Semi-Implicit Spectral Deferred Correction Method Based on the Invariant Energy Quadratization Approach for Phase Field Problems

This paper presents a high order time discretization method by combining the semi-implicit spectral deferred correction method with energy stable linear schemes to simulate a series of phase field problems.We start with the linear scheme,which is based on the invariant energy quadratization approach and is proved to be linear unconditionally energy stable.The scheme also takes advantage of avoiding nonlinear iteration and the restriction of time step to guarantee the nonlinear system uniquely solvable.Moreover,the scheme leads to linear algebraic system to solve at each iteration,and we employ the multigrid solver to solve it efficiently.Numerical re-sults are given to illustrate that the combination of local discontinuous Galerkin(LDG)spatial discretization and the high order temporal scheme is a practical,accurate and efficient simulation tool when solving phase field problems.Namely,we can obtain high order accuracy in both time and space by solving some simple linear algebraic equations.

Higher-Order Line Element Analysis of Potential Field with Slender Heterogeneities

Potential field due to line sources residing on slender heterogeneities is involved in various areas,such as heat conduction,potential flow,and electrostatics.Often dipolar line sources are either prescribed or induced due to close interaction with other objects.Its calculation requires a higher-order scheme to take into account the dipolar effect as well as net source effect.In the present work,we apply such a higher-order line element method to analyze the potential field with cylindrical slender heterogeneities.In a benchmark example of two parallel rods,we compare the line element solution with the boundary element solution to show the accuracy as a function in terms of rods distance.Furthermore,we use more complicated examples to demonstrate the capability of the line element technique.

FINITE ELEMENT APPROXIMATION OF EIGENVALUE PROBLEM FOR A COUPLED VIBRATION BETWEEN ACOUSTIC FIELD AND PLATE

We formulate a coupled vibration between plate and acoustic field in mathematically rigorous fashion. It leads to a non-standard eigenvalue problem. A finite element approximation is considered in an abstract way, and the approximate eigenvalue problem is written in an operator form by means of some Ritz projections. The order of convergence is proved based on the result of Babugka and Osborn. Some numerical example is shown for the problem for which the exact analytical solutions are calculated. The results shows that the convergence order is consistent with the one by the numerical analysis.

Numerical Validation of Asphaltene Precipitation and Deposition during CO2 miscible flooding

Asphaltene precipitation,flocculation,and deposition can significantly reduce oil production by impacting wellbores,flowlines,and more importantly,formations’pore space around the well.Any alteration in the temperature,pressure and fluid composition can trigger asphaltene deposition.The ability to predict the occurrence and magnitude of the asphaltene deposition is a major step for flow assurance.An accurate prediction of the deposition envelope enables the operator to systematically categorize different cases based on their impact on the production.This critical knowledge can be used to predict the occurrence and magnitude of asphaltene deposition,which could potentially save the expense of installing unnecessary equipment and injecting chemical inhibitors when they are not needed.Predicting asphaltene-related flow assurance issues requires robust physically-based modeling capabilities for capturing the asphaltene’s deposition tendencies as a function of the prevailing field’s operating conditions.Although available simulators are found to be useful for predicting asphaltene’s phase behavior,precipitation tendency,and instability curves,they often overlook important physical characteristics of the asphaltenes.These properties may have a detrimental role in obtaining a realistic representation of the asphaltene deposition behavior.In this paper,the experimental and the numerical investigations are combined to present a comprehensive methodology for studying the thermodynamics of asphaltene precipitation and deposition.A wide range of pressures and CO2 concentrations are covered that are relevant to actual CO2 flooding in a Middle East oil reservoir.To do so,a series of lab experiments including routine and special PVT analyses where the Asphaltene Onset Pressure(AOP)and Saturation Pressures(Psat)were measured for different mixtures of CO2 and the reservoir oil.Maximum of 50 mol%CO2 concentration mixture was tested to measure the AOP and Psat.The amount of asphaltene precipitation was found between 0.25 and 4 wt%for the mixtures of 10e50 mol%CO2 concentration.Furthermore,detailed recommendations are presented in this paper to tune an EOS for running compositional simulations when unstable asphaltene is reported based on the lab experimental measurements.