Monte simulations

Keywords deterministic methods, STOllP, GllP, reserves, ultimate recovery, net oil sands, area-depth and area-thickness methods, gross rock volume, expectation curves, probability of excedence curves, uncertainty, probability of success, annual reporting requirements, Monte-Carlo simulation, parametric method... 

A Monte Carlo simulation is fast to perform on a computer, and the presentation of the results is attractive. However, one cannot guarantee that the outcome of a Monte Carlo simulation run twice with the same input variables will yield exactly the same output, making the result less auditable. The more simulation runs performed, the less of a problem this becomes. The simulation as described does not indicate which of the input variables the result is most sensitive to, but one of the routines in Crystal Ball and Risk does allow a sensitivity analysis to be performed as the simulation is run.This is done by calculating the correlation coefficient of each input variable with the outcome (for example between area and UR). The higher the coefficient, the stronger the dependence between the input variable and the outcome. 

Figure 6.11 Schematic of Monte Carlo simulation 6.2.5 The parametric method...

The parametric method is an established statistical technique used for combining variables containing uncertainties, and has been advocated for use within the oil and gas industry as an alternative to Monte Carlo simulation. The main advantages of the method are its simplicity and its ability to identify the sensitivity of the result to the input variables. This allows a ranking of the variables in terms of their impact on the uncertainty of the result, and hence indicates where effort should be directed to better understand or manage the key variables in order to intervene to mitigate downside and/or take advantage of upside in the outcome. 

From the probability distributions for each of the variables on the right hand side, the values of K, p, o can be calculated. Assuming that the variables are independent, they can now be combined using the above rules to calculate K, p, o for ultimate recovery. Assuming the distribution for UR is Log-Normal, the value of UR for any confidence level can be calculated. This whole process can be performed on paper, or quickly written on a spreadsheet. The results are often within 10% of those generated by Monte Carlo simulation. 

Two simulation methods—Monte Carlo and molecular dynamics—allow calculation of the density profile and pressure difference of Eq. III-44 across the vapor-liquid interface [64, 65]. In the former method, the initial system consists of N molecules in assumed positions. An intermolecule potential function is chosen, such as the Lennard-Jones potential, and the positions are randomly varied until the energy of the system is at a minimum. The resulting configuration is taken to be the equilibrium one. In the molecular dynamics approach, the N molecules are given initial positions and velocities and the equations of motion are solved to follow the ensuing collisions until the set shows constant time-average thermodynamic properties. Both methods are computer intensive yet widely used. 

Orkoulas G and Panagiotopoulos A Z 1999 Phase behavior of the restricted primitive model and square-well fluids from Monte Carlo simulations in the grand canonical ensemble J. Chem. Phys. 110 1581... 

Jorgenson W L and Ravimohan C 1985 Monte Carlo simulation of the differences in free energy of hydration J. Chem. Phys. 83 3050... 

The alternative simulation approaches are based on molecular dynamics calculations. This is conceptually simpler that the Monte Carlo method the equations of motion are solved for a system of A molecules, and periodic boundary conditions are again imposed. This method pennits both the equilibrium and transport properties of the system to be evaluated, essentially by numerically solvmg the equations of motion... 

In principle, simulation teclmiques can be used, and Monte Carlo simulations of the primitive model of electrolyte solutions have appeared since the 1960s. Results for the osmotic coefficients are given for comparison in table A2.4.4 together with results from the MSA, PY and HNC approaches. The primitive model is clearly deficient for values of r. close to the closest distance of approach of the ions. Many years ago, Gurney [H] noted that when two ions are close enough together for their solvation sheaths to overlap, some solvent molecules become freed from ionic attraction and are effectively returned to the bulk [12]. 

Progress in the theoretical description of reaction rates in solution of course correlates strongly with that in other theoretical disciplines, in particular those which have profited most from the enonnous advances in computing power such as quantum chemistry and equilibrium as well as non-equilibrium statistical mechanics of liquid solutions where Monte Carlo and molecular dynamics simulations in many cases have taken on the traditional role of experunents, as they allow the detailed investigation of the influence of intra- and intemiolecular potential parameters on the microscopic dynamics not accessible to measurements in the laboratory. No attempt, however, will be made here to address these areas in more than a cursory way, and the interested reader is referred to the corresponding chapters of the encyclopedia. 

Specific solute-solvent interactions involving the first solvation shell only can be treated in detail by discrete solvent models. The various approaches like point charge models, siipennoleciilar calculations, quantum theories of reactions in solution, and their implementations in Monte Carlo methods and molecular dynamics simulations like the Car-Parrinello method are discussed elsewhere in this encyclopedia. Here only some points will be briefly mentioned that seem of relevance for later sections. 

Berne B J 1985 Molecular dynamics and Monte Carlo simulations of rare events Multiple Timescales ed J V Brackbill and B I Cohen (New York Academic Press)... 

The two main families of simulation teclmique are molecular dynamics (MD) and Monte Carlo (MC). Additionally, there is a whole range of hybrid teclmiques which combine features from both MC and MD. 

Binder K and Heermann D W 1997 Monte Carlo Simulation in Statistical Physics 3rd edn, vol 80 Solid State Sciences (Berlin Springer)... 

Bates M A and Luckhurst G R 1996 Computer simulation studies of anisotropic systems. 26. Monte Carlo investigations of a Gay-Berne discotic at constant pressure J. Chem. Phys. 104 6696-709... 

Kremer K 1996 Computer simulation methods for polymer physics Monte Carlo and Molecular Dynamics of Condensed Matter Systems vol 49, ed K Binder and G Ciccotti (Bologna Italian Physical Society) pp 669-723... 

Butler B D, Ayton C, Jepps C G and Evans D J 1998 Configurational temperature verification of Monte Carlo simulations J. Chem. Phys. fOS 6519-22... 

Gil-Villegas A, McGrother S C and Jackson G 1997 Reaction-field and Ewald summation methods in Monte Carlo simulations of dipolar liquid crystals Mol. Phys. 92 723-34... 

Manousiouthakis V I and Deem M W 1999 Strict detailed balance is unnecessary in Monte Carlo simulation J. Chem. Phys. 1102752-Q... 

Marinarl E and Parlsl G 1992 Simulated tempering a new Monte Carlo scheme Europhys. Lett. 19 451-8... 

Swendsen R H 1993 Modern methods of analyzing Monte Carlo computer simulations Physica A 194 53-62... 

Kofke D A and Glandt E D 1988 Monte Carlo simulation of multicomponent equilibria in a semigrand canonical ensemble/Wo/. Phys. 64 1105-31... 

Mon K K and Griffiths R B 1985 Chemical potential by gradual insertion of a particle in Monte Carlo simulation Phys. Rev. A 31 956-9... 

Nezbeda I and Kolafa J 1991 A new version of the insertion particle method for determining the chemical potential by Monte Carlo simulation Mol. SImul. 5 391-403... 

Harris J and Rice S A 1988 A lattice model of a supported monolayer of amphiphile molecules—Monte Carlo simulations J. Ohem. Phys. 88 1298-306... 

Panagiotopoulos A Z 1987 Direot determination of phase ooexistenoe properties of fluids by Monte Carlo simulation in a new ensemble Mol. Phys. 61 813-26... 

Panagiotopoulos A Z 1987 Adsorption and oapillary oondensation of fluids in oylindrioal pores by Monte Carlo simulation in the Gibbs ensemble Mol. Phys. 62 701-19... 

Panagiotopoulos A Z 1989 Exaot oaloulations of fluid-phase equilibria by Monte Carlo simulation in a new statistioal ensemble Int. J. Thermophys. 10 447-57... 

Esoobedo F A and de Pablo J J 1996 Expanded grand oanonioal and Gibbs ensemble Monte Carlo simulation of polymers J. Chem. Phys. 105 4391-4... 

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