A distributed acoustic sensing inversion method and system for coordinating the limit of flow restriction with the dynamic evolution of hole erosion
Patent Information
- Application Number
- CN202611545318.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-10-08
- Publication Date
- 2026-11-03
Smart Images
Figure CN123029614A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of oil and gas exploration and development technology, and in particular to a distributed acoustic sensing inversion method and system for synergistic limit flow constraint and dynamic evolution of borehole erosion. Background Technology
[0002] In horizontal well fracturing of unconventional reservoirs such as shale oil and gas, multi-cluster fracturing, flow-limited perforation technology generates additional friction by controlling the diameter and number of perforations, promoting uniform fluid ingress into each cluster. However, under high flow rates and high proppant ratios, the continuous scouring of the perforations by the proppant-carrying fluid leads to dynamic enlargement of the perforation diameter, a decrease in perforation friction, and disruption of the original flow-limiting balance. Fluid gradually concentrates in a few dominant clusters, causing uneven fracture propagation and significant differences in proppant placement. Therefore, real-time identification of differences in fluid ingress, proppant ingress, and perforation erosion among each cluster becomes crucial for evaluating the effectiveness of flow-limited fracturing and optimizing operational parameters.
[0003] Currently, distributed fiber optic acoustic sensing (DAS) technology can continuously record acoustic signals induced by orifice jets during fracturing along the wellbore, providing a new means for diagnosing inter-cluster flow distribution. Existing DAS interpretation methods are mostly based on the assumption of "constant orifice size," directly establishing a statistical relationship between DAS energy and flow rate. However, field practice shows that orifice erosion causes DAS signal attenuation; signal weakening does not equate to a decrease in flow rate. Ignoring dynamic changes in orifice size can lead to serious misjudgments of inter-cluster flow distribution characteristics. Some studies have begun to attempt to simultaneously invert flow rate and orifice size, but still treat orifice size as an independent generation at each time step, lacking physical constraints on the continuity of orifice size evolution. Under complex conditions such as low signal-to-noise ratio, interference from neighboring clusters, or cluster deactivation-reactivation, the inversion results are prone to problems such as large orifice size fluctuations, poor temporal continuity, and large errors in toe-and-heel cluster distribution.
[0004] Therefore, there is an urgent need for a DAS interpretation method that can take into account both the design intent of the limit flow restriction and the dynamic evolution of orifice erosion. This method would introduce orifice erosion as an intrinsic physical constraint into the inversion framework, enabling simultaneous and high-precision solutions for inter-cluster flow rate, orifice diameter, liquid inflow rate, and sand inflow rate, thus providing a reliable basis for real-time fracturing control and optimization of flow restriction parameters.
[0005] In view of this, the present invention is hereby proposed. Summary of the Invention
[0006] This invention proposes a distributed acoustic sensing inversion method and system that combines synergistic limit current limiting constraints with dynamic evolution of aperture erosion, aiming to overcome the shortcomings of existing DAS interpretation methods that ignore the dynamic evolution of aperture erosion and lack physical constraints, resulting in low inversion accuracy.
[0007] Specifically, the following technical solution was adopted: A distributed acoustic sensing inversion method for coordinating limit current limiting constraints and dynamic evolution of aperture erosion includes: Collect surface injection volume, proppant concentration, and construction time series, as well as distributed acoustic sensing frequency band energy data at each cluster location along the horizontal wellbore, and perform unified time alignment; Establish an acoustic correlation between distributed acoustic wave sensing frequency band energy data and the single-hole flow rate, equivalent aperture, and number of holes in each cluster; The rate of change of equivalent pore size is expressed as a function of local flow velocity and proppant concentration, making the equivalent pore size a dynamic state quantity that evolves continuously over time, and the relationship of pore erosion evolution is constructed. Establish the material conservation relationship between the total surface injection flow and the total flow of each cluster; By combining the aforementioned acoustic correlation, pore erosion evolution, and material conservation relationships, a system of differential-algebraic coupled equations is formed with the flow rate of each cluster of single pores and the equivalent pore diameter as unknowns. The differential-algebraic coupled equations are discretized in time, and the flow rate and equivalent aperture of each cluster of single holes are solved synchronously at each time step using an iterative method. The Jacobian matrix is calculated by numerical difference in the iterative solution and a convergence control strategy is introduced. Based on the single-hole flow rate obtained at each time point, the cumulative influent volume, cumulative support dose, and equilibrium index characterizing the uniformity of fluid distribution within each cluster are calculated. Output the flow rate, equivalent pore size, cumulative liquid inflow, cumulative support dose, and equilibrium index of each cluster, and issue a flow limit failure warning based on the equilibrium index.
[0008] Optionally, in the distributed acoustic sensing inversion method for collaborative limit flow constraint and dynamic evolution of aperture erosion of the present invention, the establishment of the acoustic correlation between the distributed acoustic sensing frequency band energy data and the single aperture flow rate, equivalent aperture, and number of apertures in each cluster includes: Based on the Lighthill acoustic analogy, the following correlation is constructed: ; In the formula: Let i be the single-hole flow rate of cluster i at time t. For the distributed acoustic wave sensing target frequency band energy of cluster i, Let i be the equivalent aperture diameter. and For sound school positive coefficient, For reference aperture diameter, Let i be the number of holes in cluster i. For reference, the number of holes is used.
[0009] Optionally, in the distributed acoustic sensing inversion method for synergistic limit current limiting constraint and dynamic evolution of aperture erosion according to the present invention, the acoustic correction coefficient... and Distributed acoustic sensing data from single-cluster fracturing sections or non-erosion stages were used and calibrated through least-squares fitting. The reference aperture diameter The reference number of perforations is determined by downhole measurements of the perforation gun's design diameter or minimum erosion zone. Take the actual number of holes in a single cluster.
[0010] Optionally, in the distributed acoustic sensing inversion method for synergistic limit flow constraint and dynamic evolution of aperture erosion according to the present invention, the rate of change of the equivalent aperture is expressed as a function of local flow velocity and proppant concentration, using the following aperture erosion kinetic equation: ; In the formula: Let be the equivalent aperture diameter of cluster i, and K be the erosion rate coefficient. Let i be the equivalent proppant concentration. Let be the local flow velocity in a single pore within cluster i, and m be the velocity sensitivity index.
[0011] Optionally, in the distributed acoustic sensing inversion method for synergistic limit current limiting constraint and dynamic evolution of aperture erosion according to the present invention, the equivalent proppant concentration In the absence of direct cluster-level measurements, an equivalent concentration approximation is used, calculated by ground sand ratio and inter-cluster flow distribution; the velocity sensitivity index m is calibrated through indoor erosion experiments based on the rheological characteristics of the sand-carrying fluid.
[0012] Optionally, in the distributed acoustic sensing inversion method for collaborative limit flow constraint and dynamic evolution of aperture erosion of the present invention, the material conservation relationship between the total ground injection flow and the total flow of each cluster is constructed as follows: ; In the formula: The total injection flow to the ground. Let i be the total flow of cluster i. The number of clusters.
[0013] Optionally, in the distributed acoustic sensing inversion method for synergistic limit flow constraint and dynamic evolution of orifice erosion of the present invention, when wellbore leakage or bridge plug crossflow exists, the material conservation relationship is extended to: ; In the formula, The equivalent leakage term is obtained through pressure drop analysis after pump shutdown or joint inversion of temperature anomaly segments by distributed temperature sensing.
[0014] Optionally, in the distributed acoustic sensing inversion method for synergistic limit flow constraint and dynamic evolution of orifice erosion of the present invention, the differential-algebraic coupled equation system is discretized over time, and an iterative method is used at each time step to simultaneously solve for the flow rate and equivalent aperture of each cluster of single orifices, including: The evolution equation of pore erosion is discretized using an implicit Euler scheme: ; At time step k+1, the unknown vector Substituting into the system of simultaneous equations, the flow rate and equivalent aperture of each cluster of single orifices are solved simultaneously using the Newton-Raphson iteration method. During the iteration process, the Jacobian matrix is calculated using numerical difference, and a damping factor and regularization strategy are introduced to ensure convergence. The Newton iteration format is as follows: ; in, For Jacobian matrices, The number of iterations. For the first The residual vector of the step; the Jacobian matrix is calculated using numerical difference, and the convergence control strategy includes a damping factor and a regularization strategy.
[0015] Optionally, in the distributed acoustic sensing inversion method for synergistic limit flow constraint and dynamic evolution of orifice erosion of the present invention, the calculation of the cumulative inflow, cumulative support dose, and equilibrium index of each cluster includes: The trapezoidal integral method was used to calculate the cumulative fluid intake and cumulative support dose for each cluster. The equilibrium index UI was calculated by taking the ratio of the standard deviation to the mean of the cumulative fluid intake of each cluster and multiplying it by a percentage, i.e., UI = (1-σ / μ) ×100%, where σ is the standard deviation of the cumulative fluid intake of each cluster and μ is the mean of the cumulative fluid intake of each cluster. The method of issuing a flow restriction failure warning based on the equilibrium index includes: issuing a flow restriction failure warning when the UI is lower than the threshold set according to the reservoir characteristics and construction design, and suggesting adjustment of the perforation parameters or construction flow rate of the subsequent section. The perforation parameters include the number of holes, the hole diameter, and the perforation phase.
[0016] This invention also provides a distributed acoustic sensing inversion system for synergistic limiting current constraint and dynamic evolution of aperture erosion, comprising: The data acquisition module is used to collect surface injection volume, proppant concentration, and construction time series, as well as distributed acoustic sensing frequency band energy data at each cluster location along the horizontal wellbore, and to perform unified time alignment. The acoustic correlation construction module is used to establish acoustic correlations between distributed acoustic wave sensing frequency band energy data and the single-hole flow rate, equivalent aperture, and number of holes in each cluster. The erosion evolution construction module is used to express the rate of change of equivalent aperture as a function of local flow velocity and proppant concentration, so that the equivalent aperture is a dynamic state quantity that evolves continuously over time, and to construct the aperture erosion evolution relationship. The conservation constraint construction module is used to construct the mass conservation relationship between the total surface injection flow and the total flow of each cluster. The coupled equation system construction module is used to combine the acoustic correlation, the pore erosion evolution relationship and the material conservation relationship to form a differential-algebraic coupled equation system with the single-pore flow rate and equivalent pore diameter of each cluster as unknowns. The synchronous solution module is used to discretize the differential-algebraic coupled equation system in time, and simultaneously solve the single-hole flow rate and equivalent aperture of each cluster using an iterative method at each time step. The iterative solution uses numerical difference to calculate the Jacobian matrix and introduces a convergence control strategy. The cumulative evaluation module is used to calculate the cumulative influent volume, cumulative support dose, and equilibrium index that characterizes the uniformity of fluid distribution within a section, based on the single-hole flow rate obtained at each time point. The output early warning module is used to output the flow rate of each cluster's single orifice, equivalent orifice diameter, cumulative liquid inflow, cumulative support dose, and equilibrium index, and to issue a flow limit failure warning based on the equilibrium index.
[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) The erosion of the hole is transformed from an "empirical influencing factor" to an "inherent physical constraint of the model", which significantly improves the physical consistency and temporal continuity of the inversion results.
[0018] Existing DAS interpretation methods are mostly based on the assumption of "constant aperture," directly establishing the statistical relationship between DAS energy and flow rate. While some methods attempt to simultaneously invert flow rate and aperture, they treat aperture as an independently solved algebraic quantity at each time step, lacking physical constraints on the continuity of aperture evolution. This invention introduces an aperture erosion kinetic equation, expressing the rate of change of the equivalent aperture as a function of local velocity and proppant concentration, thus elevating aperture from a "single-time inversion quantity" to a "dynamic state quantity constrained by the erosion mechanism." Consequently, aperture evolves continuously over time, overcoming the problems of large aperture fluctuations and poor temporal continuity caused by independent time-step inversion. It also maintains physical consistency of the inversion results even under complex conditions such as low signal-to-noise ratio, neighboring cluster interference, or cluster deactivation-reactivation.
[0019] (2) The implicit time discretization and iterative synchronous solution of the differential-algebraic coupled system is adopted, which has high numerical stability and fast convergence speed.
[0020] This invention combines acoustic correlations, orifice erosion evolution relationships, and mass conservation relationships to form a set of differential-algebraic coupled equations with the flow rate of each cluster's individual orifices and the equivalent orifice diameter as unknowns. The orifice erosion evolution equations are then discretized in time using an implicit Euler scheme. At each time step, the flow rate of each cluster's individual orifices and the equivalent orifice diameter are combined into an unknown vector, which is solved synchronously using an iterative method. This avoids the error accumulation caused by stepwise solutions that calculate either the flow rate first and then the orifice diameter, or vice versa. During the iteration process, the Jacobian matrix is calculated using numerical difference, and damping factors and regularization strategies are introduced to ensure robustness even when the Jacobian matrix is ill-conditioned, effectively improving the iterative stability under low signal-to-noise ratio and strong nonlinear conditions.
[0021] (3) A complete explanatory chain was constructed from DAS band energy to single-hole flow rate, equivalent orifice diameter, cumulative liquid inflow, cumulative support dose and equilibrium index, providing quantitative basis for on-site decision-making.
[0022] This invention, based on the obtained single-orifice flow rate at each time point, calculates the cumulative fluid inflow and cumulative proppant dose for each cluster using trapezoidal integrals, and further calculates the equilibrium index UI, which characterizes the uniformity of fluid distribution within a segment. The output results include curves showing the changes in single-orifice flow rate, equivalent orifice diameter, cumulative fluid inflow, cumulative proppant dose, and equilibrium index over time for each cluster. These results can be directly used to determine the uniformity of fluid distribution within a segment and identify dominant and weak clusters. When the equilibrium index falls below a set threshold, a timely warning of flow-limiting failure can be issued, and adjustments to the perforation parameters or construction flow rate of subsequent segments can be recommended. This provides a clear basis for quickly assessing the effectiveness of flow-limiting fracturing and optimizing construction parameters on-site.
[0023] (4) The original constraints of the limit flow limiting design are retained, and the attenuation of flow limiting capacity caused by erosion is taken into account, and the interpretation results are more consistent with the actual physical process.
[0024] The acoustic correlation in this invention explicitly includes the number of eyelets. Compared with the reference number of holes The ratio, in the conservation of matter, explicitly includes the number of pores in each cluster. This approach retains the original constraints of the limit flow-limiting design (number of orifices, initial orifice diameter). Simultaneously, by considering the dynamic expansion of orifice diameter and the attenuation of flow-limiting capacity caused by erosion through the orifice erosion kinetic equation, the interpretation results accurately reflect the physical process of "erosion—orifice diameter expansion—friction reduction—flow redistribution." This avoids the problem of misinterpreting signal attenuation as flow reduction due to neglecting dynamic orifice diameter changes, providing a more reliable basis for optimizing flow-limiting perforation parameters and adjusting construction discharge rates.
[0025] (5) The method is highly adaptable and can be integrated into the real-time monitoring platform for fracturing, enabling interpretation during construction.
[0026] This invention can be further extended to a real-time monitoring mode, outputting the interpretation results of each cluster step-by-step during fracturing operations and dynamically updating the equilibrium index curve to guide real-time adjustment of fracturing parameters in the field. This method is applicable to the interpretation of DAS monitoring data for various multi-cluster flow-limited fracturing processes, such as horizontal well cementing bridge plug combined fracturing, soluble bridge plug fracturing, and coiled tubing sandblasting perforation. When wellbore leakage or bridge plug crossflow exists, the mass conservation relationship can be expanded to include an equivalent leakage term. The leakage term is obtained through pressure drop analysis after pump shutdown or joint inversion of temperature anomaly segments using distributed temperature sensors, further improving the method's adaptability to complex operating conditions. Attached Figure Description
[0027] Figure 1 This is a flowchart illustrating a distributed acoustic sensing inversion method for coordinating limit current limiting constraints and dynamic evolution of aperture erosion, according to an embodiment of the present invention. Figure 2 This is a technical roadmap for a distributed acoustic sensing inversion method for coordinating limit current limiting constraints and dynamic evolution of aperture erosion, as described in an embodiment of the present invention. Detailed Implementation
[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.
[0029] Therefore, the following detailed description of embodiments of the present invention is not intended to limit the scope of the claimed invention, but merely illustrates some embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.
[0030] It should be noted that, unless otherwise specified, the embodiments and features and technical solutions in the present invention can be combined with each other.
[0031] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.
[0032] In the description of this invention, it should be noted that the terms "upper," "lower," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of this invention is in use, or the orientation or positional relationship commonly understood by those skilled in the art. These terms are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention. In addition, the terms "first," "second," etc., are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.
[0033] like Figure 1 As shown, this embodiment provides a distributed acoustic sensing inversion method for coordinating limit current limiting constraints and dynamic evolution of aperture erosion, including the following steps: Step S1: Collect surface injection volume, proppant concentration, and construction time series, as well as distributed acoustic sensing frequency band energy data at each cluster location along the horizontal wellbore, and perform unified time alignment.
[0034] Specifically, during the horizontal well multi-cluster fracturing operation, the surface injection volume is collected by instruments from the surface fracturing vehicle. The proppant concentration (sand ratio) and construction time sequence were also analyzed. Simultaneously, acoustic signals induced by orifice jets during fracturing were continuously recorded along the wellbore using distributed acoustic sensing (DAS) optical fibers deployed within the horizontal wellbore, extracting DAS frequency band energy data at each cluster location. .
[0035] Since ground construction data and DAS data may come from different acquisition systems, and their sampling frequencies and time bases may differ, it is necessary to perform unified time alignment for the two types of data. Time alignment can be achieved using interpolation or resampling methods to unify the ground construction data and DAS band energy data onto the same time base, ensuring that the injection displacement, proppant concentration, and DAS band energy at each moment correspond one-to-one in subsequent inversion.
[0036] In one specific embodiment, the DAS frequency band energy is selected from an interpretation frequency band, which has the strongest correlation with the flow-induced acoustic signal and the highest signal-to-noise ratio. The interpretation frequency band is determined through frequency domain energy spectrum analysis, selecting the main frequency band range for flow-induced acoustics. Since the main frequency band of flow-induced acoustics may differ under different well conditions, it is necessary to select a frequency band specifically for each well condition to ensure the strongest correlation between the DAS frequency band energy and flow parameters.
[0037] Step S2: Establish the acoustic correlation between the distributed acoustic wave sensing frequency band energy data and the single-hole flow rate, equivalent aperture and number of holes in each cluster.
[0038] Specifically, based on the Lighthill acoustic analogy, there is a quantitative correlation between the acoustic signal induced by orifice jet and the single-orifice flow rate, orifice diameter, and orifice number. In this embodiment, the following acoustic correlation is constructed: ; In the formula: Let i be the single-hole flow rate of cluster i at time t. For the distributed acoustic wave sensing target frequency band energy of cluster i, Let i be the equivalent aperture diameter. and For sound school positive coefficient, For reference aperture diameter, Let i be the number of holes in cluster i. For reference, the number of holes is used.
[0039] The physical meaning of this correlation is: DAS band energy. With single-orifice flow rate There is a logarithmic linear relationship between them, and the slope is determined by the acoustic correction coefficient A; equivalent aperture Relative to reference aperture The change affects the acoustic signal to the power of (7 / 4); the number of apertures Relative to the reference number of holes The changes affect the acoustic signal in a logarithmic relationship of −10A. Therefore, the acoustic correlation quantitatively correlates the DAS band energy with the single-orifice flow rate, equivalent aperture, and number of orifices, providing a physical basis for subsequent inversion.
[0040] In one specific embodiment, the acoustic correction coefficient A and DAS data from single-cluster fracturing sections or non-erosion stages were obtained through least-squares fitting calibration. Specifically, the stage at the initial stage of construction, where the proppant concentration was extremely low and the pores had not yet experienced significant erosion, was selected. At this point, the equivalent pore diameter was approximately equal to the initial pore diameter. , number of holes Equal to the actual number of holes The acoustic correlation is simplified to Using the known ground-based injection volume and DAS band energy data for this stage, the slope A and reference intercept can be obtained through least-squares fitting. .
[0041] The reference aperture diameter The perforation gun design diameter or the downhole measurement value of the minimum erosion section is used. The perforation gun design diameter is a known construction parameter and can be directly used as the reference diameter; if downhole imaging logging data is available, the measured diameter of the minimum erosion section can also be used as the reference diameter to improve calibration accuracy. The reference number of perforations... Take the actual number of holes in a single cluster.
[0042] Step S3: Express the rate of change of the equivalent pore size as a function of the local flow velocity and the proppant concentration, so that the equivalent pore size is a dynamic state quantity that evolves continuously over time, and construct the pore erosion evolution relationship.
[0043] Specifically, under conditions of high flow rate and high proppant ratio, the continuous scouring of the pores by the proppant-carrying fluid leads to dynamic enlargement of the pore size. In this embodiment, the pore size evolution is expressed as a differential equation controlled by local flow velocity and proppant concentration: ; In the formula: Let be the equivalent aperture diameter of cluster i, and K be the erosion rate coefficient. Let i be the equivalent proppant concentration. Let be the local flow velocity in a single pore within cluster i, and m be the velocity sensitivity index.
[0044] The physical meaning of this differential equation is: the rate of change of aperture. With equivalent proppant concentration Proportional to local flow velocity The erosion rate coefficient K reflects the pore material's resistance to erosion, while the velocity sensitivity index m reflects the influence of flow velocity on the erosion rate. Through this differential equation, the equivalent pore size... It is no longer an algebraic quantity that can be solved independently at each time step, but rather a dynamic state quantity that evolves continuously over time, and its evolution process is physically constrained by local flow velocity and proppant concentration.
[0045] In one specific embodiment, the equivalent proppant concentration In the absence of direct cluster-level measurements, an approximation of the equivalent concentration calculated from the surface sand ratio and inter-cluster flow distribution is used. Specifically, the surface sand ratio is known, and the flow distribution among clusters is determined by the mass conservation principle, thereby converting the surface sand ratio into the equivalent proppant concentration for each cluster. The velocity sensitivity index m is calibrated through indoor erosion experiments based on the rheological characteristics of the sand-carrying fluid, and the erosion rate coefficient K can also be obtained through indoor erosion experiments or by fitting historical field data.
[0046] Step S4: Establish the mass conservation relationship between the total surface injection flow and the total flow of each cluster.
[0047] Specifically, according to the principle of conservation of mass, the total flow rate injected to the ground is equal to the sum of the total flows rates of all clusters: ; In the formula, This represents the total injection flow rate at ground level, expressed in m³ / min. The total flow rate of cluster i is expressed in m³ / min. Let be the number of holes in cluster i; Here is the flow rate per orifice of cluster i, in m³ / min; The number of clusters.
[0048] This conservation relationship ensures that the sum of the flow distributions of each cluster equals the total flow injected to the ground, which is an important constraint on the well-posedness of the inversion problem.
[0049] In one specific implementation, when there is significant wellbore leakage or bridge plug crossflow, the mass conservation relationship is extended to: ; In the formula, The equivalent leakage term is obtained through pressure drop analysis after pump shutdown or joint inversion of temperature anomaly segments from distributed temperature sensing (DTS). Therefore, this method maintains the accuracy of mass conservation relationships even under complex operating conditions involving wellbore leakage or bridge plug crossflow.
[0050] Step S5: Combine the acoustic correlation, the pore erosion evolution relationship, and the material conservation relationship to form a set of differential-algebraic coupled equations with the flow rate of each cluster of single pores and the equivalent pore diameter as unknowns.
[0051] Specifically, the acoustic correlation from step S2, the pore erosion kinetic equation from step S3, and the mass conservation equation from step S4 are combined to form the flow rate of each cluster of single pores. and equivalent aperture The system consists of a set of nonlinear equations. Among them, the acoustic correlation equation and the matter conservation equation are algebraic equations, and the pore erosion evolution equation is a differential equation. The two equations together form a differential-algebraic coupled system.
[0052] The unknowns in this differential-algebraic coupled system are the single-orifice flow rates of each cluster. and equivalent aperture The system consists of Nc acoustic correlation equations (one per cluster), one matter conservation equation, and Nc pore erosion evolution equations (one per cluster), totaling 2Nc+1 equations. The number of unknowns is 2Nc (Nc flow rates + Nc pore diameters). Since there is only one matter conservation equation and 2Nc unknowns, time discretization is necessary to transform the differential equations into algebraic equations before a well-stressed nonlinear equation system can be formed. After time discretization, each time step has 2Nc unknowns and 2Nc equations (Nc acoustic correlation equations + Nc discretized erosion evolution equations + 1 matter conservation equation, where the matter conservation equation replaces one of the acoustic correlation equations or serves as an additional constraint), thus forming a well-stressed nonlinear equation system.
[0053] Step S6: Discretize the differential-algebraic coupled equations over time, and simultaneously solve the single-orifice flow rate and equivalent orifice diameter of each cluster using an iterative method at each time step. The iterative solution uses numerical difference to calculate the Jacobian matrix and introduces a convergence control strategy.
[0054] Specifically, the evolution equation of pore erosion is discretized in time using an implicit Euler scheme: ; In the formula, the superscript k+1 represents the (k+1)th time step, and the superscript k represents the kth time step. For clusters The equivalent aperture diameter at time step k+1, For clusters The equivalent aperture diameter at time step k, where Δt is the time step length and K is the erosion rate coefficient. For clusters The equivalent proppant concentration at time step k+1, For clusters The local flow velocity in a single orifice at time step k+1 is given by m, which is a velocity sensitivity index. K and m can be determined based on the rheological characteristics of the sand-carrying fluid through indoor erosion experiments or historical field data. In the absence of direct cluster-level measurements, an equivalent concentration approximation calculated from the ground sand ratio and inter-cluster flow distribution can be used. It can be calculated from the single-orifice flow rate and equivalent orifice diameter based on the flow area. The advantage of the implicit Euler scheme is its good numerical stability, allowing for a larger time step, making it suitable for simulating long-term fracturing operations.
[0055] At time step k+1, the unknown vector Substituting into the simultaneous equations, the flow rate and equivalent orifice diameter of each cluster are simultaneously solved using the Newton-Raphson iteration method. During the iteration process, the Jacobian matrix is calculated using numerical difference, and a damping factor and regularization strategy are introduced to ensure convergence. The Newton-Raphson iteration format is as follows: ; in, For Jacobian matrices, The number of iterations. For the first The residual vector of the step. The Jacobian matrix is calculated using numerical difference, that is, by calculating the rate of change of the residual vector through small perturbations of each unknown quantity, the Jacobian matrix is approximately obtained.
[0056] During the iteration process, a damping factor and a regularization strategy are introduced to ensure convergence. The damping factor controls the iteration step size; when the residual decreases too quickly or oscillations occur, the iteration step size is appropriately reduced to avoid iteration divergence. The regularization strategy handles the ill-conditioned case of the Jacobian matrix; when the condition number of the Jacobian matrix is too large, a regularization term is added to improve the matrix condition number and enhance iteration stability. Therefore, iteration convergence can still be guaranteed under low signal-to-noise ratio and strong nonlinearity conditions.
[0057] Step S7: Based on the single-hole flow rate obtained at each time point, calculate the cumulative influent volume, cumulative support dose, and equilibrium index that characterizes the uniformity of fluid distribution within each cluster.
[0058] Specifically, based on the single-orifice flow rate obtained at each time point... The cumulative influent volume and cumulative support dose for each cluster were calculated using trapezoidal integrals. Cumulative influent volume Single orifice flow rate The integral over time multiplied by the number of holes : ; Cumulative supportive dose Single orifice flow rate With proppant concentration The integral of the product over time multiplied by the number of eyelets : ; The trapezoidal integral method divides the time series into several small intervals and approximates the integral value with the area of a trapezoid in each small interval. It has the advantages of simple calculation and high accuracy.
[0059] The equilibrium index UI is further calculated, which is the ratio of the standard deviation to the mean of the cumulative liquid inflow of each cluster, multiplied by a percentage. UI = (1-σ / μ)×100%; Where σ is the standard deviation of the cumulative liquid inflow of each cluster, and μ is the mean of the cumulative liquid inflow of each cluster. The closer the equilibrium index UI is to 100%, the more uniform the cumulative liquid inflow of each cluster is, and the more balanced the fluid distribution within the section; the lower the UI, the greater the difference in liquid inflow of each cluster, and the worse the flow restriction effect.
[0060] Step S8: Output the flow rate of each cluster's single orifice, equivalent orifice diameter, cumulative liquid inflow, cumulative support dose, and equilibrium index, and issue a flow restriction failure warning based on the equilibrium index.
[0061] Specifically, the system outputs curves showing the changes in single-hole flow rate, equivalent orifice diameter, cumulative influent volume, cumulative support dose, and equilibrium index over time for each cluster. This allows field engineers to visually assess differences in fluid influent, sand influent, and orifice erosion among each cluster. Simultaneously, the system determines the uniformity of fluid distribution within a section based on the equilibrium index, issuing a flow-limiting failure warning when the UI falls below a set threshold.
[0062] The threshold is set based on reservoir characteristics and construction design. For example, for reservoirs with good homogeneity, the threshold can be set to 90%; for reservoirs with strong heterogeneity, the threshold can be appropriately reduced. When UI is lower than the set threshold, it indicates that the fluid distribution within the section is significantly uneven, and the flow restriction effect fails. At this time, a flow restriction failure warning is issued, and it is recommended to adjust the perforation parameters or construction flow rate of subsequent sections. The perforation parameters include the number of perforations, the perforation diameter, and the perforation phase. For example, the number of perforations of dominant clusters can be increased or their perforation diameter can be decreased to increase the perforation friction of dominant clusters and promote fluid transfer to weaker clusters; the construction flow rate can also be appropriately reduced to slow down the perforation erosion rate.
[0063] like Figure 2 As shown, the technical approach of this embodiment can be divided into four stages: The first phase involves data standardization and parameter calibration. The tasks include acquiring construction data, extracting DAS band energy, and calibrating the erosion-free section of a single cluster. Technical methods include ground parameter acquisition, DAS band energy extraction, and calibration of the erosion-free section of a single cluster. The output includes construction parameters with a unified time reference, DAS energy sequences, and a set of well completion parameters.
[0064] The second stage involves constructing a differential-algebraic coupled system. The task is to establish a set of acoustic, erosion dynamics, and mass conservation equations. Techniques include Lighthill acoustic analogy, orifice erosion differential equations, and flow conservation. The output is a set of nonlinear equations relating the single-orifice flow rate and the equivalent orifice diameter.
[0065] The third stage involves implicit discretization and Newton-Raphson iteration. The task is to simultaneously solve for the flow rate and equivalent orifice diameter of each cluster of orifices. Techniques include implicit Euler discretization, Newton-Raphson iteration, numerical Jacobian, and damping / regularization. The outputs are the flow rate, orifice diameter, and erosion rate at each time step.
[0066] The fourth stage involves cumulative volume and uniformity evaluation. The task is to calculate the cumulative liquid / sand inflow and uniformity index. Technical methods include trapezoidal integral and standard deviation / mean statistics. The outputs are the cumulative liquid inflow, cumulative support dosage, and uniformity index for each cluster. The final results serve as a basis for decision-making in diagnosing the flow restriction effect and optimizing construction.
[0067] Taking a fracturing section of a horizontal well in an oilfield as an example, DAS data interpretation was carried out according to the method of this invention. This section consists of 6 clusters, each with the same number of perforations, and the initial perforation diameter is the design value of the perforating gun. Surface construction data (injection rate, proppant concentration changes over time) and DAS frequency band energy data along the wellbore at each cluster location were collected and time-aligned.
[0068] First, the acoustic parameters are calibrated using DAS data from the early stage of construction (when the proppant concentration is extremely low), and the acoustic correlation slope A and reference intercept B_ref are obtained; the reference aperture d_ref is taken as the design value of the perforating gun, and the reference number of holes N_p,ref is taken as the actual number of holes in a single cluster.
[0069] Then, a set of coupled equations is constructed: the acoustic correlation equation establishes the relationship between DAS band energy and single-orifice flow rate, orifice diameter, and number of orifices; the orifice erosion kinetic equation expresses the orifice diameter change rate as a power function of local velocity and proppant concentration; the mass conservation equation ensures that the total flow rate injected to the ground is equal to the sum of the total flow rates of each cluster. This forms a differential-algebraic coupled system concerning the single-orifice flow rate and equivalent orifice diameter of each cluster.
[0070] The solution process employs an implicit Euler scheme to discretize the aperture evolution equation over time. At each time step, the unknowns (cluster flow rate and aperture) are grouped into a nonlinear equation system, which is then solved synchronously using the Newton-Raphson iteration method. During the iteration process, numerical difference is used to calculate the Jacobian matrix, and damping factors and regularization strategies are introduced to ensure convergence.
[0071] After solving the problem, the cumulative injection volume and cumulative proppant dosage for each cluster are calculated using trapezoidal integrals, thus obtaining the equilibrium index UI (i.e., the ratio of the standard deviation to the mean of the cumulative injection volume for each cluster, multiplied by a percentage). Taking cluster 3 as an example: the initial pore size gradually increases with proppant injection, and the flow rate per pore gradually decreases due to the increase in pore size and decrease in friction, with some flow shifting to clusters that have not been sufficiently eroded. The overall equilibrium index for this segment is 90.1%, indicating good uniformity.
[0072] To verify the interpretation results, downhole imaging logging after pressure was used to measure the actual pore diameter of each cluster. The average relative error between the final pore diameter derived from the model and the measured value was less than 4%. In contrast, the traditional algebraic inversion method, which does not consider erosion dynamics (solving only acoustic and conservation equations time-by-time), resulted in drastic fluctuations in pore diameter inversion results, exhibiting non-physical pore diameter decreases. The relative error between the cumulative fluid inflow distribution and the distributed temperature sensing (DTS) interpretation results was 12.6%, while the error of the method in this invention was only 5.2%.
[0073] The above results show that by introducing the pore erosion dynamics equation and implicit Newtonian solution, this invention significantly enhances the continuity and physical consistency of the inversion results. Even in the low signal-to-noise ratio and erosion-dominant stages, it can still stably output reliable inter-cluster flow and pore size evolution data, effectively supporting the evaluation of flow-limited fracturing effects and construction optimization decisions.
[0074] This embodiment provides a distributed acoustic sensing inversion system for coordinating limit current limiting constraints and dynamic evolution of aperture erosion, including: The data acquisition module is used to collect surface injection volume, proppant concentration, and construction time series, as well as distributed acoustic sensing frequency band energy data at each cluster location along the horizontal wellbore, and to perform unified time alignment. The acoustic correlation construction module is used to establish acoustic correlations between distributed acoustic wave sensing frequency band energy data and the single-hole flow rate, equivalent aperture, and number of holes in each cluster. The erosion evolution construction module is used to express the rate of change of equivalent aperture as a function of local flow velocity and proppant concentration, so that the equivalent aperture is a dynamic state quantity that evolves continuously over time, and to construct the aperture erosion evolution relationship. The conservation constraint construction module is used to construct the mass conservation relationship between the total surface injection flow and the total flow of each cluster. The coupled equation system construction module is used to combine the acoustic correlation, the pore erosion evolution relationship and the material conservation relationship to form a differential-algebraic coupled equation system with the single-pore flow rate and equivalent pore diameter of each cluster as unknowns. The synchronous solution module is used to discretize the differential-algebraic coupled equation system in time, and simultaneously solve the single-hole flow rate and equivalent aperture of each cluster using an iterative method at each time step. The iterative solution uses numerical difference to calculate the Jacobian matrix and introduces a convergence control strategy. The cumulative evaluation module is used to calculate the cumulative influent volume, cumulative support dose, and equilibrium index that characterizes the uniformity of fluid distribution within a section, based on the single-hole flow rate obtained at each time point. The output early warning module is used to output the flow rate of each cluster's single orifice, equivalent orifice diameter, cumulative liquid inflow, cumulative support dose, and equilibrium index, and to issue a flow limit failure warning based on the equilibrium index.
[0075] In one specific embodiment, the acoustic correlation construction module constructs acoustic correlations based on Lighthill acoustic analogies; the erosion evolution construction module adopts the porosity erosion dynamics equation. The conservation constraint construction module adopts the mass conservation law. The synchronous solution module discretizes the erosion evolution equation of the perforation using an implicit Euler scheme and solves it synchronously using the Newton-Raphson iteration method. The Jacobian matrix is calculated using numerical difference. The convergence control strategy includes a damping factor and a regularization strategy. The cumulative evaluation module calculates the cumulative amount using a trapezoidal integral, and the equilibrium index UI = (1-σ / μ) × 100%. The output early warning module issues a current limiting failure warning when UI is lower than a set threshold.
[0076] In one specific embodiment, the system can be further expanded into a real-time monitoring system that outputs the interpretation results of each cluster step by step during the fracturing operation and dynamically updates the equilibrium index curve to guide the real-time adjustment of fracturing parameters on site.
[0077] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the displayed or discussed mutual couplings, direct couplings, or communication connections may be through some interfaces; indirect couplings or communication connections between apparatuses or modules may be electrical, mechanical, or other forms.
[0078] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical modules; that is, they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.
[0079] Furthermore, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module. The integrated modules described above can be implemented in hardware or as software functional modules.
[0080] If the integrated module is implemented as a software functional module and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.
[0081] The above embodiments are only used to illustrate the present invention and are not intended to limit the technical solutions described herein. Although the present invention has been described in detail with reference to the above embodiments, the present invention is not limited to the specific embodiments described above. Therefore, any modifications or equivalent substitutions to the present invention, as well as all technical solutions and improvements that do not depart from the spirit and scope of the invention, are covered within the scope of the claims of the present invention.
Claims
1. A distributed acoustic sensing inversion method for coordinating limit current limiting constraints and dynamic evolution of aperture erosion, characterized in that, include: Collect surface injection volume, proppant concentration, and construction time series, as well as distributed acoustic sensing frequency band energy data at each cluster location along the horizontal wellbore, and perform unified time alignment; Establish an acoustic correlation between distributed acoustic wave sensing frequency band energy data and the single-hole flow rate, equivalent aperture, and number of holes in each cluster; The rate of change of equivalent pore size is expressed as a function of local flow velocity and proppant concentration, making the equivalent pore size a dynamic state quantity that evolves continuously over time, and the relationship of pore erosion evolution is constructed. Establish the mass conservation relationship between the total surface injection flow and the total flow of each cluster; By combining the aforementioned acoustic correlation, pore erosion evolution, and material conservation relationships, a set of differential-algebraic coupled equations is formed with the flow rate of each cluster of single pores and the equivalent pore diameter as unknowns. The differential-algebraic coupled equations are discretized in time, and the flow rate and equivalent aperture of each cluster of single holes are solved synchronously at each time step using an iterative method. The Jacobian matrix is calculated by numerical difference in the iterative solution and a convergence control strategy is introduced. Based on the single-hole flow rate obtained at each time point, the cumulative influent volume, cumulative support dose, and equilibrium index characterizing the uniformity of fluid distribution within each cluster are calculated. Output the flow rate, equivalent pore size, cumulative liquid inflow, cumulative support dose, and equilibrium index of each cluster, and issue a flow limit failure warning based on the equilibrium index.
2. The distributed acoustic sensing inversion method for synergistic limit current limiting constraint and dynamic evolution of aperture erosion according to claim 1, characterized in that, The establishment of the acoustic correlation between distributed acoustic wave sensing frequency band energy data and the single-aperture flow rate, equivalent aperture, and number of apertures in each cluster includes: Based on the Lighthill acoustic analogy, the following correlation is constructed: ； In the formula: Let i be the single-hole flow rate of cluster i at time t. For the distributed acoustic wave sensing target frequency band energy of cluster i, Let i be the equivalent aperture diameter. and For sound school positive coefficient, For reference aperture diameter, Let i be the number of holes in cluster i. For reference, the number of holes is used.
3. The distributed acoustic sensing inversion method for synergistic limit current limiting constraint and dynamic evolution of aperture erosion according to claim 2, characterized in that, The acoustic correction coefficient and Distributed acoustic sensing data from single-cluster fracturing sections or non-erosion stages were used to obtain the data through least-squares fitting calibration. The reference aperture diameter The reference number of perforations is determined by downhole measurements of the perforation gun's design diameter or minimum erosion zone. Take the actual number of holes in a single cluster.
4. The distributed acoustic sensing inversion method for synergistic limit current limiting constraint and dynamic evolution of aperture erosion according to claim 1, characterized in that, The rate of change of the equivalent aperture is expressed as a function of the local flow velocity and the proppant concentration, using the following aperture erosion kinetic equation: ； In the formula: Let be the equivalent aperture diameter of cluster i, and K be the erosion rate coefficient. Let i be the equivalent proppant concentration. Let be the local flow velocity in a single pore within cluster i, and m be the velocity sensitivity index.
5. The distributed acoustic sensing inversion method for synergistic limit current limiting constraint and dynamic evolution of aperture erosion according to claim 4, characterized in that, The equivalent proppant concentration In the absence of direct cluster-level measurements, an equivalent concentration approximation is used, calculated by ground sand ratio and inter-cluster flow distribution; the velocity sensitivity index m is calibrated through indoor erosion experiments based on the rheological characteristics of the sand-carrying fluid.
6. The distributed acoustic sensing inversion method for synergistic limit current limiting constraint and dynamic evolution of aperture erosion according to claim 1, characterized in that, The mass conservation relationship between the total surface injection flow and the total flow of each cluster is as follows: ； In the formula: The total injection flow to the ground. Let i be the total flow of cluster i. The number of clusters.
7. The distributed acoustic sensing inversion method for synergistic limit current limiting constraint and dynamic evolution of aperture erosion according to claim 6, characterized in that, When wellbore leakage or bridge plug crossflow occurs, the aforementioned material conservation relationship extends to: ； In the formula, The equivalent leakage term is obtained through pressure drop analysis after pump shutdown or joint inversion of temperature anomaly segments by distributed temperature sensing.
8. The distributed acoustic sensing inversion method for synergistic limit current limiting constraint and dynamic evolution of aperture erosion according to claim 1, characterized in that, The differential-algebraic coupled equations are discretized over time, and at each time step, an iterative method is used to simultaneously solve for the flow rate and equivalent aperture of each cluster of orifices, including: The evolution equation of pore erosion is discretized using an implicit Euler scheme: ； At time step k+1, the unknown vector Substituting into the system of simultaneous equations, the flow rate and equivalent aperture of each cluster of single orifices are solved simultaneously using the Newton-Raphson iteration method. During the iteration process, the Jacobian matrix is calculated using numerical difference, and a damping factor and regularization strategy are introduced to ensure convergence. The Newton iteration format is as follows: ; Where is the Jacobian matrix. The number of iterations. For the first The residual vector of the step; the Jacobian matrix is calculated using numerical difference, and the convergence control strategy includes a damping factor and a regularization strategy.
9. The distributed acoustic sensing inversion method for synergistic limit current limiting constraint and dynamic evolution of aperture erosion according to claim 1, characterized in that, The calculation of the cumulative influent volume, cumulative support dose, and equilibrium index for each cluster includes: The trapezoidal integral method was used to calculate the cumulative fluid intake and cumulative support dose for each cluster. The equilibrium index UI was calculated by taking the ratio of the standard deviation to the mean of the cumulative fluid intake of each cluster and multiplying it by a percentage, i.e., UI = (1-σ / μ) ×100%, where σ is the standard deviation of the cumulative fluid intake of each cluster and μ is the mean of the cumulative fluid intake of each cluster. The method of issuing a flow restriction failure warning based on the equilibrium index includes: issuing a flow restriction failure warning when the UI is lower than the threshold set according to the reservoir characteristics and construction design, and suggesting adjustment of the perforation parameters or construction flow rate of the subsequent section. The perforation parameters include the number of holes, the hole diameter, and the perforation phase.
10. A distributed acoustic sensing inversion system for synergistic limit current limiting constraint and dynamic evolution of aperture erosion, characterized in that, include: The data acquisition module is used to collect surface injection volume, proppant concentration, and construction time series, as well as distributed acoustic sensing frequency band energy data at each cluster location along the horizontal wellbore, and to perform unified time alignment. The acoustic correlation construction module is used to establish acoustic correlations between distributed acoustic wave sensing frequency band energy data and the single-hole flow rate, equivalent aperture, and number of holes in each cluster. The erosion evolution construction module is used to express the rate of change of equivalent aperture as a function of local flow velocity and proppant concentration, so that the equivalent aperture is a dynamic state quantity that evolves continuously over time, and to construct the aperture erosion evolution relationship. The conservation constraint construction module is used to construct the mass conservation relationship between the total surface injection flow and the total flow of each cluster. The coupled equation system construction module is used to combine the acoustic correlation, the pore erosion evolution relationship and the material conservation relationship to form a differential-algebraic coupled equation system with the single-pore flow rate and equivalent pore diameter of each cluster as unknowns. The synchronous solution module is used to discretize the differential-algebraic coupled equation system in time, and simultaneously solve the single-hole flow rate and equivalent aperture of each cluster using an iterative method at each time step. The iterative solution uses numerical difference to calculate the Jacobian matrix and introduces a convergence control strategy. The cumulative evaluation module is used to calculate the cumulative influent volume, cumulative support dose, and equilibrium index that characterizes the uniformity of fluid distribution within a section, based on the single-hole flow rate obtained at each time point. The output early warning module is used to output the flow rate of each cluster's single orifice, equivalent orifice diameter, cumulative liquid inflow, cumulative support dose, and equilibrium index, and to issue a flow limit failure warning based on the equilibrium index.