Measuring Well System Efficiency Using Tube Waves

Hydrocarbons and similar substances may exist in underground deposits and can be extracted by various means, such as drilling wells and using pumps to lift the substance to the surface. Tracking and measuring various aspects of the associated operations is important for maintaining and improving the operations. However, because many of the operations occur far beneath the surface of the earth, it can be difficult to determine the conditions that exist within the well and surrounding formation(s).

The description that follows includes example systems, methods, techniques, and program flows that embody aspects of the disclosure. However, it is understood that this disclosure may be practiced without these specific details. In some instances, well-known instruction instances, protocols, structures, and techniques have not been shown in detail in order not to obfuscate the description.

Because systems used to extract substances (e.g., hydrocarbons) from subsurface formations are located underground, downhole conditions of the well and related formation can be difficult to monitor. For example, operators may wish to track the efficiency of a system used for hydraulic fracking. One example of a condition that may impact the efficiency of a hydraulic fracking system is the condition of perforations in the casing that allow for the flow of fluids, proppant, hydrocarbons, and other substances between the wellbore and the target formation. For example, the perforations may increase in size due to erosion from the fluids, proppants, and other materials flowing through them or may become clogged due to debris.

One metric usable to determine the condition of the perforations is the resistance of the well system, which measures how much the system resists the flow of fluids and other materials. For example, clogged perforations may restrict the flow of fluids through them, thereby increasing the resistance of the system. Similarly, erosion of the perforations may increase the flow of fluids through them, thereby decreasing the resistance of the system.

One technique for measuring the resistance of the system utilizes a tube wave (sometimes referred to as a “pressure pulse” or “water hammer”). A tube wave can be generated passively or actively. For example, a tube wave may be generated passively when the pumping of fluid through the wellbore is stopped, causing a pressure differential that flows through the well system. As another example, a tube wave may be generated actively when a pressure source, such as an air gun or electrical discharge causes a pressure increase in the hydraulic fluid, resulting in a pressure differential that flows through the well system.

Once the actual resistance of the well system is determined via the tube wave (“measured resistance” or R), the measured resistance is compared to the expected resistance (“design-corrected resistance” or R) that is determined based on a number of factors, such as the expected erosion of the perforations. The comparison of the measured resistance to the design-corrected resistance can be used to generate various metrics related to the condition of the perforations. This process can be performed at various points in the operation of the well, including when the stage has been completed.

Example implementations include the measurement of stage efficiency based, at least in part, on the measured resistance and the design-corrected resistance. The measured resistance can be derived from post-stage pressure pulse ringdown analysis while the design-corrected resistance can be the estimated design resistance corrected for any erosion that is estimated from the amount of proppant that has been used during the stage. The ratio of the measured resistance and the design-corrected resistance tracks the deviation of the actual resistance of the stage from a theoretical resistance that accounts for erosion and can thus indicate the efficiency of the treatment. Incorporating the erosion effects improves the measure of efficiency relative to the system design values.

When measured as part of the post-stage pressure pulse ringdown analysis, the efficiency of each stage can be measured individually, instead of treating each stage the same. Additionally, measuring the efficiency of the system and stages can reduce waste on fluid, proppant, and other material pumped for the well, reducing costs.

As noted above, the two primary parameters generated and used in determining the stage efficiency are the measured resistance and the design-corrected resistance, which represent the two estimates of perforation resistances. Measured resistance may be generated by the tube wave measurement at the end of a stage by inverting the pressure signal generated through a tube wave, pressure pulse, water hammer, or other excitation of the wellbore.

Design-corrected resistance is generated through a simulation that uses various inputs, including inputs related to the stage design and treatment information. Some examples of stage design inputs include initial perforation count and initial perforation diameter. Some examples of treatment information inputs include slurry rate and proppant concentration over time (e.g., throughout the stage). The simulation may be based on the following equations, where Q is the injection rate, C is the proppant concentration, ρ is the fluid density, N is the number of perforations, D is the perforation diameter, Cis the discharge coefficient, α is a first scaling factor, and β is a second scaling factor:

Equation 1 provides the change in perforation diameter over time and Equation 2 provides the discharge coefficient over time as a result of erosion. The scaling factors, α and β, can be determined based on experimental data and the like. The design-corrected resistance can be calculated based on the expected perforation diameter and the discharge coefficient at the end of the stage using Equation 4:

Once the design-corrected resistance and the measured resistance is determined, the ratio R/R(“deviation ratio”) can be determined. The deviation ratio corresponds to the deviation of the actual resistance of the stage from a theoretical resistance that accounts for erosion.is a chart of the deviation ratio of a set of example stages, according to some implementations.

A deviation ratio of 1 indicates that the stage performed as expected. A deviation ratio less than 1 indicates that the stage had a condition leading to lower-than-expected resistance, such as perforations that eroded more than expected, a leak (e.g., in a plug), etc. A deviation ratio greater than 1 indicates that the stage had a condition leading to higher-than-expected resistance, such as some form of blockage. Thus, results from analyzing the deviation ratio can indicate various conditions related to the perforations and, more generally, the stage and the system.

In addition, the effective number of perforations can be determined based on the measured resistance by substituting the measured resistance for the design-corrected resistance and solving Equations 1, 2, 3, and 4 for N such that N produces a design-corrected resistance that is functionally equal to the measured resistance (e.g., |R−R|≤ε, where ε is an acceptable margin of error or similar value). The effective number of perforations is thus the number of perforations that would result in a stage having a resistance of about R. Because the amount of erosion is dependent on the rate and the rate depends on the number of perforations, the solution to the equation for Nis non-linear.

If the ratio of the effective number of perforations to the number of perforations in the actual design (“perforation deviation ratio”) is less than, then the perforation deviation ratio corresponds to the severity of conditions resulting in increased resistance (e.g., a blockage). If the perforation deviation ratio is greater than, then the perforation deviation ratio corresponds to the severity of conditions resulting in decreased resistance (e.g., greater than expected erosion or leakage).

The perforation deviation ratio can indicate a leakage within the well system (e.g., leakage of the plug used for the stage). For example, it may be determined that the measured resistance typically falls within a particular range around the design-corrected resistance, leading to a conclusion that the erosion rate is fairly consistent. Thus, if the measured resistance is unusually low, it may be inferred that there is a leak instead of an unusually high erosion rate. To put it another way, if the probability that excessive erosion has occurred is low, then a high perforation deviation ratio is more likely to indicate a leak than excessive erosion.

An eroded area deviation ratio can also be calculated using Equations 1, 2, 3,and 4. In particular, the expected area of the perforations at the end of the stage can be determined based on the sum of the expected diameter of each of the perforations at the end of the stage. The effective area of the perforations at the end of the stage can be determined based on the sum of the effective diameter of each of the perforations at the end of the stage, where the effective diameter is determined based on the measured resistance and/or the effective number of perforations. The eroded area deviation ratio is the ratio of the effective area of the perforations to the expected area of the perforations.

In some implementations, a downhole operation or attribute in the wellbore may be started, modified, or updated based on determining the efficiency of the well system. For example, an operation (at the surface or downhole) may be performed and/or directed to be performed to change a downhole operation or attribute based on the efficiency of the well system. An example of one or more downhole operations that might be performed in response to determining the well system efficiency are downhole operations to reduce leakage in the plug for a stage. Similarly, attributes of the operations in the wellbore may be set based on determining the efficiency of the well system. Examples of such attributes of the operations may include composition of the fluid, proppant concentration, injection rate, etc.

is a diagrammatic illustration of an example well system, according to some implementations. In particular,depicts a well systemthat includes a wellborein a formation. The wellboreincludes a casingand a number of perforations,in the casing. Each set of perforations,is made in a corresponding stage of a set of stagesandto allow reservoir fluids (i.e., oil, water, and gas) from the formationto flow into the wellboreand into the tubular string(the production tubing).

The well systemincludes a wellheadlocated on a pad. The padmay include a variety of equipment that varies depending on the stage of the operation, some of which may be part of the wellhead. For the purposes of the discussion herein, the padincludes a pump (not depicted) that injects fluid and other substances into the wellboreor a component therein. The well systemalso includes one or more computing systems, illustrated as computing system Aand computing system B. Computing system Aand computing system Bare communicatively coupled with one or more components of the well system. Computing system Ais located on the padwhile computing system Bis located at a different location off the padand is communicatively coupled via network.

At a particular point in time, such as when a particular stage is completed, a tube wave is generated. The tube wave travels through the wellbore(e.g., through the fluid located in the wellbore, the tubular string, etc.). The tube wave interacts with the components of the wellbore, the formation, etc. and produces reflected waves that travel back up to the wellhead. The wellheadand/or the padinclude equipment designed to measure the tube wave and transform it into a tube wave signal, such as a pressure transducer (not depicted).

The tube wave signal can be transmitted to one or more computing systems, such as computing system Aand computing system B. The computing system(s) can capture, process, and store the tube wave signal. The computing systems(s) may also use the tube wave signal to determine the efficiency of the well systemas described herein.

Although computing system Aand computing system Bare depicted as being communicatively coupled with components of the well system, some implementations may not have a computing system communicatively coupled to the components of the well systemand instead may have the tube wave signal transferred via machine-readable storage media, such as a flash drive.

depicts two computing systems (computing system Aand computing system B) to demonstrate that computing systems may be located on or off the pad. Actual implementations may have one or more computing systems located on or off the pad.

is an illustration of an example computing system for determining the efficiency of a well system, according to some implementations. In particular,depicts an example systemincluding a computing systemthat comprises a stage simulation module, a stage analysis module, and a stage efficiency analysis module. The computing systemmay be communicatively coupled with a tube wave signal generator. Computing system Aand/or computing system Bofmay be implemented in a manner similar to the computing system.

In operation, the tube wave signal generatorgenerates a tube wave signalrepresenting a tube wave. The tube wave signal generatormay be any device or system that is capable of transforming a tube wave traveling through a wellbore into a signal, such as a pressure transducer installed in a wellhead. The tube wave signal generatormay generate the tube wave signalanytime a tube wave is detected, when explicitly triggered, or a combination thereof. For example, the tube wave signalmay be generated as part of a post-stage pressure pulse ringdown analysis.

The tube wave signal generatortransmits the tube wave signalto the computing system. The tube wave signal generatormay transmit the tube wave signalusing any applicable means, such as via a computer network. In some instances, the tube wave signalis manually transferred to the computing systemby transferring the tube wave signalfrom the tube wave signal generatoronto one or more computer readable storage media and then transferring the tube wave signalfrom the one or more computer readable storage media to the computing system. The tube wave signalmay undergo additional processing during the transmission from the tube wave signal generatorto the computing system.

The stage analysis modulereceives the tube wave signaland performs operations to generate measured stage characteristics. The measured stage characteristicsrepresent the conditions of the stage as actually experienced, as contrasted with the expected stage characteristics. The measured stage characteristicscan include the measured resistance of the corresponding well system. The operations performed to generate the measured stage characteristics can include transforming the tube wave signalinto a measured resistance associated with the stage.

The stage simulation modulereceives stage design characteristics. The stage design characteristicsmay be pushed to the stage simulation module(e.g., sent to the stage simulation modulefrom data source or entered by a user) or pulled by the stage simulation module(e.g., queried from a database). The stage design characteristicscan include various characteristics of the stage design, including, but not limited to, an injection rate, a proppant concentration, a fluid density, number of perforations, perforation diameter, coefficient of discharge, and scaling factors. The stage design characteristicsmay include values that change over time and thus the stage design characteristicsmay include multiple values for individual characteristics or representations of continuous signals.

The stage simulation moduleuses the stage design characteristicsas inputs to a simulation of the stage that corresponds to the tube wave signal. Thus, as different tube wave signals are received for different stages, the stage simulation module may receive different stage design characteristics.

The implementation of the simulation can vary. For example, in some implementations the simulation may use a mathematical model consisting of Equations 1, 2, 3, and 4. In some implementations, the simulation may use other modeling techniques such as computational fluid dynamics, finite element analysis, etc.

The output of the simulation executed by the stage simulation moduleare the expected stage characteristics. The expected stage characteristicsare characteristics of the relevant stage that would be expected given the particular stage design characteristicsand thus may change depending on the stage design characteristics. The expected stage characteristicsmay include the design-corrected resistance.

The stage efficiency analysis modulecalculates the stage efficiency analysis resultsbased, at least in part, on the expected stage characteristicsand the measured stage characteristics. The stage efficiency analysis resultsmay include one or more stage efficiency metrics and may include any data relevant to determining the efficiency of the stage. For example, the stage efficiency analysis resultsmay include the deviation ratio, perforation deviation ratio, eroded area deviation ratio, etc. The stage efficiency analysis resultsmay include qualitative data as well, such as indications that the amount of erosion was greater than expected, indications that there may be leakage in the plug, etc.

Although the computing systemis depicted as a single computing system, actual implementations may vary. For example, the computing systemmay be two or more interconnected computing systems, a cloud computing system, or any other computing system capable of performing the operations described.

Further, although the operations described above are discussed in relation to analyzing the efficiency of a stage upon completion of the stage, implementations are not so limited. For example, some implementations may be configured to perform the operations anytime a tube wave is generated, not only when a tube wave is generated at stage completion.

is a flowchart depicting example operations for determining the efficiency of a well system, according to some implementations. Operations depicted in the flowchartofcan be performed by one or more machines, one or more computing systems, software, firmware, hardware, or any combination thereof. Operations of flowchartare described in reference toand. However, the operations can be adapted to other implementations. Operations of flowchartstart at block.

At block, a tube wave is generated within a well system. The tube wave may be generated via any suitable means, including passively or actively. For example, a tube wave may be passively generated by decreasing fluid pressure by cessation of pumping activity at a wellhead or may be actively generated by increasing fluid pressure using an air gun.

For example, in reference to, a pump located at the wellheadmay be disabled, causing a decrease in pressure in the wellbore. The corresponding pressure differential may propagate down the wellboreas a tube wave.

At block, the tube wave is transformed into a tube wave signal. For example, in reference to, a pressure transducer or similar mechanism may be installed within the wellbore, wellhead, or other location at which the pressure of the fluid in the system can be measured may translate the tube wave into an electrical signal.

At block, measured stage characteristics are generated based, at least in part, on the tube wave signal. For example, the tube wave signal may be analyzed and used to generate a measured resistance corresponding to the resistance of the system at stage completion. For example, in relation to, the stage analysis modulemay receive the tube wave signaland generate the measured stage characteristics.

At block, expected stage characteristics are generated based, at least in part, on a simulation of a stage using stage design characteristics corresponding to the stage. For example, with reference to, the stage simulation modulemay execute a simulation of a particular stage based on the received stage design characteristics. The simulation may result in the generation of the expected stage characteristics. In some implementations, the simulation may be performed by substituting the variables of Equations 1, 2, 3, and 4 with the corresponding values from the stage design characteristic.

At block, at least one stage efficiency metric is generated based, at least in part, on the expected stage characteristics and the measured stage characteristics. For example, with reference to, the stage efficiency analysis modulemay receive the expected stage characteristicsand the measured stage characteristicsand generate the stage efficiency analysis resultstherefrom.

In some implementations, the stage efficiency analysis results are generated by calculating at least one of the deviation ratio, the perforation deviation ratio, or eroded area ratio.

Although some of the descriptions herein describe determining the efficiency of a well system upon stage completion, operations described herein can be adapted to determine the efficiency of a well system at any point and adapted for well systems that don't have multiple stages.

While the aspects of the disclosure are described with reference to various implementations and exploitations, it will be understood that these aspects are illustrative and that the scope of the claims is not limited to them. In general, techniques for determining well system efficiency as described herein may be implemented with facilities consistent with any hardware system or hardware systems. Many variations, modifications, additions, and improvements are possible.

Plural instances may be provided for components, operations or structures described herein as a single instance. Further, boundaries between various components, operations and data stores are somewhat arbitrary, and particular operations are illustrated in the context of specific illustrative configurations. Other allocations of functionality are envisioned and may fall within the scope of the disclosure. In general, structures and functionality presented as separate components in the example configurations may be implemented as a combined structure or component. Similarly, structures and functionality presented as a single component may be implemented as separate components. These and other variations, modifications, additions, and improvements may fall within the scope of the disclosure.

The flowcharts are provided to aid in understanding the illustrations and are not to be used to limit the scope of the claims. The flowcharts depict example operations that can vary within the scope of the claims. Additional operations may be performed; fewer operations may be performed; the operations may be performed in parallel; and the operations may be performed in a different order. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by program code. The program code may be provided to a processor of a general-purpose computer, special purpose computer, or other programmable machine or apparatus.

Use of the phrase “at least one of” preceding a list with the conjunction “and” should not be treated as an exclusive list and should not be construed as a list of categories with one item from each category, unless specifically stated otherwise. A clause that recites “at least one of A, B, and C” can be infringed with only one of the listed items, multiple of the listed items, and one or more of the items in the list and another item not listed.