MEASURING WELL SYSTEM EFFICIENCY USING TUBE WAVES

Description

BACKGROUND

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).

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the disclosure may be better understood by referencing the accompanying drawings.

FIG. 1 is a diagrammatic illustration of an example well system, according to some implementations.

FIG. 2 is an illustration of an example computing system for determining the efficiency of a well system, according to some implementations.

FIG. 3 is a flowchart depicting example operations for determining the efficiency of a well system, according to some implementations.

FIG. 4 is a block diagram depicting an example computer, according to some implementations.

FIG. 5 is a chart of the deviation ratio of a set of example stages, according to some implementations.

DESCRIPTION

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_m), the measured resistance is compared to the expected resistance (“design-corrected resistance” or R_dc) 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, C_d is the discharge coefficient, α is a first scaling factor, and β is a second scaling factor:

d ⁢ D d ⁢ t = α ⁢ Cv 2 Equation ⁢ 1 d ⁢ C d d ⁢ t = β ⁢ Cv 2 ( 1 - C d C d max ) Equation ⁢ 2 v = 4 ⁢ Q N ⁢ π ⁢ d 2 Equation ⁢ 3

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:

R dc = 16 ⁢ ρ ⁢ Q o N ⁢ π 2 ⁢ C d 2 ⁢ D 4 Equation ⁢ 4

Once the design-corrected resistance and the measured resistance is determined, the ratio R_m/R_dc (“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. FIG. 5 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_dc−R_m|≤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_m. 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 1, 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 1, 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.

Example Systems

FIG. 1 is a diagrammatic illustration of an example well system, according to some implementations. In particular, FIG. 1 depicts a well system 100 that includes a wellbore 102 in a formation 101. The wellbore 102 includes a casing 104 and a number of perforations 114, 116 in the casing 104. Each set of perforations 114, 116 is made in a corresponding stage of a set of stages 130 and 132 to allow reservoir fluids (i.e., oil, water, and gas) from the formation 101 to flow into the wellbore 102 and into the tubular string 106 (the production tubing).

The well system 100 includes a wellhead 118 located on a pad 111. The pad 111 may include a variety of equipment that varies depending on the stage of the operation, some of which may be part of the wellhead 118. For the purposes of the discussion herein, the pad 111 includes a pump (not depicted) that injects fluid and other substances into the wellbore 102 or a component therein. The well system 100 also includes one or more computing systems, illustrated as computing system A 120 and computing system B 122. Computing system A 120 and computing system B 122 are communicatively coupled with one or more components of the well system 100. Computing system A 120 is located on the pad 111 while computing system B 122 is located at a different location off the pad 111 and is communicatively coupled via network 124.

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 102 (e.g., through the fluid located in the wellbore 102, the tubular string 106, etc.). The tube wave interacts with the components of the wellbore 102, the formation 101, etc. and produces reflected waves that travel back up to the wellhead 118. The wellhead 118 and/or the pad 111 include 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 A 120 and computing system B 122. 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 system 100 as described herein.

Although computing system A 120 and computing system B 122 are depicted as being communicatively coupled with components of the well system 100, some implementations may not have a computing system communicatively coupled to the components of the well system 100 and instead may have the tube wave signal transferred via machine-readable storage media, such as a flash drive.

FIG. 1 depicts two computing systems (computing system A 120 and computing system B 122) to demonstrate that computing systems may be located on or off the pad 111. Actual implementations may have one or more computing systems located on or off the pad 111.

Example Computing System

FIG. 2 is an illustration of an example computing system for determining the efficiency of a well system, according to some implementations. In particular, FIG. 2 depicts an example system 200 including a computing system 202 that comprises a stage simulation module 204, a stage analysis module 206, and a stage efficiency analysis module 208. The computing system 202 may be communicatively coupled with a tube wave signal generator 210. Computing system A 120 and/or computing system B 122 of FIG. 1 may be implemented in a manner similar to the computing system 202.

In operation, the tube wave signal generator 210 generates a tube wave signal 212 representing a tube wave. The tube wave signal generator 210 may 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 generator 210 may generate the tube wave signal 212 anytime a tube wave is detected, when explicitly triggered, or a combination thereof. For example, the tube wave signal 212 may be generated as part of a post-stage pressure pulse ringdown analysis.

The tube wave signal generator 210 transmits the tube wave signal 212 to the computing system 202. The tube wave signal generator 210 may transmit the tube wave signal 212 using any applicable means, such as via a computer network. In some instances, the tube wave signal 212 is manually transferred to the computing system 202 by transferring the tube wave signal 212 from the tube wave signal generator 210 onto one or more computer readable storage media and then transferring the tube wave signal 212 from the one or more computer readable storage media to the computing system 202. The tube wave signal 212 may undergo additional processing during the transmission from the tube wave signal generator 210 to the computing system 202.

The stage analysis module 206 receives the tube wave signal 212 and performs operations to generate measured stage characteristics 214. The measured stage characteristics 214 represent the conditions of the stage as actually experienced, as contrasted with the expected stage characteristics. The measured stage characteristics 214 can include the measured resistance of the corresponding well system. The operations performed to generate the measured stage characteristics can include transforming the tube wave signal 212 into a measured resistance associated with the stage.

The stage simulation module 204 receives stage design characteristics 216. The stage design characteristics 216 may be pushed to the stage simulation module 204 (e.g., sent to the stage simulation module 204 from data source or entered by a user) or pulled by the stage simulation module 204 (e.g., queried from a database). The stage design characteristics 216 can 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 characteristics 216 may include values that change over time and thus the stage design characteristics 216 may include multiple values for individual characteristics or representations of continuous signals.

The stage simulation module 204 uses the stage design characteristics 216 as inputs to a simulation of the stage that corresponds to the tube wave signal 212. 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 module 204 are the expected stage characteristics 218. The expected stage characteristics 218 are characteristics of the relevant stage that would be expected given the particular stage design characteristics 216 and thus may change depending on the stage design characteristics 216. The expected stage characteristics 218 may include the design-corrected resistance.

The stage efficiency analysis module 208 calculates the stage efficiency analysis results 220 based, at least in part, on the expected stage characteristics 218 and the measured stage characteristics 214. The stage efficiency analysis results 220 may 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 results 220 may include the deviation ratio, perforation deviation ratio, eroded area deviation ratio, etc. The stage efficiency analysis results 220 may 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 system 202 is depicted as a single computing system, actual implementations may vary. For example, the computing system 202 may 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.

FIG. 3 is a flowchart depicting example operations for determining the efficiency of a well system, according to some implementations. Operations depicted in the flowchart 300 of FIG. 3 can be performed by one or more machines, one or more computing systems, software, firmware, hardware, or any combination thereof. Operations of flowchart 300 are described in reference to FIG. 1 and FIG. 2. However, the operations can be adapted to other implementations. Operations of flowchart 300 start at block 302.

At block 302, 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 FIG. 1, a pump located at the wellhead 118 may be disabled, causing a decrease in pressure in the wellbore 102. The corresponding pressure differential may propagate down the wellbore 102 as a tube wave.

At block 304, the tube wave is transformed into a tube wave signal. For example, in reference to FIG. 1, a pressure transducer or similar mechanism may be installed within the wellbore 102, wellhead 118, 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 306, 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 FIG. 2, the stage analysis module 206 may receive the tube wave signal 212 and generate the measured stage characteristics 214.

At block 308, 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 FIG. 2, the stage simulation module 204 may execute a simulation of a particular stage based on the received stage design characteristics 216. The simulation may result in the generation of the expected stage characteristics 218. 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 310, 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 FIG. 2, the stage efficiency analysis module 208 may receive the expected stage characteristics 218 and the measured stage characteristics 214 and generate the stage efficiency analysis results 220 therefrom.

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.

As used herein, the term “or” is inclusive unless otherwise explicitly noted. Thus, the phrase “at least one of A, B, or C” is satisfied by any element from the set {A, B, C} or any combination thereof, including multiples of any element.

Example Computer

FIG. 4 is a block diagram depicting an example computer, according to some implementations. FIG. 4 depicts a computer 400 for measuring stage efficiency of a well system. The computer 400 includes a processor 401 (possibly including multiple processors, multiple cores, multiple nodes, and/or implementing multi-threading, etc.). The computer 400 also includes a stage efficiency analysis unit 415 which may perform the operations described herein. For example, the stage efficiency analysis unit 415 may receive stage design characteristics and/or a tube wave signal, may determine the expected stage characteristics and measured stage characteristics, and may determine the efficiency of the stage based, at least in part, on the expected stage characteristics and measured stage characteristics. Any one of the previously described functionalities may be partially (or entirely) implemented in hardware and/or on stage efficiency analysis unit 415. For example, the functionality may be implemented with an application specific integrated circuit, in logic implemented in the stage efficiency analysis unit 415, in a co-processor on a peripheral device or card, etc. Further, realizations may include fewer or additional components not illustrated in FIG. 4 (e.g., video cards, audio cards, additional network interfaces, peripheral devices, etc.). The processor 401 and the network interface 405 are coupled to the bus 403. Although illustrated as being coupled to the bus 403, the memory 407 may be coupled to the processor 401. The computer 400 includes memory 407. The memory 407 may be system memory or any one or more possible realizations of machine-readable media. The computer 400 can communicate via transmissions to and/or from remote devices via the network interface 405 in accordance with a network protocol corresponding to the type of network interface, whether wired or wireless and depending upon the carrying medium. In addition, a communication or transmission can involve other layers of a communication protocol and or communication protocol suites (e.g., transmission control protocol, Internet Protocol, user datagram protocol, virtual private network protocols, etc.).

Example Implementations

Implementation 1: A method for determining an efficiency of a well system, the method comprising: performing a simulation of a stage of the well system based, at least in part, on stage design characteristics; determining expected stage characteristics based, at least in part, the simulation; generating measured stage characteristics based, at least in part, on a tube wave signal corresponding to a tube wave that occurred in the well system; and determining at least one stage efficiency metric based, at least in part, on the expected stage characteristics and the measured stage characteristics.

Implementation 2: The method of claim 1, further comprising: generating the tube wave in the well system; and transforming the tube wave into the tube wave signal.

Implementation 3: The method according to any of the preceding Implementations, wherein said performing the simulation of the stage of the well system comprises determining a design-corrected resistance of the stage based, at least in part, on an expected perforation diameter and a discharge coefficient.

Implementation 4: The method according to any of the preceding Implementations, wherein said determining at least one stage efficiency metric comprises determining a metric that correlates with an amount of erosion in one or more perforations associated with the stage.

Implementation 5: The method according to any of the preceding Implementations, wherein said determining the metric that correlates with the amount of erosion in the one or more perforations associated with the stage comprises determining a ratio of a measured resistance of the stage to a design-corrected resistance of the stage.

Implementation 6: The method according to any of the preceding Implementations, further comprising determining a calculated number of perforations based, at least in part, on the measured stage characteristics, wherein the measured stage characteristics comprise at least a measured resistance.

Implementation 7: The method according to any of the preceding Implementations, further comprising determining a ratio of the calculated number of perforations to a design number of perforations.

Implementation 8: The method according to any of the preceding Implementations, further comprising determining an estimated eroded area based, at least in part, on the measured stage characteristics, wherein the measured stage characteristics comprise at least a measured resistance.

Implementation 9: The method according to any of the preceding Implementations, further comprising determining based, at least in part, on the at least one stage efficiency metric that one or more perforations is eroded more than expected, that one or more perforations is blocked more than expected, or that a plug has leakage.

Implementation 10: A well system comprising: one or more computing systems comprising: one or more processors; and one or more non-transitory computer-readable mediums including instructions which, when executed by the one or more processors, cause the one or more processors to determine an efficiency of the well system, the instructions including: instructions to perform a simulation of a stage of the well system based, at least in part, on stage design characteristics; instructions to determine expected stage characteristics based, at least in part, the simulation; instructions to generate measured stage characteristics based, at least in part, on a tube wave signal corresponding to a tube wave that occurred in the well system; and instructions to determine at least one stage efficiency metric based, at least in part, on the expected stage characteristics and the measured stage characteristics.

Implementation 11: The well system of claim 10, further comprising a device configured to transform the tube wave into the tube wave signal, wherein the device is communicatively coupled with the one or more computing systems.

Implementation 12: The well system according to any of the preceding Implementations, wherein the instructions to perform the simulation of the stage of the well system include instructions to determine a design-corrected resistance of the stage based, at least in part, on an expected perforation diameter and a discharge coefficient.

Implementation 13: The well system according to any of the preceding Implementations, wherein the instructions to determine at least one stage efficiency metric includes instructions to determine at least one of a deviation ratio, a perforation deviation ratio, or an eroded area deviation ratio.

Implementation 14: The well system according to any of the preceding Implementations, wherein the instructions to determine the at least one stage efficiency metric includes instructions to determine a ratio of a measured resistance of the stage to a design-corrected resistance of the stage.

Implementation 15: The well system according to any of the preceding Implementations, wherein the instructions further include instructions to determine based, at least in part, on the measured resistance and the design-corrected resistance of the stage, that one or more perforations is eroded more than predicted by the simulation, that one or more perforations is blocked more than predicted by the simulation, or that a leak may be present in a plug.

Implementation 16: One or more non-transitory computer-readable mediums including instructions which, when executed by a processor, cause the processor to determine an efficiency of a well system, the instructions comprising: instructions to perform a simulation of a stage of the well system based, at least in part, on a discharge coefficient, wherein the discharge coefficient is associated with a rate of erosion of one or more perforations in the stage; instructions to determine a design-corrected resistance of the stage based, at least in part, the simulation; instructions to generate a measured resistance of the stage based, at least in part, on a tube wave signal corresponding to a tube wave that occurred in the well system; and instructions to determine at least one stage efficiency metric based, at least in part, on the design-corrected resistance of the stage and the measured resistance of the stage.

Implementation 17: The one or more non-transitory computer-readable mediums of claim 16, wherein the instructions to determine the at least one stage efficiency metric includes instructions to determine a ratio of the measured resistance of the stage to the design-corrected resistance of the stage.

Implementation 18: The one or more non-transitory computer-readable mediums according to any of the preceding Implementations, wherein the instructions further include instructions to determine a calculated number of perforations based, at least in part, on the measured resistance of the stage.

Implementation 19: The one or more non-transitory computer-readable mediums according to any of the preceding Implementations, wherein the instructions further include: instructions to determine a design-corrected eroded area based, at least in part, on a design number of perforations; instructions to determine a calculated eroded area based on the calculated number of perforations; and instructions to determine a ratio of the calculated eroded area to the design-corrected eroded area.

Implementation 20: The one or more non-transitory computer-readable mediums according to any of the preceding Implementations, wherein the instructions further include determining a ratio of the calculated number of perforations to an expected number of perforations.