Time-dependent Finite Element Method Research Articles

A New 3D Mathematical Model for Simulating Nanofluid Flooding in a Porous Medium for Enhanced Oil Recovery.

Two-phase Darcy's law is a well-known mathematical model used in the petrochemical industry. It predicts the fluid flow in reservoirs and can be used to optimize oil production using recent technology. Indeed, various models have been proposed for predicting oil recovery using injected nanofluids (NFs). Among them, numerical modeling is attracting the attention of scientists and engineers owing to its ability to modify the thermophysical properties of NFs such as density, viscosity, and thermal conductivity. Herein, a new model for simulating NF injection into a 3D porous media for enhanced oil recovery (EOR) is investigated. This model has been developed for its ability to predict oil recovery across a wide range of temperatures and volume fractions (VFs). For the first time, the model can examine the changes and effects of thermophysical properties on the EOR process based on empirical correlations depending on two variables, VF and inlet temperature. The governing equations obtained from Darcy's law, mass conservation, concentration, and energy equations were numerically evaluated using a time-dependent finite-element method. The findings indicated that optimizing the temperature and VF could significantly improve the thermophysical properties of the EOR process. We observed that increasing the inlet temperature (353.15 K) and volume fraction (4%) resulted in better oil displacement, improved sweep efficiency, and enhanced mobility of the NF. The oil recovery decreased when the VF (>4%) and temperature exceeded 353.15 K. Remarkably, the optimal VF and inlet temperature for changing the thermophysical properties increased the oil production by 30%.

Numerical investigation of thermal residual stress distribution for the sustainability of laser welded joints of dissimilar materials

In this work, a three-dimensional (3D) time dependent finite element method is used to simulate the thermo-mechanical behavior of laser welded joints. Laser welding of two dissimilar materials (AISI 316L and Ti6Al4V) of 2 mm thickness has been considered while modeling in COMSOL multiphysics with a coupling of heat transfer and solid mechanics module. A total of six temperature dependent physical properties, i.e. density, specific heat, thermal conductivity, coefficient of thermal expansion, Young’s modulus, and Poisson’s ratio have been considered for making the numerical model more realistic. The experimental results show that AISI 316L experiences more than 2 times more maximum stresses than Ti6Al4V near the weld bead region during the process. High value of Von mishes stress in the welded zone can be observed due to high temperature gradients of welds. The simulated value of residual after one entire thermal cycle is near to 80 MPa on a point over weld bead.

Determination of individual concentration-dependent diffusivity of binary gas-mixtures in reservoir-fluid systems

Diffusion is one of the main mass transfer principles associated with a gas injection process, e.g., vapor extraction (VAPEX) and cyclic solvent injection (CSI), to reduce the viscosity of heavy oil by dissolution of light gas(es). A few efforts have been made to estimate the diffusivity of each gas component of a binary gas-mixture in heavy oil as a constant, but no attempts have been made to determine individual diffusivity of each gas component in the binary gas-mixture as concentration-dependent. In this study, the concentration-dependent diffusivities of CO2 and C3H8 in a CO2/C3H8 mixture, which preferentially diffuses in a Lloydminster heavy oil, are evaluated implicitly as a power function of gas concentration, pressure, and temperature through the oil viscosity. The coefficient and exponent of such a power function for each gas are determined once the deviations between the measured and calculated values for oil swelling factors and composition of each gas dissolved in heavy oil at the completion of a dynamic volume analysis (DVA) test are minimized by applying the 1D time-dependent finite element method (FEM). Compared with the constant diffusivities for the same test, considering concentration-dependency of the dissolved gases reproduces the experimentally measured oil swelling factors and compositions at the end of the test with a significantly enhanced accuracy. Then, such obtained concentration-dependent diffusivities are extended to reproduce the experimentally measured swelling factors of a pressure-decay test performed with another CO2/C3H8 gas-mixture and the same heavy oil. From such an evaluation, it can be inferred that the coefficient and exponent of the diffusivity correlation associated with a binary gas-mixture are functions of pressure, temperature, feed gas composition, and test duration, respectively. This is because the coefficient and exponent for one gas component may be affected by the presence of the other as the latter alters the composition of heavy oil in which the former diffuses.

Time reversal for elastic scatterer location from acoustic recording

The aim of this paper is to study the feasibility of time-reversal methods in a non homogeneous elastic medium, from data recorded in an acoustic medium. We aim to determine, from partial aperture boundary measurements, the presence and some physical properties of elastic unknown “inclusions”, i.e. not observable solid objects, located in the elastic medium. We first derive a variational formulation of the acousto-elastic problem, from which one constructs a time-dependent finite element method to solve the forward, and then, the time reversed problem. Several criteria, derived from the reverse time migration framework, are then proposed to construct images of the inclusions, and to determine their locations. The dependence of the approach to several parameters (aperture, number of sources, etc.) is also investigated. In particular, it is shown that one can differentiate between a benign and malignant close inclusions. This technique is fairly insensitive to noise in the data.

Effect of Dispersion Forces on Dynamic Stability of Electrostatically Actuated Micro/Nano-Beams in Presence of Mechanical Shocks

Dispersion forces such as van der Waals and Casimir interactions become important when the size of structures shrinks. Therefore, the effective design of micro and nano-sized structures depends on appropriate consideration of these forces. In the current research, we analyzed the effect of dispersion forces on the dynamic behavior of a micro/nanobeam actuated by electrostatic forces subject to a mechanical shock. We used the Euler–Bernoulli beam theory including nonlinearities due to mid-plane stretching in our model. The equation of motion is solved using time-dependent finite element method, and pull-in forces are calculated. The stability regimes are evaluated as the set of three force parameters in which the beam elasticity overcomes the external forces, and the beam is able to vibrate without hitting the substrate. Results show that the design of the beam should be such that the three sets of non-dimensional parameters that determine the intensity of shock, dispersion, and electrostatic force do not fall above the stability limit to avoid pull-in instability. Our results have applications in the design of electrostatically actuated micro/nanobeams in mechanical shock environments such as accelerometers.

Design and analysis of the Tesla transformer with duplex secondary winding

A Tesla transformer with duplex winding is designed. The secondary winding of the transformer is divided into two parts, a 120-turn tapered winding and a 6-turn extra winding, which combine the transient oscillation of the main tapered winding and the main gap’s trigger electrode. This configuration improves the performance of the main gap and makes the generator more compact. Two types of numerical techniques are introduced: a time-dependent finite element method model and a double transmission line lumped circuit model. To validate these models, calculated voltage signals on the extra winding are compared with the measured signal. The verification test shows that results of the two models are acceptable. Errors between the measured signal and simulation results are explained.

Modeling of chloride penetration in concrete structures under freeze-thaw cycles

PurposeThe purpose of this paper is to develop a method for predicting the chloride ingress into concrete structures, with an emphasis on the low temperature range where freeze-thaw cycles may cause damage.Design/methodology/approachThe different phenomena that contribute to the rate and amount of transported chlorides into concrete, i.e., heat transfer, moisture transport and chloride diffusion are modeled using a two-dimensional nonlinear time dependent finite element method. In modeling the chloride transport, a modified version of Fick’s second law is used, in which processes of diffusion and convection due to water movement are taken into account. Besides, the effect of freeze-thaw cycles is directly incorporated in the governing equation and linked to temperature variation using a coupling term that is determined in this study. The proposed finite element model and its associated program are capable of handling pertinent material nonlinearities and variable boundary conditions that simulate real exposure situations.FindingsThe numerical performance of the model was examined through few examples to investigate its ability to simulate chloride penetration under freeze-thaw cycles and its sensitivity to factors controlling freeze-thaw damage. It was also proved that yearly temperature variation models to be used in service life assessment should take into account its cyclic nature to obtain realistic predictions.Originality/valueThe model proved promising and suitable for chloride penetration in cold climates.

A Theoretical Study on Surfactant Adsorption Kinetics: Effect of Bubble Shape on Dynamic Surface Tension

A planar or spherical fluid-liquid interface was commonly assumed on studying the surfactant adsorption kinetics for a pendant bubble in surfactant solutions. However, the shape of a pendant bubble deviates from a sphere unless the bubble's capillary constant is close to zero. Up to date, the literature has no report about the shape effect on the relaxation of surface tension due to the shape difference between a pendant bubble and a sphere. The dynamic surface tension (DST), based on the actual shape of a pendant bubble with a needle, of the diffusion-controlled process is simulated using a time-dependent finite element method in this work. The shape effect and the existence of a needle on DST are investigated. This numerical simulation resolves also the time-dependent bulk surfactant concentration. The depth of solution needed to satisfy the classical Ward-Tordai infinite-solution assumption was also studied. For a diffusion-controlled adsorption process, bubble shape and needle size are two major factors affecting the DST. The existence of a needle accelerates the bulk diffusion for a small bubble; however, the shape of a large pendant bubble decelerates the bulk diffusion. An example using this method on the DST data of C12E4 is illustrated at the end of this work.

Melt pool shape and dilution of laser cladding with wire feeding

Dilution is an important factor to influence the properties of laser cladding. To get high quality clad layer, low dilution is required. During laser cladding, heat will accumulate near the melt pool before quasi-steady state is reached. So dilution will become larger and larger. In this paper the melt pool of laser cladding is modeled by time-dependent finite element method (FEM). Adaptive mesh is used to adapt the mesh to the melt pool shape, which changes during cladding. Relative reference frames are used. The reference frames are first attached to the laser power during cladding period and then attached to the workpiece at a certain cladding time. Dilutions and melt pool shapes at different cladding times are calculated by a two-dimensional FEM model. Experiment of laser cladding with wire feeding is done. The influences of cladding time and cladding speed on dilution and melt pool shape are checked. The FEM results coincide with the experimental results.

Time-dependent FEM simulation of dilution control of laser cladding by adaptive mesh method

Dilution is an important factor which influences the properties of clad layer. In this paper the change of dilution during laser cladding and the control of dilution are simulated by a finite element method. The adaptive mesh method is adopted for the time-dependent finite element method computation so that the shape of melt pool can be well represented. The situation of the width control of melt pool is also simulated, which indicates that the dilution can be controlled if the width of melt pool is controlled. Computational results indicate that if a line energy (input energy per unit distance) remains constant the dilution will increase with time, especially at the beginning. Simulation results show that it is possible to control dilution in a certain range if the line energy decreases with time. Experiment of Nd: YAG laser cladding with wire feeding is performed. Experiment results coincide well with the FEM results.

Frost-induced deformations and stresses in pipelines

Forst-induced soil-pipeline interaction is modelled using a time-dependent thermo-mechanical process. A simplified one-dimensional frost heave model is used to evaluate frost heave, and a beam on elastic foundation finite element is used to model the buried pipeline. The time-dependent creep displacements of frozen soil are determined based on the elastic theory for the multi-layer half space. The frost-related soil stiffness is obtained using an average elastic modulus and treating the freezing soil as a multi-layer half space. The contact pressure exerted on the pipeline by frost heave and by creep effects in the frozen soil is represented by a simple distributed load. A computer program based on the time-dependent finite element method is developed which can be used to calculate frost-induced stresses and deformations of the pipe. A numerical example is presented which demonstrates reasonable agreement between the results from the proposed analysis and available experimental data.

Time-dependence of diffusion-controlled currents of a soluble redox couple at interdigitated microarray electrodes

Abstract Chronoamperometric curves for a soluble redox couple at the interdigitated array electrode (IDA) were computed by the time-dependent finite element method for various combinations of electrode geometry. In the simulated system involving the reduced species, a positive potential was applied to one pair of the IDA and the potential was stepped simultaneously negatively to the other electrode of the pair. The anodic current at first decayed following Cottrellian behavior, was then subjected to the edge effect, influenced by electrolysis at the neighboring electrodes and finally approached a steady-state value. The cathodic current began to flow with a lapse, which corresponded to the time of travel for the oxidized species from the anode to the cathode. The cathodic transient curve was characterized by the time at half of the steady-state current. The time was related directly to the square of the effective electrode gap. Six kinds of platinum IDAs, each microband electrode being 3–10 μm, were constructed by photolithography. The observed transient curves were in agreement with the computed ones.

TRANSIENT THERMAL CHANGE ON A SOLID SURFACE: COUPLED DIFFUSION OF HEAT AND MOISTURE

Abstract The sudden change of moisture and/or temperature on a solid can significantly disturb the resulting stresses and strains and cause material damage. This investigation is concerned with the sudden rise (or drop) of temperature over a finite segment of a half-space that is free of tractions. The mutual dependence of moisture and temperature is examined by coupled equations such that the hygrothermal stresses and strains are transient in character. The moisture, temperature, and stress are computed by a time-dependent finite-element method and are found to peak and oscillate as a function of time in the vicinity where the surface temperature is altered. These effects are displayed for the 5208 epoxy resin material commonly used in fiber-reinforced composities. The locations of possible failure sites are also determined by application of the strain-energy density criterion. This assumes that the peaks and valleys of the strain-energy density function dW/dV within the solid are associated with materia...