Dynamometer Card Research Articles

An Intelligent Diagnosis Method of the Working Conditions in Sucker-Rod Pump Wells Based on Convolutional Neural Networks and Transfer Learning

In recent years, deep learning models represented by convolutional neural networks have shown incomparable advantages in image recognition and have been widely used in various fields. In the diagnosis of sucker-rod pump working conditions, due to the lack of a large-scale dynamometer card data set, the advantages of a deep convolutional neural network are not well reflected, and its application is limited. Therefore, this paper proposes an intelligent diagnosis method of the working conditions in sucker-rod pump wells based on transfer learning, which is used to solve the problem of too few samples in a dynamometer card data set. Based on the dynamometer cards measured in oilfields, image classification and preprocessing are conducted, and a dynamometer card data set including 10 typical working conditions is created. On this basis, using a trained deep convolutional neural network learning model, model training and parameter optimization are conducted, and the learned deep dynamometer card features are transferred and applied so as to realize the intelligent diagnosis of dynamometer cards. The experimental results show that transfer learning is feasible, and the performance of the deep convolutional neural network is better than that of the shallow convolutional neural network and general fully connected neural network. The deep convolutional neural network can effectively and accurately diagnose the working conditions of sucker-rod pump wells and provide an effective method to solve the problem of few samples in dynamometer card data sets.

Using the motor power and XGBoost to diagnose working states of a sucker rod pump

In oilfiled production, the dynamometer cards are usually used to diagnose the downhole conditions of the pumping well. They record changes in the rod load versus rod displacement. However, the measurement has deficiencies such as poor real-time performance and high maintenance costs. Aiming at the problems, a novel method based on motor power for fault detection of the sucker rod pump is proposed in this paper. In this method, the motor power curves of seven working states are obtained by transforming the dynamometer cards into motor power curves. The characteristics of the motor power curves under different working states are analyzed combining with the theoretical motor power curve. Furthermore, the novel sixteen features are extracted in time and frequency domains with the analysis of the working mechanism of the sucker rod pump. Subsequently, the Extreme Gradient Boosting (XGBoost) algorithm, machine learning algorithm, is employed to classify and identify working states of the sucker rod pumps. At last, this paper uses the dataset collected from the oil field to corroborate the proposed method. The experimental results showing the proposed method gives 98% correct diagnosis, proves a higher accuracy to SVM and KNN. Moreover, the final engineering practice also proves the effectiveness of the method proposed in this paper.

A real-time diagnosis method of reservoir-wellbore-surface conditions in sucker-rod pump wells based on multidata combination analysis

This paper proposes a real-time diagnosis method that addresses the limitations of traditional “dynamometer cards” used for sucker-rod pump performance analysis. The “power vs. position plots” are proposed to demonstrate an improved diagnostic method for rod pump performance. On this basis, the working condition diagnosis plate of the sucker-rod pump well is created. The eigenvalues of dynamometer cards and “power vs. position plots” under different working conditions are extracted, and a combined diagnosis model based on feature recognition is established. The model not only diagnoses the wellbore condition but also the surface condition, which improves the diagnosis effect and expands the diagnosis range. In addition, considering the surface dynamometer card as the known condition, the one-dimensional damping wave equation is used to solve the downhole pump dynamometer card. By analyzing the change law of the pump-load slope-time relationship curve, the opening and closing points of the pump valve are accurately extracted, and the load difference between the upstroke and downstroke, and the effective stroke of the downhole pump dynamometer card are determined. On this basis, a calculation model of the dynamic fluid level and fluid production is established to determine the change in reservoir energy and analyze the supply and discharge relationship of the sucker-rod pump wells. Combined with the online collection of the surface dynamometer cards and “power vs. position plots,” the real-time diagnosis of oil well production systems can be realized. This can effectively improve the timeliness of sucker-rod pump performance analysis, reduce production management costs, and improve the production efficiency and benefits of the oilfield.

Calculation Method for Inflow Performance Relationship in Sucker Rod Pump Wells Based on Real-Time Monitoring Dynamometer Card

Based on the informatization and intelligent construction of an oilfield, this paper proposes a new method for calculating inflow performance relationship in sucker rod pump wells, which solves the limitations of current IPR curve calculation method in practical application. By analyzing the forming principle of the dynamometer card, the plate of abnormal dynamometer card is created innovatively, and the recognition model of abnormal dynamometer card based on “feature recognition” is established to ensure the accuracy of the dynamometer card. By analyzing the curvature of each point on the curve of downhole pump dynamometer card, the opening and closing points of standing valve and traveling valve are determined, and the models for calculating fluid production and bottom hole flowing pressure are established to obtain the data of fluid production and bottom hole flowing pressure of sucker rod pump wells. Finally, a calculation model of inflow performance relationship fitted with the calculated fluid production and bottom hole flowing pressure data based on genetic algorithm is established to realize calculation of oil well inflow performance relationship curve. The field application and analysis results show that the inflow performance relationship curve calculated by the model in this paper fits well with the measured data points, indicating that the calculation model has high accuracy and can provide theoretical and technical support for the field. Moreover, the real-time acquisition of dynamometer cards can provide real-time data source for this method, improve the timeliness of oil well production analysis, and help to reduce the production management costs and improve the production efficiency and benefit.

Nonlinear Finite Element Analysis of Rod String in Rod Pumping System

Rod pumping is the main oil recovery method at home and abroad. The corresponding displacement and load of the sucker rod section are important parameters in the system. This paper uses the advantages of the finite element method to solve the three nonlinear problems in the rod string model, and establishes its finite element analysis model. According to the upper and lower boundary conditions and initial conditions, the software is used to program and calculate. The surface dynamometer card of multi-level steel rod columns and glass fiber reinforced plastics-steel hybrid rod string is predicted, and the calculation results with and without considering mass nonlinearity are compared and analyzed. The feasibility of predicting the surface dynamometer card by the finite element method is verified. It is proved that the coupling has a great influence on the mechanical properties of the glass fiber reinforced plastics-steel hybrid rod string.

A Novel Method for Diagnosis of Sucker-Rod Pumping Systems Based on the Polished-Rod Load Vibration in Vertical Wells

Summary The pump dynamometer card is a direct reflection of the operating conditions of the downhole pump, which is important for the diagnosis of sucker-rod pumping systems. In this paper, we propose a novel diagnostic method based on the estimation of the parameters from the polished-rod load vibration signal of sucker-rod pumping systems in a vertical well. In this study, we deduce a new analytic solution of the 1D wave equation of the sucker-rod string, which can be used for the predictive and diagnostic analyses. The relationship between the polished-rod load vibration and the pump equivalent impulse load based on the analytic solution is studied, and the diagnostic parameter estimating method is proposed. Therefore, the pump dynamometer card calculated method based on the surface dynamometer card is realized. This study shows that the method is efficient.

Development and application of pumping unit monitoring system based on wireless dynamometer sensor node

For the problems of the complicated installation and removal of dynamometer card detection equipment, high cost, not convenient for real-time detection, prone to failure and maintenance workload, a kind of low cost wireless dynamometer is developed. With the implement of wireless transmission gateway, comprehensive monitoring software is programmed. This system consists of a pumping dynamometer, gateway, monitoring software and indicator diagram measuring algorithm. Finally, the wireless dynamometer was installed at RenQiu oil field, and the data shows that the system works well and can be used for the long-term working and operating state of pumping oil field monitoring.

Research on the Coupled Axial-Transverse Nonlinear Vibration of Sucker Rod String in Deviated Wells

The coupled axial-transverse nonlinear vibration simulation model of sucker rod sting (SRS) in deviated wells is established. Based on the simulation results, the nonlinear vibration phenomenon of SRS is analyzed, and the influence of centralizer arrangement on the nonlinear vibration of SRS is discussed. The mechanical simulation model of the coupled axial-transverse vibration of SRS in deviated wells can be simplified to the coupled axial-transverse vibration model of longitudinal and transverse curved beam with initial bending under borehole constraints. In this paper, when establishing the simulation model of the coupled axial-transverse vibration of SRS, it is proposed that the bending borehole trajectory is a main excitation of the vibration of SRS. Based on the theory of elastic vibration, a nonlinear dynamic simulation model of the coupled axial-transverse vibration of SRS in deviated well is established. Then the fourth-order Runge–Kutta method is used to solve the simulation model. The nonlinear vibration phenomenon of the SRS is studied by example analysis. The simulation results show that: (1) the simulation curve of polished rod dynamometer card is in good agreement with the test curve, and the error value of polished rod maximum load and minimum load is within 5%, which shows that the coupled axial-transverse vibration simulation model of SRS established in this paper has high accuracy. (2) When the centralizer is not arranged, the chaotic motion of SRS mainly occurs in the compression section of SRS, which shows that the instability of SRS is the main reason for the chaotic motion of SRS. (3) The arrangement of centralizer can improve the bending rigidity of SRS, restrain or even eliminate the chaotic motion of SRS.

Determination of lower sucker-rod breakage in wells equipped with sucker-rod pumps

Development of mature oilfields of the Ural-Volga region is performed primarily by means of downhole sucker-rod pumping units (UShSN). The most characteristic failures of these installations are breakdowns and twist-offs and pump valve failures [1-5]. The ways of the elimination of these accidents vary significantly: rod breakage or twist-off implies pulling out of downhole equipment, and elimination of “sticking” of the pump’s shut-off valve assembly requires rehabilitation of downhole equipment through flushing with water, hot petroleum or a solvent. Failure to identify a malfunction leads to incorrect planning of wellbore equipment rehabilitation activities and, eventually, to economic losses.The cause of downhole equipment malfunctions is usually determined through analysis of dynamometer cards (DC). However, in the majority of cases, the dynamometer cards do not allow to distinguish the rods’ tail end twist-off from the rod pump valve failure. In the paper presented the method is considered for rapid detection of rod breakage and twist-offs (RBT) in the wellbore, which involves creation of an electrical circuit “rod string - tubing string” and monitoring of its integrity. To determine the failure type, the synchronization module measures the system’s resistance on the dielectric coupling via an electromagnetic conduit. In case of RBT, the electrical resistance of “tubing - pump - rod string” circuit will be much higher (over 2 Ohm) than in case of absence of this failure (0…2 Ohm).

A novel method of output metering with dynamometer card for SRPS under fault conditions

Remote monitoring of sucker rod pumping system (SRPS) based on polished rod dynamometer cards (DC) is an effective means to reduce the operating costs and realize the real-time control. Nevertheless, how to obtain the working process and the production rate of SRPS from polished rod DC is always a puzzle because of complex down-hole motions. The typical solution for this problem is deriving the pump DC via the wave equation to achieve the effective stroke of plunger. But some key parameters involved in this approach such as valve leakage and the fill factor are difficult to determine accurately, especially under fault conditions, which may influence the accuracy of output metering.In order to address this tough issue, in this paper, a novel method of output metering with DC is proposed based on quantitative analysis of fault. The method consists of two parts, the first part is an approach to simulate the working process of SRPS under fault conditions, specifically it's an improved simulation model characterized by a set of fault parameters, which is presented through analyzing the mechanisms of sucker rod pumps at normal and several faulty scenarios. And the second part is a method implemented by genetic optimization algorithm to determine the fault parameters set of the actual SRPS.Using parameters of typical well, the analysis of effects of faults on SRPS is carried out. The simulation results show that valves leakage reduces the flow rate of liquid significantly in the period of effective stroke, which leads to the distortion of output metering results of effective stroke method. Compared with single faults, coupling faults aggravate the production reduction of SRPS. Furthermore, when the well fluid contains gas, the impact of traveling valve leakage on the reduction of production is greater than that of standing valve leakage, but the consequence is opposite when formation energy is insufficient. Besides, the carbon fiber rod and fiberglass rod SRPS are more sensitive to valve leakage, while the steel rod and wire rope SRPS are more sensitive to the condition of insufficient liquid supply.Eventually, the proposed method is verified experimentally through the productive parameters and measured DC of actual wells collected from an oilfield. The obtained results demonstrate the effectiveness of the proposed method for output metering and fault diagnosis as well.

Identification of Downhole Conditions in Sucker Rod Pumped Wells Using Deep Neural Networks and Genetic Algorithms (includes associated discussion)

Summary In this paper, deep learning artificial neural networks (ANNs) are used to analyze the features of downhole dynamometer cards and identify the sucker rod pumping system conditions. A description model for the dynamometer cards, using Fourier descriptors, was established for card feature extraction. Then, neural networks were trained to generate failure prediction models to recognize downhole faults of the rod pumping systems. The failure prediction models were validated and tested with a large database of previously interpreted cards. The proposed model is trained by using 4,467 dynamometer cards—29.2% of these cards represent sucker rod pumping systems of normal conditions, while the rest (70.8%) represent faulty sucker rod pumping systems. Genetic algorithms (GAs) were used to search for the best deep ANN structure that gives highest accuracy for the testing data. Accuracy of the proposed ANN model was measured with 1,915 cards that were not used in developing the ANN. The proposed model identified the sucker rod system failure successfully with very high accuracy (99.69%).

Dynamometer-Card Classification Uses Machine Learning

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 194949, “Beam-Pump Dynamometer Card Classification Using Machine Learning,” by Sayed Ali Sharaf, Tatweer Petroleum; Patrick Bangert, SPE, Algorithmica Technologies; and Mohamed Fardan, Tatweer Petroleum, et al., prepared for the 2019 SPE Middle East Oil and Gas Show and Conference, Manama, Bahrain, 18–21 March. The paper has not been peer reviewed. In reciprocating rod pumping systems, analysis of dynamometer-card data can deliver valuable insight into the status of the pump, and can indicate if future action is required. The complete paper explains the steps taken to improve surveillance of beam pumps using dynamometer-card data and machine-learning techniques, and reviews lessons learned from executing the operator’s first artificial intelligence (AI) project. Background The oldest and most widely used method of artificial lift is called beam pumping, or the sucker-rod lift method. A dynamometer is a device used on beam pumps that measures load on the polished rod (top) and plots the load in relation to the rod position as the pumping unit moves through a stroke cycle. This plot is known as the surface card. A pump card is a plot of load vs. position on the pump’s plunger. The pump card is more useful for surveillance purposes because it filters effects of anything above the plunger and provides standard pump card shapes for interpreting pump operating conditions. Identification and diagnosis of beam pumps using the pump card is an expensive human visual-interpretation process, not only requiring significant labor time but also deep expertise in the domain. Use of machine-learning techniques for pattern recognition can help automate the visual interpretation process, increasing efficiency and reducing maintenance activities resulting from missed early diagnosis. Data Collection Sucker-rod pumps are widely deployed in the Bahrain Field. There are two different types of communication layers used across the field, radio and optical fiber. Almost 300 optical-fiber- connected beam-pump units (BPUs) have been selected for surveillance and advanced analysis. Fiber is used to avoid any communication issues during data collection for the AI project. The sampling rate of collection for each pump is one reading per 20 seconds, thus covering three pump cards per minute. All BPUs are connected to a central server that converts hardware-communication protocol used by a programmable logic controller into the open-platform-communication (OPC) protocol. Fig. 1 shows the details of the 209 values representing a single pump card being read from a BPU and stored in the operator database. During the data-collection period, a total of 5,380,163 pump cards from 297 BPUs were collected and stored in the database. Data Labeling and Preparation In machine learning, an important step after data collection is data labeling, which is usually performed manually by experts. The labeled data set is used to feed machine-learning algorithms that detect patterns specific to each class. A total of 35,292 pump cards has been labeled (more than 1,000 cards per day on average). A useful feature of the labeling software is that it allows labeling an entire time period of cards in one shot, although such labeling should be performed with care.

ДВУХУРОВНЕВЫЙ МЕТОД ДИАГНОСТИКИ ТЕХНИЧЕСКОГО СОСТОЯНИЯ ШТАНГОВЫХ НАСОСНЫХ УСТАНОВОК

Актуальность. Значительное число крупнейших нефтяных месторождений в России находится на завершающей стадии разработки, характеризующейся снижением объемов добычи, увеличением доли осложненного фонда скважин. Одним из наиболее распространенных способов эксплуатации скважин малодебитного фонда являются штанговые насосные установки. Эксплуатация штанговых установок в осложненных условиях эксплуатации в ряде случаев сопровождается снижением межремонтного периода работы, повышением удельных энергетических и экономических затрат при добыче. В этих условиях одной из наиболее актуальных является задача обеспечения рентабельной разработки скважин за счет своевременной диагностики технического состояния и условий работы насосного оборудования. Объекты: штанговая насосная установка, работающая в нефтяных добывающих скважинах, в том числе при наличии осложняющих факторов, и устьевая динамограмма работы штанговой установки, отражающая техническое состояние и условия работы внутрискважинного оборудования. Цель: разработка нового подхода к диагностике состояния штанговых насосных установок по динамограмме, базирующаяся на решении обратных задач динамики штанговой установки. Методы: методы численного решения уравнений в частных производных для прямых задач, включающих моделирование теоретической динамограммы работы штанговой установки; методы решения обратных задач, направленных на определение параметров модели, характеризующих работу штанговой установки. Результаты. Разработан двухуровневый метод диагностирования состояния штанговых насосных установок по динамограмме. Предлагаемый метод диагностики включает: на первом уровне обработку практических динамограмм системой распознавания образов и на втором уровне – количественное определение последствий неисправностей решением задачи динамики штанговой установки, исходя из физических законов формирования конфигурации динамограмм. Путем анализа конфигурации динамограмм при эксплуатации насосного оборудования (нормальная работа, высокое содержание газа на приеме насоса, утечки в нагнетательном клапане насоса, низкая посадка плунжера в цилиндре) показаны примеры решения задач количественной диагностики и выдачи рекомендаций по корректировке технологического режима на основе разработанного алгоритма.

A New Intermittent Pumping Design for Fluid Shortage Wells

Low oil price requires oil companies to reduce costs and increase benefits. The wells with deficient fluid supplies approximately account for 20–30% of all producing wells, and this situation is even worse in the old oilfields. Intermittent production is an effective way to reduce the cost and increase the system efficiency to overcome the shortage of oil supply from the reservoir. The key is to optimize the intermittent pumping scheme, i.e., to design reasonable shut-in and operating periods. In this study, this is achieved using the dynamic change of the fluid level in the wellbore. From the electrical power curve to the dynamometer card, the dynamic drop of the fluid level can be obtained, and thus the optimal operation time of the well; at last, from the inflow performance of the well, the optimal shut-in period can be obtained. This method shows a good application in the field through a case study.

Fault Diagnosis of Sucker Rod Pump Based on Deep-Broad Learning Using Motor Data

Conventional fault diagnosis methods of sucker rod pump (SRP) mainly focus the operating status of oil well by identifying the dynamometer cards (DCs), which are limited by the sensor maintenance and calibration, battery replacement and safety hazards for staff. Motor power, as the most basic parameter providing the energy source for the oil well, is directly related to the real-time operation state of oil well. Therefore, a novel deep and broad learning system (DBLS) based on motor power data for fault diagnosis of sucker rod pump is proposed in this paper. Considering the key parameters such as mechanical wear and balance weight, the motor power data are labeled by the DCs with typical working conditions. Furthermore, CNN-based feature extractor is designed to make up for the lack of expert experience in motor power, which is obtained by merging the output of the CNNs with the manual features extracted based on mechanical analysis. And then the broad learning system is employed as the classifier to solve the problem of real-time update of system structure. Finally, a dataset containing six different working states collected from the oilfield by a self-developed device is employed to verify the proposed method experimentally and compared with other methods.

A Method for Diagnosing Formation Fluid Leakage During the Operation of Sucker Rod Pumps and a Device for Its Implementation

The operation of oil sucker rod pumps (SRP) is known to be one of the most common and basic methods of oil production, especially for marginal wells. However, rapid wear of the plunger pair, tubing and sucker rods caused by friction, leading to a decline in equipment performance, as well as to labor intensity of replacement and repair of deep-well pumps, determines the relevance of developing methods for diagnosing the technical condition of sucker rod pumping units (SRPU) and formation fluid (FF) leakage during the operation of SRPU as an indicator of the technical condition of SRPU in particular. As one of the controlled parameters, leakage value is important for the operational control of well performance and increasing the efficiency of oil production. The authors consider the impacts of well product leakage both in the pump itself (the “cylinder-plunger” clearance, valves) and on the path of the pump product from the cylinder to the orifice (through threaded connections of the tubing string (TS) of the well, through possible pipe breakdowns caused by wear due to rubbing against the rods, etc.). In the existing literature, formulas are given for calculating the amount of fluid leakage through the clearance between the working surfaces of the plunger and the cylinder of a SRP during laminar flow in the clearance (laminar regime is the most probable), with the clearance as the main parameter, cubed. However, this formula requires determining the size of the clearance directly, which is an extremely difficult (impossible) task in an operating SRPU. And results of determining leakage from dynamometer cards and piezograms have low accuracy. In view of the above, the paper proposes a new method and a device for its implementation, which involves measuring the pressure on the well flow line and at two points of the tubing string (TS) of the well, one of which is located at the TS orifice, and the second lower at a distance of half the height of the cylinder of the pump being used, the FF leakage from downhole pumping equipment being calculated by the algorithms given in the text. It is shown that the proposed diagnostic method makes it possible to more accurately and reliably, in comparison with the existing methods, determine the formation fluid leakage during the operation of SRPU.

Techniquesof Oil Well Equipment Diagnostics Using Dynamomemter Card

Currently, the most widely used equipment to oil extraction is a sucker rod pump. More than 70% of oil wells are equipped with this mechanism. The advantages a sucker rod pump are usage simplicity and high efficiency, but the main drawback is difficulties with diagnostics and repairing. So providing continuous operation of oil well equipment is the key issue in oil well maintain process. Nowadays, the most efficient method of oil well equipment diagnostics is building and an analysis of dynamometer card, namely dependency of load on rod string on polished rod displacement. This diagnostic method is widely used due to simplicity of its implementation, as well as clarity and easy interpretation of the results. If there are any problems in sucker rod pump operation, shape of dynamometer card changes. Moreover each specific fault in operation has unique characteristic shape of dynamometer card. In this article author proposes techniques overview of oil well equipment diagnostic using dynamometer card, the use of which is a big step in “Industry 4.0” model implementation in the oil production field.

Component-oriented acausal modeling of the dynamical systems in Python language on the example of the model of the sucker rod string.

Typically, component-oriented acausal hybrid modeling of complex dynamic systems is implemented by specialized modeling languages. A well-known example is the Modelica language. The specialized nature, complexity of implementation and learning of such languages somewhat limits their development and wide use by developers who know only general-purpose languages. The paper suggests the principle of developing simple to understand and modify Modelica-like system based on the general-purpose programming language Python. The principle consists in: (1) Python classes are used to describe components and their systems, (2) declarative symbolic tools SymPy are used to describe components behavior by difference or differential equations, (3) the solution procedure uses a function initially created using the SymPy lambdify function and computes unknown values in the current step using known values from the previous step, (4) Python imperative constructs are used for simple events handling, (5) external solvers of differential-algebraic equations can optionally be applied via the Assimulo interface, (6) SymPy package allows to arbitrarily manipulate model equations, generate code and solve some equations symbolically. The basic set of mechanical components (1D translational “mass”, “spring-damper” and “force”) is developed. The models of a sucker rods string are developed and simulated using these components. The comparison of results of the sucker rod string simulations with practical dynamometer cards and Modelica results verify the adequacy of the models. The proposed approach simplifies the understanding of the system, its modification and improvement, adaptation for other purposes, makes it available to a much larger community, simplifies integration into third-party software.

Sucker Rod Pump Working State Diagnosis Using Motor Data and Hidden Conditional Random Fields

In oil exploitation, the short maintenance period and the poor real-time performance of dynamometer card sensors limit the timely working state diagnosis for sucker rod pumps (SRP). The motor is the power source of the SRP that provides all the energy required to lift the oil from underground to surface. The motor power output is highly associated with the working state of the entire equipment. Thus, this article proposes a new strategy to predict the working state of SRP based on motor power. First, seven novel features are extracted from motor power data to support the modeling and diagnosing processes, with the consideration of the significant parameters such as valve's working points and the operating cycle of SRP. Moreover, a custom-designed multiple hidden conditional random fields model with time window is employed as the classifier to identify different working states. At last, the proposed method is validated by a set of motor power data collected from wells by a self-developed device. The experimental result demonstrates the effectiveness of the proposed method for the working state diagnosis of SRPs.

Sucker rod string dynamics in deviated wells

Beam pumping is the most common artificial lift system. The down-hole dynamometer card, calculated using surface measurements, is an important tool to determine the pump operating condition and optimize the well production strategy. The description of the dynamics of a vertical sucker rod string has been well understood since S. G. Gibbs paper in the sixties [1]. The vertical well problem can be easily solved because the rod string is accurately approximated by a 1D linear elastic model, where the fluid drag is also linear with velocity. This can be solved in closed form and the parameters inferred from it, such as the down-hole card or pump fillage factor, have been widely used as the basis of most automatic well controllers.The number of deviated wells in the world has been steadily increasing since new technologies such as directional drilling became available and unlocked the potential of unconventional resources, where the possibility of drilling horizontal wells or multipad directional wells is critical for field development. These directional wells many times are produced using beam pumps after the primary depletion stage. Thus the description of the dynamics of a sucker rod string in non-vertical cases has become an important problem in recent years. These wells need to be analyzed including the effects of the non-vertical well trajectory and its consequent rod-tubing Coulomb friction losses. Coulomb friction is a highly non-linear phenomena that introduces very important dynamical effects. The increase in the complexity of this system is probably the cause of a lack of a consensus on how to deal with the problem. This fact has a clear impact on the industry, most well controllers do not include the possibility of calculating the down-hole card for a deviated well and many patents with different numerical schemes trying to solve the system have been disclosed recently.In this article a new model for the system that includes all the relevant physical mechanism that need to be incorporated in the description is proposed. The model is fully self contained and can be solved by numerical means, giving an accurate representation of the sucker rod string dynamics for directional wells. In contrast to other approaches to the problem, this model solves a closed system of equations without any external estimation of the variables in the system. Using this framework both the forward, or predictive, scheme, useful in the design of the rod string, and the down-hole card problem, needed to monitor down-hole conditions (diagnostic mode) are solved. This theory is used to move one step ahead and predict new effects not previously discussed in the literature, such as multiple micro sticking events of the rod string that are generated by static Coulomb friction.Field cases are analyzed and agree with the predictions of the model. These examples demonstrate that it is critical to take into account Coulomb friction to properly describe qualitative and quantitative features, that cannot be approximated by any means using a one dimensional vertical well approximation.