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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.Keywords: Rod string, sucker rod pump, dynamometer cards, petroleum artificial lift, finite difference method. RESUMENEl 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.Palabras clave: sarta de varillas, bombeo mecánico, carta dinamométrica, ele...
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.Keywords: Rod string, sucker rod pump, dynamometer cards, petroleum artificial lift, finite difference method. RESUMENEl 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.Palabras clave: sarta de varillas, bombeo mecánico, carta dinamométrica, ele...
Summary There are nearly 920,000 oil-producing wells worldwide, approximately 87% of which are operated with an artificial-lift method. A rough distribution of these wells shows that 71% use a beam-pumping system, 16% use electrical submersible pumps, 7% use gas lift, and 6% use other forms of lifting systems (Alemi et al. 2011; Liu and Qi. 2011; Ghareeb et al. 2007; Xu et al. 2012). The great majority of the world's oil wells are on artificial lift; therefore, they require large amounts of external electric energy to produce hydrocarbons because the available formation energy is not sufficient to move the well fluids to the surface. On the basis of the 920,000 wells, with 10 kW/hr of consumed power for each well and oil production for 350 days of the year, beam-pumping systems consume approximately 4.77×1010 kW-hr of power per year worldwide. If the power consumption can be decreased by 20% with an energy-saving technique, that alone will help to save 0.95×1010 kW-hr of electricity per year around the world. Therefore, enormous economic benefits will be created by enhancing the system efficiency and reducing the consumption of energy. In this paper, a new comprehensive simulation method of efficiency optimization for a sucker-rod pumping system is presented. Our new method combines a slip model of the surface-transmission system (STS) with a closely coupled model of the downhole rod-string vibration to provide an improved method for calculating the motion of a rod string and the power requirements for a conventional sucker-rod pumping system. The new model proposed in this paper will provide an improved prediction of the power requirements for conventional sucker-rod pumping systems, and the results will be significantly improved as the amount of slip in the STS increases. The new model is verified by comparing it with the available analytical solutions, and good agreement is found. Real application in a high-energy-consumption oil field shows that the new model in this paper will result in significant improvements in system design, especially when the oil wells have a small-diameter pump and high stroke frequency.
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