Published
Numerical simulation of the sucker-rod pumping system
Simulación numérica de un sistema de bombeo mecánico
Keywords:
Rod string, sucker rod pump, dynamometer cards, petroleum artificial lift, finite difference method. (en)sarta de varillas, bombeo mecánico, carta dinamométrica, elevación artificial de petróleo, diferencias finitas (es)
The sucker rod pump is an artificial lift method frequently applied in onshore petroleum wells. This system can be described using a numerical simulation based on the behavior of a rod string. In the past, the elastic behavior of the rod string made it difficult to model the system. However, since the 1960s and with the advent of digital computers, it has been modeled numerically. The rod string behaves like a slender bar, and thus, the propagation of elastic waves along the bar can be represented by a one-dimensional equation. Gibbs (1963) presented a mathematical model based on the wave equation, which is described on the basis of the analysis of forces on the rod string and is incorporated into a boundary value problem involving partial differential equations. The use of the finite difference method allows for a numerical solution by the discretization of the wave equation developed in the mathematical formulation with appropriate boundary and initial conditions. This work presents a methodology for implementing an academic computer code that allows simulation of the upstroke and downstroke motion of the rod string described by the wave equation under ideal operating conditions, assuming a harmonic motion of the rod at one end and downhole pump at the other end. The goal of this study is to generate the downhole dynamometer card, an important and consolidated tool that controls the pump system by diagnosing operational conditions of the downhole pump.
El bombeo mecánico es un método de elevación artificial, utilizado principalmente en campos terrestres. Este sistema, puede ser entendido mediante la simulación numérica del comportamiento de la sarta de varillas, que conecta la superficie con la bomba en el subsuelo. En el pasado, el comportamiento elástico de la sarta de varillas era difícil de modelar, sin embargo, desde 1960 con el surgimiento de los computadores digitales este proceso fue facilitado.
La sarta de varillas se comporta como una barra esbelta, donde la propagación de las ondas elásticas es representada por una ecuación unidimensional y trascendente, la cual fue propuesta por Gibbs (1963), así mismo, el método de diferencias finitas permite obtener la solución numérica de dicha ecuación. En este trabajo, se explica la metodología para la implementación de un código computacional académico, que permite simular el movimiento alternativo de la sarta de varillas descrita matemáticamente por la ecuación de las ondas de Gibbs. De esta manera, se consideran como condiciones de entorno: el movimiento armónico en la superficie y la presencia de la bomba de fondo en el subsuelo, en condiciones ideales de operación.
Finalmente, el objetivo es obtener la carta dinamométrica de fondo, que es una importante y consolidada herramienta de control y diagnóstico para las condiciones operacionales de la bomba de fondo.
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Copyright (c) 2014 Oldrich Joel Romero, Paula Almeida
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