Method for determining perforation erosion and related parameters from tube waves induced in a well

Abstract

A method for determining well perforation erosion during pumping a treatment includes measuring pressure in a well during pumping the treatment and for a first change in flow rate of the pumping, determining a first well pipe friction pressure loss and a first perforation friction pressure loss using tube wave events in the measured pressure. A number of effective perforations using the first perforation friction pressure loss. A second change in flow rate of the pumping is made and a second well pipe friction pressure loss and a second perforation friction pressure loss are determined using tube wave events in the measured pressure. A number of perforations remaining effective is determined using the second determined perforation friction pressure loss. A volume distribution of fluid among the remaining effective perforations is determined, and using the volume distribution, an entry hole diameter of the remaining effective perforations is determined.

Description

METHOD FOR DETERMINING PERFORATION EROSION AND RELATED PARAMETERS FROM TUBE WAVES INDUCED IN A WELL BACKGROUND

[0001] This disclosure relates to the field of treatment of subsurface wells used to extract valuable minerals such as hydrocarbons from subsurface formations. More particularly, the present disclosure relates to specific uses for parameters determinable using pressure measurements made during pumping fluid treatments such as hydraulic fracturing treatments used to enhance production rates and fluid recovery from such wells.

[0002] US Patent Application Publication No. 2023 / 0228185 filed by Dunham et al.discloses a method for using induced tube waves caused by flow rate changes of fluid in a pipe (e.g., a casing or liner in a well) to determine frictional fluid pressure loss along the pipe and through perforations in the pipe that connect the well hydraulically to formations outside the well. By being able to calculate such frictional fluid pressure losses, it is possible to determine the fluid pressure at the mouth of one or more fractures in the formations. Such pressure is important in conducting and evaluating hydraulic fracture treatment parameters such as fluid density, fluid viscosity, pumping rate, pumping pressure and proppant concentration during pumping.

[0003] During pumping a treatment, some of the perforations may become ineffective (lose permeability to further fluid movement through them). Continued pumping at any given rate will therefore result in greater flow rate through the remaining effective perforations. Increased flow may result in corresponding increase in erosion of the perforations. It is desirable to have a method for determining which perforations remain effective, and how such effectiveness affects perforation erosion during the treatment procedure.SUMMARY

[0004] According to one aspect of the present disclosure, a method for determining well perforation erosion during pumping a treatment includes measuring pressure in a well during pumping the treatment and for a first change in flow rate of the pumping, idetermining a first well pipe friction pressure loss and a first perforation friction pressure loss using tube wave events in the measured pressure. A number of effective perforations using the first perforation friction pressure loss. A second change in flow rate of the pumping is made and a second well pipe friction pressure loss and a second perforation friction pressure loss are determined using tube wave events in the measured pressure. A number of perforations remaining effective is determined using the second determined perforation friction pressure loss. A volume distribution of fluid among the remaining effective perforations is determined, and using the volume distribution, an entry hole diameter of the remaining effective perforations is determined.

[0005] In some implementations, the determining the number of effective perforations at either the first or second flow rate change comprises determining a friction coefficient of the perforations. The determining the friction coefficient of the perforations comprises initializing a value of the friction coefficient of the perforations, modeling a pressure with respect to time of a reflected tube wave in the well, comparing the measured pressure to the modeled reflected tube wave pressure, adjusting the friction coefficient of the perforations and repeating modeling the reflected tube wave pressure until a difference between the modeled tube wave pressure and a change in measured pressure from the reflected tube wave falls below a selected threshold.

[0006] Some implementations further comprising repeating the determining the entry hole diameter as above at selected times during pumping the treatment, and determining changes in the entry hole diameter over time.

[0007] Some implementations further comprise determining existence of a leaking plug in the well.

[0008] Some implementations further comprise either (i) increasing a rate of the pumping or (ii) terminating pumping based on a determined plug leak magnitude.

[0009] Some implementations further comprise terminating the pumping when the entry hole diameter exceeds a selected threshold.

[0010] Some implementations further comprise terminating the pumping when a runaway fracture is detected.

[0011] A non-transitory computer readable medium according to another aspect of the present disclosure has logic stored thereon operable to cause a programmable computer to perform actions to carry out the method of the prior aspect of the present disclosure and its various implementations as set forth above.

[0012] Other aspects and possible advantages will be apparent from the description and claims that follow.BRIEF DESCRIPTION OF THE DRAWINGS

[0013] FIG. 1 shows example implementations of equipment that may be used to acquire signals usable with a method according to the present disclosure.

[0014] FIG. 2 illustrates the principle of Uniformity Index (UI).

[0015] FIG 3 shows a graph with respect to time during pumping a fracture treatment of pressure, volume of proppant and frac fluid pumping rate.

[0016] FIG. 4 shows a graph of perforation efficiency with respect to time during pumping of a fracture treatment.

[0017] FIG. 5 shows a graph of volumes of fracture fluid accepted by each of a plurality of perforation clusters in a fracture treatment stage and an associated UI.

[0018] FIG. 6 shows a graph of measured pressure in a well compared to predicted pressure in the well.

[0019] FIG. 7 shows a graph of measured pressure in the well compared to predicted pressure in the well in the case of a leaking plug in the well.

[0020] FIG. 8 shows a graph of measured pressure in the well compared to predicted pressure in the well in the case of unexpectedly high erosion of perforations in a well casing.

[0021] FIG. 9 shows an example of the continuous UI values during the treatment stage.

[0022] FIG. 10 shows an example of cluster level proppant volumes and the calculated proppant UI at the end of a treatment stage.

[0023] FIG. 11 shows an example of the Near Wellbore (NWB) pressure drop variation during the stage.

[0024] FIG. 12 shows an example of the cluster level perforation entry hole diameter (EHD) at the end of the stage. For this example the initial EHD of all clusters were 0.44 inch.

[0025] FIG. 13 shows a graph of predicted surface pressure compared to predicted surface pressure when there are no problems with the well or the treatment.

[0026] FIG. 14 shows a graph of predicted surface pressure compared to predicted surface pressure when a plug at the bottom of a stage is leaking.

[0027] FIG. 15 is a graph of predicted surface pressure compared to measured surface pressure where there is substantial perforation erosion.

[0028] FIG. 16 shows schematically a computer system that may be used in accordance with the present disclosure.DETAILED DESCRIPTION

[0029] FIG. 1 is a schematic diagram of an example well data acquisition system (“system”) that may be used in some implementations. The system 100 comprises components associated with a well including one or more fluid pumps 101, such as hydraulic fracturing fluid pumps or other fluid treatment pumps; sensors such as hydrophones or pressure transducers 102 in fluid pressure communication with the well; a data acquisition and processing apparatus 103 (described in more detail below); a well pipe 104, e.g., a casing or liner disposed in a well drilled through a reservoir formation; a plug or wellbore bottom 106; fracture network 107 in hydraulic communication with the well through perforations 108 made in the well pipe (e.g., casing or liner) 104. A nearby well 109 may be present in the area of interest. One or more water hammer pulses 105 may be generated by the pumps 101, such as by a step change in the rate of pumping, or a pressurepulse may be generated by other means such as a fluid pressure pulse generator. In any case, the pressure pulses induce tube waves in the well. The pressure pulse(s) therefore travel along the well in the form of tube waves. The sensors 102 may be nonintrusive devices such as pressure transducers, accelerometers, and hydrophone(s), any or all of which may be disposed in a location on or near the top of the well (e.g., the wellhead) to measure pressure, pressure time derivative and / or particle motion of fluid in the well continuously before, during, and after pumping of a treatment such as an hydraulic fracture treatment. Characteristics of such data may be analyzed as explained below to obtain parameters such as frictional pressure loss along the well and through the perforations also as will be explained in more detail below.

[0030] One attribute of pumping a treatment such as a fracture treatment is that fluid being pumped into one or more specific axial intervals in the well (a “stage”) may include variations between fluid movement rates among spaced apart groups (“clusters”) of perforations, in each of which are a number of perforations spaced apart by relatively small distances (e.g., 1 to 6 inches). The clusters may be separated from each other by several feet to several tens of feet. Thus, some clusters may accept relatively large fractions of the total fluid flow, while others may accept little to none. FIG. 2 illustrates the principle. In the upper part of FIG. 2, all perforation clusters in a stage accept the same fractional amount (e.g., 10 barrels / min) of a total fluid pumping rate (e g., 50 barrels / min). A “uniformity index” (UI) in such case is unity (1). The lower part of FIG. 2 illustrates that the various perforation clusters accept differing fractional amounts of the total fluid flow. In such case the UI will be less than unity.

[0031] During pumping of treatments such as hydraulic fracture treatments, fluid properties and fluid pumping rates may be changed to cause the fluid pumping to obtain specific results. In FIG. 3, such changes in the pumping rate 303 and accompanying fluid pressure 301 may take place at the initiation of a first pad segment 300, early in the proppant ramp at 302, later in the proppant injection at 304 and near the end of proppant injection at 306, and near the end of the fracture stage pumping at 308. Corresponding fluid flow rates are shown at 303, and cumulative volumes of proppant are shown at curve

[0032] As will be readily apparent from the disclosure in US Pat. App. Pub. No.2023 / 0228185 filed by Durham et al. and incorporated herein by reference, each such flow rate change and accompanying pressure change may induce tube waves (105 in FIG. 1) in the well (104 in FIG. 1). Characteristics of the tube waves may be used, as explained in the ‘185 publication, to determine frictional pressure loss in the well pipe and in the perforations. Thus, during pumping a fracture treatment stage at varying flow rates, it is possible to determine pipe and perforation friction at each of such times over the course of pumping the fracture stage.

[0033] FIG. 4 illustrates that for each flow rate change, and accompanying calculations of pipe friction pressure loss and perforation friction pressure loss, it is possible to calculate a perforation efficiency. Perforation efficiency represents how many of the perforations in the stage being pumped are taking fluid or are active (perforation efficiency = number of active perforations / total number of perforations). In the present method, the peroration frictional pressure loss may be calculated using the method disclosed in the ‘185 publication, and the foregoing calculated perforation friction pressure loss is compared to the ideal perforation friction loss. Ideal perforation frictional pressure loss is the pressure loss that would be expected if all the perforations were taking fluid. Such expected fluid pressure loss may be determined, e.g., using mathematical models of fluid flow through various size apertures with reference to the hydraulic properties of the fluid being pumped. If the number of perforations that take fluid is less than all of the perforations, then the perforation friction loss will be larger. How much larger will determine the perforation efficiency as follows:

[0034] The foregoing perforation efficiency may be used in determining the UI. In a method according to the present disclosure, the UI may be determined as follows.

[0035] The method for determining pipe friction pressure loss and perforation friction pressure loss as set forth in the ‘185 publication may be performed during a fracture stage for a plurality of pumping rate changes.

[0036] Perforation efficiency may be calculated each time the frictional pressure losses are determined during the stage, using, e.g., the above formula. Such multiple calculations of perforation efficiency enable determining the variation of perforation efficiency over the entire fracture treatment stage.

[0037] The perforation efficiency determinations and the fracture treatment total injected fluid volume data may be used to determine the evolution of the fluid volume for each perforation cluster in the stage Vi.

[0038] Use the cluster-level volumes Vi to determine a proxy for the uniformity of each fracture stage using the following expression:UI = 1 - STD(Vi) / (mean(Vi) ) (2) where STD is the standard deviation.

[0039] The fluid volume taken through each perforation cluster Vi may be obtained as follows. The perforation efficiency values calculated as above will be used to calculate the number of the effective perforations, Nperfe^ at any time during pumping.Nperfeff(t) = eperf (f) * Nperf(3)

[0040] where eperf is the perforation efficiency, and Nperf is the total number of perforations within the entire stage. Here it is assumed all the perforations are the same hydraulically, and it is not known which of the perforations in the stage and various clusters are effective; it is known from eperf only how many of the total number perforations are taking fluid. With the number of how many of the perforations are taking fluid, it is possible to calculate the slurry volume increment for each perforation.

[0041] Where AVtot(t) is total slurry volume pumped at each time increment (e.g., 1 effsecond) and Al^eris the slurry volume increment for each perforation. Note that only effective perforations are taking fluid, and the fluid volume attributable to the inactive perforations remains constant. Because the volume contribution for each perforation isdeterminable, it is then possible calculate the volume attributable to each effective perforation at the end of each time increment (At) as follows:

[0042] Finally, the volume of fluid accepted by each of the perforations may be used to calculate the volume of fluid accepted by each cluster in the stage by adding the volumes taken by all the perforations within each cluster. Expressed alternatively, the individual perforation fluid volumes may be multiplied by the number of perforations in a specific cluster to obtain the fluid volume for such cluster. The same type of calculation can be used to calculate the proppant volume accepted by each cluster in the stage.

[0043] FIG. 5 shows an example calculation of cluster level volumes and the calculated UI at the end of the stage. For this example, the end of stage UI was determined as 0.835. Such determinations may be made at a plurality of times, e.g., at the time of one or more flow rate changes, during pumping or one or more stages in a fracture treatment.

[0044] FIG. 9 shows an example of the continuous UI values during the treatment stage.FIGS. 9 through 13 show different attributes of the same treatment stage.

[0045] FIG. 10 shows an example of cluster level proppant volumes and the calculated proppant UI at the end of the stage. For this example, the end of stage UI was determined to be 0.53.

[0046] As will be readily apparent from the disclosure in US Pat. App. Pub. No.2023 / 0228185 filed by Durham et al. and incorporated herein by reference, each such flow rate change and accompanying pressure change may induce tube waves (105 in FIG. 1) in the well (104 in FIG. 1). Characteristics of the tube waves may be used, as explained in the ‘185 publication, to determine frictional pressure loss in the well pipe and in the perforations in the casing or liner in the well. Thus, during pumping a fracture treatment stage at varying flow rates, it is possible to determine pipe and perforation friction, and consequent pressure loss at each of such times over the course of pumping the fracturestage. The measured pressure in the well and the determined frictional pressure losses at such times may be used to calibrate other pressure parameters in the well. Such calibrated pressure parameters may be used to estimate or predict the expected measured pressure (surface pressure) at times intermediate the times at which the friction parameters and associated pressures are determined. The predicted pressure may be compared to the measured pressure to evaluate certain mechanical properties of the well and certain mechanical faults in the well.

[0047] The method disclosed in the ‘ 185 patent, while not limiting the scope of the present disclosure, may be generally characterized as follows. Fluid, e.g., hydraulic fracturing slurry is moved through a well pipe (e.g., well casing or liner) and perforations in the well pipe at a first rate, e.g., during pumping a fracture treatment. A pressure of the fluid is measured, typically proximate the top of the well, while the fluid is moving at the first rate. The rate of moving fluid is changed to a second rate so as to induce tube waves in the well pipe. Pressure of the fluid flowing at the second rate is measured. The measured pressure flowing at the first rate and at the second rate are used to determine frictional fluid pressure loss in the well pipe and frictional fluid pressure loss through the perforations based on pressure change with respect to time and characteristics of propagating tube waves in the well.

[0048] The determining fluid pressure loss in the well pipe comprises determining a pipe friction factor based on pressure change with respect to time after the changing flow rate, and prior to a reflected tube wave reaching a position of the measuring pressure.

[0049] The determining pipe friction factor comprises initializing a value of the friction factor, modeling the pressure change with respect to time based on the initialized pipe friction factor, comparing the modeled pressure change to the measured pressure change, and adjusting the pipe friction factor and repeating the modeling until a difference between the modeled pressure change and the measured pressure change falls below a selected threshold.

[0050] The determining frictional fluid pressure loss in the perforations comprises determining a friction coefficient of the perforations. The determining the frictioncoefficient of the perforations comprises initializing a value of the friction coefficient of the perforations, modeling a pressure with respect to time of a reflected tube wave in the well based on the initialized value of friction factor, comparing the measured pressure to the modeled reflected tube wave pressure, adjusting the friction coefficient of the perforations and repeating modeling the reflected tube wave pressure until a difference between the modeled tube wave pressure and a change in measured pressure from the reflected tube wave falls below a selected threshold.

[0051] Surface pressure in a well during pumping fluid into a formation fracture adjacent to the well is a result of other well pressure parameters, and may be represented by the following equation:wherein, ps= surface (measured) pressure, Pfrac=formation fracture pressure, pH= hydrostatic pressure of the column of fluid in the well, pPipe= pipe friction pressure loss, Pperf=perforation friction pressure loss, PNWB= nearwellbore (NWB) friction pressure loss.

[0052] In a method according to the present disclosure, to calculate the expected surface pressure with respect to time (ps(t)) it is necessary to calculate the variation of all the foregoing pressure components in Eq. (7) with respect to time. The foregoing may be obtained by performing the following actions:1. perform the method disclosed in the ‘185 publication at each of two or more fluid flow rate changes (“steps”) during pumping a “stage” of the fracture treatment, and calculate the friction pressure loss components at each of these flow rate changes, namely, pipe friction pressure loss, perforation friction pressure loss and near wellbore (NWB) friction pressure loss.2. The foregoing friction pressure loss components may then be used to calculate the fracture pressure at the particular time (p, superscript step) of each of the one or more fluid flow rate changes. The foregoing may be calculated using the following equation: step step . step step step stepzr)Pfrac = Ps + PH ~ Ppipe ~ Pperf ~ PNWB (8)in which ptep= represents the measured (surface) pressure, pf]tep= hydrostatic pressure, which may be obtained as the product of true vertical depth of the well and the fracture fluid slurry density, which may be measured or obtained from the fracture treatment operator, PpipP= pipe friction pressure loss obtained as explained above, Pper / =perforation friction pressure loss obtained as explained above, and p^^B= NWB friction pressure loss obtained as explained above.

[0053] To obtain values of Pfrac(t) at times intermediate the time of the rate changes, the determined values of P / rac(t) may be interpolated. In the present example implementation, the interpolation may be based on the assumption that the fracture pressure changes linearly between the times of the flow rate changes. Using such assumption, an interpolated value of Pfrac(.t) may be calculated for any time intermediate the times of the flow rate changes, where an explicit value of fracture pressure may be determined as explained above. Once the intermediate values of Pfrac(.t) are determined, it is then possible to calculate the other pressure components change with respect to time during the fracture treatment pumping. The main variables in the foregoing pressure components are slurry density, slurry pumping rate, and the pipe friction factor. The flow rate may be obtained from the fracture treatment operator or a separate flowmeter placed in the pumping line from the pumping unit (101 in FIG. 1). The fluid slurry density and the pipe friction factor variations may be calculated based on the fracture treatment data obtained from the fracture treatment operator and previously determined pipe friction functions. This action will provide the following:pipe friction coefficient during the stage f(t), slurry density during the stage p(t)

[0054] It then being known how the fluid slurry density and pipe friction factor change during the treatment, known equations for pipe friction, perforation friction, NWB friction and hydrostatic pressure may be used to calculate the variation of the foregoing pressure components during the fracture treatment. These equations have certain unknown parameters. Frictional pressure loss calculations made at the times of fluid flow rate changes, made as explained above with reference to the ‘185 publication may be used tocalculate the unknown parameters in these equations. The foregoing will provide the following parameters:

[0055] Finally, the calculated variation of the pressure components during the fracture treatment may be used to calculate the expected surface pressure during the treatment at times intermediate the times of the flow rate changes. The following equation may be used:

[0056] FIG. 6 is a graph comparing predicted surface pressure to measured surface pressure. The internal stress shadow at the end of pumping ntiadow=350 pounds per square inch (psi) which shows multiple fractures are growing (normal) in the formations adjacent to the well.

[0057] FIG. 7 is a graph of measured pressure compared to predicted surface pressure in which it has been determined that the bottom-of-stage well casing plug has leaks; the measured surface pressure is lower than the predicted surface pressure. When there is a plug issue, some of the fluid can leak past the plug; the perforations of the previous treatment stage(s), deeper in the well, if such is the case, can become active. This will cause a rapid drop of the measured pressure. This rapid drop of the measured pressure will result in a deviation from the predicted pressure. In this example, at a time of around 2000 seconds, the plug started to leak and the measured pressure became much lower than the predicted pressure. Usually, a plug leak causes a fast drop in the measured pressure, but later in the stage the measured pressure comparison to the predicted pressure will appear normal.

[0058] FIG. 8 shows a graph of measured pressure compared to predicted pressure wherein ^intshadow^ Psh which indicates mainly that only one fracture is growing, which itself indicates very low perforation cluster efficiency and possibility of a fracture “hit.” Such incidence may also be referred to as a “runaway fracture.” When a runaway fracture takes place, it reduces the amount of treatment fluid available to affect the remaining fractures. Thus, the remaining fractures stop propagating and the treatment stage effectiveness iscompromised. The well operator may decide to terminate such stage to avoid any communication with offset wells through the runaway fracture.

[0059] In a method according to the present disclosure, the following actions may be performed:First, calculate variation of the NWB pressure drop and perforation friction during the stage treatment.Next, the calculated perforation friction values may be used to calculate the perforation efficiency variation during the stage.Next, the calculated perforation efficiency values may be used the determine cluster level proppant / fracture fluid volumes during the stage treatment. The cluster level fracture fluid / proppant volumes may be used to determine cluster level entry hole diameter increase (erosion of the perforations) during treatment.Finally, the calculated perforation efficiency values will be used to determine the cluster level fluid / proppant slurry volumes and variation of the uniformity index during the stage. The various actions stated above will be explained in more detail following:

[0060] Surface pressure is the sum of various pressures as stated in the following equationPpipeCO "b Pper / (0 "b Pwwzs(f) (11) wherein, ps= surface pressure, Pfrac=fracture pressure, pH= hydrostatic pressure, pptpe= pipe friction (as determined by tube wave analysis), pperf = perforation friction pressure, PNWB=NWB friction pressure. The objective is to determine the variation of the perforation friction, thus eq. (11) may be rewritten as:

[0061] To determine the variation of the perforation friction during the treatment, the following actions may be performed:First, determine the fracture pressure at the end of the stage using one of the following two ways:Use instantaneous shut-in pressure (ISIP) at the end of the current fracture treatment stage (Use the ISIP pressure values from previous treatment stages to estimate the fracture pressure of the current stage (predictive model).Next, assume the fracture pressure varies linearly from beginning of the stage until the end as function of slurry volume:wherein Vsiurry= pumped fracture treatment slurry volume at time ( / ) and Vsiurry=pumped slurry volume at the end of the stage

[0062] Next, perform tube wave friction analysis as explained in the ‘185 publication for each of two or more flow rate changes during pumping the treatment stage, and calculate the pipe friction and perforation friction at each flow rate change (for example, at least one analysis at or near the beginning of the treatment and one at or near the end is needed).

[0063] Next, calculate the NWB pressure drop at each of the tube wave friction analysis (FA) points:PNWB = PsA- Pfrac + PHA- Ppfpe - Pperf (14)

[0064] Between the FA points, a linear relationship may be assumed for NWB pressure drop as a function of the pumped fracture treatment slurry volume. However, initially, for the first approximately 10 minutes after the time that proppant reaches the bottom of the well it may be allowed that the NWB pressure drop decreases due to flow path tortuosity decrease. During these initial approximate 10 minutes the principal part of the surface pressure change is assumed to be due to NWB pressure change. The following equation may be used to determine the effect of the treatment injection rate on the NWB pressure drop. At the end of this action PNWB( ) is defined.

[0065] KNWBis calculated at the FA points. Between FA points a linear relationship for KNWB may be assumed. FIG. 11 shows an example of the NWB pressure drop variation during the stage. As it can be observed in FIG. 11, when the proppant first enters the perforations, NWB pressure drops suddenly as a result of tortuosity reduction Proppant enters the perforations at about 3800 seconds, leading to erosion within the near wellbore and an abrupt drop in NWB frictional pressure drop.

[0066] Then it is necessary to calculate how the other surface pressure components change with respect to time during the treatment stage. The principal pressure components are slurry density, slurry flow (pumping) rate, and pipe friction coefficient. The pumping rate is known from the fracture treatment parameters. The fracture treatment slurry density and pipe friction coefficient variations may be calculated based on the treatment parameters and previously calibrated friction curves. This will provide the following:pipe friction coefficient during the stage (t),slurry density during the stage (t)

[0067] Because it is known how the slurry density and pipe friction coefficient change over time during the stage, known equations for pipe friction and hydrostatic pressure may be used to calculate the variation of these pressure components during the stage. These equations have some unknown parameters. FA results obtained at the times of rate changes may be used to calculate the unknown parameters in these equations (FA will be used to calibrate). This will provide the following:PH( » PpipeW)Finally, the perforation friction variation can be calculated as:

[0068] The foregoing actions may be summarized as follows:Perform a first friction analysis (FA), e.g., according to the ‘ 185 publication at a first flow rate change to obtain bottom hole pressure drop;Compute pipe and perforation frictional pressure drop using the first FA;Determine (from perforation frictional pressure drop) one of:number of perforations receiving fluid at that time;equivalent entry hole diameter of perforations receiving fluid.Conduct a second FA at a later time to determine the number of perforations remaining open at the later time.Distribute materials injected into the well among the total number of open perforations (an even distribution would be Q_per _perf = Q Jotal / N _perf for example).Between the first and second FAs, each of which provides a determination of the number of open perforations, vary the number of open perforations with respect to time (one way is to assume a linear distribution with time between the FAs) between N1 the number of open perforations at the time T1 of the first FA and N2 the number of open perforations at the time of the second FA, T2.Compute a change in perforation (entry) hole diameter due to the erosive effect of (mostly) proppant entering the perforation based on amount injected into each perforation in the interval between T1 and 72Repeat the foregoing starting at the second FA until the end of the fracture treatment stage.

[0069] FIG. 12 shows an example of the cluster level perforation entry hole diameter (EHD) at the end of the stage. For this example the initial EHD of all clusters were 0.44 inch.

[0070] The foregoing assumes, between each measurement, that all perforations erode as if each receives the same amount of fluid, even though it may be understood that those perforations which shut down end up taking less fluid, leading to more fluid going to those that remain open. As a result, the remaining open perforations will erode more than if the others did not shut down.

[0071] The above description does not explain how the “normal erosion” is computed. A number of publications provide empirical equations to relate the perforation erosion rate asa function of the volume of fluid and / or proppant injected into that perforation. See, e.g., Cramer, SPE 16189 (Cramer, D. D. 1987a. The Application of Limited-Entry Techniques in Massive Hydraulic Fracturing Treatments. SPE Production Operations Symposium, Oklahoma City, Oklahoma, USA, 8-10 March. SPE-16189-MS.https: / / d0i.0rg / l 0.2118 / 16189-M S.). To better account for perforation erosion wherein some perforations close during a treatment stage, the following procedure may be used:

[0072] Assume at a first time Ta the diameter of and the number of open perforations are known based on having performed the above using FA.

[0073] A second determination of perforation pressure drop at a later time Th is determined, e.g., using FA.

[0074] Using the above described surface pressure prediction, then compute the perforation pressure drop as a function of time between Ta and Th, as in Eq. (16).

[0075] Then iterate to separate the combined effect on Pperf of changes in Nperf and of changes in perforation entry hole diameter (EHD) due to erosion.

[0076] Knowing Pperfif), first assume all perforations erode as if all receive fluid throughout; that is Qperf= 0 / Nperf This allows determining erosion as a function of time between Ta and Tb, which provides an estimate of “average” EHD( / ) by rearranging Eq. (17) below:With the new estimate of “average” F.HD(z) it is possible to derive an estimate of Nperfif).

[0077] Knowing Nperfif) and total fluid flow rate it is possible to calculate a new measure of cluster level volume with respect to time, from which can be derived a new perforation erosion with respect to time. From the new erosion with respect to time it is possible then to recalculate a new EHD with respect to time. The foregoing is repeated to obtain repeated estimates of Nperfif) and the foregoing is iterated until convergence is obtained at consistent values of Nperf and EHD.

[0078] Alternatively, initial entry hole diameter may be determined from properties of the perforating system (e.g., perforating gun type, shaped charge size, gun orientation, etc.).

[0079] The improved determinations of Nperf EHD, and injected volumes per perforation as a function of time obtained as above can be used to obtain improved determinations of uniformity, fluid distribution, proppant distribution, and end stage eroded perforation hole diameter.

[0080] FIG. 13 shows a graph of predicted surface pressure compared to measured surface pressure when there are no problems with the well or the treatment.

[0081] FIG. 14 shows a graph of predicted surface pressure compared to measured surface pressure when a plug at the bottom of a stage is leaking. If it is determined that a plug is leaking, the well operator may choose, for example, to increase the pumping rate of the treatment fluid to offset fluid loss through the leaking plug so that the treated zone (stage) will receive sufficient treatment fluid. If the plug leak is sufficiently large, the well operator may choose to terminate the treatment stage as a result of inability to pump sufficient treatment fluid into the rock formations within the stage.

[0082] FIG. 15 is a graph of predicted surface pressure compared to measured surface pressure where there is substantial perforation erosion. When extreme erosion is detected, e.g., increase of the EHD above a selected threshold, the well operator has to carefully monitor wellbore integrity. The well operator should be prepared to stop pumping the treatment stage if a sudden pressure drop from extreme erosion is observed, as this could indicate potential failure in the well casing or liner.

[0083] It will be appreciated that any or all aspects of the foregoing methods may be implemented in any form of programmable computer which is capable of reading a non- transitory computer readable medium having stored on it logic operable to cause the programmable computer to implement the actions described above for determining pressure, etc. Thus, another aspect of this disclosure is a non-transitory computer readable medium having such instructions stored on it. FIG. 16 shows an example computing system 200 in accordance with some implementations. Actions described above with reference to example implementations may be carried out on a computer or computer system, whereinpressure measurements made as described may be entered into the computer or computer system and processed in the computer or computer system as explained above. The computing system 200 may be an individual computer system 201 A or an arrangement of distributed computer systems. The individual computer system 201A may include one or more analysis modules 202 that may be configured to perform various tasks and controls according to some implementations, such as the tasks explained with reference to FIGS. 2- 15. To perform these various tasks, the analysis module 202 may operate independently or in coordination with one or more processors 204, which may be connected to one or more storage media 206. A display device 205 such as a graphic user interface of any known type may be in signal communication with the processor 204 to enable user entry of commands and / or data and to display results of execution of a set of instructions according to the present disclosure.

[0084] The processor(s) 204 may also be connected to a network interface 208 to allow the individual computer system 201 A to communicate over a data network 210 with sensors, one or more additional individual computer systems and / or computing systems, such as 201B, 201C, and / or 201D. Note that computer systems 201B, 201C and / or 201D may or may not share the same architecture as computer system 201 A, and may be located in different physical locations, for example, computer systems 201A and 201B may be at a well drilling location, while in communication with one or more computer systems such as 201C and / or 20 ID that may be located in one or more data centers on shore, aboard ships, and / or located in varying countries on different continents.

[0085] A processor may include, without limitation, a microprocessor, microcontroller, processor module or subsystem, programmable integrated circuit, programmable gate array, or another control or computing device.

[0086] The storage media 206 that captures data in a tangible medium may be implemented as one or more computer-readable or machine-readable storage media. Note that while in the example implementation of FIG. 16 the storage media 206 are shown as being disposed within the individual computer system 201 A, in some implementations, the storage media 206 may be distributed within and / or across multiple internal and / or external enclosures ofthe individual computing system 201A and / or additional computing systems (e.g., 201B, 201C, 20 ID), or over a network (“cloud”). Storage media 206 may include, without limitation, one or more different forms of memory including semiconductor memory devices such as dynamic or static random access memories (DRAMs or SRAMs), erasable and programmable read-only memories (EPROMs), electrically erasable and programmable read-only memories (EEPROMs) and flash memories; magnetic disks such as fixed, floppy and removable disks; other magnetic media including tape; optical media such as compact disks (CDs) or digital video disks (DVDs); or other types of storage devices. Note that computer instructions to cause any individual computer system or a computing system to perform the tasks described above may be provided on one computer- readable or machine-readable storage medium, or may be provided on multiple computer- readable or machine-readable storage media distributed in a multiple component computing system having one or more nodes. Such computer-readable or machine- readable storage medium or media may be considered to be part of an article (or article of manufacture). An article or article of manufacture can refer to any manufactured single component or multiple components. The storage medium or media can be located either in the machine running the machine-readable instructions or located at a remote site from which machine-readable instructions can be downloaded over a network for execution.

[0087] It should be appreciated that computing system 200 is only one example of a computing system, and that any other implementation of a computing system may have more or fewer components than shown, may combine additional components not shown in the example implementation of FIG. 16, and / or the computing system 200 may have a different configuration or arrangement of the components are shown in FIG. 16. The various components shown in FIG. 16 may be implemented in hardware, software, or a combination of both hardware and software, including one or more signal processing and / or application specific integrated circuits.

[0088] Further, the acts of the processing methods described above may be implemented by running one or more functional modules in information processing apparatus such as general purpose processors or application specific chips, such as ASICs, FPGAs, PLDs, or other appropriate devices. These modules, combinations of these modules, and / or theircombination with general hardware are all included within the scope of the present disclosure.

[0089] In light of the principles and example implementations described and illustrated herein, it will be recognized that the example implementations can be modified in arrangement and detail without departing from such principles. The foregoing discussion has focused on specific implementations, but other configurations are also contemplated. In particular, even though expressions such as in “an implementation," or the like are used herein, these phrases are meant to generally reference implementation possibilities, and are not intended to limit the disclosure to particular implementation configurations. As used herein, these terms may reference the same or different implementations that are combinable into other implementations. As a rule, any implementation referenced herein is freely combinable with any one or more of the other implementations referenced herein, and any number of features of different implementations are combinable with one another, unless indicated otherwise. 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. Accordingly, all such modifications are intended to be included within the scope of this disclosure as defined in the following claims.

Claims

CLAIMSWhat is claimed is:

1. A method for determining well perforation erosion during pumping a treatment, comprising:(a) measuring pressure in a well during pumping the treatment;(b) for a first change in flow rate of the pumping, determining a first well pipe friction pressure loss and a first perforation friction pressure loss using tube wave events in the measured pressure induced by the first change in flow rate;(c) determining a number of effective perforations using the first perforation friction pressure loss;(d) for a second change in flow rate of the pumping, determining a second well pipe friction pressure loss and a second perforation friction pressure loss using tube wave events in the measured pressure induced by the first change in flow rate;(e) determining a number of perforations remaining effective using the second determined perforation friction pressure loss;(f) determining a volume distribution of fluid among the remaining effective perforations;and(g) using the volume distribution, determining an entry hole diameter of the remaining effective perforations.

2. The method of claim 1 wherein the determining the number of effective perforations at either the first or second flow rate change comprises determining a friction coefficient of the perforations, the determining the friction coefficient of the perforations comprising initializing a value of the friction coefficient of the perforations, modeling a pressure with respect to time of a reflected tube wave in the well, comparing the measured pressure to the modeled reflected tube wave pressure, adjusting the friction coefficient of the perforations and repeating modeling the reflected tube wave pressure until a difference between the modeled tube wave pressure and a change in measured pressure from the reflected tube wave falls below a selected threshold.

3. The method of claim 1 further comprising repeating (a) through (g) at selected times during pumping the treatment and determining changes in the entry hole diameter.

4. The method of claim 1 further comprising determining existence of a leaking plug in the well.

5. The method of claim 4 further comprising either (i) increasing a rate of the pumping or (ii) terminating pumping based on a determined plug leak magnitude.

6. The method of claim 1 further comprising terminating the pumping when the entry hole diameter exceeds a selected threshold.

7. The method of claim 1 further comprising terminating the pumping when a runaway fracture is detected.

8. A non transitory computer readable medium having stored thereon logic operable to cause a programmable computer to perform acts, comprising:(a) accepting as input to the computer, pressure measured in a well during pumping the treatment;(b) for a first change in flow rate of the pumping, determining a first well pipe friction pressure loss and a first perforation friction pressure loss using tube wave events in the measured pressure induced by the first change in flow rate;(c) determining a number of effective perforations using the first perforation friction pressure loss;(d) for a second change in flow rate of the pumping, determining a second well pipe friction pressure loss and a second perforation friction pressure loss using tube wave events in the measured pressure induced by the first change in flow rate;(e) determining a number of perforations remaining effective using the second determined perforation friction pressure loss;(f) determining a volume distribution of fluid among the remaining effective perforations;and(g) using the volume distribution, determining an entry hole diameter of the remaining effective perforations.

9. The computer readable medium of claim 8 wherein the determining the number of effective perforations at either the first or second flow rate change comprises determining a friction coefficient of the perforations, the determining the friction coefficient of the perforations comprising initializing a value of the friction coefficient of the perforations, modeling a pressure with respect to time of a reflected tube wave in the well, comparing the measured pressure to the modeled reflected tube wave pressure, adjusting the friction coefficient of the perforations and repeating modeling the reflected tube wave pressure until a difference between the modeled tube wave pressure and a change in measured pressure from the reflected tube wave falls below a selected threshold.

10. The computer readable medium of claim 8 further comprising logic operable to cause the programmable computer to perform at selected times, repeating (a) through (g) and determining changes in entry hole diameter.

11. The computer readable medium of claim 8 further comprising instructions operable to cause the computer to perform determining existence of a leaking plug in the well.

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