¿Determinísticamente probable o probabilísticamente determinista?

Este trabajo presenta la revisión de algunos modelos que conocemos como determinísticos o como estocásticos, así como algunas relaciones entre ellos, las cuales resultan interesantes. Vemos cómo las caminatas aleatorias generan algunas ecuaciones diferenciales parciales tales como la ecuación de calor; se presenta la ecuación de Laplace resuelta usando el juego Tour du wino; es decir, simulación Montecarlo para obtener los valores de una función armónica, como los promedios de su valores en la frontera obtenidos por diferentes trayectorias. Se revisan los modelos de Black and Scholes, así como el método de funciones generadoras de probabilidad para mostrar como determinados problemas probabilísticos pueden resolverse usando métodos determinísticos basados en ecuaciones diferenciales ordinarias y parciales.Palabras clave: modelos determinísticos, modelos probabilísticos, Montecarlo, caminatas aleatorias, Black and ScholesAbstract This work presents a review of some deterministic and stochastic models, interesting rela­tionships between them, are also discussed. Random walks give rise to partial differential mo­dels such as the heat equation. A Tour du wino game is introduced to approximate a solution to Laplace equation, here a Monte Carlo simulation is used to obtain the values of an harmonic function as the average of its boundary values using random trajectories. We review the Black & Scholes and the probability generating functions models to show how some probabilistic pro­blems can be solved using deterministics methods (based on ordinary and partial differential equations).Keywords: BDeterministic models; Stochastic models; Monte Carlo; random walk; Black and Scholes

Numerical Calculation of NMR Response for the 3D Digital Core Constructed with CT Images of the Tight Rock

The tight rock often has low porosity, low permeability and poor pore connectivity, which it is difficult for formation evaluation. Nuclear Magnetic Resonance (NMR) logging is widely used in fluid typing and reservoir parameters determination to provide the information of porosity, permeability and pore size distribution. NMR relaxation mechanisms are characterized by the pore-scale petrophysical models. Monte Carlo algorithm describes the Brownian motion of fluid molecules in pore space. In the paper we setup a 3D digital core of the tight sandstone with X-ray computer tomography (CT) images to model NMR response with Monte Carlo random walk algorithm. We compared T2 distributions from the numerical calculated pulse echo trains from the measurements. The results show that the simulated NMR response is consisted with the experiment.