Two stochastic versions of the Arps curve decline

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.

Figures (4)

• Figure 1: Simulations of the first stochastic models
• Figure 2: Simulations of the second stochastic models
• Figure 3: Approximation of the pdf of the hitting time for the second model
• Figure 4: Simulations of the cumulative stochastic models

Theorems & Definitions (12)

• Proposition 1
• proof
• Proposition 2
• proof
• Definition 1
• lemma 1
• Proposition 3
• proof
• Proposition 4
• proof