Two stochastic versions of the Arps curve decline

TL;DR

This paper introduces two stochastic models based on the Arps decline curve for oil production, analyzing their theoretical properties, simulations, and parameter inference methods to improve understanding of decline behavior.

Contribution

The paper presents two novel stochastic models for the Arps decline curve, including their theoretical analysis, simulation results, and methods for statistical parameter inference.

Findings

Derived first passage time distributions for the models

Provided simulation results demonstrating model behavior

Discussed statistical inference techniques for parameter estimation

Abstract

Based on the Arps equation, we propose two stochastic models for curve decline useful in oil engineering context. Theoretical properties and simulations of these models are provided. The first passage time distribution of these stochastic models to a constant level is then studied. In conclusion, we discuss about statistical inference of the parameters from the observations of the oil production cumulative rate.