Method for determining frictional pressure losses due to fluid flow through a well, perforations in the well, and near wellbore regions from water hammer analysis

Abstract

A method for determining fluid friction pressure loss in a well pumping fluid includes measuring fluid pressure in the well while pumping at a first flow rate. The first flow rate is changed to a second flow rate and the fluid pressure is measured for a selected time. A modeled pressure response of the well is performed using selected values of parameters related to pipe friction factor. The modeled pressure response is compared to the measured pressure. The values of the parameters related to pipe friction factor are adjusted and the modeling and comparison are repeated until the modeled pressure response substantially matches the measured pressure. The first flow rate is changed and the measuring, modeling, comparing, adjusting the parameters related to pipe friction factor, and repeating the modeling and comparison are repeated to determine a relationship between the values of the parameters related to pipe friction factor and the first flow rate.

Description

Technical Field

[0001] This disclosure relates to the field of pumping fluids into underground wells to treat the well and a reservoir hydraulically connected to the well. More specifically, this disclosure relates to methods for determining the amount of fluid pressure loss during the pumping of such treatment fluids in order to characterize the effects of pumping such treatment fluids on the well and on the hydraulically connected reservoir. Background Technology

[0002] Fluids are injected into subsurface soil formations through a well for purposes including hydraulic fracturing and other well enhancement processes. Hydraulic fracturing is performed to enhance reservoir permeability (increasing the effective radius of the wellbore within the reservoir), thereby facilitating the extraction of oil and gas, or creating flow paths for heat exchange in geothermal energy production. Creating hydraulic fractures through fluid injection is a subcategory of well enhancement. During multi-stage hydraulic fracturing, where multiple sections of the well are to be fractured in different zones of the reservoir, the portion of the well penetrating the reservoir can be divided into shorter axial segments called "segments." During enhancement, the segment currently being treated is isolated from any and all lower (deeper) segments, for example, by placing plugs in the wellbore. The wellbore can then be perforated in a cluster of perforations—that is, openings are created in the well casing or tubing—and fluid is injected into the well and then through the perforations to create hydraulic fractures in the formation.

[0003] The effectiveness of hydraulic fracturing depends heavily on controlling the fluid pressure within the well, particularly around the perforation, and the fluid pressure in the subsurface formation surrounding the well and at a certain lateral distance from it—the so-called "near-wellbore zone." However, measuring the pressure inside and outside the well is difficult, expensive, and in some cases impossible. Determining formation and wellbore fluid pressures using pressure measurements taken at convenient locations along the well (e.g., near the wellhead at the surface) is challenging because fluid flow through the well, perforation, and near-wellbore zone is accompanied by viscous drag and energy dissipation and pressure losses due to turbulence.

[0004] Fluid pressure in hydraulic fractures of the reservoir The following expression relates to wellhead pressure. Related (see, for example, Economides et al., 2002; Cramer et al., 2019; Mondal et al., 2021): (1) in It is the hydrostatic pressure of the fluid column inside the well. This is due to frictional pressure loss caused by flow within the well (pipe friction, typically expressed as pressure loss per unit distance along the pipe). (to quantify) This is due to the frictional pressure loss caused by the flow through the perforation orifice (perforation friction), and This is due to frictional pressure loss caused by the tortuous path of the flow through the near-wellbore region (near-wellbore friction). These pressure losses are volumetric flow rates. Functions: (2) in It is the depth measured along the well. It is the Darcy-Weisbach friction coefficient (e.g., Moody, 1944; Chen, 1979). It is fluid density. is the inner diameter of the well; (3) in This is the perforation friction coefficient (e.g., Cramer, 1987; Crump and Conway, 1988); and (4) in It is the near-wellbore friction coefficient, and It is the near-wellbore index, which is typically between 0.25 and 1 (see, for example, Cramer et al., 2019; Mondal et al., 2021).

[0005] Several known methods exist for determining these frictional pressure losses. Pipe friction is most commonly determined by empirical or theoretical models calibrated from experimental data of the flow loop (see, for example, Lord and McGowan, 1986; Keck et al., 2002; Yang et al., 2018). Theoretical models are based on the understanding that the Darcy-Weisbach pipe friction coefficient... The Reynolds number depends on the Reynolds number of the injected fluid (see, for example, Moody, 1944; Chen, 1979) and the pipe through which the fluid flows. The Reynolds number is related to the injection flow rate. The coefficient of friction is directly proportional to and inversely proportional to the fluid viscosity. The pipe friction coefficient also depends on the roughness of the pipe surface. In many hydraulic fracturing processes, chemicals known as friction modifiers are added to water or brine to suppress turbulence and reduce pipe friction. The reduction in pipe friction is influenced by the chemical composition and concentration of the friction modifier (see, e.g., Virk, 1975; Lord and McGowan, 1986; Keck et al., 2002; Yang et al., 2018). Pipe friction is also affected by the composition of the water or brine, measured, for example, by the total dissolved solids concentration, when produced water or brine from underground formations is used as the injected fluid or in the injected fluid, and this composition can interact with the friction modifier chemicals (see, e.g., Yang et al., 2018). All these factors contribute to considerable uncertainty in pipe friction (see, e.g., Cramer et al., 2019).

[0006] The uncertainty of pipe friction using the methods described above can be reduced by measuring pipe friction in a specific well of interest and with a specific fluid being used. Pipe friction measurements can be performed by placing two or more pressure sensors at different depths in the well, for example, one pressure sensor at the wellhead and another at a selected depth below the surface; determining the difference in pressure measured under different fluid flow conditions; and taking into account the hydrostatic pressure difference between the sensors. Due to the difficulties associated with deploying sensors within the well, especially at reservoir depths, the aforementioned methods are not widely used.

[0007] Perforation friction and near-wellbore friction are typically measured using a stepped-down flow rate test. In this test, the injected fluid flow rate is reduced in a series of steps and kept constant at each flow rate until the wellhead pressure stabilizes. The stabilized wellhead pressure is measured for different injected flow rates. The difference in wellhead pressure at different flow rates is attributed to the difference between pipe friction, perforation friction, and near-wellbore friction. After correcting for pipe friction, regression is typically performed on the pressure measurements using an empirical model as previously explained to determine perforation friction and near-wellbore friction (see, for example, Cramer et al., 2019; Mondal et al., 2021). If the measurements span a wide range of flow rates, perforation friction and near-wellbore friction can be uniquely separated because their dependence on flow rate differs. One challenge in applying this method is... Any pipe friction error that is directly proportional to the error will also lead to... Positive perforation friction error.

[0008] All of the foregoing considerations lead to the desire for an inexpensive and non-invasive method (meaning that the method does not require placing sensors below the surface in the well, but only at the wellhead) that can uniquely determine pipe friction, perforation friction, and near-wellbore friction. Summary of the Invention

[0009] One aspect of this disclosure is a method for determining fluid friction pressure loss in a well into which fluid is pumped. The method according to this aspect includes measuring the fluid pressure in the well while pumping at a first flow rate. The first flow rate is changed to a second flow rate, and the fluid pressure is measured again for a selected time. The pressure response of the well is modeled using selected values ​​of a parameter related to the pipe friction coefficient f. The modeled pressure response is compared with the measured pressure. The value of the parameter related to f is adjusted, and the modeling and comparison are repeated until the modeled pressure response substantially matches the measured pressure. The first flow rate is changed, and the measurement, modeling, comparison, adjustment of the parameter related to f, and repetition of modeling and comparison are repeated to determine the relationship between the value of the parameter related to f and the first flow rate.

[0010] Some implementations also include: continuing pressure measurement until a reflected pipe wave event is detected. At least for the first flow rate, the hydraulic impedance Z of the section is used. s The selected value of Z or a similar parameter describing the reflection (e.g., the reflection coefficient R) is used to model the pressure response of the well. s The value of Z is determined, and the pressure response is modeled repeatedly for the first and second flow rates until the modeled pressure response substantially matches the measured pressure. The first flow rate is changed and the aforementioned steps are repeated to determine the relationship between the first flow rate and Z. s The relationship between them, and using Z s The relationship between the first flow rate and the frictional pressure loss through the perforation and the frictional pressure loss in the near-wellbore region is used to estimate the values.

[0011] Some implementations also include determining the design frictional pressure loss through the well perforation and using the estimated frictional pressure loss through the well perforation to obtain a value for the perforation cluster efficiency.

[0012] Some implementations also include changing at least one composition parameter of the fluid pumped into the well, and repeating the modeling to determine the relationship between the at least one composition parameter and the relationship between f and the first flow rate.

[0013] Some implementations also include using the relationship between the following two to determine the optimal value of at least one component parameter: at least one component parameter, and the relationship between the parameter associated with f and the first flow rate.

[0014] Some implementations also include using the relationship between the value of the parameter related to f and the first flow rate to determine the optimal value of the first flow rate.

[0015] According to another aspect of this disclosure, a method for determining fluid frictional pressure loss in a well to which fluid is pumped includes measuring the fluid pressure in the well while pumping fluid at a first flow rate. The first flow rate is changed to a second flow rate different from the first flow rate, and fluid pressure is continued to be measured after the change for a selected time. The pressure response of the well is modeled using selected values ​​of a parameter associated with the pipe friction coefficient f. The modeled pressure response is compared with the measured pressure. The value of the parameter associated with f is changed, and the modeling and comparison are repeated until the modeled pressure response substantially matches the measured pressure. At least one component parameter of the pumped fluid is changed, and the foregoing operations are repeated, and the relationship between the value of the parameter associated with f and the at least one component parameter is determined.

[0016] Some implementations also include using the relationship to determine the optimal value of at least one component parameter.

[0017] Some implementations also include: continuing pressure measurement until a reflected pipe wave event is detected. At least for the first flow rate, the hydraulic impedance Z of the section is used. s The selected value of Z or a similar parameter describing the reflection (e.g., the reflection coefficient R) is used to model the pressure response of the well. s The value of Z is determined, and the pressure response is modeled repeatedly for the first and second flow rates until the modeled pressure response substantially matches the measured pressure. The first flow rate is changed and the aforementioned steps are repeated to determine the relationship between the first flow rate and Z. s The relationship between them, and using Z s The relationship between the first flow rate and the frictional pressure loss through the perforation and the frictional pressure loss in the near-wellbore region is used to estimate the values.

[0018] Some implementations also include determining the design frictional pressure loss through the well perforation and using the estimated frictional pressure loss through the well perforation to obtain a value for the perforation cluster efficiency.

[0019] According to another aspect of this disclosure, a method for determining the fluid frictional pressure loss in a well to which fluid is pumped includes measuring the fluid pressure in the well while pumping fluid at a first flow rate. The first flow rate is changed to a second flow rate different from the first flow rate, and fluid pressure is measured again after the change from the first flow rate to the second flow rate, at least until a first reflected wave event is detected in the measured pressure. The second flow rate is changed to a third flow rate different from the first and second flow rates, and fluid pressure is measured again after the change from the second flow rate to the third flow rate, until a second reflected wave event is detected in the measured pressure. The fluid pressure in the well is modeled using selected initial values ​​of the frictional pressure loss in the well, the frictional pressure loss in the wellbore perforation, and the frictional pressure loss in the near-wellbore region of the reservoir. The modeled pressure is compared with the measured pressure. The initial values ​​of the frictional pressure loss in the well, the frictional pressure loss in the wellbore perforation, and the frictional pressure loss in the near-wellbore region are adjusted, and the modeling of the fluid pressure in the well is repeated for all of the first, second, and third flow rates until the modeled fluid pressure in the well matches the measured pressure in the well.

[0020] Some implementations also include determining the design frictional pressure loss through the well perforation and using the estimated frictional pressure loss through the well perforation to obtain a value for the perforation cluster efficiency.

[0021] Some implementations also include changing at least one composition parameter of the fluid and repeating the modeling and comparison to determine the relationship between at least one composition parameter and frictional pressure loss in the well, frictional pressure loss in the wellbore perforation, and frictional pressure loss in the near-wellbore zone.

[0022] Other aspects of this disclosure include a non-transitory computer-readable medium having logic stored thereon that can be used to cause a programmable computer to perform actions, including actions performed in response to various measurements of fluid pressure within a well, the measurements being performed in a manner described with reference to the various methods disclosed herein.

[0023] Other aspects and potential advantages will become apparent from the following description and the appended claims. Attached Figure Description

[0024] Figure 1 Example implementations for generating and acquiring signals that can be used according to this disclosure are shown.

[0025] Figure 2 This shows a representative water hammer measurement at the wellhead using a high sampling rate pressure sensor.

[0026] Figure 3A and Figure 3B Showing the cause Figure 2An enlarged view of the water hammer caused by the decrease in the fourth fluid injection flow rate, as shown in the figure. Figure 3B The pressure measured at the wellhead is shown, and Figure 3A The injection flow rate is shown as the flow rate that is presumed to have caused water hammer.

[0027] Figure 4 and Figure 5 Examples of regressions of the friction coefficient as a function of flow rate Q and pressure loss per unit distance are shown graphically.

[0028] Figure 6A and Figure 6B The graph shows two water hammer sequences resulting from multiple consecutive flow rate drops during well shut-in.

[0029] Figure 7A and Figure 7B Showing targets Figure 6A The example shown is a magnified view of the water hammer reflection from the segment. Figure 7C and Figure 7D Showing targets Figure 6B The example shown is a magnified view of the water hammer reflection from the segment. Figure 7B and Figure 7D The pressure measured at the wellhead is shown, and Figure 7A and Figure 7C The injection flow rate is shown as the flow rate that is presumed to have caused water hammer.

[0030] Figure 8A The pressure loss due to perforation friction and near-wellbore friction is shown as a function of flow rate. Figure 8B The figure shows the flow rate as a function of the initial flow rate, with the flow rate decreasing. The reflection coefficient of the tube wave is bbl / minute. Figure 8C This shows the error in the reflection coefficient caused by neglecting near-wellbore friction.

[0031] Figure 9 The graph shows the wellhead pressure during the production enhancement period of a fracturing stage.

[0032] Figures 10A to 10D Showing the cause Figure 9 The image shows an enlarged view of the water hammer caused by two flow rate drops during the production ramp-up period, as marked in the image. Figure 10B and Figure 10D The pressure measured at the wellhead is shown, and Figure 10A and Figure 10C The injection flow rate is shown as the flow rate that is presumed to have caused water hammer.

[0033] Figures 11A to 11H Showing traffic from the same segment but with different initial flows The curves of the initial four water hammer events. Figure 11B , Figure 11D, Figure 11F and Figure 11G The pressure measured at the wellhead is shown, and Figure 11A , Figure 11C , Figure 11E and Figure 11H The injection flow rate is shown as the flow rate that is presumed to have caused water hammer.

[0034] Figure 12A and Figure 12B An example of flow rate reduction is shown, which is too slow to uniquely determine pipe friction and perforation friction. However, for this situation, a modified acoustic friction analysis using a calibrated pipe friction model can be employed to determine perforation friction and near-wellbore friction. Figure 12B The pressure measured at the wellhead is shown, and Figure 12A The injection flow rate is shown as the flow rate that is presumed to have caused water hammer.

[0035] Figure 13 An example computing system is shown that various methods can be implemented according to this disclosure. Detailed Implementation

[0036] This disclosure provides a method known as “acoustic tribology analysis” to determine frictional pressure losses caused by the wellbore, perforations in the wellbore, and near-wellbore formations using water hammer (tube wave) analysis. Typically, the method according to this disclosure can be performed in conjunction with pumping fluid into the well and measuring the fluid pressure in the well. Fluid pumping can be performed, for example, in conjunction with hydraulic fracturing, which is performed on the well in one or more zones or sections of a reservoir fluidly connected to the well. Fluid is pumped (injected) into the well at a certain flow rate, which can be determined either by direct measurement (e.g., via a flow meter) or by inference from indirect measurements (e.g., the operating flow rate of the fluid pump). This flow rate is the one referred to below in the description of how the method according to this disclosure is implemented. Pressure can be measured near the upper end of the well (e.g., at the wellhead) using a fast-response sensor, such as a quartz pressure transducer. Such measurements can be digitally sampled for processing as described herein; for such purposes, the digital sampling rate of pressure measurements may be 10 Hz or greater, but the sampling rate, sensor type, or sensor location does not limit the scope of this disclosure.

[0037] A. Signal acquisition used in conjunction with the method according to this disclosure Figure 1This is a schematic diagram of an example well data acquisition system (“System”) that may be used in some implementations. System 100 includes components associated with a well, including: one or more fluid pumps 101, such as hydraulic fracturing fluid pumps or other fluid processing pumps; sensors in communication with well fluid pressure, such as hydrophones or pressure transducers 102; and data acquisition and processing equipment 103 (refer to below). Figure 13 (Described in more detail); well conduit 104, for example, a casing or liner disposed in a well permeating the reservoir; plug or wellbore bottom 106; formation fracture network 107, which is hydraulically connected to the well through perforations 108 formed in the well conduit (e.g., casing or liner) 104. Nearby wells 109 may exist in the area of ​​interest. One or more water hammer pulses 105 may be generated by pump 101, for example, by a step change in pump flow rate. The water hammer pulses 105 travel along the well in the form of tube waves. Sensor 102 may be, for example, but not limited to, non-invasive devices such as pressure transducers, accelerometers, and hydrophones or optical fibers, any one or all of which may be disposed at or near the top of the well (e.g., the wellhead) to continuously measure the pressure, pressure-time derivative, and / or particle motion of the fluid in the well before, during, and after pumping of a treatment fluid (e.g., hydraulic fracturing treatment fluid). The characteristics of such data can be analyzed to obtain parameters, such as frictional pressure loss along the well and through the perforation, as explained below, which will be explained in more detail below.

[0038] Reference Figure 13 Further interpretation of the computer or computing system can be achieved by implementing various example methods for pressure measurements as described herein to obtain values ​​related to friction and pressure losses due to friction in various parts of the well and surrounding reservoir.

[0039] B. Acoustic Friction Analysis Dunham et al. (2023) described a method for determining wellbore and perforation friction, which uses wellhead pressure measurements to determine friction during water hammer caused by sudden changes in the injection flow rate of fluid entering the well, such as during fracturing. Water hammer includes tubular waves, a type of wave that travels at a velocity... The propagating pressure wave, the velocity of which depends on the fluid density ρ, fluid compressibility, and well compliance. Wave propagation in the well is governed by the following expression (see, Wylie et al., 1993): (5) (6) in It is time. It is volumetric flow rate, and It is the pressure at a depth x in the well minus the hydrostatic pressure. It also requires... and The initial conditions and two boundary conditions, one of which is at the wellhead ( At the location of the second boundary condition, and at the depth of the fracturing section under study (along the axial position of the well) ( The initial conditions correspond to steady flow under constant injection flow rate. (7) (8) in This is the pressure at the wellhead before the flow rate change that causes water hammer. f represents the pipe friction coefficient. At the wellhead, the fluid injection flow rate is specified as a boundary condition. At time... The injected traffic changes rapidly; in this example, reducing the amount... , so that: (9) in It is a unit step function.

[0040] The method described in this paper does not require a step function (instantaneous) flow rate change (decline), but the flow rate change does need to be fast enough to isolate certain waveform features used in the analysis. The boundary conditions for this section are expressed by the following expression: (10) The total pressure loss caused by perforation friction and near-wellbore friction in a specific treatment section is defined by the following expression: (11) Already from fracturing pressure Subtract hydrostatic pressure ,because It is defined as the pressure that is adjusted to remove hydrostatic pressure.

[0041] Pipe waves can be generated in a well, for example, by such rapid (“step”) changes in fluid flow rate that can induce so-called water hammer; the resulting pipe waves propagate along the well and interact with any hydraulic fractures in the perforation, near-wellbore region, and formation, in a manner that can ultimately induce reflected pipe waves that propagate upwards along the well back to the wellhead.

[0042] Figure 2The diagram illustrates the fluid pressure in a well undergoing fluid injection, for example, during the pumping of hydraulic fracturing fluid, with variations in the fluid injection (flow) rate at selected times. The pressure response to the flow rate variation represents the water hammer from pressure measurements taken, for example, near the wellhead using a fast-response (capable of high-frequency response) pressure sensor. Pressure measurements should be sampled at sufficiently high flow rates to properly sample the waveform characteristics used in this analysis and avoid aliasing (see, for example, Wang et al., 2008; Dung et al., 2021).

[0043] The representative water hammer oscillations generated during the shut-in process at the end of the hydraulic fracturing enhancement treatment, resulting from four consecutive drops in fluid injection flow rate, were observed. Figure 2 The curves in the figure are shown. Although the decrease in flow rate is comparable in magnitude, the water hammer differs in oscillation amplitude and number of oscillations. These differences are caused by the nonlinear dependence of the initial fluid injection (flow) flow rate before the flow rate change. Figure 1 Each of the four water hammer events shown is achieved by injecting flow rates from... Rapidly reduce to And thus it is generated. Each type of water hammer has considerable... , but with different value, The injection flow rate prior to the change in injection flow rate is indicated. The following description is interpreted in relation to a decrease in fluid injection flow rate; it should be clearly understood that, in principle, the method according to this disclosure can be performed using an increase in injection flow rate, provided that the change in injection flow rate is sudden enough to induce tubular waves in the well.

[0044] Figure 3A and Figure 3B Showing the cause Figure 2 An enlarged view of the water hammer caused by the decrease in the fourth fluid injection flow rate, as shown in the figure. Figure 3B Shown by Figure 2 The image shows a magnified view of the water hammer caused by the fourth injection flow rate drop. Key features used in the following acoustic tribology analysis are marked. Figure 3B The features marked as [1], [2] and [3] are, respectively, the pressure drop accompanying the decrease in flow rate, the further pressure drop caused by pipeline friction, and the reflection from the specific fracturing section under construction.

[0045] As in Figure 3A and Figure 3B It can be observed that the decrease in injected flow rate is accompanied by a decrease in the amount of injected flow rate. The pressure decreases proportionally ( Figure 3B The features in [1]), where Z can be determined by the following expression. T : (12) Represents the hydraulic impedance of the pipe wave, where This is the cross-sectional area of ​​the well (e.g., well casing or liner). As the pipe wave propagates along the well, it is attenuated due to pipe friction. This attenuation is represented in wellhead pressure as an additional decrease in pressure after the initial pressure drop accompanying a decrease in injected flow rate. Figure 3B Features in [2]). Measurements of the slope of the pressure drop “ramp” can provide measurements of pipe friction (see Dunham et al., 2023). Reflection ( Figure 3B The analysis of the features in [3] can provide constraints on perforation friction and near-wellbore friction, as explained below.

[0046] C. Calibrated model for pipe friction Pipeline friction measurements can be performed using acoustic friction analysis of water hammer sampling at different fluid injection flow rates. This analysis can be performed for multiple water hammers within a fracturing section and / or multiple water hammers across multiple sections within a single well. The foregoing provides information for different fluid injection (flow) rates. The pipe friction value, quantified as, for example, pressure loss per unit distance. or coefficient of friction Or related parameters. Regressions can be performed on these data to provide a mathematical model for pipe friction or pressure loss as a function of flow rate (see, for example, Virk, 1975). Regressions can also include data across a range of fluid compositions or friction modifier concentrations, where parameters quantifying these fluid compositions or friction modifier concentrations are included in the model.

[0047] Figure 4 and Figure 5 Examples of regressions of the friction coefficient and pressure loss per unit distance as a function of the injection flow rate Q are shown graphically. Figure 4 This shows the friction coefficient of the Darcy-Weisbach pipeline under different flow rates. A compilation of acoustic friction measurements (indicated by circles). Figure 4 The curve in the middle is... The best-fit model (deterministic expression) of the form, where the model parameters and It can be determined through nonlinear least squares regression.

[0048] Figure 5 This shows the pipe friction pressure loss per unit distance, in psi / ft, performed at different injection flow rates, in bbl / min. A compilation of acoustic friction calculations (indicated by circles). Figure 5 The curve in the figure is the best-fit quadratic polynomial obtained through linear least squares regression: .

[0049] Tube wave reflection Next, consider the reflection of tube waves from the fracturing section (characteristic in Figure 3 [3]). Reflection coefficient Defined as the ratio of the amplitude of the pressure change carried by the reflected tube wave to the amplitude of the pressure change carried by the incident wave. For tube waves with sufficiently small amplitudes, the reflection from this section is determined by the hydraulic impedance of the tube wave and the hydraulic impedance of the fracturing section. The ratio is controlled. In this case, the reflectance coefficient is given by the following expression (see, for example, Paillet and White, 1982): (13) The hydraulic impedance of the treatment section is contributed by perforation friction and near-wellbore friction. These components of the system are hydraulically connected in series, making... (14) in It is the hydraulic resistance of the perforation, and This refers to the hydraulic resistance in the near-wellbore region. For sufficiently small flow rate changes, hydraulic resistance is defined as the ratio of pressure change to flow rate change, or... Therefore, according to equations (3) and (4) in the background section of this paper: (15) and (16) The reflection coefficient can also be calculated for pipe waves of arbitrary amplitude. This is done by solving the pipe wave equations (5) and (6) near the fracturing treatment section where reflection occurs. Near the relevant treatment section, the pressure and flow rate within the well are obtained using a characteristic method with the following expressions: (17) (18) The penultimate term in equations (17) and (18) is the incident wave, and the last term is the reflected wave with relative amplitude. In these expressions for incident and reflected waves, pipe wave attenuation due to pipe friction is neglected because calculating the reflection coefficient is unnecessary, as reflection depends only on processes occurring near that section. However, if the measured depth to that section is long enough that the pipe wave amplitude decreases significantly from its amplitude near the wellhead, the flow rate carried by the pipe wave decreases (as shown in the above expressions). The reflection coefficient (indicated by the wellhead flow rate drop) may be less than the flow rate drop at the wellhead. The expression for the reflection coefficient provided below should be evaluated using the decaying flow rate drop, but using the wellhead flow rate drop will only introduce a small error. At the location of the fracturing section ( At point ), pressure and flow rate are given by the following expressions: (19) (20) Reflectance coefficient This can be obtained by solving the following nonlinear equation: .(twenty one) The expression for the pressure drop on the left is obtained as follows: first, using the initial flow rate, then using the flow rate at reflection given by the last term in equation (20), the pressure at that segment given by equation (10) is evaluated, and then the pressure difference is determined. Assume the hydrostatic pressure... and fracturing pressure Difference and frictional pressure The change is relatively small. The pressure drop on the right comes from the last term in equation (19). Equation (21) can be solved using the bisection method, the secant method, or Newton's law. Use any scalar root-finding method, such as the Newton-Raphson method, to solve it. When When the flow rate is sufficiently small, the left side of equation (21) can be approximated by performing a Taylor series expansion of the flow rate around the initial flow rate, resulting in the following expression: ,(twenty two) in Therefore, we can conclude that: ,(twenty three) As stated in equation (13).

[0050] Figure 6A and Figure 6B A comparison of two examples with different perforation cluster designs is provided, both from the same well in the Bakken Formation, North Dakota. Figure 6A The example shown has 14 clusters and 28 perforations, and Figure 6B The example shown has only one cluster and three perforations. All perforation diameters are identical. The perforation friction coefficient... It is inversely proportional to the square of the number of perforations, so for a cluster design, And therefore The expected value is 87 times higher. This difference in perforation friction is... Figure 7B and Figure 7D The magnified view of the water hammer reflection shown is clearly evident. For Figure 6A , Figure 7A and Figure 7B The 14-cluster design shown has a negative reflectance ( This indicates that the hydraulic impedance of this section is less than the hydraulic impedance of the pipe wave. ).for Figure 6B , Figure 7C and Figure 7D The cluster design shown has a positive reflectance ( ). This indicates that the hydraulic impedance of this section is greater than the hydraulic impedance of the pipe wave. This aligns with the increased perforation resistance and therefore perforation friction of the cluster design.

[0051] Figures 7A to 7D Showing targets Figure 6A and Figure 6B The two examples shown are magnified views of water hammer reflections from each segment. Reflections from a segment with 14 clusters and 28 perforations exhibit low... The resulting negative reflection coefficient, which in Figure 7B As shown in the image. Figure 7D The reflection from a segment with one cluster and three apertures is shown to have a high [missing information - likely a typo, should be "high"]. The resulting positive reflection coefficient. Figure 7A and Figure 7C The diagram shows the change in injection flow rate that causes water hammer.

[0052] The relative contributions of the perforation and near-wellbore regions during the reflection process can be quantified as a function of flow rate using the expression provided above. Figures 8A to 8C Examples of parameters representing a limited-access hydraulic fracturing design are shown (listed in Table 1). These parameters give frictional pressure losses of 2000 psi from the perforation and 500 psi from the near-wellbore region at an injection flow rate of 100 bbl / min, which is typical for increased production.

[0053] Table 1 Representative parameters used to calculate the reflection coefficient in Figure 7

[0054] Figure 8A The pressure loss due to perforation friction and near-wellbore friction is shown as a function of flow rate, and... Figure 8B The figure shows the flow rate as a function of the initial flow rate, with the flow rate decreasing. The reflection coefficients of the tube waves at bbl / min. The reflection coefficients labeled “perf+NWB” are calculated by solving equation (21), and the reflection coefficients labeled “linearized” are calculated using equation (13). The reflection coefficients calculated according to equation (21) when near-wellbore friction is ignored are also shown (labeled “perf only”). Figure 8C The reflection coefficient error is shown when near-wellbore friction is ignored. It is obtained as the difference between the "perf only" reflection coefficient and the "perf+NWB" reflection coefficient.

[0055] As in Figures 8A to 8C It can be observed that at sufficiently high flow rates, the wave reflection characteristics are mainly affected by the perforation, with the contribution from the near-wellbore region being negligible. Dunham et al. (2023) analyzed the water hammer generated by the flow rate drop during the shut-in process when perforation friction was assumed to control wave reflection. The background flow rate was high enough to justify neglecting near-wellbore friction.

[0056] Calculation of improved through-hole cluster efficiency using an erosion model The friction coefficient of the perforation depends on the fluid density. Number of perforations in this section and perforation diameter : ,(twenty four) in This is a dimensionless flow coefficient that quantifies the effect of flow contraction or expansion through a perforation. Typical values ​​for the flow coefficient range from 0.6 to 0.95 (e.g., Cramer, 1987; Crump and Conway, 1988). The method described by Dunham et al. (2023) or its variations described below can be used. The measured values ​​are used to provide an estimate of the number of open perforations in a segment. This is called the perforation cluster efficiency and is defined as: (25) The "design" value is evaluated using the number and diameter of perforations in the well completion design according to equation (24), and the "measured" value is obtained through acoustic friction analysis. The values ​​used in the design calculation are assumed to be... , and Representing the actual value, then It is the ratio of the actual number of perforations to the designed number.

[0057] However, it is well known that erosion caused by the turbulent flow of fluid and proppant through the perforation increases the perforation diameter. The flow coefficient is also thought to increase, but this effect is usually much smaller than the change in diameter. Therefore, accurate calculation of perforation cluster efficiency requires the use of an erosion model. Several available models are documented in the literature, such as Cramer (1987), which has been validated using downhole pressure gauge data and ultrasonic measurements of perforation diameter (Cramer et al., 2023). These models provide a function of the total injected proppant. and The expression is as follows. The following examples use an erosion model similar to Cramer's (1987).

[0058] Measurements during production enhancement (fracturing) Acoustic friction analysis can be performed during production ramp-up using, for example, the decrease in fluid injection flow rate that occurs when one or more pumps temporarily slow down or stop. By performing this method at different times during production ramp-up, the evolution of pipe friction and perforation friction, as well as perforation cluster efficiency, can be monitored. This monitoring can be used to measure changes in pipe friction when the composition of the injected fluid is altered, for example, by adjusting the concentration of the anti-friction agent. It can also be used to monitor perforation cluster efficiency and detect sand blockage when proppant blocks one or more perforation clusters. Figure 9 and Figures 10A to 10D An example of the aforementioned method is shown.

[0059] Figure 9 A graph showing wellhead pressure during production enhancement in a fracturing stage is presented. The two times marked with arrows correspond to the flow rate decrease that generates water hammer, which has characteristics required for acoustic triboanalysis. Figures 10A to 10D Showing the cause Figure 9 The arrows in the image indicate magnified views of the water hammer caused by two flow rate drops during the production ramp-up. Acoustic friction analysis provides... The value, used in conjunction with a perforation erosion model, is used to calculate perforation cluster efficiency. The efficiency is close to 100% during the first water hammer that occurs near the start-up of a production ramp-up, but drops to approximately 50% by the time the second water hammer occurs. This suggests that half of the clusters may experience "sand blockage" midway through the production ramp-up.

[0060] Determine both perforation friction and near-wellbore friction When analyzing reflected pipe waves, there may be instances where the injected flow rate is too low to justify ignoring near-wellbore impedance. This typically occurs when the injected flow rate decreases through a series of flow rate drops (e.g., ...). Figure 2 (As shown in the diagram) The reduced step-down flow rate test occurs during shut-in periods when the injected flow rate drops to zero. Under conditions where the segment impedance has significant contributions from both perforation friction and near-wellbore friction, analysis of water hammer caused by a single flow rate drop is insufficient to uniquely determine perforation friction and near-wellbore friction. However, the perforation contribution and near-wellbore contribution can be separated by analyzing multiple water hammers at different initial fluid flow rates (injection flow rates).

[0061] First, consider multiple water hammers, each starting with a different initial fluid flow rate (injection flow rate). For measurement... The injected flow is represented as Assume these have sufficiently small amplitudes to justify using equation (13) to determine the reflection coefficient. For each water hammer, the background discharge... The hydraulic impedance of the lower section can be determined by measuring the amplitude of the reflected pipe wave; or by combining the impedance boundary conditions of the section and numerically solving the pipe wave equations (5) and (6), wherein the impedance boundary conditions are described by the following expressions: (26) Instead of the boundary conditions given by equation (10), we next use equations (14)-(16) for segment impedance to formulate the unknowns. , and The regression problem. The residual of each measurement is defined as: (27) Furthermore, regression problems determine the unknowns by minimizing a certain norm of the residuals. For example, the L2 norm can be used to obtain nonlinear least squares problems.

[0062] Figures 11A to 11H Showing traffic from the same segment but with different initial flows The initial four water hammer events are shown in the graphs. The water hammer equations are solved for each segment, and the segment impedance is adjusted. The best-fit data was then determined by minimizing the mismatch between the segment impedance and the sum of the perforation impedance and the near-wellbore impedance. , and The value of . For this example, the best-fit value is , and .

[0063] If the water hammer amplitude is not small enough to guarantee the use of equation (13) to calculate the reflection coefficient, it can be determined by joint waveform inversion. , and Solving the water hammer equation (10) with bottom boundary conditions for multiple water hammers, and adjusting... , and This aims to minimize a suitable mismatch (e.g., the L2 norm of the difference between the numerical solution obtained by summing all water hammer data and the wellhead pressure data). This is similar to the previously described method, but instead of performing waveform inversion for each segment individually, waveform inversion is performed simultaneously for all segments. This method avoids introducing impedance boundary conditions and separate regression steps.

[0064] Alternatively, after correcting for the attenuation caused by pipe friction, the reflection coefficient can be calculated by solving equation (21) for each water hammer. Then, a regression can be established in a similar manner as before, but now using the nonlinear reflection coefficient equation (21) instead of the impedance equation (14).

[0065] Slow flow rate decreases (changes) There is a decrease or change in fluid injection flow rate that is too gradual to produce [results]. Figure 3BThe waveform characteristics shown are as follows. For example, the initial pressure drop ramp caused by pipe friction may overlap with reflections caused by perforation friction and near-wellbore friction. Under high flow conditions, when near-wellbore friction is negligible, the pressure response of water hammer is controlled by the combined effects of pipe friction and perforation friction. Both of these depend on the square of the flow rate, making it challenging or impossible to uniquely separate them. Figure 12A and Figure 12B An example of this situation is shown in the figure.

[0066] Example implementations of the methods according to this disclosure The method according to this disclosure may include some or all of the following actions: 1. Inject initial (first) traffic. The fluid is pumped into the well.

[0067] 2. Change the injection flow rate (increase or decrease) to a second injection flow rate. It should be noted that The sign depends on whether the injected flow rate is increasing or decreasing. The injected flow rate can be changed, for example, by altering the speed of the fluid pump, closing or opening a valve, adding or removing a pump from the flow, or any combination thereof. As explained earlier, the change in injected flow rate should have a sufficiently short duration to induce pipe waves to propagate in the well.

[0068] 3. Measure the fluid pressure in the well using a pressure sensor that is in fluid communication with the fluid in the well, such as a quartz pressure transducer, an optical fiber with a Bragg grating, or any other suitable pressure sensor. The well fluid pressure may originate from... Become This is caused by changes in the injection flow rate. Fluid pressure can be determined by measuring the pressure during pumping at the initial injection flow rate, followed by measuring the pressure after the injection flow rate changes. The pressure sensor can be placed at any convenient location in the well; it should be understood that proximity to the surface end of the well, such as in or near the wellhead, may be more convenient than other locations along the well. The pressure measurement following the flow rate change should be sustained for a sufficient period to determine the properties of the pressure, particularly the gradual pressure drop following the flow rate change. Figure 3B The slope of the feature in the well [2]). In fact, pressure can be measured until a pipe wave reflection from a deeper feature in the well is detected, as indicated below.

[0069] 4. Determine the hydraulic impedance of the pipe wave. For example, equation (12) is used to calculate the pipe wave generated by the change in injection flow rate. As shown in equation (12), Z is determined. TThe values ​​for fluid density, wave velocity, and well cross-sectional area are required. Fluid density can be determined by combining the known liquid phase density of the fluid (e.g., water) with the amount and density of proppant and / or other additives in the fluid pumped into the well. Wave velocity can be determined, for example, based on the bidirectional travel time of the wave to the end of the fracturing section and back to the pressure sensor. The bidirectional travel time can be determined from the measured well fluid pressure data as the time of reflection arrival minus the time of flow drop. Wave velocity can also be determined according to a known expression (see, for example, Norris, 1990), which includes the density and compressibility of the fluid in the well (which are well-known or readily determined) and the well's flexibility (which depends on the thickness of the well tubing or casing, the elastic modulus of the casing and the elastic modulus of the formation, and other parameters). The well cross-sectional area is known because it is part of the well's engineering design.

[0070] 5. Determine the changes in flow rate. This can be achieved, for example, by using a sensor such as a flow meter to measure changes in flow rate, determining changes in the operating flow rate of the fluid pump or the opening of a control valve, or by using the determined pipe wave hydraulic impedance to calculate the changes in flow rate. .

[0071] 6. Model the pipe wave propagation from the time of flow rate change up to the time of detection of the first reflection in the pressure measurement (as explained with reference to Figure 3). Such a model can be generated by solving equations (5)-(9) to obtain a set of expected well fluid pressures relative to time based on the inputs of the above equations. The aforementioned equations can be solved from the time of flow rate change up to the time of detection of the pipe wave reflection or longer, as will be explained further below. The pipe wave reflection occurs after the injection flow rate change. The time has arrived. The measured depth of the fractured section during well assessment. Known from the well's engineering design, the wave velocity *c* can be estimated at least as explained by the reference method for determining the wave hydraulic impedance. For the purpose of limiting the scope of this part of the method, it is not necessary to model the wave propagation until reflection. Modeling the wave propagation for a certain amount of time after the initial flow rate change is sufficient to determine the reference method. Figure 3B The slope of the pressure drop characteristic in the wellhead pressure measurements [2] is explained. However, using all pressure data during the flow rate variation up to the time of reflection arrival makes it possible to obtain a more accurate determination of the slope in the pressure data of characteristic [2].

[0072] 7. Will be by The modeled well fluid pressure, expressed relative to time, is compared with the measured well fluid pressure relative to time. The pipe friction coefficient in the pipe wave propagation model can be adjusted. The modeled pressure is recalculated and can be repeatedly compared with the measured well pressure until the modeled fluid pressure in the well substantially matches the measured fluid pressure in the well.

[0073] 8. Then, the injection flow rate can be adjusted for one or more different initial fluid flows. Repeat steps 1-7, changing the injection flow rate after each different initial injection flow rate. Pressure measurements corresponding to the various initial injection flow rates and subsequent changes in injection flow rate can be used to obtain the value of f corresponding to the initial injection flow rate Q. The foregoing may include a set of data points corresponding to the initial injection flow rate and the associated friction coefficient f. As a non-restrictive example, Figure 2 The graph in the figure represents the well fluid pressure, where the flow rate of the fluid moving into the well decreases four times in succession, where the initial flow rate of each successive flow rate decrease corresponds to a different value of the initial fluid injection flow rate, and the flow rate decrease after the initial fluid injection flow rate can induce pipe waves in the well.

[0074] 9. This set of data points can be... Perform regression analysis to determine the flow to be used as the initial injection flow. The function The parameters in the mathematical model (e.g., a deterministic expression or relation). In some implementations, the relation can be used to determine the optimal value of the initial injected (flow) flow.

[0075] 10. In some implementation schemes, the pipe friction coefficient determined as explained above is used. Then you can target the initial injected traffic. Each value determines the pipe friction pressure loss per unit distance. For this set of data points Perform regression analysis to determine the flow to be used as the initial injection flow. The function Parameters in the mathematical model (e.g., a deterministic expression or relation). Frictional pressure loss per unit distance. It can be used, for example, to calculate or determine the well fluid pressure at any location along the well during fluid pumping. In one instance, the well fluid pressure at a perforation in the well casing or tubing can be determined.

[0076] 11. In some implementations, actions 1-7 can be repeated for different fluid compositions. Or targeting Alternatively, a regression can be performed using similar metrics related to pipe friction, this time considering the dependence on fluid composition in addition to the initial fluid flow rate. That is, one or more parameters related to the composition of the pumped fluid (e.g., viscosity, proppant concentration, amount of anti-friction agent) can be adjusted, and the process repeated to obtain a relationship between one or more composition parameters and pipe friction parameters. In some embodiments, this relationship can be used to determine optimal values ​​for the composition parameters. For example, but not limited to, the relationship can be used to determine the anti-friction agent concentration that produces the lowest total fluid pumping financial cost.

[0077] 12. In some implementation schemes, the wave velocity is determined. In some implementations, the wave velocity is determined during the operation of determining the wave hydraulic impedance, as explained above.

[0078] 13. In some embodiments, and using c as determined above or otherwise obtained, the pipe wave propagation over an additional time period is modeled, the pipe wave propagation including pipe wave reflections from the well treatment section under evaluation. The modeled pipe wave propagation is compared with measured pressure data from before the time the injection flow rate changes from the initial injection flow rate until after the detection of reflected pipe waves.

[0079] 14. In some implementation schemes, the hydraulic resistance of the fracturing section is adjusted. Or any other quantitative measure of the reflection conditions at the fracturing section, and repeat the modeling of the tube wave propagation and comparison with the measured pressure until the modeled well fluid pressure matches the measured well fluid pressure as closely as possible.

[0080] 15. In some implementations, different initial injection flows are considered. Repeat steps 1-7 and 12-14 to obtain a set of data points. Section hydraulic impedance It can be replaced by any other quantitative measure of the reflection condition.

[0081] 16. In some implementation schemes, execution Regression of data points to determine the perforation friction coefficient Near-wellbore friction coefficient and the friction index near the wellbore In this part of the method, the hydraulic resistance of the section... This can be replaced by any other quantitative measure of the reflection conditions at that point. (Perforation friction coefficient) Near-wellbore friction coefficient and the friction index near the wellbore This can be used, for example, to determine the fluid pressure in any one or more fractures in a reservoir that is hydraulically connected to the well, for example, through perforations in the well casing or tubing. As explained in the Background section of this document, determining such pressures is important for the design and execution of hydraulic fracturing procedures.

[0082] 17. In some implementations, fluid density may be used. Number of perforations in sections, zones, or wells and individual perforation diameter To calculate or determine the perforation friction coefficient The design value. Perforation diameter. It can be determined, for example, by measurement, based on information published by the perforation projectile manufacturer, or by using a perforation corrosion model.

[0083] 18. Use the perforation friction coefficient explained above. The determined value and the explanation above. Calculate the perforation cluster efficiency using design values. The value of perforation cluster efficiency can be used, for example, to determine when a perforated section or zone in a well becomes partially or completely blocked, where the well operator can choose to reperforate the poorly performing section. Perforation cluster efficiency can also indicate when the perforation diameter increases from its previous value. Excessive expansion due to erosion. In another example use, well operators can decide to stop pumping if they determine low perforation efficiency midway through a production enhancement process, in order to prevent fractures from becoming longer than expected and to save on fluid and proppant costs as well as pump energy.

[0084] In some implementations, f (or ), , and The value can be determined through the following operations: Repeat steps 1-7 as explained above, with pressure measurements continuing until a reflected tube wave event is detected.

[0085] For the bottom boundary conditions, use equation (10), using f (or ), , and The initial values ​​are selected to model the propagation of the tube wave during reflection. Equation (10) has the function defined in Equation (11). Equation (11) has the function defined in Equations (3) and (4). Then, for all values ​​of the initial flow rate, the modeled pressure response is compared with the measured pressure response. That is, for such... Figure 2 The entire set of pressure measurements shown is compared.

[0086] Adjust f (or ), , and The value of is determined until, simultaneously for all different flow rates, the modeled pressure response matches the measured wellhead pressure. Because this uses data from multiple initial flow rates, the three parameters f (or ), and .

[0087] In some implementations, once all friction parameters f (or ), , and Then, the fluid pressure in the subsurface reservoir can be estimated based on the measured fluid pressure (e.g., at the wellhead) and flow rate. Such pressure can be used, for example, to predict fracturing behavior during a fracturing process, or to determine the optimal fluid flow rate for pumping successive fracturing stages.

[0088] In some implementations, perforation cluster efficiency can be used to estimate a fraction of the total fluid volume pumped into the well through multiple perforation clusters during pumping of a treatment fluid (e.g., hydraulic fracturing treatment fluid). For each section or zone in the treated well, the perforation friction coefficient can be determined, as explained above, by detecting the corresponding reflected tube wave event for each section during multiple flow rate variations during pumping of the treatment fluid. It can be The value and The perforation efficiency is obtained by comparing the engineering design values ​​with the perforation efficiency. This is determined through repeated testing during the process. The variation in the perforation efficiency over time can be determined during pumping of one or more segments. Repeatedly determining the perforation friction coefficient may include subsequent flow rate variations and pressure measurements during segment pumping, as explained herein. The calculated variation in perforation efficiency can be used to allocate a portion of the total number of perforations or perforation clusters in that segment to the total fluid flow entering that segment, corresponding to the perforation efficiency calculated for that state with reference to the total number of perforations or perforation clusters in that segment.

[0089] Figure 12 illustrates an example of a flow rate decrease that is too slow for acoustic friction analysis as explained above, as is typically performed using waveform inversion to compare with... Figure 3B The waveform feature matching shown is used to uniquely separate pipe friction and perforation friction. This situation can be handled by using a calibrated model to determine pipe friction, leaving perforation friction as a residual unknown in the acoustic friction waveform inversion.

[0090] In such cases, perforation friction from water hammer can still be determined if an independent constraint on pipe friction exists. One way to obtain this constraint is to perform acoustic tribology analysis to develop a calibrated model for pipe friction as a function of flow rate and fluid type (e.g., type and concentration of anti-friction agent, proppant concentration), as previously explained. Waveform inversion is performed as described by Dunham et al. (2023) or as previously shown. However, the calibrated model is used for pipe friction, leaving perforation friction as a remaining unknown (and near-wellbore friction is also unknown if the injection flow rate is sufficiently low). These unknowns become the model parameters in the inversion, which are tuned to best fit the water hammer data.

[0091] Figure 13 An example computing system 1200 according to some embodiments is shown. The actions described above with reference to the example embodiments can be performed on a computer or computer system, wherein pressure measurements obtained as described can be input into and processed in the computer or computer system, as explained above. The computing system 1200 can be an individual computer system 1201A or an arrangement of distributed computer systems. The individual computer system 1201A may include one or more analysis modules 1202, which can be configured to perform various tasks and controls according to some embodiments, such as the tasks explained with reference to Figures 3-12. In order to perform these various tasks, the analysis module 1202 can operate independently or in coordination with one or more processors 1204, which can be connected to one or more storage media 1206. For example, a display device (1205) of any known type of graphical user interface can signal to the processor 1204 to enable the user to input commands and / or data and display the execution results of a set of instructions according to this disclosure.

[0092] Processor 1204 can also be connected to network interface 1208 to allow individual computer system 1201A to communicate with sensors, one or more additional individual computer systems and / or computing systems (e.g., 1201B, 1201C, and / or 1201D) via data network 1210. It should be noted that computer systems 1201B, 1201C, and / or 1201D may or may not share the same architecture as computer system 1201A and may be located in different physical locations. For example, computer systems 1201A and 1201B may be located at a drilling site while communicating with one or more computer systems (e.g., 1201C and / or 1201D), which may be located on shore, on a ship, in one or more data centers, and / or in different countries on different continents.

[0093] A processor may include, but is not limited to, a microprocessor, a microcontroller, a processor module or subsystem, a programmable integrated circuit, a programmable gate array, or other control or computing device.

[0094] The storage medium 1206, which captures data in a tangible medium, can be implemented as one or more computer-readable or machine-readable storage media. It should be noted that, although in Figure 13 In the example implementation, storage medium 1206 is shown as being disposed within a personal computer system 1201A. However, in some implementations, storage medium 1206 may be distributed within and / or across multiple internal and / or external housings of the personal computing system 1201A and / or additional computing systems (e.g., 1201B, 1201C, 1201D), or distributed via a network (“cloud”). Storage medium 1206 may include, but is not limited to, one or more different forms of memory, including semiconductor memory devices such as dynamic or static random access memory (DRAM or SRAM), erasable and programmable read-only memory (EPROM), electrically erasable and programmable read-only memory (EEPROM), and flash memory; magnetic disks, such as fixed disks, floppy disks, and removable disks; other magnetic media, including magnetic tape; optical media, such as optical discs (CDs) or digital video discs (DVDs); or other types of storage devices. It should be noted that computer instructions used to cause any individual computer system or computing system to perform the tasks described above may be set on a single computer-readable or machine-readable storage medium, or may be set on multiple computer-readable or machine-readable storage media distributed across a multi-component computing system having one or more nodes. Such one or more computer-readable or machine-readable storage media may be considered part of an article (or article of manufacture). An article or article of manufacture may refer to any single component or multiple components manufactured. The one or more storage media may be located in a machine that executes the machine-readable instructions, or at a remote site from which the machine-readable instructions may be downloaded via a network for execution.

[0095] It should be understood that computing system 1200 is only one example of a computing system, and any other implementation of the computing system may have more or fewer components than those shown, and may be combined. Figure 13 Additional components not shown in the example implementation, and / or the computing system 1200 may have Figure 13 The different configurations or arrangements of the components shown in the figure. Figure 13 The various components shown can be implemented in hardware, software, or a combination of both, and include one or more signal processing and / or application-specific integrated circuits.

[0096] Furthermore, the processing methods described above can be implemented by one or more functional modules in an information processing device that run, for example, a general-purpose processor, or by a dedicated chip such as an ASIC, FPGA, PLD, or other suitable device. These modules, combinations of these modules, and / or combinations thereof with general hardware are all included within the scope of this disclosure.

[0097] In addition to determining the fluid friction pressure loss through perforations in the wellbore or casing and near the wellbore (in formations close to the well), the method according to this disclosure can also determine the fluid friction pressure loss at any location along the entire well. This method may include determining perforation efficiency, wherein perforations on the wellbore or casing adjacent to the fracturing section can be evaluated, and re-perforating of poorly performing areas in the well if deemed necessary by the well operator.

[0098] Based on the principles and exemplary embodiments described and illustrated herein, it will be appreciated that modifications in arrangement and detail of the exemplary embodiments may be made without departing from such principles. The foregoing discussion focuses on particular embodiments, but other configurations are also contemplated. In particular, even when expressions such as “implementation” are used herein, these phrases imply the general possibility of reference to embodiments and are not intended to limit this disclosure to specific embodiment configurations. As used herein, these terms may refer to the same or different embodiments that can be combined into other embodiments. Generally, unless otherwise specified, any embodiment referenced herein can be freely combined with any one or more other embodiments referenced herein, and any number of features of different embodiments can be combined with each other. Although only a few examples have been described in detail above, those skilled in the art will readily appreciate that many modifications are possible within the scope of the described examples. Therefore, all such modifications are intended to be included within the scope of this disclosure as defined in the appended claims.

[0099] References cited in this disclosure Chen, NH (1979). An explicit equation for friction factor in pipe. Industrial&Engineering Chemistry Fundamentals, 18(3), 296-297. Cramer, D. D. (1987). The application of limited-entry techniques inmassive hydraulic fracturing treatments. Presented at the SPE ProductionOperations Symposium, Oklahoma City, Oklahoma, 8-10 March. SPE-16189-MS. Cramer, D., Friehauf, K., Roberts, G.,&Whittaker, J. (2019).Integrating DAS, treatment pressure analysis and video-based perforationimaging to evaluate limited entry treatment effectiveness. Presented at theSPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands,Texas, USA, February 2019. SPE-194334-MS. Cramer, D., White, M.,&Douglas, C. (2023). Correlating Surface andDownhole Perforation Entry-Hole Measurements Lead to Development of ImprovedPerforating Systems. Paper presented at the SPE Hydraulic FracturingTechnology Conference and Exhibition, The Woodlands, Texas, USA, January2023. SPE-212335-MS. Crump, J. B.,&Conway, M. W. (1988). Effects of perforation-entryfriction on bottomhole treating analysis. Journal of Petroleum Technology, 40(08), 1041-1048. Dung, N., Cramer, D., Danielson, T., Snyder, J., Roussel, N.,&Ouk, A.(2021). Practical applications of water hammer analysis from hydraulicfracturing treatments. Paper presented at the SPE Hydraulic FracturingTechnology Conference and Exhibition, Virtual, May 2021. SPE-204154-MS. Dunham, E. M., Zhang, J.,&Moos, D. (2023). Constraints on PipeFriction and Perforation Cluster Efficiency from Water Hammer Analysis.Presented at the SPE Hydraulic Fracturing Technology Conference andExhibition, The Woodlands, Texas, USA, February 2023. SPE- 212337-MS. Economides, M., Oligney, R.,&Valkó, P. (2002). Unified fracturedesign: Bridging the gap between theory and practice. Orsa Press. Keck, R. G., Nehmer, W. L.,&Strumolo, G. S. (1992). A new method forpredicting friction pressures and rheology of proppant-laden fracturingfluids. SPE Production Engineering, 7(01), 21-28. Lord, D. L.,&McGowen, J. M. (1986). Real-time treating pressureanalysis aided by new correlation. Paper presented at the SPE AnnualTechnical Conference and Exhibition, New Orleans, Louisiana, October 1986.SPE-15367-MS Mondal, S., Zhang, M., Huckabee, P., Ugueto, G., Jones, R., Vitthal,S., Nasse, D.,&Sharma, M. (2021). Advancements in step down tests to guideperforation cluster design and limited entry pressure intensities-Learningsfrom field tests in multiple basins. SPE Hydraulic Fracturing TechnologyConference and Exhibition. SPE-204147-MS. Moody, L. F. (1944). Friction factors for pipe flow. Trans. ASME, 66,671-684. Paillet, F. L.,&White, J. E. (1982). Acoustic modes of propagation inthe borehole and their relationship to rock properties. Geophysics, 47(8),1215-1228. Ugueto C, G. A., Huckabee, P. T., Molenaar, M. M., Wyker, B.,&Somanchi, K. (2016). Perforation cluster efficiency of cemented plug and perflimited entry completions; Insights from fiber optics diagnostics. SPEHydraulic Fracturing Technology Conference. SPE-179124-MS. Virk, P. S. (1975). Drag reduction fundamentals. AIChE Journal, 21(4), 625-656. Wang, X., Hovem, K., Moos, D.,&Quan, Y. (2008). Water hammer effectson water injection well performance and longevity. Paper presented at the SPEInternational Symposium and Exhibition on Formation Damage Control,Lafayette, Louisiana, USA, February 2008. SPE-112282-MS. Wylie, E. B., Streeter, V. L.,&Suo, L. (1993). Fluid transients insystems. Englewood Cliffs, NJ: Prentice Hall. Yang, B., Zhao, J., Mao, J., Tan, H., Zhang, Y.,&Song, Z. (2019).Review of friction reducers used in slickwater fracturing fluids for shalegas reservoirs. Journal of Natural Gas Science and Engineering, 62, 302-313.

Claims

1. A method for determining fluid frictional pressure loss in a well into which fluid is pumped, comprising: a. Measure the fluid pressure in the well while pumping fluid at the first flow rate; b. Change the first flow rate to a second flow rate different from the first flow rate, and measure the fluid pressure for a selected time after the change; c. Model the well pressure response using selected values ​​of parameters related to the pipe friction coefficient f; d. Compare the modeled pressure response with the measured pressure; e. Adjust the values ​​of the parameters related to f and repeat the modeling and comparison until the modeled pressure response substantially matches the measured pressure; f. Change the first flow rate and repeat (a) to (e), and determine the relationship between the value of f and the first flow rate.

2. The method according to claim 1, further comprising: g. Continue measuring the pressure until a reflected tube wave event is detected; h. At least for the first flow rate, the pressure response of the well is modeled using selected values ​​of parameters related to the reflection coefficient; i. Adjust the parameters related to the reflection coefficient and repeatedly model the pressure response for the first flow rate and the second flow rate until the modeled pressure response substantially matches the measured pressure; j. Change the first flow rate and repeat (h) and (i) to determine the relationship between the first flow rate and the parameters related to the reflection coefficient; as well as k. Use the relationship between parameters related to f and the first flow rate, and the relationship between parameters related to the reflection coefficient and the first flow rate, to estimate the values ​​of frictional pressure loss through the perforation and frictional pressure loss in the near-wellbore region.

3. The method of claim 2 further includes determining the design frictional pressure loss of the well perforation and using the estimated frictional pressure loss through the well perforation to obtain a value of the perforation cluster efficiency.

4. The method of claim 3 further includes using the perforation cluster efficiency to distribute fluid flow to the perforation clusters that account for a corresponding proportion of the total number of perforation clusters.

5. The method of claim 4, further comprising repeatedly acquiring values ​​of the perforation cluster efficiency and distributing fluid flow rates at selected times during the pumping of the treatment fluid into the well.

6. The method of claim 2, wherein the parameters related to the reflection coefficient include the hydraulic impedance of the fractured section in the well.

7. The method according to claim 1, further comprising: Change at least one composition parameter of the fluid being pumped into the well; as well as Repeat (a) through (f) to determine the relationship between at least one component parameter and the relationship between f and the first flow rate.

8. The method of claim 7, further comprising using the relationship between the at least one component parameter and the relationship between the parameter associated with f and the first flow rate to determine the optimal value of the at least one component parameter.

9. The method of claim 1, further comprising determining an optimal value for the first flow rate using the relationship between the value of a parameter related to f and the first flow rate.

10. A method for determining fluid frictional pressure loss in a well into which fluid is pumped, comprising: a. Measure the fluid pressure in the well while pumping fluid at the first flow rate; b. Change the first flow rate to a second flow rate different from the first flow rate, and measure the fluid pressure after the change for a selected time; c. Model the well pressure response using selected values ​​of parameters related to the pipe friction coefficient f; d. Compare the modeled pressure response with the measured pressure; e. Adjust the values ​​of the parameters related to f and repeat the modeling and comparison until the modeled pressure response substantially matches the measured pressure; f. Change at least one composition parameter of the pumped fluid and repeat (a) to (e), and determine the relationship between the value of the parameter associated with f and the at least one composition parameter.

11. The method of claim 10, further comprising using the relationship to determine the optimal value of the at least one component parameter.

12. The method of claim 10, further comprising: g. Continue measuring the pressure until a reflected tube wave event is detected; h. At least for the first flow rate, the pressure response of the well is modeled using selected values ​​of parameters related to the reflection coefficient; i. Adjust the values ​​of the parameters related to the reflection coefficient, and repeatedly model the pressure response for the first flow rate and the second flow rate until the modeled pressure response substantially matches the measured pressure; j. Change the first flow rate and repeat (h) and (i) to determine the relationship between the first flow rate and the parameters related to the reflection coefficient; as well as k. Use the relationship between parameters related to f and the first flow rate, and the relationship between parameters related to the reflection coefficient and the first flow rate, to estimate the values ​​of frictional pressure loss through the perforation and frictional pressure loss in the near-wellbore region.

13. The method of claim 12, further comprising determining the design frictional pressure loss of the well perforation, and using the estimated frictional pressure loss through the well perforation to obtain a value for the perforation cluster efficiency.

14. The method of claim 12, wherein the parameters associated with the reflection coefficient include the hydraulic impedance of the fractured section in the well.

15. A method for determining fluid frictional pressure loss in a well into which fluid is pumped, comprising: a. Measure the fluid pressure in the well while pumping fluid at the first flow rate; b. Change the first flow rate to a second flow rate different from the first flow rate, and measure the fluid pressure after changing from the first flow rate to the second flow rate, at least until a first reflected tube wave event is detected in the measured pressure; c. Change the second flow rate to a third flow rate that is different from the first flow rate and the second flow rate, and measure the fluid pressure after changing from the second flow rate to the third flow rate until a second reflected tube wave event is detected in the measured pressure; d. Model the fluid pressure in the well using selected initial values ​​for frictional pressure loss in the well, frictional pressure loss in the wellbore perforation, and frictional pressure loss in the near-wellbore zone of the reservoir; e. Compare the measured pressure with the modeled fluid pressure, and adjust the initial values ​​of frictional pressure loss in the well, frictional pressure loss in the wellbore perforation, and frictional pressure loss in the near-wellbore area, and repeat the modeling of fluid pressure in the well; as well as f. For all of the first flow rate, the second flow rate, and the third flow rate, repeat (e) until the modeled fluid pressure in the well matches the measured pressure in the well.

16. The method of claim 15, further comprising determining the design frictional pressure loss of the well perforation, and using the estimated frictional pressure loss through the well perforation to obtain a value for the perforation cluster efficiency.

17. The method of claim 15, further comprising changing at least one composition parameter of the fluid and repeating (a) to (f) to determine the relationship between the at least one composition parameter and frictional pressure loss in the well, frictional pressure loss in the wellbore perforation, and frictional pressure loss in the near-wellbore zone.

18. A non-transitory computer-readable medium storing instructions thereon, the instructions being operable to cause a programmable computer to perform a method for determining fluid frictional pressure loss in a well into which fluid is pumped, the method comprising actions including: a. To make the computer accept the measured value of the fluid pressure in the well as obtained when the fluid is pumped at a first flow rate as input; b. Make the computer accept as input the measured value of the fluid pressure in the well obtained after the first flow rate is changed to a second flow rate different from the first flow rate and at least until the pressure change lasts for a selected time; c. In a computer, the pressure response of the well is modeled using selected values ​​of parameters related to the pipe friction coefficient f; d. In the computer, compare the modeled pressure response with the measured pressure; e. In the computer, adjust the values ​​of the parameters related to f and repeat the modeling and comparison until the modeled pressure response substantially matches the measured pressure; f. Accept the pressure measurement obtained after changing the first flow rate as input to the computer, and repeat (a) to (e) in the computer, and determine the relationship between the value of the parameter related to f and the first flow rate.

19. The non-transitory computer-readable medium of claim 18, further comprising logic capable of operating to cause a computer to perform actions, said actions including: g. Accept measurements of fluid pressure in the well obtained up to the detection of a reflected wave event as input to the computer; h. In a computer, at least for the first flow rate, the pressure response of the well is modeled using selected values ​​of a parameter related to the reflection coefficient; i. In a computer, adjust the values ​​of parameters related to the reflection coefficient and repeatedly model the pressure response for the first flow rate and the second flow rate until the modeled pressure response substantially matches the measured pressure; j. In a computer, the first flow rate is varied and (h) and (i) are repeated to determine the relationship between the first flow rate and the parameters related to the reflection coefficient; as well as k. In the computer, the values ​​of frictional pressure loss through the well perforation and frictional pressure loss in the near-wellbore region are estimated using the relationship between parameters related to f and the first flow rate, and the relationship between parameters related to the reflection coefficient and the first flow rate.

20. The non-transitory computer-readable medium of claim 19, further comprising logic capable of operating to cause a computer to perform actions, said actions including determining the design frictional pressure loss of the well perforation and using the estimated frictional pressure loss through the well perforation to obtain a value for the perforation cluster efficiency.

21. The non-transitory computer-readable medium of claim 20, further comprising logic capable of operating to cause a computer to perform actions, said actions including distributing fluid flow rates to a corresponding proportion of the total number of perforation clusters using the perforation cluster efficiency.

22. The non-transitory computer-readable medium of claim 21, further comprising logic capable of operating to cause a computer to perform actions, said actions including repeatedly acquiring values ​​of perforation cluster efficiency and distributing fluid flow rates at selected times during the pumping of the processing fluid into the well.

23. The non-transitory computer-readable medium of claim 19, wherein the parameters related to the reflection coefficient include the hydraulic impedance of the fracturing section in the well.

24. The non-transitory computer-readable medium of claim 18, further comprising logic capable of operating to cause a computer to perform actions, said actions including: After at least one compositional parameter of the fluid pumped into the well changes; as well as Repeat (a) through (f) to determine the relationship between the following two: the at least one component parameter, and the relationship between the parameter associated with f and the first flow rate.

25. The non-transitory computer-readable medium of claim 18, further comprising logic for causing the computer to perform actions, the actions including determining, in the computer, an optimal value for the at least one component parameter using the relationship between the at least one component parameter and the relationship between the parameter associated with f and the first flow rate.

26. The non-transitory computer-readable medium of claim 18, further comprising logic capable of operating to cause a computer to perform actions, said actions including: In a computer, the optimal value of the first flow rate is determined by using the relationship between the value of a parameter related to f and the first flow rate.

27. A non-transitory computer-readable medium storing instructions thereon, the instructions being operable to cause a programmable computer to perform a method for determining fluid frictional pressure loss in a well into which fluid is pumped, the method comprising actions including: a. Accepts measurements of the fluid pressure in the well obtained when pumping fluid at a first flow rate as input to the computer; b. Accept measurements of fluid pressure in the well obtained during a selected time period after the first flow rate is changed to a second flow rate different from the first flow rate as input to the computer; c. In a computer, the pressure response of the well is modeled using selected values ​​of parameters related to the pipe friction coefficient f; d. In the computer, compare the modeled pressure response with the measured pressure; e. In the computer, adjust the values ​​of the parameters related to f and repeat the modeling and comparison until the modeled pressure response substantially matches the measured pressure; f. In a computer, at least one composition parameter of the pumped fluid is changed and (a) to (e) are repeated, and the relationship between the value of the parameter associated with f and the at least one composition parameter is determined.

28. The non-transitory computer-readable medium of claim 27, further comprising logic capable of operating to cause a computer to perform an action, said action including using the relationship to determine an optimal value for the at least one component parameter.

29. The non-transitory computer-readable medium of claim 27, further comprising logic capable of operating to cause a computer to perform actions, said actions including: g. Accept measurements of fluid pressure in the well obtained up to the detection of a reflected wave event as input to the computer; h. In a computer, at least for the first flow rate, the pressure response of the well is modeled using selected values ​​of a parameter related to the reflection coefficient; i. In a computer, adjust the values ​​of parameters related to the reflection coefficient and repeatedly model the pressure response for the first flow rate and the second flow rate until the modeled pressure response substantially matches the measured pressure; j. In a computer, the first flow rate is varied and (h) and (i) are repeated to determine the relationship between the first flow rate and the parameters related to the reflection coefficient; as well as k. In the computer, the values ​​of frictional pressure loss through the well perforation and frictional pressure loss in the near-wellbore region are estimated using the relationship between parameters related to f and the first flow rate, and the relationship between parameters related to the reflection coefficient and the first flow rate.

30. The non-transitory computer-readable medium of claim 27, wherein the parameters related to the reflection coefficient include the hydraulic impedance of the fracturing section in the well.

31. The non-transitory computer-readable medium of claim 27, further comprising logic capable of operating to cause a computer to perform actions, said actions including, in the computer, determining the design frictional pressure loss of the well perforation, and using the estimated frictional pressure loss through the well perforation to obtain a value for the perforation cluster efficiency.

32. A non-transitory computer-readable medium storing instructions thereon, the instructions being operable to cause a programmable computer to perform a method for determining fluid frictional pressure loss in a well into which fluid is pumped, the method comprising actions including: a. Accepts measurements of the fluid pressure in the well obtained when pumping fluid at a first flow rate as input to the computer; b. Accept measurements of fluid pressure in the well obtained at least until a first reflected tube wave event is detected in the measured pressure after the first flow rate is changed to a second flow rate different from the first flow rate; c. Accept measurements of fluid pressure in the well obtained after the second flow rate is changed to a third flow rate different from the first flow rate until a second reflected tube wave event is detected in the measured pressure as input to the computer; d. In the computer, the fluid pressure in the well is modeled using selected initial values ​​of frictional pressure loss in the well, frictional pressure loss in the wellbore perforation, and frictional pressure loss in the near-wellbore zone of the reservoir; e. In the computer, the measured pressure is compared with the modeled fluid pressure, and the initial values ​​of frictional pressure loss in the well, frictional pressure loss in the wellbore perforation, and frictional pressure loss in the near-wellbore area are adjusted. The modeling of fluid pressure in the well is then repeated. f. For all of the first flow rate, the second flow rate, and the third flow rate, repeat (e) until the modeled fluid pressure in the well matches the measured pressure in the well.

33. The non-transitory computer-readable medium of claim 32, further comprising logic capable of operating to cause a computer to perform actions, said actions including, in the computer, determining the design frictional pressure loss of the well perforation and using the estimated frictional pressure loss through the well perforation to obtain a value for the perforation cluster efficiency.

34. The non-transitory computer-readable medium of claim 32, further comprising logic capable of operating to cause a computer to perform actions, said actions including, after changing at least one composition parameter of the fluid, repeating (a) to (f) to determine the relationship between said at least one composition parameter and frictional pressure loss in the well, frictional pressure loss in the wellbore perforation, and frictional pressure loss in the near-wellbore zone.

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