been developed for a steam liquid system including a solid phase in the liquid and a non-condensable component in the steam. A proper choice of a dependent-variables vector yields an extremely simple working form of the system of PDEs not necessitating any simplifying assumptions. The critical mass flow rate and/or the critical flow conditions corresponding to the assumptions above are determined. With the assumption of either dispersed or homogeneous flow the model offers identifiable characteristics and path lines. For the inhomogeneous flow the flow describing system is transformed into the canonical form.

A transient-state model of dielectric relaxation accounting for lag of many-body effect

A transient-state model of dielectric relaxation accounting for lag of many-body effect