A quantitative evaluation method for the fracturing efficiency of wellbore perforation

Abstract

The present invention discloses a method for quantitatively evaluating the fracturing efficiency of wellbore perforations, comprising the following steps: Step 1, dividing the wellbore casing into several sections, setting several perforation clusters in each section, and setting several perforations in each perforation cluster; Step 2, injecting fracturing fluid and fracturing proppant into the wellbore under high pressure, and the fracturing fluid and fracturing proppant enter the formation from the perforations to erode the perforations; Step 3, after flushing the wellbore, collecting perforation image data through an image acquisition device; Step 4, analyzing the perforation image data to obtain the erosion angle of the perforations, the relationship between the erosion area of each perforation and the amount of fracturing proppant entering, the relationship between the erosion area of perforations within each section / cluster and the amount of fracturing proppant entering within each section / cluster, and the quantitative value of the fracturing efficiency of perforations within each section / cluster. The method of the present invention simply and accurately calculates the fracturing efficiency and distribution of perforations, and can greatly promote the research in this field.

Description

Technical Field

[0001] The present invention relates to the technical field of borehole detection, and particularly to a method for quantitatively evaluating the fracturing efficiency of wellbore perforations. Background Art

[0002] Billions of dollars are invested in hydraulic fracturing every year. Operating companies understand that different fracturing volumes and different perforation cluster designs will affect productivity. However, how to optimize perforation cluster design parameters such as stage spacing and cluster spacing, number of clusters per stage, number of perforations per cluster; how to optimize fracturing design parameters, volume of fracturing fluid and proppant per stage, and temporary plugging, etc., is still unclear at present. Research in this field is still in its infancy in China and has not been reported in the newspapers. To solve the blank of related technologies in China, the present invention proposes a new method for quantitatively evaluating the fracturing efficiency of wellbore perforations. Summary of the Invention

[0003] The purpose of the present invention is to solve the problems mentioned in the background art and provide a method for quantitatively evaluating the fracturing efficiency of wellbore perforations.

[0004] To achieve the above technical purpose, the technical solution adopted by the present invention is

[0005] A method for quantitatively evaluating the fracturing efficiency of wellbore perforations, characterized by comprising the following steps:

[0006] Step 1: Divide the wellbore casing into several sections, set several perforation clusters in each section, and set several perforations in each perforation cluster;

[0007] Step 2: Inject fracturing fluid and proppant into the wellbore under high pressure. The fracturing fluid and proppant enter the formation from the perforations and erode the perforations;

[0008] Step 3: After washing the wellbore, collect perforation image data through an image acquisition device;

[0009] Step 4: Analyze the perforation image data to obtain the perforation erosion angle, the relationship between the erosion area of each perforation and the amount of proppant entering, the relationship between the perforation erosion area within each section / cluster and the amount of proppant entering within each section / cluster, and the quantitative value of the fracturing efficiency of the perforations within each section / cluster.

[0010] To optimize the above technical solution, the specific measures taken also include:

[0011] In Step 3, the image acquisition device is a logging tool with circumferential imaging technology including optics, X-rays, acoustic waves, or array sensors, etc.

[0012] The image acquisition device is an array ring-scanning high-definition imaging logging instrument. The array ring-scanning high-definition imaging logging instrument has multiple ring-scanning lenses, and adjacent ring-scanning lenses have overlapping fields of view, capable of capturing high-resolution images of the 360° circumference of the wellbore wall.

[0013] In step 4, the theoretical model of borehole erosion is adopted to determine the borehole erosion angle. The theoretical model of borehole erosion is as follows:

[0014] dL m (t) = ρ m ·c(t)dt = ρ m ·H·(1 - ε(t))·a e (t)·dt

[0015] Where

[0016]

[0017]

[0018] When tanθ2(t) ≈ tanθ1(t) = tanθ(t), and tanθ(t) is the borehole erosion angle;

[0019] L m (t): The mass of metal erosion loss at time t, with the unit of g,

[0020] ρ m : The density of metal, a constant, taking 7.8 g / cm 3 ,

[0021] c(t): The volume of eroded metal loss in the time interval (t, t + dt),

[0022] H: The thickness of the casing, with the unit of cm,

[0023] ε(t): The erosion coefficient,

[0024] a e (t): The borehole erosion area in the time interval (t, t + dt),

[0025] h: The height calculated for the infinitesimal volume, h ∈ [0, H],

[0026] θ1(t), θ2(t): The erosion angles at times t and t + dt,

[0027] When tanθ2(t) ≈ tanθ1(t) = tanθ(t), and tanθ(t) is the borehole erosion angle,

[0028] e(t): The borehole erosion width at time t, with the unit of cm,

[0029] A e : The erosion area of a single borehole, that is, the difference between the measured area of a single borehole and the base borehole area, with the unit of cm 2 ,

[0030] e(T): The final erosion width, in cm.

[0031] d(T): The final perforation diameter, in cm.

[0032]

[0033] d BH : The base perforation diameter, in cm.

[0034] In Step 4, the relationship between the erosion area of a single perforation in the wellbore and the amount of fracturing proppant entering is calculated using the PSE formula. The PSE formula is:

[0035] M s = γA e

[0036]

[0037] Where:

[0038] γ: The erosion sand influx coefficient, i.e., the relationship between the erosion area of a single perforation in the wellbore and the amount of fracturing proppant.

[0039] A e : The erosion area of a single perforation, i.e., the difference between the measured area of a single perforation and the base perforation area.

[0040] M s : The amount of proppant entering a single perforation during the steady-state erosion process.

[0041] C p : The average value of the release coefficient, which is a constant in the range of 0.95 - 0.9 during the steady-state erosion process.

[0042] The weighted erosion coefficient of the average erosion area

[0043] The mean value of λP for this perforation pf Mean value

[0044] λ: The erosion coefficient, a constant.

[0045] P pf : The perforation erosion pressure drop.

[0046] ρ s : The density of the fracturing proppant, a constant.

[0047] In Step 4, the relationship between the erosion area of perforations within a stage / cluster and the amount of fracturing proppant entering the stage / cluster is calculated using the SED formula. The SED formula is:

[0048] Ms,SCP = γ SCP A e,SCP

[0049]

[0050] Wherein

[0051] A e,SCP : The final erosion area of all perforations within a stage / cluster, that is, the difference between the measured area of all perforations within a stage / cluster and the corresponding reference perforation area.

[0052] γ SCP : The erosion sand influx coefficient within a stage / cluster, that is, the relationship between the erosion area of perforations within each stage / cluster and the amount of fracturing proppant entering each stage / cluster.

[0053] M s,SCP : The amount of proppant entering all perforations within a stage / cluster.

[0054] The weighted erosion coefficient of the average erosion area within a stage / cluster

[0055] The average value of λP within a stage / cluster pf of.

[0056] In step 4, the fracturing efficiency of perforations within a stage / cluster is calculated using the FEI index or the EGI index. The FEI index is the ratio of the standard deviation of the amount of proppant entering a single perforation within a stage / cluster to the average value of the amount of proppant entering a single perforation within a stage / cluster. The EGI index is the ratio of the standard deviation of the final erosion area of a single perforation within a stage / cluster to the average value of the final erosion area of a single perforation within a stage / cluster.

[0057] According to the range of FEI, the fracturing efficiency of perforations within a stage / cluster is divided into uniform sand influx distribution, selective sand influx distribution, discrete sand influx distribution, and pulsed sand influx distribution.

[0058] The uniform sand influx distribution means that after the sand fluid breaks through a certain perforation within a stage with a high probability, it spreads to the surrounding area and finally forms a relatively uniform sand influx distribution. Whether in terms of space or the amount of proppant entering, it shows an even distribution. From the perspective of fractures, multiple fractures are likely to form, and the stress cloud interference between fractures is low. Therefore, there is a relatively complex connection of main fractures. From the perspective of the reservoir, there is a complex fracture network between fractures, and the SRV volume is significantly increased, and the fracturing efficiency is good.

[0059] Selective sand injection shows distributed sand injection in a certain area within the stage, while there is insufficient sand injection in other areas, indicating a weak stress cloud effect between holes or clusters. When selecting the perforations or perforation clusters for proppant injection, complex fracture networks can be formed outside the wellbore and sufficient fracture network volumes can be achieved. However, for the perforations or perforation clusters without selected proppant injection, the amount of proppant entering is low, complex fracture networks cannot be formed, and the fracture network volume is low. From the perspective of fractures, selective sand injection only forms complex fracture networks in a certain area, and there are no effective fracture networks in other areas. From the perspective of the reservoir, selective sand injection only realizes volume stimulation in a certain area within the stage, with a certain SRV scale. However, from the entire stage, the fracturing efficiency is medium, subdivided into medium-preferred, medium, and medium-poor;

[0060] Discrete sand injection shows a certain degree of distribution or selective distribution, and the overall sand injection distribution is discrete, indicating a strong stress cloud effect between holes or clusters, resulting in difficult coupling between the fractures that initiate, and most of the space outside the wellbore cannot form complex fracture networks, and the fracture network volume is low. From the perspective of the reservoir, the SRV volume is limited, and the fracturing efficiency is medium-poor;

[0061] Pulsed sand injection shows that 1 - 5 perforations have strong excessive sand injection, occupying more than 30% of the total sand injection volume, resulting in no sand injection or very limited sand injection in other perforations within this stage. From the perspective of fractures, pulsed sand injection is a concrete manifestation of linear fractures, indicating that after some perforations are broken through, peripheral expansion cannot be achieved and excessive sand injection occurs, resulting in severe underpressure in other perforations. From the perspective of the reservoir, the stress cloud effect is severe, resulting in the inability to form a fishbone effect in a single fracture, and it can only extend continuously along the maximum principal stress perpendicular plane towards the far end, with a probability of causing well interference and no SRV volume of scale can be formed, and the fracturing efficiency is poor.

[0062] The FEI of the described distributed sand injection is in the range of 0 - 0.7, and the overall evaluation of the fracturing effect is good. Selective sand injection is divided into strong selective sand injection, selective sand injection, and weak selective sand injection. The FEI of weak selective sand injection is in the range of 0.7 - 1.0, and the overall evaluation of the fracturing effect is medium-preferred. The FEI of selective sand injection is in the range of 1.0 - 1.4, and the overall evaluation of the fracturing effect is medium. The FEI of discrete sand injection or strong selective sand injection is in the range of 1.4 - 1.8, and the overall evaluation of the fracturing effect is medium-poor. The FEI of pulsed sand injection is greater than 1.8, and the overall evaluation of the fracturing effect is poor. The EGI index has the same division definition as the FEI index.

[0063] The described fracturing proppant is quartz sand, or ceramsite, or chemically coated and modified proppant, or a combination of quartz sand, ceramsite, and chemically coated and modified proppant.

[0064] The advantages of the present invention are as follows:

[0065] The present invention discloses a theoretical model of borehole erosion, PSE formula, SED formula, and FEI index. With the help of high-resolution optical imaging technology, it accurately measures and interprets the borehole size before and after fracturing. It quantitatively calculates the borehole erosion angle using the borehole erosion theoretical model, quantitatively calculates the relationship between the erosion area of a single borehole and the amount of proppant entering using the PSE formula, quantitatively calculates the relationship between the borehole erosion area within a stage / cluster and the amount of fracturing proppant entering within the stage / cluster using the SED formula, and quantitatively evaluates the fracturing efficiency of boreholes within a stage / cluster using the FEI index. The method disclosed by the present invention simply and accurately calculates the fracturing efficiency and distribution of boreholes, and can greatly promote the research in this field.

[0066] The present invention classifies the sand entry distribution into four types, namely spread sand entry distribution, selective sand entry distribution, discrete sand entry distribution, and pulsed sand entry distribution. The fracturing efficiency of wellbore boreholes can be simply and quickly judged through the FEI index. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 is a schematic structural diagram of Well A;

[0068] Figure 2 is a 13-stage distribution diagram, selective sand entry distribution;

[0069] Figure 3 is a 14-stage distribution diagram, spread sand entry distribution;

[0070] Figure 4 is a 15-stage distribution diagram, pulsed sand entry distribution;

[0071] Figure 5 is a 16-stage distribution diagram, selective sand entry distribution;

[0072] Figure 6 is a 17-stage distribution diagram, selective sand entry distribution;

[0073] Figure 7 is an 18-stage distribution diagram, discrete or strongly selective sand entry distribution;

[0074] Figure 8 is a 19-stage distribution diagram, discrete or strongly selective sand entry distribution;

[0075] Figure 9 is a 20-stage distribution diagram, discrete or strongly selective sand entry distribution;

[0076] Figure 10 is a 21-stage distribution diagram, selective sand entry distribution.

[0077] Figure 11 is a schematic diagram of an overpressure borehole;

[0078] Figure 12 is a schematic diagram of a fully pressurized borehole;

[0079] Figure 13 It is a schematic diagram of underpressure perforations. Specific implementation manners

[0080] The embodiments of the present invention will be further described in detail below in conjunction with the accompanying drawings.

[0081] A method for quantitatively evaluating the fracturing efficiency of wellbore perforations in the present invention includes the following steps:

[0082] Step 1: Divide the wellbore casing into several sections, set several perforation clusters in each section, and set several perforations in each perforation cluster;

[0083] Step 2: Inject fracturing fluid and fracturing proppant into the wellbore under high pressure. The fracturing fluid and fracturing proppant enter the formation from the perforations and erode the perforations;

[0084] Step 3: After washing the wellbore, collect perforation image data through an image acquisition device;

[0085] Step 4: Analyze the perforation image data to obtain the perforation erosion angle, the relationship between the erosion area of each perforation and the amount of fracturing proppant entering, the relationship between the perforation erosion area within each section / cluster and the amount of fracturing proppant entering within each section / cluster, and the quantitative value of the fracturing efficiency of the perforations within each section / cluster.

[0086] Steps 1 and 2 are the existing wellbore perforation fracturing steps. The innovation points of the present invention lie in Steps 3 and 4.

[0087] In Step 3, the image acquisition device preferably used is an array side-looking high-definition imaging logging instrument. The latest development of downhole optical imaging technology makes it possible to measure before and after fracturing perforations during routine operations. Currently, two types of downhole imaging technology tools are known: one is to use a front camera for perforation evaluation. This kind of lens will seriously distort the image, and perforation measurement requires model inversion, and the test accuracy is doubtful. The other type of tool has a side-looking camera that can rotate at a fixed point, and the measurement period is too long, and there is a well control risk. In order to accurately measure the perforation image, it is preferred to use a lens of an array side-looking circumferential scanning logging instrument parallel to the casing wall to capture the perforation image of the entire 360-degree circumference of the casing.

[0088] The present invention adopts a perforation erosion theoretical model to determine the perforation erosion angle. The reasoning steps of the perforation erosion theoretical model are as follows:

[0089] Since the transient erosion process will not enlarge the perforation hole, but only make the outer periphery of the perforation smooth, the amount of proppant entering can be ignored during this process. In fact, the amount of proppant entering during this process can be described as follows,

[0090]

[0091] M L: Mass loss of metal, unit: g,

[0092] θ i : Erosion angle during transient erosion process, unit: degree,

[0093] ρ: Metal density, unit: g / cm 3 ,

[0094] μ: Mass erosion coefficient during transient erosion process, cm 3 / degree,

[0095] According to measurements, at the end of the transient erosion process, θi is very small and does not exceed π / 12. M L is small and the variation between holes is not significant. We assume that during this process, the amount of proppant entering all perforations is very small and can be ignored. Our goal will focus on the steady-state erosion process, which smooths and enlarges the perforations.

[0096] Assume the perforation diameter is d(t), the casing thickness is H, and the erosion angle at time t is θ1(t).

[0097] During a small time interval (t, t+dt), erosion further smooths the perforation and enlarges the hole. Let the erosion angle change from θ1(t) to θ2(t), and the perforation diameter change from d to d(t)+e(t).

[0098] The mass loss of the casing metal during this time interval is the loss volume multiplied by the metal density. To calculate the volume loss, we will use the finite element analysis (FEA) method to divide the cone into an infinite number of layers. The height of each layer is dh. The volume loss is equal to the volume of the cone at time t+dt minus the volume of the cone at time t. Then, calculus is performed from h = 0 to h = H. The total volume loss during the time interval (t, t+dt) is given. To calculate the total volume loss, integration needs to continue from t = 0 to t = t (total fracturing time). The total metal loss due to erosion will be given.

[0099]

[0100] ae(t): Perforation erosion area during the time interval (t, t+dt), unit: cm 2 ,

[0101] d(t): Perforation diameter at time t, unit: cm,

[0102] e(t): Perforation erosion width at time t, unit: cm,

[0103] Based on the above theory, we can write the differential volume loss:

[0104]

[0105] c(t): The volume of eroded metal loss in the time interval (t, t + dt).

[0106] θ1(t), θ2(t): Erosion angles at times t and t + dt.

[0107] h: The height for infinitesimal volume calculation.

[0108] Integrating with respect to h ∈ [0, H], we can obtain the volume of eroded metal in (t, t + dt).

[0109]

[0110] When we have tanθ2(t) ≈ tanθ1(t) = tanθ(t)

[0111]

[0112] Defining as the erosion coefficient, we have

[0113] c(t) = H·(1 + ε(t))·a e (t) (3)

[0114] The metal loss caused by erosion can be written as:

[0115] dL m (t) = ρ m ·c(t)dt = ρ m ·H·(1 + ε(t))·a e (t)·dt (4)

[0116] where

[0117] L m (t): The mass of metal erosion loss at time t, in grams.

[0118] ρ m : The metal density, a constant, taken as 7.8 g / cm 3 ,

[0119] ε(t): The erosion coefficient.

[0120] H: The casing thickness, in cm.

[0121] a e (t): The erosion area at time t, in cm 2 ,

[0122] Equation (4) represents the relationship between the metal loss of the eroded casing, the erosion coefficient, and the erosion area. This method is applicable to the entire fracturing process and has time-varying characteristics.

[0123] Integrating Equation (4), we have

[0124]

[0125] A e : The erosion area of a single hole, i.e., the difference between the measured area of a single hole and the base hole area

[0126] The mean erosion area weighted erosion coefficient

[0127] For engineering applications, we will estimate ε by the difference between the base hole diameter and the final hole radius

[0128]

[0129]

[0130] By measuring that e(t) is smaller than d(t), so we have to neglect all terms in the quadratic equation

[0131]

[0132] Note that

[0133] When We simplify Equation (6) to

[0134]

[0135] Therefore, we write

[0136]

[0137] e(T): The final erosion width, in cm

[0138] d(T): The final hole diameter, in cm

[0139] Since

[0140]

[0141] From (8) and (5), we deduce that

[0142]

[0143] (9) and (10) are the equations we finally obtain representing the relationship between the final erosion area and the metal loss. Since all parameters can be measured and calculated, we can calculate the hole erosion angle for each hole.

[0144] The present invention uses the PSE formula to calculate the relationship between the overall wellbore perforation erosion area and the amount of fracturing proppant. The derivation process is as follows:

[0145] Erosion is mainly caused by fluid kinetic energy. According to the research of Cramer (D.D. Cramer, 1988), the metal erosion caused by fluid penetration into the formation is mainly due to the sand erosion of the fracturing fluid. The fracturing fluid has no effect on metal erosion. The conclusion of this paper is verified by experiments. Based on this understanding, we can simply write

[0146] dL m (t) = λ·m s (t)·v s 2 (t)·dt (11)

[0147] L m (t): The metal loss of the casing at time t, in g,

[0148] λ: Erosion dynamic coefficient, which is a constant within the section,

[0149] m s (t): The amount of proppant entering the perforation at time t, in MT,

[0150] v s (t): The flow rate of the fracturing proppant at time t, in m / s,

[0151] According to the perforation pressure drop calculation formula proposed by Veatch (R.W. Veatch 1983),

[0152]

[0153] where

[0154] P pf (t): The perforation erosion pressure drop, in psi,

[0155] Q(t): The pump discharge at time t, in m 3 / min,

[0156] A(t): The perforation area at time t, in cm 2 ,

[0157] C p (t): The release coefficient at time t, time-varying,

[0158] ρ s : The density of the fracturing proppant, a constant, which can be taken as 2.65 g / cm 2 ,

[0159] Since we are now studying a single perforation, the proppant entry velocity is equal to the sand volume divided by the perforation area, and we obtain

[0160]

[0161] Combining equations (7) and (6)

[0162]

[0163] The erosion process is divided into a transient erosion process and a steady-state erosion process. See the detailed analysis by Grose. During the transient erosion process, the erosion does not enlarge the perforation, but only smooths the inner diameter of the casing and increases the slope. During this process, the release coefficient C p (t) and the erosion pressure drop P pf (t) vary with time. However, compared with the steady-state erosion process, this process lasts for a short time. During the steady-state erosion process, the perforation enlarges and at the same time makes the area around the perforation smooth. During this process, the release coefficient remains between 0.9 and 0.95, and the erosion pressure drop remains stable between 150 and 300 psi. Since the transient process does not enlarge the perforation diameter, the erosion area defined in this paper is zero. We have

[0164]

[0165] where

[0166] L m : Mass loss of casing metal erosion during the fracturing process, in g,

[0167] M s : Proppant entry volume for a single perforation during the steady-state erosion process, in MT,

[0168] C p : Mean value of the release coefficient. During the steady-state erosion process, the release coefficient is 0.9 - 0.95,

[0169] The average value of λP for this perforation pf ,

[0170] Combining (10) and (15)

[0171]

[0172] Define

[0173] as the erosion sand entry coefficient, and equation (14) can be written as

[0174] M s = γA e (17)

[0175] Among them,

[0176] A e : The erosion area of a single perforation, that is, the difference between the measured area of a single perforation and the base perforation area,

[0177] M s : The amount of proppant entering a single perforation during the steady-state erosion process, in MT,

[0178] The weighted erosion coefficient of the average erosion area,

[0179] The average value of λP for this perforation, pf Average value,

[0180] γ: Erosion sand influx coefficient (SEC),

[0181] (17) is called the perforation sand influx (PSE) formula, abbreviated as the PSE formula. This method is applied to a single perforation, indicating that the sand influx is related to the ratio of the erosion area.

[0182] The PSE formula describes the nearly linear relationship between the sand influx of a single perforation and the erosion area.

[0183] Since the latest downhole camera technology can accurately measure the base perforation and the perforation diameters and areas before and after fracturing. The parameters in the PSE formula can be calculated using the measured data.

[0184] The present invention uses the SED formula to calculate the relationship between the perforation erosion area in a stage / cluster and the amount of fracturing proppant entering the stage / cluster. The derivation process is as follows:

[0185] Definition:

[0186]

[0187] M s,SCP =γ SCP A e,SCP (18)

[0188] Among them, A e,SCP : The final erosion area of the stage / cluster perforations, that is, the difference between the measured areas of all perforations in the stage / cluster and the corresponding base perforations, in cm 2 ,

[0189] γ SCP : Stage / cluster erosion sand influx coefficient (ESEC), variable,

[0190] M s,SCP : The amount of proppant entering the stage / cluster perforations, MT,

[0191] Mean value of λP within segment / cluster pf which is

[0192] (18) is called the sand entry distribution (SED) formula, or simply the SED formula for short.

[0193] The SED formula reveals the sand entry distribution of perforation clusters and perforation segments. More than 10 sets of on-site working data show good accuracy.

[0194] Let's add up the proppant entry amounts for the entire segment. This is

[0195]

[0196] From (8), we get

[0197]

[0198]

[0199] Through (8) and (9), we can obtain

[0200] Combined with (17), we use to represent the average value of perforations within the segment, and we have

[0201]

[0202] is the total proppant entry amount for the fracturing segment.

[0203] Since A e,SCP and can be measured and calculated, can be calculated,

[0204] Therefore, the erosion sand entry coefficient for the segment / cluster, that is, the relationship between the erosion area of perforations within the segment / cluster and the proppant entry amount within the segment / cluster, can be written as

[0205]

[0206] Since the erosion area of each segment / cluster perforation can be measured, the proppant entry amount for each segment / cluster perforation can be given by the SED formula.

[0207] The FEI index of the present invention is used to calculate the fracturing efficiency of perforations within a stage / cluster. The FEI index is basically very similar to the EGI index, which is the standard deviation of the erosion area of a stage divided by the average erosion area of each perforation in a stage. The difference between these two metrics for a stage is relatively small, often less than a 2%-5% deviation. Physically, the EGI index is a parameter describing the uniformity of the erosion area distribution of a certain stage, while the FEI index is a parameter describing the uniformity of the proppant influx. The reason why these two metrics are so similar is that in most cases, the variation of the erosion and sand influx coefficient γ between different perforations is small. Calculating γ for each perforation in a stage shows that the numerical variation between perforations is very small.

[0208]

[0209] I FEI,SC : The fracturing efficiency of a stage / cluster, also known as the FEI index,

[0210] Var SC : The standard deviation of the proppant influx into the perforations of a stage / cluster,

[0211] The average value of the proppant influx into the perforations of a stage or cluster,

[0212] Over 100 operations have proven that when the FEI is in the range of 0 to 0.7, the fracturing efficiency is good; when it is in the range of 0.7 to 1, the fracturing efficiency is moderately good; when it is in the range of 1 to 1.4, the fracturing efficiency is medium; when it is in the range of 1.4 to 1.8, the fracturing efficiency has a medium deviation; and when it is above 1.8, the fracturing efficiency is poor.

[0213] Definitions of some terms related to the present invention:

[0214] The erosion area defined in this article refers to the area expanded due to erosion. It does not include the casing mass loss caused by the smoothing of the perforation periphery due to erosion. Practice has shown that many eroded perforations have smooth steps. Perforations under saturated pressure are often accompanied by smooth transitions. Therefore, it is difficult and inaccurate to determine the smooth area. It is relatively easy to measure the perforation area before and after fracturing. So, we define

[0215] Erosion area: The difference between the measured perforation area after fracturing and the base perforation area.

[0216] According to the research of Grose (R. Grose, 1985), Cramer (D. D. Cramer, 1988), Crump and Conway (J. B. Crump, M. W. Conway 1988), the erosion process can be divided into the following two stages (transient erosion process and steady-state erosion process).

[0217] Transient erosion process: This erosion occurs in the initial stage of fracturing, only causing the circumference of the perforation to be smoothed without causing perforation enlargement. Compared with the entire fracturing process, the time required for this process is shorter.

[0218] Steady-state erosion process: This erosion occurs after transient erosion, causing perforation enlargement and further smoothing. This process occupies most of the fracturing cycle and approaches steady erosion with a stable erosion pressure drop and a stable sand influx rate.

[0219] Under-pressured perforation: The amount of proppant entering the perforation is lower than the average amount of proppant entering the perforation.

[0220] Over-pressured perforation: The amount of proppant entering the perforation is greater than the average amount of proppant entering the perforation but less than the designed maximum amount.

[0221] Over-pressured perforation: The amount of proppant entering the perforation exceeds the maximum designed amount.

[0222] Pulsed sand influx distribution: A small number of perforations (such as 1 - 5 perforations) in a fracturing stage have a proppant influx exceeding 30% or more of the total pumped proppant influx in the fracturing stage, and the sand influx distribution looks like a delta function within the entire fracturing stage. The pulsed sand influx distribution has poor fracturing efficiency. It reflects that the fracturing volume breaks through from one point and cannot expand to other perforations. The FEI index value of the pulsed sand influx distribution tends to be greater than 1.8, indicating a strong heterogeneity in the sand influx distribution of a certain stage. The reservoir in the fracturing stage has strong heterogeneity, and the stress field between perforations and clusters is strong. The fracturing fluid and proppant cannot be shared among all perforations in a fracturing stage but are concentrated in a few perforations. The fractures in those over-pressured perforations should be long and linear. The SRV volume should be less than expected.

[0223] Discrete sand influx distribution: Many perforations have sand influx, but the proppant-entering perforations after fracturing are not continuously distributed within a stage. The discrete sand influx distribution has relatively poor fracturing efficiency. It reflects that the fracturing volume breaks through from multiple points but cannot expand to nearby perforations. The FEI index of the discrete sand influx distribution is usually between 1.4 - 1.8. It also indicates the existence of a stress field between perforations. The fracturing fluid and proppant are shared by multiple perforations in a fracturing stage, but some perforations cannot carry enough proppant due to the stress field. The fractures in the well's production-increasing perforations should be non-linear and provide a certain SRV.

[0224] Selective proppant entry distribution: Proppant entry occurs in some clusters, and the perforations within the clusters show continuous proppant entry. Selective proppant entry distribution refers to medium or average fracturing efficiency. It reflects the non-uniform distribution of the fracture volume within the well section. However, between these clusters, the perforations cannot achieve sufficient proppant entry. The FEI index of selective proppant entry distribution is usually between 0.7 - 1.8. This also indicates that there are stress clouds between these clusters. Valuable fracturing fluid and proppant can be shared in most of the perforations of the wellbore fracturing clusters. Between these clusters with good fracturing effects, the stress clouds block the interconnections. The fractures of these fracturing clusters are relatively complex, and the SRV volume is relatively high.

[0225] Spread proppant entry distribution: All clusters and perforations show continuous proppant entry. Spread proppant entry distribution has good fracturing efficiency. It reflects the uniform distribution of the fracture volume within the section. The FEI index value of spread proppant entry distribution is less than 0.7, indicating good reservoir homogeneity and minimal stress field effects. Fracturing fluid and proppant are shared in most of the perforations in this section. The fractures throughout the section are complex, with a good total SRV volume.

[0226] Proppant entry distribution is a concentrated reflection of fracturing efficiency. Since there are always some errors in measurement, individual perforation measurements may not be accurate. However, a small number of inaccurate perforation measurements will not affect the distribution. In short, compared with individual perforation measurements, SED can more accurately judge fracturing efficiency. It also reveals how the fracture volume struggles with the formation and how it breaks through along the fracture section. Obviously, a better distribution is undoubtedly better than a worse (lower uniformity) distribution. Since the amount of proppant pumped into the formation is determined in the absence of plugging problems, a better distribution can be obtained in most of the producing formations. From this perspective, SED can become the main indicator for evaluating the effectiveness of fracturing.

[0227] Job case:

[0228] Figure 1 It is a schematic diagram of Well A. The horizontal well starts from the heel at 3400 m MD and extends to the toe at 4700 m. A total of 9 sections were recorded and analyzed. The measurement sections started from Section 13 to Section 21. Above Section 21, 16 un-fractured "base" perforations were shot, also called "base value perforations", and they were named Section 22 for analysis.

[0229] Table 1

[0230]

[0231] Table 1 shows the fracturing design of Well A. Each fracturing section includes the number of fracturing clusters, the number of perforations in each cluster, the total number of perforations in each fracturing section, the depth of the fracturing clusters and fracturing sections, the setting depth of the bridge plug, the number of perforations per meter, the fracturing fluid volume and proppant mass, and the temporary plugging agent for each fracturing section.

[0232] The operating company designed 9 fracturing stages, with 48 perforations in each stage. 6, 8, or 12 clusters were designed in these stages. The fracturing fluid volume and proppant volume were divided into low volume and high volume. No bridging agent was pumped in one of the stages, while bridging agents were pumped in all other stages.

[0233] After sufficient wellbore flushing, the operation was successfully completed. Among the 448 designed perforations, 385 perforations were actually measured, and 271 perforations were measured erosion holes. All the eroded perforations were measured, and the SED analysis gave the data shown in Table 2.

[0234] Table 2

[0235]

[0236] From the FEI and EGI indices, the average distribution of Stage 14 tended to be good. The average distribution of Stage 13 was poor. The distributions of all other stages were very poor. From the ratio of underpressure - saturation pressure - overpressure, Stage 14 was the best, Stage 13 performed better in the overpressure and saturation pressure ratios but was poorly evaluated in the underpressure ratio. Stage 15 performed well in overpressure and was average or below average in saturation pressure and underpressure. Stage 18 performed well in saturation pressure and underpressure and was average in overpressure. However, from the perspective of the proppant layer distribution, Stage 15 had a pulsed distribution with a low proppant efficiency. Stage 18 was discrete and there was no proppant entry at the toe.

[0237] The proppant distributions of all 9 fracturing stages are as Figures 2 - 10 shown. Among them,

[0238] Figure 2 is the distribution map of Stage 13, selective proppant distribution;

[0239] Figure 3 is the distribution map of Stage 14, spreading proppant distribution;

[0240] Figure 4 is the distribution map of Stage 15, pulsed proppant distribution;

[0241] Figure 5 is the distribution map of Stage 16, selective proppant distribution;

[0242] Figure 6 is the distribution map of Stage 17, selective proppant distribution;

[0243] Figure 7 is the distribution map of Stage 18, discrete or strongly selective proppant distribution;

[0244] Figure 8 is the distribution map of Stage 19, discrete or strongly selective proppant distribution

[0245] Figure 9It is a 20-segment distribution map, with discrete or strongly selective sand influx distribution;

[0246] Figure 10 It is a 21-segment distribution map, with selective sand influx distribution.

[0247] Through the analysis of the above operation results:

[0248] a. The fracture distribution in the 14th segment is relatively wide, and the average fracturing efficiency is close to a good level. The 13th, 17th, 16th, and 21st segments have selective sand influx distribution, with medium fracturing efficiency. The 18th, 19th, and 20th segments have discrete or strongly selective sand influx distribution, with medium to poor fracturing efficiency. The 15th segment has pulsed sand influx distribution, with poor fracturing efficiency. Both the 13th and 14th segments adopt an 8x6 (number of perforations x number of perforation clusters) design. In one segment, reducing rather than increasing the clusters will help improve the uniform distribution.

[0249] b. The fracturing dosage in the 13th and 14th segments is relatively low. This also indicates that a high fracturing volume may not help provide a good sand influx distribution.

[0250] c. The SED level in the 13th segment is average, but no temporary plugging agent is injected! From the analysis of this well, we cannot prove that the temporary plugging agent can improve the uniform distribution. On the contrary, it may deteriorate the uniform distribution.

[0251] Finally, Figures 11 - 13 The conditions of overpressured, saturated-pressure, and underpressured perforations are given. These images are taken by downhole logging instruments and are also very clear to the operators.

[0252] The segment / cluster erosion sand influx coefficient γ in the SED formula SCP varies little with the number of perforations in the same segment of perforations. Especially for this well, the γ of all perforation holes SCP The calculation results are summarized as the minimum value, average value, and maximum value for each segment. In addition, the standard variance of γ for each segment is also calculated. See Table 3: SCP

[0253]

[0254] ​SED analysis provides comprehensive data analysis of the proppant influx per perforation. It shows the sand influx distribution for each fracturing stage. From the SED perspective, Stage 14 is relatively the best among the 9 stages, followed by Stage 13. Stages 15, 18, 19, and 20 are the worst among the 9 stages. Especially for Stage 15, the fracturing energy broke through from the first perforation of Cluster 11, and proppant continuously entered this perforation during the entire fracturing process. This reflects that the formation stress may be non-uniform, and the fracturing energy can only be overcome through this perforation and cannot spread to other perforations. As a result, a total of 74 MT of proppant entered this perforation, accounting for approximately 23% of the total proppant mass used. Based on this information, the fracture length and height of this stage will far exceed the numerical simulation data and may reach the far end of the formation. Wells near this well may experience unexpected low productivity because oil and gas will be discharged through this unexpected long linear fracture length and height.

[0255] Generally speaking, the fracturing efficiency of Well A is not satisfactory. The low fracturing efficiency may be related to the fracturing volume. When Well A was designed, the fracturing fluid volume and proppant content were large. Most of the high-pressure fracturing stages did not produce better SED. SED analysis determined that in a stage, the fewer the number of clusters, the better the uniform distribution. And the temporary plugging agent did not increase the uniform distribution.

[0256] Through SED analysis, the operator can carefully design the fracturing construction parameters, determine the fracturing efficiency through SED data, optimize the reservoir and engineering parameters, and then use the SED data to determine the fracturing efficiency. Continuously optimize the reservoir and engineering parameters in this way to achieve a more optimized fracturing design.

[0257] The above is only the preferred implementation mode of the present invention. The protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the idea of the present invention belong to the protection scope of the present invention. It should be noted that for those of ordinary skill in the art of this technology, several improvements and refinements made without departing from the principle of the present invention should be regarded as within the protection scope of the present invention.

Claims

1. A quantitative evaluation method for the fracturing efficiency of wellbore gun perforation, characterized in that: It includes the following steps: Step 1: Divide the wellbore casing into several sections, set several perforation clusters in each section, and set several perforations in each perforation cluster; Step 2: Inject fracturing fluid and fracturing proppant into the wellbore under high pressure. The fracturing fluid and fracturing proppant enter the formation from the perforations and erode the perforations; Step 3: After washing the wellbore, collect perforation image data through an image acquisition device; Step 4: Analyze the perforation image data to obtain the quantitative values of the perforation erosion angle, the relationship between the erosion area of each perforation and the amount of fracturing proppant entering, the relationship between the erosion area of perforations in each section or cluster and the amount of fracturing proppant entering in each section or cluster, and the fracturing efficiency of perforations in each section or cluster; In Step 4, use the perforation erosion theoretical model to determine the perforation erosion angle. The perforation erosion theoretical model is: dL m (t) = ρ m ·c(t)dt = ρ m ·H·(1 + ε(t))·a e (t)·dt Where When t ∈ [t, t + dt] and lim dt→0 dt = 0, there is tanθ2(t) ≈ tanθ1(t) = tanθ(t), where tanθ(t) is the borehole erosion angle; L m (t): The mass of metal erosion loss at time t, unit: g ρ m : Metal density, constant, take 7.8 g / cm 3 , c(t): The volume of eroded metal loss in the time interval (t, t + dt); H: The casing thickness, in cm; ε(t): The erosion coefficient; a e (t): Eroded area of the blast hole in the time interval (t, t+dt), h: The height calculated for an infinitesimal volume, h ∈ [0, H]; θ1(t), θ2(t): The erosion angles at times t and t + dt; When t ∈ [t, t + dt] and lim dt→0 dt = 0, there is tanθ2(t) ≈ tanθ1(t) = tanθ(t), where tanθ(t) is the hole erosion angle. e(t): The perforation erosion width at time t, in cm; A e : The erosion area of a single blast hole, which is the difference between the measured area of a single blast hole and the base blast hole area, with the unit of cm 2 , e(T): The final erosion width, in cm; d(T): The final perforation diameter, in cm; d BH : Base value of blasthole diameter, unit is cm; In Step 4, the relationship between the erosion area of a single perforation in the wellbore and the amount of fracturing proppant entering is calculated using the PSE formula. The PSE formula is: M s = γA e Where γ: The erosion sand entry coefficient, that is, the relationship between the erosion area of a single perforation in the wellbore and the amount of fracturing proppant; A e : The erosion area of a single blast hole, that is, the difference between the measured area of a single blast hole and the reference blast hole area M s : Proppant influx into a single perforation during the steady-state erosion process C p : The average value of the release coefficient, steady-state erosion process, with a value of 0.9 - 0.95 and stable as a constant, Weighted erosion coefficient of mean erosion area, Mean value of blasthole λP pf and λ: The erosion coefficient, a constant; P pf : Pressure drop due to borehole erosion, ρ s : proppant density, constant; In Step 4, the relationship between the erosion area of perforations in a section or cluster and the amount of fracturing proppant entering in the section or cluster is calculated using the SED formula. The SED formula is: M s,SCP = γ SCP A e,SCP Where A e,SCP : The final erosion area of all the holes within a segment or cluster, i.e., the difference between the measured area of all the holes within the segment or cluster and the corresponding reference hole. γ SCP : Erosion sand influx coefficient in a stage or cluster, i.e., the relationship between the erosion area of perforations in each stage or cluster and the amount of fracturing proppant entering each stage or cluster M s,SCP : The amount of proppant entering all the perforations within a stage or cluster, Weighted erosion coefficient of the average erosion area in a segment or cluster, Mean value of λP within segment or cluster pf ; In Step 4, the fracturing efficiency of perforations in a section or cluster is calculated using the FEI index or the EGI index. The FEI index is the ratio of the standard deviation of the proppant entry amount of a single perforation in the section or cluster to the average value of the proppant entry amount of a single perforation in the section or cluster. The EGI index is the ratio of the standard deviation of the final erosion area of a single perforation in the section or cluster to the average value of the final erosion area of a single perforation in the section or cluster.

2. The quantitative evaluation method for the fracturing efficiency of wellbore gun perforation according to claim 1, characterized in that: In Step 3, the image acquisition device is an optical, X-ray, acoustic, or array sensor logging tool with circumferential imaging technology.

3. A quantitative evaluation method for the fracturing efficiency of wellbore gun perforation according to claim 2, characterized in that: The image acquisition device is an array ring-scanning high-definition imaging logging instrument. The array ring-scanning high-definition imaging logging instrument has multiple ring-scanning lenses, and adjacent ring-scanning lenses have overlapping fields of view, capable of capturing high-resolution images of the 360° circumference of the wellbore wall.

4. A method for quantitatively evaluating the fracturing efficiency of wellbore perforation pressure according to claim 3, characterized in that: The fracturing efficiency of perforations in a section or cluster is divided into a spread sand entry distribution, a selective sand entry distribution, a discrete sand entry distribution, and a pulsed sand entry distribution according to different ranges of the FEI; The spread sand entry distribution means that after the sand fluid breaks through a certain perforation in the section, it spreads to the surrounding area and finally forms a relatively uniform sand entry amount distribution. Whether in terms of space or the amount of proppant entering, it shows an even distribution. From the perspective of fractures, multiple fractures are formed, and the stress cloud interference between the fractures is low. Therefore, there is a relatively complex connection of the main fractures. From the perspective of the reservoir, there is a complex fracture network between the fractures, the SRV volume is significantly increased, and the fracturing efficiency is good; Selective sand injection is presented as spreading sand injection in a certain area within the stage, while there is insufficient sand injection in other areas, reflecting a weak stress cloud effect between pores or clusters. When selecting the perforations or perforation clusters for proppant injection, a complex fracture network and sufficient fracture network volume can be formed outside the wellbore. However, in the perforations or perforation clusters where proppant injection is not selected, the amount of proppant entering is low, and a complex fracture network cannot be formed, and the fracture network volume is low. From the perspective of fractures, selective sand injection is only distributed to form a complex fracture network in a certain area, and there is no effective fracture network in other areas. From the perspective of the reservoir, selective sand injection only realizes volume stimulation in a certain area within the stage, with a certain SRV scale. However, from the perspective of the entire stage, its fracturing efficiency is medium, which is subdivided into medium-preferred, medium, and medium-deviated. Discrete sand injection distribution has a certain spreading or selective distribution, and the overall sand injection distribution is discrete, reflecting a strong stress cloud effect between pores or clusters, resulting in difficult coupling between the fractures that initiate, and most of the space outside the wellbore cannot form a complex fracture network, and the fracture network volume is low. From the perspective of the reservoir, the SRV volume is limited, and the fracturing efficiency is medium-deviated. Pulsed sand injection distribution reflects that 1-5 perforations have strong excessive sand injection, occupying more than 30% of the total sand injection volume, resulting in no sand injection or very limited sand injection in other perforations within this stage. From the perspective of fractures, pulsed sand injection distribution is a concrete manifestation of linear fractures, indicating that after some perforations are broken through, peripheral expansion cannot be achieved and excessive sand injection occurs, resulting in severe underpressure in other perforations. From the perspective of the reservoir, the stress cloud effect is severe, resulting in the inability to form a fishbone effect in a single fracture, and it can only continuously extend along the maximum principal stress perpendicular plane to the far end, with a probability of causing well interference, and a large-scale SRV volume will not be formed, and the fracturing efficiency is poor.

5. A method for quantitatively evaluating the fracturing efficiency of wellbore gun perforation according to claim 4, characterized in that: The FEI of the spreading sand injection distribution described above is in the range of 0 to 0.7, and the overall evaluation is good fracturing efficiency. Selective sand injection distribution is divided into strong selective sand injection distribution, medium selective sand injection distribution, and weak selective sand injection distribution. The FEI of the weak selective sand injection distribution is in the range of 0.7 to 1.0, and the overall evaluation is medium-preferred fracturing efficiency. The FEI of the medium selective sand injection distribution is in the range of 1.0 to 1.4, and the overall evaluation is medium fracturing efficiency. The FEI of the discrete sand injection distribution or strong selective sand injection distribution is in the range of 1.4 to 1.8, and the overall evaluation is medium-deviated fracturing efficiency. The FEI of the pulsed sand injection distribution is greater than 1.8, and the overall evaluation is poor fracturing efficiency. The EGI index has the same division definition as the FEI index.

6. The quantitative evaluation method for the fracturing efficiency of wellbore gun perforation according to claim 5, characterized in that: The fracturing proppant described above is quartz sand, or ceramsite, or chemically coated and modified proppant, or a combination of quartz sand, ceramsite, and chemically coated and modified proppant.

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