1FEBRUARY 2005 Javier Pérez

PHASE DIAGRAM PREDICTION OF ACID GAS PHASE DIAGRAM PREDICTION OF ACID GAS MIXTURES BY MOLECULAR SIMULATIONMIXTURES BY MOLECULAR SIMULATION

Javier Pérez PelliteroJavier Pérez Pellitero††,, P. UngererP. Ungerer‡‡,, Allan D. MackieAllan D. Mackie††

†† Departament d’Enginyeria Química, ,Univ. Rovira i Virgili

‡‡ Institut Français du Pétrole

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INTRODUCTION HISTOGRAM REWEIGHTING

THE IDEA COLLECTING DATA REWEIGHTING DATA CALCULATING PHASE EQUILIBRIA

FINITE SIZE SCALING GENERAL CONSIDERATIONS BINDER’S PARAMETER

RESULTS CONCLUSIONS

INDEX:

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INTRODUCTION:

Binary mixtures containing acid gases are of interest in the crude reinjection process of the petroleum industry.

Gibbs ensemble technique is not useful in the critical region where industry demands predictions

In this work histogram reweighting and finite size scaling techniques are presented to compute phase diagrams and to complete the phase envelope in the critical region.

Phase diagrams and critical constants has been computed for the:

Long range corrected Lennard-Jones fluidBinary Lennard-Jones mixture

Pot

enti

al

r

612

4rr

r

4N U

H

SIMULATIONS:

1. Monte Carlo simulations are performed in the Grand Canonical ensemble μi , V, T = constants

1. Information about the visited states in the system is recorded in histograms.

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HISTOGRAM REWEIGHTING: THE IDEA

Method to combine results taken at different state conditions Histograms are combined according to the method outlined

by Ferrenberg and Swendsen. This method is based on the minimization of error in the microcanonical density of states

The main idea:

Combine simulation data at different temperatures to improve quality of all data via their mutual relation to (U)

smicrostate

NVU 1,,

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HISTOGRAM REWEIGHTING: COLLECTING AND REWEIGHTING DATA

N U

HH is the number of times the system visits a given state during a simulation

Pure Compound Binary mixture

H (N,U) H (N1,N2,U)

μ , V, T μ1 , μ2 , V, T

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#U

#N

HISTOGRAM REWEIGHTING: COLLECTING AND REWEIGHTING DATA

Different phase space regions are sampled with different simulations keeping “overlap” between them

#N is the maximum number of particles allowed in the system

and #U the maximum number of intervals (bins) for the energy.

Farrenberg & Swendsen: error minimization in the calculation of (U)

Knowledge of the whole phase space of interest

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HISTOGRAM REWEIGHTING: CALCULATING PHASE EQUILIBRIA

Equilibrium is calculated tuning chemical potential until equal area (equal pressure) is obtained for both phases.

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FINITE SIZE SCALING STUDY: CALCULATING THE CRITICAL PARAMETERS I

P

;22

4

LU

•For T>>Tc and L = large , we find UL 3

•For T<<Tc and L = large , we find UL 1

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Lennard-Jones fluid L1= 7.9, L2=5.3

L1 = 7.9

L2 = 5.3

FINITE SIZE SCALING STUDY: CALCULATING THE CRITICAL PARAMETERS II• For T Tc we can show that UL = universal number . This

holds for large L. For small L there will be corrections in the form L-x with x > 0. This means:

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RESULTS I: PURE FLUIDS:

Cumulant intersection L1= 7.9, L2=5.3

1,3136This work

1,326Caillol (1998)

1,3120Potoff & Panagiotopoulos (1998)

1,3145Shi and Johnson (2001)

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RESULTS II: LENNARD-JONES BINARY MIXTURES

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RESULTS II: LENNARD-JONES BINARY MIXTURES

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CONCLUSIONS:

Histogram reweighting techniques combined with finite size scaling studies improve the behaviour of Gibbs ensemble near the critical region and allow for an accurately calculation of the critical constants.

The results are in good agreement with Gibbs ensemble simulations in the region of appliance of the last technique

Application of histogram reweighting techniques allows for the calculation of binary mixture pressure-temperature-composition phase diagrams from a relative small number of simulations.

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