Experimental Steady-state Data Research Articles

Reaction Kinetics Determined from Coreflooding and Steady-State Principles for Stevns Klint and Kansas Chalk Injected with MgCl2 Brine at Reservoir Temperature

Summary A methodology is presented for determining reaction kinetics from coreflooding: A core is flooded with reactive brine at different compositions with injection rates varied systematically. Each combination is performed until steady state, when effluent concentrations no longer change significantly with time. Lower injection rate gives the brine more time to react. We also propose shut-in tests where brine reacts statically with the core for a defined period and then is flushed out. The residence time and produced brine composition are compared with the flooding experiments. This design allows characterization of the reaction kinetics from a single core. Efficient modeling and matching of the experiments can be performed as the steady-state data are directly comparable to equilibrating the injected brine gradually with time and do not require spatial and temporal modeling of the entire dynamic experiments. Each steady-state data point represents different information that helps constrain parameter selection. The reaction kinetics can predict equilibrium states and time needed to reach equilibrium. Accounting for dispersion increases the complexity by needing to find a spatial distribution of coupled solutions and is recommended as a second step when a first estimate of the kinetics has been obtained. It is still much more efficient than simulating the full dynamic experiment. Experiments were performed injecting 0.0445 and 0.219 mol/L MgCl2 into Stevns Klint (Denmark) and Kansas (USA) chalks at 100 and 130°C (North Sea reservoir temperature). Injection rates varied from 0.25 to 16 pore volume per day (PV/D), while shut-in tests provided equivalent rates down to 1/28 PV/D. The results showed that Ca2+ ions were produced and Mg2+ ions retained (associated with calcite dissolution and magnesite precipitation, respectively). This occurred in a substitution-like manner, where the gain of Ca was similar to the loss of Mg2+. A simple reaction kinetic model based on this substitution with three independent tuning parameters (rate coefficient, reaction order, and equilibrium constant) was implemented together with advection to analytically calculate steady-state effluent concentrations when injected composition, injection rate, and reaction kinetic parameters were stated. By tuning reaction kinetic parameters, the experimental steady-state data were fitted efficiently. The parameters were determined to be relatively accurate for each core. The roles of reaction parameters, pore velocity, and dispersion were illustrated with sensitivity analyses. The determined reaction kinetics could successfully predict the chemical interaction in reservoir chalk and outcrop chalk containing oil with strongly water-wet or mixed-wet state. The steady-state method allows computationally efficient matching even with complex reaction kinetics. Using a comprehensive geochemical description in the software PHREEQC, the kinetics of calcite and magnesite mineral reactions were determined by matching the steady-state concentration changes as function of (residence) time. The simulator predicted close to the identical production of Ca as loss of Mg. The geochemical software predicted much higher calcite solubility in MgCl2 than observed at 100 and 130°C for Stevns Klint and Kansas. The methodology supports reactive flow modeling in general, but especially oil-bearing chalk reservoirs, which are chemically sensitive to injected seawater in terms of wettability and rock strength.

Simulation of supercritical water oxidation reactor in transitory state: Application to time-dependent processes

Supercritical Water Oxidation (SCWO) is a powerful process for the treatment of organic wastewater. It has already been studied for decades and, nowadays there are several demonstration and industrial plants under construction worldwide. Simulation tools play an important role, both to predict and optimize the operating conditions during the process and to evaluate its economic viability. In the case of SCWO, transitory state models are sparse in the literature. In order to exhaustively know the behavior of the SCWO process during time-dependent applications, a transitory tubular reactor model has been built. That model has been developed by the finite difference method in two dimensions. It takes into account the reaction of wastewater along the reactor and the heat loss from the fluid to the atmosphere in a radial way, both along the pipe and through the isolation material.In order to validate the model, a set of experiments under different operating conditions were carried out in a pilot plant. Their aim was to characterize the heat loss in the system to fit both simulated and experimental data in steady state. Then, the transitory model is tested and typically time-dependent applications at industrial scale are analysed under different operating conditions (varying feed concentrations, reactor inlet temperature or amount of cooling water injection). In each case, the model results are collected and they show the time variation according to the changes in operating parameters such as temperature, feed concentration or heat loss along the reactor. The model developed can also be used for other technologies based on supercritical water, such as supercritical water gasification.

Void fraction correlations analysis and their influence on heat transfer of helical double-pipe vertical evaporator

An analysis of 50 void fraction correlations available in the literature was performed to describe two-phase flow mechanism inside two helical double-pipe vertical evaporators. The evaporators considered water as working fluid connected in countercurrent so the change of phase was carried out into the internal tube. The discretized equations of continuity, momentum and energy in each flow were coupled using an implicit step by step method. The selection of the void fraction correlations for the mathematical model was based on inclusion of some theoretical limits. The results of this analysis were compared with the experimental data in steady state for two different evaporators, obtaining good agreement in the evaporation process for only 7 void fraction correlations. The Armand and Massena correlation had a mean percentage error (MPE) of 3.08%, followed by Rouhanni and Axelsson I adquired MPE=3.16%, Chisholm and Armand obtained MPE=3.18%, Steiner as well as Rouhanni and Axelsson II with MPE=3.19%, Bestion reached MPE=3.20% and Flanigan presented MPE=3.21%. Furthermore, the experimental and simulated heat flux were acceptable (R2=0.939). Finally, the results showed that the drift flux parameter was important to evaluate the void fraction.

CFD analysis of the effect of rolling motion on the flow distribution at the core inlet

The flow distribution at the core inlet in rolling motion is investigated with software CFX12.0. The calculation results were in agreement with experimental data in steady state. As the increasing of rolling amplitude and the decreasing of rolling period, the effect of rolling motion on the flow distribution factor and the flowing behavior increases. In rolling motion, the variation of flow distribution factor is not regular. The rolling motion could decrease the minimum flow distribution factor. The effect of rolling motion on the coolant field and flow distribution diminishes with the Reynolds number increasing. The effect of rolling motion on the flow distribution in the case of single loop operation is more significant than that in the case of double loops operation.

Theoretical analysis of the fluid mixing at the core inlet in rolling motion

► The fluid mixing at the reactor core in rolling motion is investigated. ► The theoretical results are validated with experimental data in steady state. ► The variation of fluid mixing factor increases with the increasing of additional force. ► The effect of rolling motion might be limited by the increasing of Reynolds number. The fluid mixing at the reactor core in rolling motion and steady state is investigated numerically with CFX12.0. The CFD results are validated with experimental data in steady state. In rolling motion, the fluid mixing factor at the center of the core oscillates in a cosine function, but the variation of the fluid mixing factor surrounding the core is not regular. The variation amplitude of the fluid mixing factor next to the boundary line of fluid mixing is the most significant. The variation of fluid mixing factor increases with the increasing of additional force. The increasing of Reynolds number could depress the effect of rolling motion on the fluid mixing.

Relative Permeability Calculations from Two-Phase Flow Simulations Directly on Digital Images of Porous Rocks

We present results from a systematic study of relative permeability functions derived from two-phase lattice Boltzmann (LB) simulations on X-ray microtomography pore space images of Bentheimer and Berea sandstone. The simulations mimic both unsteady- and steady-state experiments for measuring relative permeability. For steady-state flow, we reproduce drainage and imbibition relative permeability curves that are in good agreement with available experimental steady-state data. Relative permeabilities from unsteady-state displacements are derived by explicit calculations using the Johnson, Bossler and Naumann method with input from simulated production and pressure profiles. We find that the nonwetting phase relative permeability for drainage is over-predicted compared to the steady-state data. This is due to transient dynamic effects causing viscous instabilities. Thus, the calculated unsteady-state relative permeabilities for the drainage is fundamentally different from the steady-state situation where transient effects have vanished. These effects have a larger impact on the invading nonwetting fluid than the defending wetting fluid. Unsteady-state imbibition relative permeabilities are comparable to the steady-state ones. However, the appearance of a piston-like front disguises most of the displacement and data can only be determined for a restricted range of saturations. Relative permeabilities derived from unsteady-state displacements exhibit clear rate effects, and residual saturations depend strongly on the capillary number. We conclude that the LB method can provide a versatile tool to compute multiphase flow properties from pore space images and to explore the effects of imposed flow and fluid conditions on these properties. Also, dynamic effects are properly captured by the method, giving the opportunity to examine differences between steady and unsteady-state setups.

Modelling of an infrared halogen lamp in a rapid thermal system

The heat flux distribution of an infrared halogen lamp in a Rapid Thermal Processing (RTP) equipment is studied. An overview of lamp modelling in RTP systems is given and for the first time, the infrared lamp bank is modelled by taking into consideration with accuracy a lamp portion in the bank environment. A three-dimensional (3D) lamp model, with a fine filament representation is largely presented. The model assumptions are in particular exposed with focusing on the thermal boundary conditions. The lamp temperature is calculated by solving the radiative heat transfer equation by means of the Monte-Carlo method for ray tracing. Numerical calculations are performed with the finite volume method. A very good agreement is found with experimental data in steady state. The heat amount provided by the lamp is also determined. As a first development, transient calculations are performed with the validated model and the dynamic behaviour of the lamp during heating process is determined with precision. Lastly, the model is discussed and further developments are proposed.

Heat transfer of a helical double-pipe vertical evaporator: Theoretical analysis and experimental validation

A predictive model is developed to describe heat transfer and fluid dynamic behavior of a helical double-pipe vertical evaporator used in an absorption heat transformer integrated to a water purification process. The evaporator uses water as working fluid connected in countercurrent. Heat transfer by conduction in the internal tube wall is considered; in addition the change of phase is carried out into the internal tube. The dynamic model considers equations of continuity, momentum and energy in each flow. The discretized governing equations are coupled using an implicit step by step method. The results of this model are compared with the experimental data in steady state, obtaining good agreement in the evaporation process. The model is also evaluated of form dynamic to determine the principal operation variables that affect the evaporator with the main objective to optimize and control the system.

Rate-Dependent Elastoslide Model for Magnetorheological Damper

A rate-dependent elastoslide model is developed to study the quasi-steady and dynamic behavior of a magnetorheological damper. This time-domain model uses a rate-dependent slide and a parallel viscous damping to describe the practical yield behavior demonstrated by field-activated magnetorheological fluids, and it uses a stiff spring in series with the slide to represent the preyield stiffness of the damper. A method of determination of the model parameters is developed using single-frequency hysteresis data of the magnetorheological damper. The model parameters are determined using virtual loading curves identified from the force-displacement and force-velocity hysteretic diagrams. A relationship between current controllable parameters and current input is established. The fidelity of the model is justified by a good correlation between modeling results and experimental steady-state data over a broad amplitude and moderate-frequency range. Significantly, this model captures nonlinear amplitude- and frequency-dependent behavior of magnetorheological dampers using constant model parameters and trivial computational effort.

A numerical simulation model for plate-type, roll-bond evaporators

This study presents a first-principles mathematical model developed to investigate the thermal behavior of a plate-type, roll-bond evaporator. The refrigerated cabinet was also taken into account in order to supply the proper boundary conditions to the evaporator model. The mathematical model was based on the mass, momentum and energy conservation principles applied to each of the following domains: (i) refrigerant flow through the evaporator channels; (ii) heat diffusion in the evaporator plate; and (iii) heat transmission to the refrigerated cabinet. Empirical correlations were also required to estimate the shear stresses, and the internal and external heat transfer rates. The governing partial differential equations were discretized through the finite-volume approach and the resulting set of algebraic equations was solved by successive iterations. Validation of the model against experimental steady-state data showed a reasonable level of agreement: the cabinet air temperature and the evaporator cooling capacity were predicted within error bands of ±1.5 °C and ±6%, respectively.

RATE-DEPENDENT ELASTO-SLIDE MODEL FOR SINGLE AND DUAL FREQUENCY MR LAG DAMPER BEHAVIOR

In order to capture MR lag damper behavior accurately in the context of helicopter rotor dynamic analyses, a physically motivated rate-dependent elasto-slide model was developed based on the Bingham plastic model. This time-domain model uses a rate-dependent slide and a parallel viscous damper to simulate the yield behavior of the MR fluid and uses a stiff spring in series with the slide to represent the preyield stiffness. A method of determination of the model parameters was introduced using MR damper single frequency hysteresis data. The fidelity of the model was justified by the good correlation between modeling results and experimental steady-state data over a wide amplitude and moderate frequency range. Significantly, the rate-dependent elasto-slide model is applicable in predicting response under single and dual frequency loading conditions encountered by an MR lag damper.

Identification of a nonlinear compressor model

In this article, a technique for the identification of a nonlinear compressor performance model exhibiting bifurcation phenomena is presented. The approach consists of employing the modal form of the compressor flow equations along with derived linear and nonlinear stability results. When the identified steady-state model is used in the system, bifurcation analysis tools predict stable solutions in accord with experimental steady-state data.

5605051 Automotive air conditioner having condenser and evaporator provided within air duct

This study presents a first-principles mathematical model developed to investigate the thermal behavior of a plate-type, roll-bond evaporator. The refrigerated cabinet was also taken into account in order to supply the proper boundary conditions to the evaporator model. The mathematical model was based on the mass, momentum and energy conservation principles applied to each of the following domains: (i) refrigerant flow through the evaporator channels; (ii) heat diffusion in the evaporator plate; and (iii) heat transmission to the refrigerated cabinet. Empirical correlations were also required to estimate the shear stresses, and the internal and external heat transfer rates. The governing partial differential equations were discretized through the finite-volume approach and the resulting set of algebraic equations was solved by successive iterations. Validation of the model against experimental steady-state data showed a reasonable level of agreement: the cabinet air temperature and the evaporator cooling capacity were predicted within error bands of ±1.5 °C and ±6%, respectively.

Transient natural convection over a heat generating vertical cylinder

A numerical solution for the transient natural convection over heat generating vertical cylinders of various thermal capacities and radii is presented. A fully implicit finite difference technique is used to solve the non-linear set of equations. The rate of propagation of the leading edge effect is given special consideration. It is found that this rate, predicted by the one-dimensional conduction solution, is slower than that resulting from the boundary layer solution. Also, it increases as the radius and thermal capacity of the cylinder decrease, and as the surface heat flux increases. The transient boundary layer thickness is found to exceed its steady-state value while the transient average heat transfer coefficient is found to reach a minimum, as low as 53% of its steady-state value for the highest value of the modified Grashof number studied. Excellent agreement with previous experimental steady-state data as well as with one-dimensional theoretical results is obtained.

Experimental and modelling investigations of steady-state and dynamic characteristics of ethylene hydrogenation on Pt/Al 2O 3

A robust strategy based on fluid-phase measurements is described for the testing and development of kinetic models for heterogeneous catalytic reactions. Steady-state, step-response, feedback-induced Hopf bifurcation and forced concentration cycling experiments were applied to ethylene hydrogenation over 0.05% Pt/Al 2O 3 in a CSTR at 80°C. Two versions of a reaction mechanism that differ in the order for hydrogen adsorption describe the experimental steady-state data. However, only one of these models adequately describes the system responses to step changes in the feed composition. Step-response experiments were used to identify a time scale of 5000 s which is associated with chemisorbed hydrogen. Conversely, feedback-induced Hopf bifurcation data indicate this time scale to be of the order of 1 s in magnitude. In the overall strategy of dynamic modelling, the two techniques are complementary since each inherently focuses on an opposite region in the spectrum of time scales for the reactor system. A detailed method for analysing feedback-induced Hopf bifurcation with a time delay is presented. The dynamic model based upon steady-state, step-response and bifurcation data was found to be inadequate for describing the results from cycled-feedstream experiments. Cycling the feedstream composition resulted in an improvement of the time-average reaction rate for the ethylene hydrogenation reaction compared to steady-state reactor operation. Rate improvement was observed for the entire range of ethylene feed concentrations that were tested, including conditions which give rise to a maximum in the steady-state reaction rate surface.

Crystal size distributions in continuous crystallizers when growth rate is size dependent

AbstractEmpirical size‐dependent growth rate models are studied for their effect on the population density distributions from a continuous, mixed suspension, mixed product removal (CMSMPR) crystallizer. The growth rate models and/or their corresponding population density distributions are examined for continuity, convergence of moments, versatility, and their ability to fit experimental data.A new empirical size‐dependent growth rate model is proposed which has properties superior to those of previous models. Experimental steady state data are presented to illustrate the application of the model to actual CMSMPR crystallization systems.