A method and a system for determining height of fluid in an annulus of an oil well

Abstract

The present invention discloses a method and a system for determining the height of the fluid in an annulus of an oil well. The method involves receiving invariant values for one or more first parameters associated with characteristics of the oil well, and receiving first and second values for one or more second parameters defining the oil well's characteristics at distinct time intervals after the well is shut in. By analyzing variations between these values, the method defines changes in the characteristics of the oil well. A height of the fluid in the annulus is then determined at a third time interval using a predetermined relationship based on these values. This method enables accurate assessment and determination of the fluid level, enhancing decision- making for oil well management and optimization.

Description

A METHOD AND A SYSTEM FOR DETERMINING HEIGHT OF FLUID IN AN ANNULUS OFAN OIL WELLTechnical Field:

[0001] The present invention relates to a method and a system for determining height of the fluid in the annulus of an oil well or wellbore, and more particularly relates to the method and the system for determining height of the fluid in the annulus of an oil well in any variable time ‘t’ during shut-in period of the well.Background:

[0002] Oil wells are integral installations for the extraction of oil and gas from subterranean reservoirs. Their operational effectiveness significantly depends on the ability to accurately manage the dynamics of reservoir pressure and productivity index. One aspect of managing these dynamics involves measuring the height of the fluid within the annulus of the oil well at various time intervals over the lifespan of the oil well, which is essential for adjusting production rates and optimizing overall well performance. Traditionally, these measurements require extended shut-in periods, which significantly delay the resumption of well operations and impact the economic and operational efficiency of oil wells. Additionally, the use of sophisticated, costly equipment like echoshot guns during these shut-in periods introduces further delays and additional costs, increasing the inefficiencies, especially in low productivity wells. The reliance on extended shut-ins and expensive, repetitive measurements leads to reduced production rates and diminished profitability for oil and gas companies.Summary

[0003] In accordance with a first aspect of the present invention, there is provided a method for determining height of fluid in an annulus of an oil well. The method involves receiving a value for one or more first parameters associated with characteristics of the oil well, where these parameters are an invariant representation of the characteristic. It also includes acquiring a first value for one or more second parameters defining characteristics of the oil well at a first time interval after the well is shut in, and a second value for the one or more second parameters at a second time interval when the well is shut in. The variations in the second value relative to the first value for each of the second parameters indicate the change in the characteristics of the oil well. The height of the fluid in the annulus is then determined at a third time interval based on the received values of the first parameters and the first and second values of the second parameters, using a predetermined relationship. This method provides the advantage of leveraging data from multiple time intervals, which significantly enhances the accuracy of predicting well behavior. This improvedprediction capability allows for better decision-making in well management and optimization, potentially improving production efficiency and reducing operational costs.

[0004] In some exemplary embodiments of the present invention, the method may further include the first parameter encompassing at least one of a density of the fluid in the annulus of the oil well and a total capacity of the oil well. This allows for a comprehensive understanding of the fluid dynamics within the well, crucial for accurate fluid height measurements.

[0005] In some exemplary embodiments of the present invention, the method may further include the second parameter encompassing at least one of the casing head pressure, height of fluid after well shut-in, and hydrostatic pressure of a gas column in the annulus of the oil well at the first- and second-time intervals. This inclusion enables a detailed analysis of the well's pressure dynamics and fluid behavior of the well, essential for accurate assessments of well integrity and performance.

[0006] In some exemplary embodiments of the present invention, the method may further include determining the height of the fluid in the annulus of the oil well using an echoshot gun.

[0007] In some exemplary embodiments of the present invention, the method may further include determining the casing head pressure using a pressure gauge. This approach ensures accurate and timely monitoring of pressure changes, which is vital for maintaining well safety and efficiency. The advantage here is the ability to continuously monitor well pressures, facilitating early detection of anomalies that could lead to significant operational issues, thus ensuring a safer and more stable well operation.

[0008] In some exemplary embodiments of the present invention, the method may further include determining the height of the fluid in the annulus of the oil well at time ‘t’ during shut in period of the well by a predetermined relation:H(t) = (hl - h2 * (eA(m))n) / (1 - (eA(m))n)) - (1)Where: hl = b - A / D / (1.6 * pfA2) h2 = b + " D / (1.6 * pfA2) m = (Qmax * A / D * t) / (0.8 * C * pfA2) n = (hi - hl) / (hi - h2)A / D = (bA2 - 4ac) = 1.8 * Pr * pf b = -0.2 * pf * Pr - 1.64 * pfA2 - 1.6 * CHP * p * Pr - 1.6* pgc * pfHere,H(t): Final height of the fluid in the annulus of the oil well at the shut-in time (t).pf: Well fluid density (psi / ft).Pr: Reservoir pressure (psi). CHP: Casing head pressure (psi). Pgc: Gas column hydrostatic pressure (psi). Hi: Pump submergence or initial column height (ft). T: Shut-in time in days.C: Well capacity (bbl / ft).

[0009] In some exemplary embodiments of the present invention, the method include determining pump intake pressure by using the relation PIP(t) = CHP(t) + Pgc + pf • H(t), where PIP(t) represents the pump intake pressure at any shut-in time t, CHP(t) is the casing head pressure at any shut-in time, Pgc denotes the hydrostatic pressure of the gas column, pf is the well fluid density, and H(t) is the variable pump submergence height at any shut-in time, with Hi indicating the column height prior to shut-in or immediately after shut-in. This inclusion allows for a precise calculation of the pump intake pressure, essential for effective pump operation and fluid management within the well.

[0010] In accordance with a second aspect of the present invention, a system is provided for determining the height of fluid in an annulus of an oil well. The system comprises a memory and one or more processors coupled with the memory. The processors are configured to receive a value for one or more first parameters associated with characteristics of the oil well, where these parameters are an invariant representation of the characteristic. The processors also receive a first value for one or more second parameters defining characteristics of the oil well at a first-time interval after the well is shut in. Additionally, the processors receive a second value for the one or more second parameters at a second time interval when the well is shut in, wherein the variations in the second value relative to the first value for each of the second parameters define the change in the characteristics of the oil well. The processors then determine the height of the fluid in the annulus at a third time interval based on the received values of the first parameters and the first and second values of the second parameters at the first- and second-time intervals respectively, using a predetermined relationship.

[0011] In some exemplary embodiments of the present invention, the system may include one or more first parameters such as the density of the fluid in the annulus of the oil well and the total capacity of the oil well.

[0012] In some exemplary embodiments of the present invention, the system may include one or more second parameters including at least one of the casing head pressure, the height of fluid after the well is shutin, and the hydrostatic pressure of a gas column in the annulus of the oil well at the first- and second-time intervals.

[0013] In some exemplary embodiments of the present invention, the system may determine the height of the fluid in the annulus of the oil well using an echoshot gun.

[0014] In some exemplary embodiments of the present invention, the system may determine the casing head pressure using a pressure gauge. This approach ensures precise and continuous monitoring of pressure conditions, vital for the safe and efficient operation of the well.

[0015] In some exemplary embodiments of the present invention, the system may further determine the height of the fluid in the annulus of the oil well by a predetermined relation:H(t) = (hl - h2 * (eA(m))n) / (1 - (eA(m))n)) -(1)Where: hl = b - A / D / (1.6 * pfA2) h2 = b + " D / (1.6 * pfA2) m = (Qmax * A / D * t) / (0.8 * C * pfA2) n = (hi - hl) / (hi - h2)A / D = (bA2 - 4ac) = 1.8 * Pr * pf b = -0.2 * pf * Pr - 1.64 * pfA2 - 1.6 * CHP * p * Pr - 1.6* pgc * pfHere,H(t): Final height of the fluid in the annulus of the oil well at the shut-in time (t). pf: Well fluid density (psi / ft).Pr: Reservoir pressure (psi).CHP: Casing head pressure (psi).Pgc: Gas column hydrostatic pressure (psi). hi: Pump submergence or initial column height (ft).T: Shut-in time in days.C: Well capacity (bbl / ft).

[0016] In some exemplary embodiments of the present invention, the system may be configured to determine pump intake pressure (PIP) at any shut-in time using the formula: PIP(t) = CHP(t) + Pgc + pf • H(t), where PIP(t) represents the pump intake pressure at any shut-in time, CHP(t) denotes the casing head pressure, Pgc is the hydrostatic pressure of the gas column, pf indicates the well fluid density, and H(t) is thevariable pump submergence height, with Hi showing the pump submergence / column height prior to or immediately after shut-in. This configuration facilitates accurate and real-time monitoring of pump intake pressures, enhancing the operational efficiency and safety of the oil well.Brief Description of Drawings:

[0017] The accompanying drawings are included in order to more clearly illustrate the embodiments of the present disclosure and the related art. The drawings included herein provide a further understanding of the disclosure and are incorporated in and constitute a part of the present disclosure. It is appreciable that the drawings illustrate implementations of the disclosure and, together with the description, serve to explain the principles of the disclosure. It is apparent that the drawings are merely embodiments of the present disclosure, a person having ordinary skill in this field can obtain other figures according to these figures.

[0018] FIG. 1 illustrates a cross-sectional view of a conventional oil well with situation or conditions suitable to illustrate current invention.

[0019] FIG. 2 illustrates a block diagram of a system for determining height of the fluid in the annulus of an oil well, in accordance with an exemplary embodiment of the present invention.

[0020] FIG. 3 illustrates a flowchart of a method for determining height of the fluid in the annulus of an oil well, in accordance with an exemplary embodiment of the present invention.

[0021] FIG. 4 illustrates a graphical representation of comparative experimental outcomes obtained from the method of present invention and field measured data.

[0022] The summary above, as well as the following detailed description of illustrative embodiments, is better understood when read in conjunction with the appended drawings. For the purpose of illustrating the present disclosure, exemplary constructions of the disclosure are shown in the drawings. However, the disclosure is not limited to specific methods and instrumentalities disclosed herein. Moreover, those in the art will understand that the drawings are not to scale. Wherever possible, like elements have been indicated by identical numbers.Detailed Description:

[0023] Detailed embodiments and implementations of the claimed subject matters are disclosed herein in detail with the technical matters, structural features, achieved objects, and effects with reference to the accompanying drawings as follows. It shall be understood that the disclosed embodiments and implementations are merely illustrative of the claimed subject matters which may be embodied in various forms. The present disclosure may, however, be embodied in many different forms and should not be construed as limited to the exemplary embodiments and implementations set forth herein. Rather, these exemplary embodiments and implementations are provided so that description of the present disclosure is thorough and complete and will fully convey the scope of the present disclosure to those skilled in the art. Specifically, the terminologies in the embodiments of the present disclosure are merely for describing the purpose of the certain embodiment, but not to limit the disclosure. In the description below, details of well- known features and techniques may be omitted to avoid unnecessarily obscuring the presented embodiments and implementations.

[0024] An embodiment of the present invention introduces a method and a system for determining height of a fluid in an annulus of an oil well. This exemplary embodiment includes a system and a method designed to accurately measure the height of the fluid or the fluid column within the annulus of the oil well, alongside monitoring trends such as pump intake pressure. The method and system provided herein give insights into well behavior, even under challenging reservoir conditions, thus aiding in the optimization of well performance and protecting the economic interests of oil and gas companies.

[0025] The fluid column within the annulus encompasses all the fluids present in the wellbore, extending from the bottom of the well to the surface facilities. This column consists of various fluid components, including crude oil, natural gas, and formation water, each with unique properties such as density, viscosity, and phase behavior. The height and behavior of the fluid column are influenced by several factors, including reservoir pressure, fluid composition, wellbore geometry, and the rate of production. Accurately determining this height is essential for effective well management and operational efficiency, particularly in settings where conventional measurement techniques may fall short.

[0026] Figure 1 depicts a detailed cross-sectional view of a conventional oil well, illustrating the pathway for fluid migration from a reservoir. Over time, this pathway may experience sand accumulation (170), which, if not managed, could obstruct the flow of fluids. Situated within the downhole section of the wellbore, a pump (110) is employed to extract liquids that may be mixed with sand and gasses from the reservoir into the annulus of the oil well (130). Within the annulus, the fluid ascends to a specified level(134), with an additional indicator marked as (138), accounting for the height inclusive of foam (136). The space above this fluid level is occupied by gasses, which exert pressure on the underlying fluid.

[0027] The figure shows fluid being drawn from the reservoir, as depicted by arrow (150), subsequently lifted to the surface by the pump as indicated by arrow (162), while gas slugs (132) exit the reservoir through the annulus of the oil well, as shown by arrow (164). The increase in pressure within the annulus after shut-in is primarily due to gas compression and the behavior of fluids under constrained conditions. Gasses trapped in the annulus compress as their available space diminishes, leading to an increase in pressure according to the principles of gas laws which state that pressure increases as volume decreases if the temperature remains constant. Additionally, any fluid in the well, which might still seep slowly from the formation, contributes to this pressure. Since the fluid cannot escape, any dissolved gasses in the fluid may come out of solution, further increasing the volume of gas in a confined space and adding to the pressure buildup.

[0028] Over time, this heightened pressure influences the contents of the annulus, including the compression of any foam layer present (136). As the foam compresses, the actual height of the fluid within the annulus (130) becomes more apparent. This dynamic is critical for accurately assessing the fluid level within the well, which is essential for proper well management and ensuring the integrity and safe operation of the oil well post shut in.

[0029] Additionally, the wellbore is outfitted with an array of sensors, including an A-annulus pressure sensor (112), a B-annulus pressure sensor (114), a flowing THP pressure sensor (116), a pump suction pressure sensor (optional) (118), and a pump discharge pressure sensor (optional) (120). These devices (250) are strategically placed to continuously measure critical parameters such as pump submergence, pump intake pressure (PIP), and casing head pressure (CHP). This extensive instrumentation allows for comprehensive monitoring and analysis of well performance.

[0030] Figure. 2 illustrates a system (200) for determining height of the fluid in the annulus of an oil well. In one exemplary embodiment of the present invention, the system (200) may include a control unit (270) that serves as a central component or processor (230) for overseeing and managing the operations of the system. The control unit (270) may be implemented as either a general-purpose computer or a dedicated circuit. In some exemplary embodiments of the present invention, the control unit may be configured to receive parameters for defining the well bore characteristics. Specifically, the control unit may receive input parameters including but not limited to reservoir pressure (Pr), productivity index (J), flowing reservoirpressure (Pwg), casing head pressure (CHP), gas column hydrostatic pressure (Pgc), well capacity (c), well fluid density (pf), shut-in time (T) and pump submergence or initial column height (Hi).

[0031] In some exemplary embodiments of the present invention, the control unit (270) may include components, such as a Central Processing Unit (CPU) or processors (230), memory, and input / output devices (260). The inclusion of a CPU or processor (230) may enable the control unit to execute complex algorithms and process data in real-time. The memory (240) may be located either in the cloud or internally within the system, may store relevant data, including user preferences, well characteristic data history, safety protocols etc. The ability to store relevant data may ensure continuity and efficiency during multiple sessions, as the system may retrieve and compare different wellbore configurations.

[0032] In some exemplary embodiments of the present invention, the control unit (270) may feature user-friendly input / output devices, providing an intuitive and interactive interface for users. The interface may include a display (220) screen, buttons, touch panels, or other intuitive input methods. Using the input / output device, users may conveniently input parameters regarding well bore characteristics. The display screen may provide real-time feedback and display determined unknown parameters.

[0033] A memory (240) may be any form of storage either within or outside the device. The memory may include a database. In some embodiments of the present disclosure, the memory may also be a combination of one or more storage available internally or externally. For example, flash memory, randomaccess memory (RAM), read-only memory (ROM), compact disc read-only memory (CDROM), electro- optical memory like compact disk or digital versatile disk (DVD), smart card magneto-optical memory, erasable programmable read-only memory (EPROM), and electrically-erasable programmable read-only memory (EEPROM), and / or the like. In some embodiments of the present disclosure, the memory may store or carry the source code or instruction for executing required tasks. In some embodiments of the present disclosure, a carrier wave may carry content or data including those used in transmitting and receiving electronic data such as electronic mail (e-mail) or in accessing a computer network such as the Internet or a local area network (LAN). In some embodiments of the present disclosure, the memory may be a cloud storage and / or the like that may be accessible via the internet.

[0034] A display (220) may be a touch-sensitive or presence-sensitive display. In some embodiments of the present disclosure, the display includes an input / output interface module (I / O interface module). In some embodiments of the present disclosure, the display may provide an output to the user, for example, display contents, including without limitation, an image or a video image and / or the like. In some embodiments of the present disclosure, the display may include or be integrated with a touch screen or touchsensitive overlay for receiving touch input from the user. In some embodiments of the present disclosure, the display may also be capable of receiving a user input from a stylus, fingertip, or other means of gesture input. In some embodiments of the present disclosure, the display may be a computer monitor, for example, a personal computer, with an internal or external display operatively connected. In yet another exemplary embodiment, the display may be a display device, such as an LCD TV or projector and / or the like.

[0035] An Input / Output interface module (I / O interface module) refers to any means or set of commands or menus through which a user may communicate with the device. In some embodiments of the present disclosure, the I / O interface module may be a virtual keyboard or any other means through which a user may input information to the device. The I / O interface module may enable the device to communicate with the user for exchanging data or for establishing connection with the devices. The I / O interface module may enable the device to connect with various I / O peripherals. The peripherals, for example may include keyboard, mouse, camera, touch screen (e.g., display), a microphone, and may also include one or more output devices such as a display screen (e.g., display) and a speaker. The I / O interface module may enable the user to navigate, view, edit and perform several other operations to notification banners, badges, application program interface (API), files and documents such as portable document format (PDF) files, word files, spreadsheets, powerpoint presentations, screenshots, JPEG (Joint Photographic Experts Group), PNG (Portable Network Graphics), GIF (Graphics Interchange Format), SVG (Scalable Vector Graphics), MP4 (Moving Picture Experts Group) and / or the like.

[0036] In some exemplary embodiment of the present invention, the control unit (270) may determine the height of the fluid in the annulus of an oil well over time.

[0037] In some exemplary embodiments of the present invention, the system (200) may include a tight oil well. Tight wells are characterized by reservoir rocks with very low permeability, significantly restricting fluid flow. These wells require specialized techniques, such as hydraulic fracturing, to improve fluid flow and enhance production efficiency. In the development and operation of tight wells, advanced methods are employed to manage the limited fluid flow and high-pressure differentials. The implementation of these techniques ensures optimized recovery strategies and effective production from tight formations. In some exemplary embodiments of the present invention, the system may include a packerless well. Packerless wells are wells that do not use packers, devices that typically isolate sections of the wellbore to manage fluid flow and pressure. This design allows for production from multiple zones within the well, offering a flexible and efficient approach to hydrocarbon extraction. However, managing a packerless well requires careful consideration of pressure and flow dynamics to prevent cross flow between different zones. The operationof packerless wells involves advanced monitoring and control techniques to ensure safe and efficient production from multiple reservoir zones.

[0038] In some exemplary embodiments of the present invention, the system may include a low productivity well that is defined as a well that yields relatively small quantities of oil or gas compared to high productivity wells. These wells typically produce lower volumes of hydrocarbons, which makes them less economically viable and more difficult to manage. Low productivity may result from various factors, including poor reservoir quality, low permeability, high water saturation, or depletion of the hydrocarbon- bearing formation.

[0039] Low productivity wells may present significant challenges due to their reduced output. These wells often experience issues such as increased water cut, which is the ratio of water produced compared to the volume of total liquids produced. High water cut may complicate the extraction process and increase operational costs, as more effort and resources are required to separate and dispose of the produced water.

[0040] Low productivity wells may require more frequent interventions and maintenance to sustain production levels. For instance, the buildup of paraffin and scale within the wellbore may restrict fluid flow, necessitating regular cleaning and treatment. Additionally, artificial lift systems, such as sucker rod pumps (SRPs) (210), may need to be optimized or replaced more frequently to maintain efficiency in these wells. They may face economic challenges due to the higher cost per barrel of oil or cubic foot of gas produced. The lower output may lead to a higher break-even price, making these wells less attractive for investment, especially in fluctuating market conditions. Operators may need to implement cost-saving measures and optimize production strategies to ensure the economic viability of these wells.

[0041] Low productivity wells often experience extended times for fluid stabilization due to the inherently low permeability and poor quality of the reservoir. The slow stabilization means that when these wells are shut in, it may take weeks for the fluid height to stabilize and provide accurate data. The prolonged shut-in period is necessary so that the measurements of the fluid height reflect the true conditions within the well, as rapid changes in fluid height are less pronounced in low productivity wells. Consequently, the extended shut-in time may result in significant operational delays and economic losses, highlighting the need for more efficient methods to determine the height of the fluid in the annulus of an oil well.

[0042] To address challenges in traditional measurement methods, the present invention integrates a column-rise equation with real-time monitoring of pump submergence, using the modified Vogel methodology. This innovative approach reduces the time required for fluid stabilization by swiftly adapting to changing reservoir conditions. It significantly curtails the need for extended stabilization periods andeliminates the repetitive use of echoshot guns for measuring fluid heights in subsequent assessments. This methodology enhances the efficiency of the measurement process, allowing for more frequent updates on fluid levels without the extensive downtime typically associated with traditional methods.

[0043] Upon well shut-in, the system immediately starts monitoring and analyzing fluid height data, employing the modified Vogel equation to track the rise or fall trajectory of the fluid within the annulus. This approach enables the system to assess fluid height changes promptly, reducing dependency on traditional, slower methods. The continuous comparison of real-time measurements with the results determined by the modified Vogel methodology allows the system to quickly ascertain when the fluid column has reached a stable level, thereby streamlining the monitoring process and reducing the time typically required for reliable data collection.

[0044] Additionally, the system adjusts operational parameters in response to dynamic reservoir conditions influenced by observed fluid height. These adjustments might involve modifying pump speeds, altering injection rates, or adapting pressure management strategies to maintain well performance. By dynamically responding to changes, the present invention not only simplifies the fluid height measurement process but also contributes to more effective well management and operational cost reductions. This proactive adjustment ensures that the well operates efficiently, maximizing output while minimizing unnecessary expenditures and operational disruptions. The system's ability to react quickly to changes in fluid height enables operators to fine-tune operations almost in real-time, thereby optimizing the extraction process based on the most current data. This continuous adaptation is crucial during varying production phases and contributes significantly to maintaining optimal operating conditions, preventing issues such as over-pumping and the resultant stresses on the well structure.

[0045] The present invention ensures that the fluid height data is accurate without the need for extended shut-in periods. Moreover, the ability of the invention to process and interpret fluid height data quickly minimizes operational delays and reduces economic losses associated with prolonged shut-in times, thus improving well management and operational efficiency. By delivering accurate and timely data, the system enhances decision-making processes, allowing for better strategic planning and operational adjustments that align with the current state of the well. This leads to optimized resource utilization and improved overall performance of oil well operations.

[0046] In some exemplary embodiments of the present invention, the system (200) may include a sucker rod pump (SRP). The sucker rod pump (210) is positioned in a downhole portion of the wellbore.

[0047] A sucker rod pump is a widely recognized and extensively utilized artificial lift system in the oil and gas industry. The sucker rod pump comprises several key components, including a downhole pump assembly, sucker rods, and surface drive equipment. The downhole pump assembly, typically positioned at the bottom of the wellbore, consists of a pump barrel, plunger, standing valve, and traveling valve. The sucker rods, connected in a series, transmit reciprocating motion from the surface drive to the downhole pump, facilitating fluid lifting from the reservoir to the surface.

[0048] In some exemplary embodiment of the present invention, the system (200) may include a plurality of sensors. In some exemplary embodiments of the present invention, the system may include a pressure sensor transmitter located at the tubing head for measuring flowing tubing head pressure (FTHP), for determining pump intake pressure and for a comprehensive assessment of performance of the well.

[0049] In some exemplary embodiment of the present invention, the system may include a pressure gauge or pressure sensor or pressure transducer sensor at the surface of the well for measuring the casing head pressure.

[0050] In some exemplary embodiment of the present invention, an echoshot gun may be used for measuring pump submergence or initial height of the fluid in the annulus of the oil well.

[0051] An echoshot gun is a specialized device used to generate acoustic signals within a wellbore. These signals travel through the well fluid and reflect off the fluid surface and other well components, providing vital data on the internal conditions of the well. These echoshot guns are used for conducting a survey which involves using the echoshot gun to measure the height of the fluid within the annulus of the oil well at specific instances. The acoustic signals emitted by the gun are analyzed upon reflection, allowing operators to determine the precise fluid levels and other characteristics within the wellbore.

[0052] The present invention optimizes the value of echoshot surveys by leveraging initial measurements of key parameters, such as the height of the fluid in the annulus, for prolonged periods. Following an initial echoshot survey conducted at two distinct instances, the invention utilizes derived relationships to determine changes in the height of the fluid in the annulus of the oil well over time. The approach of the present invention reduces the necessity for frequent echoshot surveys, leading to substantial cost reductions. By harnessing the initial dataset and established correlations, the invention provides reliable assessments of the fluid height.

[0053] In some exemplary embodiments of the present invention, the control unit (270) may receive any one of the parameters including but not limited to reservoir pressure (Pr), productivity index (J), casinghead pressure (CHP), gas column hydrostatic pressure (Pgc), well capacity (c), well fluid density (pf), shut- in time (T) and pump submergence or initial column height (Hi).

[0054] In some exemplary embodiments of the present invention, the control unit (270) may determine the height of the fluid within the annulus of the oil well using, for example, relations derived from the modified Vogel methodology. The height of the fluid in the annulus of the oil well may be determined by a predetermined relationship:H(t) = (hl - h2 * eA(m)n) / (1 - eA(m)n)) - (1)Where: hl = b - A / D / (1.6 * pfA2) h2 = b + " D / (1.6 * pfA2) m = (Qmax * A / D * t) / (0.8 * C * pfA2) n = (hi - hl) / (hi - h2)A / D = (bA2 - 4ac) = 1.8 * Pr * pf b = -0.2 * pf * Pr - 1.64 * pfA2 - 1.6 * CHP * p * Pr - 1.6* pgc * pfWherein,H(t): Final height of the fluid in the annulus of the oil well at the shut-in time (ft). pf: Well fluid density (psi / ft).Pr: Reservoir pressure (psi).CHP: Casing head pressure (psi).Pgc: Gas column hydrostatic pressure (psi). hi: Pump submergence or initial column height (ft). t: Shut-in time (days). c: Well capacity (bbl / ft).

[0055] The Vogel methodology is an established concept in petroleum engineering that explains the relationship between reservoir conditions and fluid behavior in the wellbore. This methodology provides insights into oil and gas well management, aiding in reservoir analysis and production management. It utilizes a mathematical model to examine the dynamics of fluid from a reservoir into a wellbore. Key factors considered in the Vogel methodology include reservoir pressure, fluid density, wellbore geometry, and pump efficiency, focusing on evaluating the fluid height in the annulus. Applying the Vogel methodology helpsoperators to adjust production strategies, assess reservoir characteristics, and improve well productivity. This method is useful for enhancing operational decisions and optimizing well output.

[0056] Reservoir pressure (Pr) is the pressure within the reservoir containing oil or gas. It plays a role in analyzing well behavior, impacting both the rate of production and the overall performance of the reservoir. This pressure influences the rate at which fluids flow into the wellbore and is crucial for predicting the total recoverable resources from the well. Generally, high reservoir pressure suggests a robust potential for producing fluids, whereas a decrease in reservoir pressure could indicate depletion of the reservoir.

[0057] Well fluid density (pf) refers to the density of fluids within the wellbore, which affects how fluids flow and how pressures are distributed within the system. This density, measured in psi / ft, is vital for accurately determining pressures and understanding the behavior of fluids in the wellbore.

[0058] Casing head pressure (CHP) is the pressure at the top of the well casing, used for evaluating the overall pressure profile within the wellbore and its effects on fluid dynamics. Casing head pressure, which can incorporate factors like fluid density, wellbore geometry, and production rates, influences the pressure conditions at the wellhead. External elements such as atmospheric pressure and temperature changes can also affect casing head pressure. High casing head pressure may indicate substantial support for fluid production, whereas low casing head pressure could point to issues such as fluid migration — unwanted movement of fluids between geological formations that might lead to contamination and inefficient hydrocarbon production — or insufficient reservoir pressure support, which can necessitate the use of artificial lift techniques.

[0059] Gas column hydrostatic pressure (Pgc) is the pressure exerted by the gas in the wellbore. This pressure is used for assessing the overall pressure balance in the well and its influence on fluid flow. Gas column hydrostatic pressure reflects the weight of the gas above the fluid level, affecting pressure conditions and fluid dynamics within the wellbore. Factors such as gas density, well depth, and production rates can alter gas column hydrostatic pressure. Understanding this pressure is important for managing gas influx and optimizing production strategies.

[0060] Pump submergence or initial height of the fluid in the annulus of the oil well (Hi) indicates how deep the pump is submerged in the wellbore fluid, affecting pressure distribution and fluid movement. For instance, a pump submerged 100 feet deep may indicate certain well configurations that dictate fluid flow and overall well performance.

[0061] Shut-in time (T) is the period during which the well is closed and not producing, affecting pressure build-up and allowing for the evaluation of reservoir conditions. A typical shut-in period might last three days, during which the pressure dynamics and reservoir behavior are monitored.

[0062] Well capacity (c) represents the total volume of fluid that the wellbore and annulus can hold per unit length. Higher well capacity suggests that the wellbore and annulus can hold more fluid, potentially leading to increased production rates. Conversely, a lower well capacity might limit fluid flow and affect production outcomes. Adjustments to well capacity can be made based on wellbore geometry, tubing dimensions, and fluid properties, such as enlarging tubing diameter or expanding the annular space to enhance fluid storage and boost production capabilities.

[0063] In some exemplary embodiments of the present invention, the control unit may determine pump intake pressure at any shut-in time ‘t’ in a well after the well shut-in using:PIP(t) = CHP(t) + Pgc + H(t) * pf -(2)

[0064] The pump intake pressure (PIP) represents the pressure at the pump intake prior to the well being shut in. Pump intake pressure accounts for factors such as fluid height, casing head pressure (CHP), and gas column hydrostatic pressure (Pgc). For instance, pump intake pressure incorporates the casing head pressure, which represents the pressure at the top of the well casing, and the gas column hydrostatic pressure, which accounts for the pressure exerted by the gas column in the wellbore. By considering factors like casing head pressure and gas column hydrostatic pressure, the pressure conditions within the wellbore and their impact on fluid flow dynamics may be understood. A higher pump intake pressure may indicate a greater pressure gradient driving fluid production, resulting in higher production rates. Conversely, a lower pump intake pressure may suggest issues such as fluid migration, wellbore integrity problems, or insufficient reservoir pressure. The change in pump intake pressure over time may offer information about well performance and potential issues. Pressure buildup within the wellbore may be assessed and reservoir characteristics may be evaluated by monitoring pump intake pressure during shut-in periods. Analyzing variations in pump intake pressure during production may help identify changes in fluid behavior, such as gas influx or liquid migration, enabling proactive measures to optimize production and mitigate risks.

[0065] When an oil well is shut down, a series of changes occur that impact the pressure within the well and the surrounding reservoir. Initially, the pressure inside the reservoir is higher than in the wellbore, mainly because the active pumping out of fluids creates a pressure difference. This difference helps push the oil towards the well. However, once the well is shut in and pumping stops, this pressure difference starts to decrease as the system seeks to balance itself.

[0066] As the well remains inactive, the pressures between the reservoir and the wellbore begin to equalize. This equalization is a slow process that depends on how easily fluids can move through the reservoir rock, which is influenced by the rock’s permeability and the fluid's viscosity. Over time, as no more fluids are being removed, the reservoir pressure, which might have dropped due to previous extraction activities, starts to recover. This recovery happens because the fluid movement within the reservoir slows down, allowing pressures throughout the reservoir to stabilize.

[0067] During this time, the liquid column inside the wellbore may begin to rise. This rise is affected by several factors: the physical properties of the reservoir (like its size and how easily fluids can flow through it), the characteristics of the fluid in the well (such as its weight and thickness), and how long the well stays shut in. If the well is closed for a longer period, there's more time for pressures to balance out, possibly causing a more noticeable rise in the liquid column. This rising of the liquid column during the shut-in period can provide valuable information about the reservoir’s conditions and help in managing the well more effectively in the future.

[0068] Fig. 3 illustrates a non-limiting example of a flowchart of a method for determining the height of the fluid in the annulus of an oil well, in accordance with an exemplary embodiment of the present invention. At block 310, the method may include receiving a value of one or more first parameters associated with characteristics of the oil well. The value of the one or more first parameters represents a constant representation of said characteristic. The value of these parameters may remain invariant, regardless of the operational state of the oil well. The one or more first parameters may include but are not limited to the density of the fluid in the annulus of the oil well and the total capacity of the oil well.

[0069] For example, the present invention starts by initially receiving invariant values of the first parameters of the well. In this scenario, the well operators record the well fluid density (pf) as 0.85 psi / ft and the total capacity (c) of the well as 1500 bbl / ft. These parameters remain unchanged regardless of whether the well is active or shut in, providing a stable baseline for future comparisons.

[0070] At block 320, the method may further include receiving a first value for one or more second parameters defining characteristics of the oil well at a first-time interval after the well is shut in. The values for the one or more second parameters may respond to the state of the oil well. These values may change not only if the well is operational but also vary with the duration of the shut-in. The one or more second parameters may include but are not limited to casing head pressure, the height of fluid after well shut-in, as well as hydrostatic pressure of a gas column in the annulus of the oil well. As the shut-in period extends,variations in these parameters may significantly affect the dynamics within the annulus of the oil well, highlighting the need to monitor these changes precisely.

[0071] For example, after the well has been shut in for 24 hours, the first set of values for the second parameters may be measured. The measured second parameter may include, for example, the casing head pressure (CHP) at 500 psi, and the hydrostatic pressure of the gas column in the annulus (Pgc) at 200 psi. The initial fluid height in the annulus (hi) of the oil well may be at 100 ft. This data is crucial as it reflects the immediate response of the well's internal environment to the shut-in condition.

[0072] In some exemplary embodiments of the present invention, the method may include receiving any one of the parameters such as reservoir pressure (Pr), productivity index (J), flowing reservoir pressure (Pwg), casing head pressure (CHP), gas column hydrostatic pressure (Pgc), well capacity (c), well fluid density (pf), shut-in time (T) and pump submergence or initial column height (Hi).

[0073] In some exemplary embodiments of the present invention, the method may include receiving pressure data from a plurality of sensors. In some exemplary embodiments of the present invention, the method may include measuring a flowing tubing head pressure using a pressure sensor positioned at the tubing head. In some exemplary embodiments of the present invention, the method may include determining oil rate at surface of the oil well by a multiphase flowmeter. The measured oil rate is a parameter reflecting the actual oil production from the oil well. In some exemplary embodiment of the present invention, an echoshot gun may be used for measuring pump submergence or initial height of the fluid in the annulus of the oil well.

[0074] At block 330, the method may include receiving a second value for the one or more second parameters at a second time interval when the well is shut in. This step may involve assessing how the characteristics of the oil well evolve over time by comparing these values, thereby mapping any significant changes from the first to the second interval.

[0075] In some exemplary embodiments of the present invention, the method may include receiving any one of the parameters such as reservoir pressure (Pr), productivity index (J), flowing reservoir pressure (Pwg), casing head pressure (CHP), gas column hydrostatic pressure (Pgc), well capacity (c), well fluid density (pf), shut-in time (T) and pump submergence or initial column height (Hi).

[0076] For example, 48 hours from the initial shut-in, a second set of values of the second parameters may be measured to assess further changes in the environment of the oil well. The casing head pressure is now slightly decreased to 490 psi, indicating a natural progression towards pressure stabilization. The hydrostatic pressure of the gas column is measured at 195 psi, and the fluid height has risen to 105 ft. Theseobservations are key to understanding the evolving dynamics within the well during the extended shut-in period.

[0077] At block 340, the method may include determining the height of the fluid in the annulus of the oil well at a third time interval based on the received values of the one or more first parameters and both the first and second values of the one or more second parameters observed at the previous intervals. This determination may use a predetermined relationship to accurately gauge the fluid height, which is essential for effective well management and operational optimization. Such measurements might involve using tools like an echoshot gun for precise determination and a pressure gauge for monitoring the casing head pressure, ensuring reliable data collection and analysis.

[0078] For example, the data collected from the earlier assessments may be applied to a predetermined relationship to determine the height H(t) of the fluid at a third time interval. The calculations incorporate changes observed in the parameters to model the final height. Factors such as b, D, m, b, n are calculated based on updated pressures and the well fluid properties. These values are then applied in the relation -H(t) = (hl - h2 * (eA(m))n) / (1 - (eA(m))n)) - (1)Where: hl = b - A / D / (1.6 * pfA2) h2 = b + " D / (1.6 * pfA2) m = (Qmax * A / D * t) / (0.8 * C * pfA2) n = (hi - hl) / (hi - h2)A / D = (bA2 - 4ac) = 1.8 * Pr * pf b = -0.2 * pf * Pr - 1.64 * pfA2 - 1.6 * CHP * p * Pr - 1.6* pgc * pfWherein,H(t): Final height of the fluid in the annulus of the oil well at the shut-in time (ft). pf: Well fluid density (psi / ft).Pr: Reservoir pressure (psi).CHP: Casing head pressure (psi).Pgc: Gas column hydrostatic pressure (psi). hi: Pump submergence or initial column height (ft). t: Shut-in time (days). c: Well capacity (bbl / ft).

[0079] Relation (1) may be used to analyze the height of the fluid in the annulus of the oil well within the wellbore during shut-in. By incorporating known values for parameters such as reservoir pressure, casing head pressure, pump submergence and shut-in time, prediction for the final height of the fluid in the annulus of the oil well may be determined for any given time of the future.

[0080] This method may utilize data across multiple time intervals to more reliably determine changes in the condition of the oil well, enhancing decision-making processes for well management and optimization, potentially improving production efficiency and minimizing operational costs.

[0081] In some exemplary embodiments of the present invention, the method may be implemented in oil wells for example a tight oil well, a packerless well or a low productivity well that is defined as a well that yields relatively small quantities of oil or gas compared to high productivity wells.

[0082] In some exemplary embodiments of the present invention, the method may include determining by the control unit, pump intake pressure after the well is shut. The determination of pump intake pressure after the well is shut-in involves various factors derived from relationships related to wellbore pressure dynamics. One such relation is represented as relation (2) i.e. PIP(t) = CHP(t) + Pgc + H(t) * pf, where PIP(t) denotes the pump intake pressure at a specific shut-in time (t), CHP(t) denotes the casing head pressure at the same time, Pgc represents the gas column hydrostatic pressure, H(t) represents the final height of the fluid in the annulus of the oil well at the shut-in time, and p represents the well fluid density.

[0083] In some exemplary embodiments of the present invention, the authenticity of a predetermined relationship for determining the height of the fluid in the annulus of an oil well is verified through the establishment and validation of boundary conditions. These conditions serve as benchmarks for comparing the predicted or determined heights against actual measurements, thus determining the accuracy and reliability of the relation in practical applications. One embodiment involves setting specific initial or boundary values for the variables in the relation, reflecting real-world scenarios or constraints relevant to the well's operational environment. These boundary conditions might include physical limitations, environmental factors, or system constraints inherent to the operation of the oil well.

[0084] In the process of determining the height of the fluid in the annulus of an oil well, setting appropriate boundary conditions is essential for accurate modeling and analysis. These boundary conditions typically include constraints on well fluid density, annulus pressure, and the geometric configuration of the wellbore. Well fluid density affects how fluid particles interact and move within the space, while annulus pressure influences the overall stability and movement of the fluid. The geometric configuration of the wellbore, such as its diameter and the shape of its interior surfaces, also plays a crucial role in how fluidsbehave and move. Together, these factors are essential for defining the physical limits and operational conditions within which the mathematical models operate. Once established, these boundary conditions allow for the numerical or analytical solving of relations that predict how the fluid will behave under various conditions.

[0085] Before these boundary conditions can be effectively set, it is important to establish the initial conditions of the well. This typically involves gathering comprehensive data after a period of well shut-in, to ensure that the measurements reflect a stable state of the well's internal environment. For example, the depth of pump submergence is a critical measurement and is recorded with precision, such as noting the pump is submerged at -243 meters from True Vertical Depth (mTVD). This specific data helps in calibrating the model accurately, ensuring that the subsequent analysis reflects true well conditions.

[0086] The application of these boundary conditions yields valuable insights into the dynamic behavior of the fluid at specific times. Initially, a mathematical relation, such as relation (1), uses parameters like hl and h2, which are adjusted based on the initial boundary conditions to represent different physical aspects of the well setup. Factors m and n are determined to account for dynamic changes over time, influenced by variables such as pump depth pressure, casing head pressure, and gas column hydrostatic pressure, all normalized by the fluid density. Over time, as the system approaches a steady-state condition — represented as infinite time in theoretical models — the fluid height reaches a point influenced solely by these pressures, adjusted for fluid density. At this stage, the liquid production rate decreases to zero, indicating a cessation of fluid flow into the well. Analyzing these outcomes against established boundary conditions serves as a benchmark for assessing both the accuracy and the effectiveness of the mathematical models used in predicting the fluid's behavior in the well. These insights are critical for ongoing well management and for making informed decisions about future operations and interventions.

[0087] Reference is made to FIG. 4 illustrating a non-limiting example of a curve which serves as a visual aid in validating a model as presented in the present invention aimed at predicting column rise within the realm of oil and gas extraction. The graph visualizes the relationship between well shut-in time and the rise in the height of the fluid in the annulus of the oil well, pertinent to oil and gas extraction operations. The X-axis represents well shut-in time measured in minutes, while the Y-axis displays the pressure in the annulus (in mTVD) based on the modified Vogel methodology. The scatter plot comprises multiple data points, indicative of measurements taken over the duration of the shut-in.

[0088] The plotted curve aligns well with the observed data points for multiple dates throughout the displayed range. Specifically, the curve matches the observed data, for example on August 18th, 2022,August 21st, 2022, and August 24th, 2022. This close correspondence between the values predicted using the method as disclosed in the present invention and the field-tested / observed measurements suggests that the measurement technique is accurate and reliable. Overall, visualization facilitates the validation of predictions of a mathematical model against observed height of the fluid in the annulus of oil well, aiding in the assessment of the accuracy and practical applicability of the present invention.

[0089] For instance, consider the measurements recorded at 13:00 and 14:00. At 13:00, the fluid level in the annulus (Hl) is 34.00 meters, while the fluid density (pf) is -972.03 psi / ft. The casing head pressure (CHP) at this time is 3.066 psi, and the hydrostatic pressure of the gas column (Pgc) is 16,191 psi. By 14:00, the fluid level has risen to 38.00 meters, the fluid density remains relatively unchanged at -972.15 psi / ft, and the casing head pressure has slightly decreased to 2.984 psi. The hydrostatic pressure of the gas column also slightly decreased to 16,182 psi.

[0090] Applying the present method, these changes in fluid level and pressures over the one-hour interval can be analyzed to assess the dynamics within the well. The method may use a predefined mathematical model to determine the rate of fluid rise, taking into account the measured pressures and fluid density. For example, using the predetermined relationship:H(t) = (hl / (1 - eA(m)n)) - (1) where: hl = b - A / D / (1.6 * pfA2) h2 = b + A / D / (1.6 * pfA2) m = (Qmax * A / D * t) / (0.8 * C * pfA2) n = (hi - hl) / (hi - h2)A / D = (bA2 - 4ac) = 1.8 * Pr * pf b = -0.2 * pf * Pr - 1.64 * pfA2 - 1.6 * CHP * p * Pr - 1.6 * pgc * pf wherein, pf: Well fluid density (psi / ft).Pr: Reservoir pressure (psi).CHP: Casing head pressure (psi).Pgc: Gas column hydrostatic pressure (psi). hl: Pump submergence or initial column height (ft).T: Shut-in time in days. c: Well capacity (bbl / ft).

[0091] The plotted curve aligns well with the observed data points across the displayed range. This close correspondence between the values predicted using the method as disclosed in the present invention and the field-tested / observed measurements suggests that the measurement technique is accurate and reliable. Overall, this visualization facilitates the validation of predictions of the mathematical model against observed column rise data, aiding in the assessment of the accuracy and practical applicability of the present invention.

Claims

AMENDED CLAIMS received by the International Bureau on 10 April 2026 ( 10.04.2026)We claim:

1. A method for determining height of the fluid in an annulus of an oil well, the method comprising: receiving (310) a value for one or more first parameters associated with characteristics of the oil well, wherein the value for the one or more first parameters is an invariant representation of said characteristic; receiving (320), a first value for one or more second parameters defining characteristics of the oil well at a first-time interval after the well is shut in; receiving (330), a second value for the one or more second parameters defining characteristics of the oil well at a second time interval when the well is shut in, wherein the variations in the second value with respect to the first value for each of the one or more second parameters defines the change in the characteristics of the oil well associated with the corresponding second parameter due to pressure buildup within the annulus following shut-in of the well; and determining (340), height of the fluid in the annulus at a third time interval based on the received values of the one or more first parameters and the first value and the second value of the one or more second parameters defining the characteristics of the oil well at the first-time interval and the second time interval respectively, using a predetermined relationship that determines the height of the fluid in the annulus at any given shut-in time.

2. The method as claimed in claim 1, wherein the first parameter includes at least one of a density of the fluid in the annulus of the oil well and a total capacity of the oil well.

3. The method as claimed in claim 1, wherein the second parameter includes at least one of a casing head pressure, height of fluid after well shut in, and hydrostatic pressure of a gas column in the annulus of the oil well at the first-time interval and the second time interval.

4. The method as claimed in claim 3, wherein the height of the fluid in the annulus of the oil well is determined using an echoshot gun.

5. The method as claimed in claim 3, wherein the casing head pressure is determined using a pressure gauge.

6. The method as claimed in claim 1 , wherein the height of the fluid in the annulus of the oil well is determined by the predetermined relationship as given below: H(t) = (hl - h2 * e' (.ni)n) / (1 - Where:m = (Qmax * VD * t) / (0.8 * C * pfA2) n = (hi - hl) / (hi - h2) VD = V(bA2 - 4ac) = 1.8 * Pr * pf b = -0.2 * pf * Pr - 1.64 * pfA2 - 1.6 * CHP * pf * Pr - 1.6 * Pgc * pf wherein, pf: Well fluid density (psi / ft). Pr: Reservoir pressure (psi). CHP: Casing head pressure (psi). Pgc: Gas column hydrostatic pressure (psi), hl : Pump submergence or initial column height (ft), t: Shut-in time in days. c: Well capacity (bbl / ft).

7. The method as claimed in claim 1, wherein the method includes determining pump intake pressure by:PIP(t) = CHP(t) + Pgc + pf H(t), whereinPIP(t): Pump intake pressure at any shut in time (t) (psi)CHP(t): Casing head pressure at any shut in time (psi)Pgc: Hydrostatic gas column pressure (psi) pf: Well fluid density (psi / ft)H(t): Variable pump submergence height at any shut in time (t) hi: Pump submergence / column height prior to shut-in or immediately after shut in time (t).

8. A system for determining height of the fluid in an annulus of an oil well, the system comprising: a memory; and one or more processors (230) coupled with the memory, wherein the one or more processors(230) are configured to:receive (310) a value for one or more first parameters associated with characteristics of the oil well, wherein the value for the one or more first parameters is an invariant representation of said characteristic; receive (320) a first value for one or more second parameters defining characteristics of the oil well at a first time interval after the well is shut in; receive (330) a second value for the one or more second parameters defining characteristics of the oil well at a second time interval when the well is shut in, wherein the variations in the second value with respect to the first value for each of the one or more second parameters defines the change in the characteristics of the oil well associated with the corresponding second parameter due to pressure buildup within the annulus following shut-in of the well; and determine (340) the height of the fluid in the annulus at a third time interval based on the received values of the one or more first parameters and the first value and the second value of the one or more second parameters defining the characteristics of the oil well at the first time interval and the second time interval respectively, using a predetermined relationship that determines the height of the fluid in the annulus at any given shut-in time.

9. The system (200) as claimed in claim 8, wherein the one or more first parameters include at least one of the density of the fluid in an annulus of the oil well and the total capacity of the oil well.

10. The system (200) as claimed in claim 8, wherein the one or more second parameters include at least one of the casing head pressure, height of fluid after well shut in, and hydrostatic pressure of a gas column in the annulus of the oil well at the first time interval and the second time interval.

11. The system (200) as claimed in claim 10, wherein the height of the fluid in the annulus of the oil well is determined using an echoshot gun.

12. The system (200) as claimed in claim 10, wherein the casing head pressure is determined using a pressure gauge.

13. The system (200) as claimed in claim 8, wherein the one or more processors (230) are configured to determine the height of the fluid in the annulus of the oil well at any shut-in time, using the predetermined relationship as given below:H(t) = (hl - h2 * e' (.ni)n) / (1 - eA(mJ''n))Where:m = (Qmax * VD * t) / (0.8 * C * pfA2) n = (hi - hl) / (hi - h2) VD = V(bA2 - 4ac) = 1.8 * Pr * pf b = -0.2 * pf * Pr - 1.64 * pfA2 - 1.6 * CHP * pf * Pr - 1.6 * Pgc * pf wherein, pf: Well fluid density (psi / ft). Pr: Reservoir pressure (psi). CHP: Casing head pressure (psi). Pgc: Gas column hydrostatic pressure (psi), hi: Pump submergence or initial column height (ft), t: Shut-in time in days. c: Represents the well capacity (bbl / ft).

14. The system (200) as claimed in claim 8, wherein the one or more processors (230) are configured to determine pump intake pressure (PIP) at any shut-in time, by using the formula: PIP(t) = CHP(t) + Pgc + pf H(t), whereinPIP(t): Pump intake pressure at any shut in time, t (psi)CHP(t): Casing head pressure at any shut in time (psi)Pgc: Hydrostatic gas column pressure (psi) pf: Well fluid density (psi / ft)H(t): Variable pump submergence height at any shut in time (t) hi: Pump submergence / column height prior to shut-in or immediately after shut in time (t).

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