Ahmad Salim Kadoura

Constraining a compositional flow model with flow‐chemical data using an ensemble‐based Kalman filter

Isothermal compositional flow models require coupling transient compressible flows and advective transport systems of various chemical species in subsurface porous media. Building such numerical models is quite challenging and may be subject to many sources of uncertainties because of possible incomplete representation of some geological parameters that characterize the systems processes. Advanced data assimilation methods, such as the ensemble Kalman filter (EnKF), can be used to calibrate these models by incorporating available data. In this work, we consider the problem of estimating reservoir permeability using information about phase pressure as well as the chemical properties of fluid components. We carry out state-parameter estimation experiments using joint and dual updating schemes in the context of the EnKF with a two-dimensional single-phase compositional flow model (CFM). Quantitative and statistical analyses are performed to evaluate and compare the performance of the assimilation schemes. Our results indicate that including chemical composition data significantly enhances the accuracy of the permeability estimates. In addition, composition data provide more information to estimate system states and parameters than do standard pressure data. The dual state-parameter estimation scheme provides about 10% more accurate permeability estimates on average than the joint scheme when implemented with the same ensemble members, at the cost of twice more forward model integrations. At similar computational cost, the dual approach becomes only beneficial after using large enough ensembles.

A conservative and a hybrid early rejection schemes for accelerating Monte Carlo molecular simulation

Molecular simulation could provide detailed description of fluid systems when compared to experimental techniques. They can also replace equations of state; however, molecular simulation usually costs considerable computational efforts. Several techniques have been developed to overcome such high computational costs. In this paper, two early rejection schemes, a conservative and a hybrid one, are introduced. In these two methods, undesired configurations generated by the Monte Carlo trials are rejected earlier than it would when using conventional algorithms. The methods are tested for structureless single-component Lennard–Jones particles in both canonical and NVT-Gibbs ensembles. The computational time reduction for both ensembles is observed at a wide range of thermodynamic conditions. Results show that computational time savings are directly proportional to the rejection rate of Monte Carlo trials. The proposed conservative scheme has shown to be successful in saving up to 40% of the computational time in the canonical ensemble and up to 30% in the NVT-Gibbs ensemble when compared to standard algorithms. In addition, it preserves the exact Markov chains produced by the Metropolis scheme. Further enhancement for NVT-Gibbs ensemble is achieved by combining this technique with the bond formation early rejection one. The hybrid method achieves more than 50% saving of the central processing unit (CPU) time.

An Efficient Method of Reweighting and Reconstructing Monte Carlo Molecular Simulation Data for Extrapolation to Different Temperature and Density Conditions

This paper introduces an efficient technique to generate new molecular simulation Markov chains for different temperature and density conditions, which allow for rapid extrapolation of canonical ensemble averages at a range of temperatures and densities different from the original conditions where a single simulation is conducted. Obtained information from the original simulation are reweighted and even reconstructed in order to extrapolate our knowledge to the new conditions. Our technique allows not only the extrapolation to a new temperature or density, but also the double extrapolation to both new temperature and density. The method was implemented for Lennard-Jones fluid with structureless particles in single-gas phase region. Extrapolation behaviors as functions of extrapolation ranges were studied. Limits of extrapolation ranges showed a remarkable capability especially along isochors where only reweighting is required. Various factors that could affect the limits of extrapolation ranges were investigated and compared. In particular, these limits were shown to be sensitive to the number of particles used and starting point where the simulation was originally conducted.

Accelerating Monte Carlo molecular simulations by reweighting and reconstructing Markov chains: Extrapolation of canonical ensemble averages and second derivatives to different temperature and density conditions

Accurate determination of thermodynamic properties of petroleum reservoir fluids is of great interest to many applications, especially in petroleum engineering and chemical engineering. Molecular simulation has many appealing features, especially its requirement of fewer tuned parameters but yet better predicting capability; however it is well known that molecular simulation is very CPU expensive, as compared to equation of state approaches. We have recently introduced an efficient thermodynamically consistent technique to regenerate rapidly Monte Carlo Markov Chains (MCMCs) at different thermodynamic conditions from the existing data points that have been pre-computed with expensive classical simulation. This technique can speed up the simulation more than a million times, making the regenerated molecular simulation almost as fast as equation of state approaches. In this paper, this technique is first briefly reviewed and then numerically investigated in its capability of predicting ensemble averages of primary quantities at different neighboring thermodynamic conditions to the original simulated MCMCs. Moreover, this extrapolation technique is extended to predict second derivative properties (e.g. heat capacity and fluid compressibility). The method works by reweighting and reconstructing generated MCMCs in canonical ensemble for Lennard-Jones particles. In this paper, systems potential energy, pressure, isochoric heat capacity and isothermal compressibility along isochors, isotherms and paths of changing temperature and density from the original simulated points were extrapolated. Finally, an optimized set of Lennard-Jones parameters (e, σ) for single site models were proposed for methane, nitrogen and carbon monoxide.

Speeding up Monte Carlo molecular simulation by a non-conservative early rejection scheme

Monte Carlo (MC) molecular simulation describes fluid systems with rich information, and it is capable of predicting many fluid properties of engineering interest. In general, it is more accurate and representative than equations of state. On the other hand, it requires much more computational effort and simulation time. For that purpose, several techniques have been developed in order to speed up MC molecular simulations while preserving their precision. In particular, early rejection schemes are capable of reducing computational cost by reaching the rejection decision for the undesired MC trials at an earlier stage in comparison to the conventional scheme. In a recent work, we have introduced a ‘conservative’ early rejection scheme as a method to accelerate MC simulations while producing exactly the same results as the conventional algorithm. In this paper, we introduce a ‘non-conservative’ early rejection scheme, which is much faster than the conservative scheme, yet it preserves the precision of the method. The proposed scheme is tested for systems of structureless Lennard-Jones particles in both canonical and NVT-Gibbs ensembles. Numerical experiments were conducted at several thermodynamic conditions for different number of particles. Results show that at certain thermodynamic conditions, the non-conservative method is capable of doubling the speed of the MC molecular simulations in both canonical and NVT-Gibbs ensembles.

Switching Between the NVT and NpT Ensembles Using the Reweighting and Reconstruction Scheme

Abstract Recently, we have developed several techniques in order to accelerate Monte Carlo (MC) molec- ular simulations. For that purpose, two strategies were followed. In the first, new algorithms were proposed as a set of early rejection schemes performing faster than the conventional al- gorithm while preserving the accuracy of the method. On the other hand, a reweighting and reconstruction scheme was introduced that is capable of retrieving primary quantities and sec- ond derivative properties at several thermodynamic conditions from a single MC Markov chain. The latter scheme, was first developed to extrapolate quantities in NV T ensemble for struc- tureless Lennard-Jones particles. However, it is evident that for most real life applications the NpT ensemble is more convenient, as pressure and temperature are usually known. Therefore, in this paper we present an extension to the reweighting and reconstruction method to solve NpT problems utilizing the same Markov chains generated by the NV T ensemble simulations. Eventually, the new approach allows elegant switching between the two ensembles for several quantities at a wide range of neighboring thermodynamic conditions.

Multi-scale Coupling between Monte Carlo Molecular Simulation and Darcy-Scale Flow in Porous Media

Abstract In this work, an efficient coupling between Monte Carlo (MC) molecular simulation and Darcy- scale flow in porous media is presented. The cell centered finite difference method with non- uniform rectangular mesh were used to discretize the simulation domain and solve the governing equations. To speed up the MC simulations, we implemented a recently developed scheme that quickly generates MC Markov chains out of pre-computed ones, based on the reweighting and reconstruction algorithm. This method astonishingly reduces the required computational times by MC simulations from hours to seconds. To demonstrate the strength of the proposed coupling in terms of computational time efficiency and numerical accuracy in fluid properties, various numerical experiments covering different compressible single-phase flow scenarios were conducted. The novelty in the introduced scheme is in allowing an efficient coupling of the molecular scale and the Darcys one in reservoir simulators. This leads to an accurate description of thermodynamic behavior of the simulated reservoir fluids; consequently enhancing the confidence in the flow predictions in porous media.

Single-site Lennard-Jones models via polynomial chaos surrogates of Monte Carlo molecular simulation.

In this work, two Polynomial Chaos (PC) surrogates were generated to reproduce Monte Carlo (MC) molecular simulation results of the canonical (single-phase) and the NVT-Gibbs (two-phase) ensembles for a system of normalized structureless Lennard-Jones (LJ) particles. The main advantage of such surrogates, once generated, is the capability of accurately computing the needed thermodynamic quantities in a few seconds, thus efficiently replacing the computationally expensive MC molecular simulations. Benefiting from the tremendous computational time reduction, the PC surrogates were used to conduct large-scale optimization in order to propose single-site LJ models for several simple molecules. Experimental data, a set of supercritical isotherms, and part of the two-phase envelope, of several pure components were used for tuning the LJ parameters (ε, σ). Based on the conducted optimization, excellent fit was obtained for different noble gases (Ar, Kr, and Xe) and other small molecules (CH4, N2, and CO). On the other hand, due to the simplicity of the LJ model used, dramatic deviations between simulation and experimental data were observed, especially in the two-phase region, for more complex molecules such as CO2 and C2 H6.

An NPT Monte Carlo Molecular Simulation-Based Approach to Investigate Solid-Vapor Equilibrium: Application to Elemental Sulfur-H2S System

Abstract In this work, a method to estimate solid elemental sulfur solubility in pure and gas mixtures using Monte Carlo (MC)molecular simulation is proposed. This method is based on Isobaric-Isothermal (NPT) ensemble and the Widom insertion technique for the gas phase and a continuum model for the solid phase. This method avoids the difficulty of having to deal with high rejection rates that are usually encounteredwhen simulating using Gibbs ensemble. The application of this method is tested with a system made ofpure hydrogen sulfide gas (H 2 S) and solid elemental sulfur. However, this techniquemay be used for other solid-vapor systems provided the fugacity of the solid phase is known (e.g., through experimentalwork). Given solid fugacity at the desired pressureand temperature, the mole fraction of the solid dissolved in gas that would be in chemical equilibrium with the solid phase might be obtained. In other words a set of MC molecular simulation experiments is conducted on a single box given the pressure and temperature and for different mole fractions of the solute.The fugacity of the gas mixture is determined using the Widom insertion method and is compared with that predetermined for the solid phase until one finds the mole fraction which achieves the required fugacity. In this work, several examples of MC have been conducted and compared withexperimental data. TheLennard-Jones parameters related to the sulfur molecule model ( , ) have been optimized to achieve better match with the experimental work.)© 2013The Authors. Published by Elsevier B.V.Selection and/or peer-review under responsibility of the organizers ofthe 2013 International Conference on ComputationalScience