Prediction method of offshore well production and sand production rate in unconsolidated sandstone considering the effect of screen pipe

Abstract

The method for predicting offshore well production and sand production of unconsolidated sandstone considering the influence of screen pipe relates to the technical field of oil and gas development, and mainly comprises the following steps: obtaining well logging data and historical production data of a target well, establishing a dynamic physical model of comprehensive sand production effect, multiphase flow and screen pipe-reservoir seepage coupling influence, constructing a screen pipe comprehensive integrity evolution model, calculating the comprehensive model prediction value of oil, water and sand production rate and screen pipe comprehensive integrity at any time point, and based on the calculation result of the above model and the historical production data, constructing a characteristic vector training machine learning regression model to obtain a machine learning prediction value, and performing weighted fusion on the two types of prediction values to obtain the final prediction result of the oil, water and sand production rate and screen pipe comprehensive integrity at each time point; the weighted fusion of the comprehensive model prediction result and the result of the machine learning regression model realizes the deep fusion of the physical model and the data-driven method, and effectively improves the prediction accuracy of the model on a long time scale.

Description

Technical Field

[0001] This invention relates to the field of oil and gas development technology, specifically to a method for predicting production and sand output of offshore wells in loose sandstone considering the influence of screens. Background Technology

[0002] Loose sandstone reservoirs are an important type of global petroleum resource, mainly distributed in offshore areas such as the Bohai Sea, South China Sea, and Gulf of Mexico. These reservoirs are characterized by loose cementation, high porosity (typically >30%), and high permeability (typically >1000 mD), making them prone to sand production during production, which seriously threatens the long-term stable production of oil wells. Currently, screen pipe sand control completion technology is commonly used in loose sandstone wells. However, during long-term production, the screen pipe system undergoes various degradation processes such as mechanical wear, hydraulic performance decline, and chemical corrosion, leading to a gradual decrease in sand control capability. Especially during the oil-water co-production stage, the increase in water cut will cause complex physicochemical effects such as rock softening and changes in interfacial tension, further exacerbating the risk of sand production.

[0003] The existing technology has the following problems:

[0004] First, traditional sand output prediction models do not consider the dynamic degradation effect of the screen system. Existing methods typically assume constant screen performance and cannot predict screen failure time and subsequent output spikes, leading to a cumulative increase in prediction error over time.

[0005] Second, there is a lack of a complete mathematical description of the oil-water two-phase flow and the screen-reservoir coupling. Existing studies have mostly treated reservoir seepage, wellbore flow, and screen filtration as independent processes, neglecting the bidirectional coupling and dynamic feedback relationships between them.

[0006] Third, the long-term performance degradation mechanism of offshore loose sandstone wells is unclear. Existing models are unable to explain phenomena such as "intensified delayed sand production" and "abnormal production decline during high water cut periods" observed in the field.

[0007] Fourth, both pure physics models and data-driven models have their limitations. Pure physics models have numerous parameters, are computationally complex, and are highly sensitive to parameters; pure data-driven models lack physical constraints and have poor extrapolation capabilities.

[0008] Therefore, there is an urgent need to develop a new method that can accurately describe the coupling mechanism of screen-reservoir-fluid, consider the time evolution of screen integrity, and achieve high-precision prediction of long-term production dynamics of offshore loose sandstone wells with a lifespan of 20 years. Summary of the Invention

[0009] Therefore, the main objective of this invention is to provide a method for predicting production and sand production of offshore wells in loose sandstone that takes into account the influence of screen pipes, so as to solve the above-mentioned problems in the prior art, realize accurate prediction of long-term production dynamics of oil and water wells in loose sandstone, and provide a scientific basis for sand control completion design and production optimization.

[0010] The technical solution of this invention is a method for predicting the production and sand output of offshore wells in loose sandstone considering the influence of screens, comprising the following steps:

[0011] S1: Obtain logging data and historical production data of the target well, calculate the relative permeability of oil and water, and combine the water softening effect and Biot coefficient to correct the stress path coefficient and porosity changes caused by compaction, update the reservoir permeability, and obtain the corrected porosity, permeability, stress path coefficient and relative permeability parameters.

[0012] S2: Considering the influence of flow field disturbance near the screen tube and the sand control efficiency of the screen tube on sand production, a dynamic physical model integrating sand production effect, multiphase flow model and screen tube-reservoir seepage coupling effect is established.

[0013] S3: Combining mechanical damage, hydraulic performance degradation and chemical corrosion factors, construct an evolution model of the overall integrity of the screen tube and calculate the relationship between the overall integrity of the screen tube and time.

[0014] S4: Combine the dynamic physical model and the screen tube integrity evolution model to calculate the comprehensive model prediction value of oil, water, sand production and screen tube integrity at any time point;

[0015] S5: Based on the calculation results of the dynamic physical model and the screen pipe integrated integrity evolution model, as well as well logging data and historical production data, feature vectors are constructed to train a machine learning regression model;

[0016] S6: Using a machine learning regression model, the oil, water, and sand yields and the overall integrity of the screen tube are iteratively predicted at a set time step to obtain the machine learning prediction value at any time point.

[0017] S7: The two types of predicted values ​​obtained in steps S4 and S6 are weighted and fused, and then rolled correction is performed using Kalman filtering combined with measured production data to obtain the final predicted results of oil, water, and sand yields and screen tube integrity at each time point.

[0018] The technical effects of this invention are:

[0019] (1) This invention establishes a dynamic prediction system for screen tube-reservoir complete coupling. It weightedly integrates the prediction results of the comprehensive model obtained by the dynamic physical model and the screen tube comprehensive integrity model with the results of the machine learning regression model, realizing the deep integration of physical model and data-driven method, truly reflecting the bidirectional coupling relationship between screen tube system and reservoir, and significantly improving prediction accuracy.

[0020] (2) This invention proposes a multi-mechanism sand discharge superposition model, which organically combines four mechanisms: pressure drive, water softening, fluid shearing and fatigue accumulation. It can accurately predict the main control sand discharge mechanism conversion at different production stages and can be used to effectively explain the abnormal sand discharge phenomenon observed in current on-site production.

[0021] (3) This invention can predict the failure time of screen tubes by coupling calculation of mechanical integrity, hydraulic integrity and chemical integrity, and provides a scientific basis for sand control well completion design and maintenance plan.

[0022] (4) The machine learning regression model in this invention improves the accuracy and robustness of long-term predictions while maintaining physical interpretability through multi-dimensional feature vector extraction and Kalman filter dynamic correction.

[0023] (5) By introducing stress and water content corrections to porosity and permeability, the abnormal decline in yield during high water content periods was explained, which improved the reliability of predictions on a long-term scale. Attached Figure Description

[0024] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below.

[0025] Figure 1 This is an overall flowchart of the present invention;

[0026] Figure 2 This shows the actual state of the screen pipe in the target well in the embodiment. Detailed Implementation

[0027] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings.

[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. The described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] See Figure 1A method for predicting production and sand output of offshore wells in loose sandstone, taking into account the influence of screens, includes the following steps:

[0030] Step S1: Acquire logging data and historical production data of the target well. This step involves acquiring and processing the logging data and historical production data of the target well to construct a basic formation property model that dynamically reflects changes in formation seepage capacity and mechanical strength. This model provides input parameters for multiphase flow simulation, sand production mechanism analysis, and screen-reservoir coupling calculations. Specifically, it includes five sub-steps: logging data preprocessing, relative permeability calculation, stress path coefficient determination, porosity evolution caused by compaction, and dynamic permeability updating.

[0031] Acquire reservoir logging data for the target well, including formation physical parameters such as porosity, permeability, uniaxial compressive strength, cohesion, and friction angle. Then, perform layer segmentation, outlier removal, and interpolation smoothing on the data to form a continuous physical property curve at depth z.

[0032] The reservoir porosity and permeability are introduced with stress and water cut corrections, wherein the initial water saturation is based on depth. S wi (z) The calculation method is as follows:

[0033] in S wi Z represents the bound water saturation, obtained from rock physical parameters derived from well logging data; Z represents the current depth. Z max This indicates the maximum logging depth of the target well, obtained from the measurement depth derived from the logging data. Z min This indicates the minimum logging depth of the target well, which is obtained from the measurement depth derived from the logging data. Δp This represents the porosity effect term. This formula is used to give the water aquifer distribution field at the beginning of the layer.

[0034] To fully reflect the key role of water content in sand production mechanism, pore structure softening, permeability renewal and screen performance degradation, a dynamic evolution model of water saturation with time and depth was established.

[0035] A first-order leading-edge propulsion model is adopted:

[0036] in F(z,t) The water drive leading edge function is a time-dependent function that can be determined based on production history or material balance. S wimax This represents the maximum bound water saturation, obtained from rock physical parameters derived from well logging data. S wf ( z ,t () indicates the water saturation at the water drive front.

[0037] Water saturation at depth z at time t S w (z,t) Historical water production, water cut, or WOR data can be used to invert or correct the water cut. Water cut also redistributes between layers due to local permeability and pressure differences, so a disturbance term can be added. The calculation method is shown in the following formula:

[0038] in λ(t) These are the historical fitting coefficients. δw (z,t) It is used to describe the effects of uneven water flooding, shear-induced sand carrying, or gravity differentiation.

[0039] Effective water saturation S wef (z,t) The calculation method is shown in the following formula:

[0040] In the formula, S or This represents the residual oil saturation.

[0041] oil-water relative permeability k ro (z,t), k rw (z,t) The calculation method is shown in the following formula:

[0042] In the formula, k rwmax 、k romax These represent the maximum relative water permeability and the maximum relative oil permeability, respectively, obtained from the rock physical parameters obtained during well logging. n w Corey index in aqueous phase; n o Corey index in the oil phase.

[0043] Considering the effect of water softening on the skeleton Poisson's ratio v ef (z,t) The revised calculation method is shown in the following formula:

[0044] In the formula, v fr (z) This represents the initial skeleton Poisson's ratio at depth z, obtained from the rock physical parameters obtained during well logging.

[0045] Corrected Biot coefficient α ef (z,t) The calculation method is shown in the following formula:

[0046] In the formula, α(z) This represents the initial Biot coefficient at depth z, obtained from the rock physical parameters obtained during well logging.

[0047] For horizontal stress path coefficient γ h (z,t) The calculation method is shown in the following formula:

[0048]

[0049] Vertical stress path coefficient γ v (z,t) The calculation method is shown in the following formula:

[0050] In the formula, e Indicates the aspect ratio of the oil reservoir;

[0051] Effective stress σ ef (z,t) The evolution over time is calculated as follows:

[0052] In the formula σv(z) This represents the overburden pressure at depth z, obtained from the rock physical parameters obtained during well logging. P p (z,t) This refers to pore pressure. Effective stress drives compaction, determines rock strength, and influences mechanical damage to the screen.

[0053] During the production process, as pore pressure decreases and effective stress increases, the formation undergoes compaction deformation, and porosity gradually decreases. To quantitatively describe this process, a porosity evolution model considering effective stress and water softening is established.

[0054] For elastic modulus based on water softening effect E ef (z,t) The calculation method is shown in the following formula:

[0055] In the formula, E(z) This represents the basic elastic modulus of the rock skeleton, which is obtained from the rock physical parameters obtained during well logging. F soft This indicates the calibration water softening coefficient, taken as 0.65; S w (z, t () represents the water saturation at depth z at time t; S wi ( z () represents the initial water saturation at depth z;

[0056] For formation pressure difference ​ 2 ​ The calculation method is shown in the following formula:

[0057] In the formula, P e (z) This represents the reservoir pressure at depth z, obtained from well logging data; P w ​ This represents the bottom-hole flow pressure at depth z at time t, obtained from historical production data;

[0058] For compaction factor ​ The calculation method is shown in the following formula:

[0059]

[0060] For the porosity change Δ ​ The calculation method is shown in the following formula:

[0061] In the formula, λ por To calibrate the influence coefficient of water softening on porosity.

[0062] Based on the calculated porosity change Δ ​ Updated layer porosity ​ The calculation method is shown in the following formula:

[0063] In the formula, ​ This indicates the updated reservoir porosity; ​ 0 (z) Indicates initial porosity; Δ ​ Indicates changes in porosity;

[0064] Based on the new porosity and taking into account the complex effects of the aquifer environment, the updated reservoir permeability is... k The calculation method is shown in the following formula:

[0065] In the formula, ​ This represents the corrected reservoir permeability; k 0 (z) Indicates the initial reservoir permeability; ​ Indicates the water content effect factor;

[0066] Among them, water content effect factor ​ The calculation method is shown in the following formula:

[0067] In the formula, S w ​ This represents the water saturation at depth z at time t.

[0068] Step S2: Considering the influence of flow field disturbance near the screen tube and the sand control efficiency of the screen tube on sand production, establish a dynamic physical model that integrates sand production effect, multiphase flow model and screen tube-reservoir seepage coupling effect.

[0069] Based on the acquisition of formation physical parameters, production parameters, and wellbore structural parameters, this step establishes a dynamic physical model capable of simultaneously characterizing multi-mechanism sand production behavior, formation multiphase seepage patterns, the intervention of the screen pipe on the flow field and sand production, and the sand particle transport and settling process in the wellbore. This model achieves deep coupling between the sand production process and the seepage process, and incorporates the dynamic influence of screen pipe performance into the core equations as time-varying parameters, providing a physical basis for accurate dynamic prediction of production and sand production.

[0070] The presence of screens alters the near-wellbore flow field distribution. At screen openings or slots, fluid convergence leads to local velocities significantly higher than the average formation seepage velocity. To accurately describe this effect, a flow field disturbance model near the screens is established:

[0071] In the formula, ​ Let be the velocity potential function; ​ Total flow; r Radial distance; N This represents the total number of openings in the sieve tube; ​ These are the coordinates of the observation point in the complex plane; ​ i It is the first i The location of each opening on the complex plane; A i It is the fluid source strength coefficient corresponding to the opening.

[0072] Therefore, considering the local velocity amplification effect at the screen opening, the velocity at the screen opening... ​ The calculation method is shown in the following formula:

[0073] In the formula, D s Indicates the outer diameter of the sieve tube; L s Indicates the length of the sieve tube; ​ q represents the aperture ratio of the sieve tube; s i (z,t) represents the screen tube-reservoir exchange volumetric flow rate density;r w The radius of the oil well; ​ Indicates the first j The boundary of each hole; A i This represents the fluid source strength coefficient corresponding to the opening; n Indicates the direction of the normal.

[0074] The sand production effect mentioned above is a multi-mechanism coupled sand production. The sand production mechanism includes pressure driving sand production, water softening and interfacial tension affecting sand production, fluid shearing and spalling affecting sand production, and fatigue accumulation affecting sand production. First, the original sand production rate of the formation is calculated, and then it is corrected according to the interception efficiency of the screen pipe to obtain the net sand production rate entering the wellbore.

[0075] The primary sand production rate model for the formation is shown in the following equation:

[0076] In the formula, R t ​ This represents the total sand output rate at depth z at time t; R p ​ This represents the sand output rate at depth z at time t due to the pressure-driven effect. R w (z, t) The sand discharge rate at time t at depth z is represented by the effect of water softening and interfacial tension. R s ​ The sand discharge rate at depth z and time t is represented by the effect of fluid shear spalling. R f ​ The output sand rate represents the cumulative effect of fatigue at depth z at time t, which is the output sand rate that develops according to the process of "increase in production calendar time → accumulation of pressure cycles → microcrack propagation → particle fatigue shedding".

[0077] Among them, the sand output rate at time t at depth z is affected by the pressure drive. R p ​ The calculation method is shown in the following formula:

[0078] In the formula, k p Indicates the pressure sand output coefficient; Δ P ( z , t ) represents the pressure difference between the reservoir and the screen at time t at depth z; Δ P c ( z , t) represents the critical sand discharge pressure difference at depth z and time t. This calculation formula is only effective when the absolute value of ΔP(z,t) is greater than the absolute value of ΔPc(z,t).

[0079] The pressure difference Δ between the reservoir and the screen at time t at depth z P ( z , t The calculation method for ) is shown in the following formula:

[0080] In the formula, P e (z) This represents the reservoir pressure at depth z, obtained from well logging data; P s ​ This represents the pressure inside the screen tube at depth z at time t.

[0081] The method for calculating the pressure inside the screen tube is shown in the following formula:

[0082] In the formula, P wh Indicates wellhead pressure; ​ mix This indicates the mixed density of the oil and water phases; z wh Indicates the wellhead depth; z Indicates the current depth; f s The coefficient of friction of the sieve tube depends on the flow regime and the roughness of the inner wall of the sieve tube. Q t ( z , t () represents the total fluid flow rate at depth z at time t; D s Indicates the inner diameter of the sieve tube; ​ This is the wellbore inclination correction term, used to characterize the gravity component along the well section direction.

[0083] Sand production considering the effects of water softening: Sand production rate at depth z and time t influenced by water softening and interfacial tension. R w ​ The calculation method is shown in the following formula:

[0084] In the formula, S w ( ​ () represents the water saturation at depth z at time t; S wi ( z () represents the initial water saturation at depth z; kin The equivalent amplification factor representing the effect of interfacial tension is used to characterize the combined enhancing effect of increased water content and decreased interfacial tension on sand production. In practical calculations, it can be determined jointly by the water content softening function and the interfacial sand-carrying term; exp[-2(S w (z,t)-S wi (z))] represents the softening factor. Similarly, the formula must satisfy: S w ( ​ (greater than) S wi ( z ),and S w ( ​ () Greater than 0.4; To avoid negative values ​​that would not match actual production conditions, if there are parts that do not meet this condition, the parts that do not meet the condition are directly taken as 0.

[0085] The effect of fluid shear spalling on sand production rate at depth z at time t R s ​ The calculation method is shown in the following formula:

[0086] In the formula, ​ i This represents the hydrodynamic viscosity of phase i; L c (z) The characteristic length representing the pore throat size can be estimated based on permeability; ​ c Represents the critical Reynolds number, which is the minimum threshold value for the occurrence of self-maintaining transport and shear stripping; ​ Indicates the shear sand production coefficient; ​ ( z , t The pore Reynolds number at time t at depth z is defined as: In the formula, ​ i For fluid density;

[0087] The effect of fatigue accumulation on sand production rate at time t at depth z R f ​ The calculation method is shown in the following formula:

[0088] In the formula, k f Indicates the fatigue coefficient; t p ( t ) indicates from production to t The number of calendar days that have elapsed since the beginning of the moment; fh ( z ) represents the heterogeneity factor at depth z, ranging from 0.5 to 1.5.

[0089] The overall sand control efficiency of the screen tube ​ s ​ Its interception efficiency is determined by its size, flow rate capture efficiency, and its own integrity.

[0090] In the formula, ​ 1 Indicates size interception efficiency; ​ 2 Indicates flow rate capture efficiency; ​ 3 This indicates the integrity of the sieve tube itself, and is numerically equal to the overall integrity of the sieve tube. I i ( z , t ).

[0091] The sieve tube ​ 1 The method for calculating size interception efficiency is shown in the following formula:

[0092] In the formula, ​ This refers to the sieve tube slot width or aperture. d The particle size of the formation sand; ​ The grain size distribution function of the formation sand is usually represented by a log-normal distribution.

[0093] The sieve tube ​ 2 ​ The calculation method for flow velocity capture efficiency is shown in the following formula:

[0094] In the formula, v c The critical flow velocity required to lift or wash away sand particles of a specific size can be calculated based on Stokes' law.

[0095] The sieve tube ​ 3 ​ Its integrity depends directly on the current overall integrity of the sieve tube (defined in step S3).

[0096] After considering the sand control efficiency of the screen tube, the final net sand discharge rate entering the screen tube-annular system is... R t,net ​ The calculation method is shown in the following formula:

[0097] In the formula,R ss ​ The rate of particle shedding due to erosion and corrosion of the screen tube itself cannot be ignored in the later stages of production.

[0098] Under multiphase flow conditions, the fluids within the reservoir are predominantly oil and water, and the flow of each phase is controlled by a multiphase flow model, particularly the relative permeability between the fluid phases. The multiphase flow behavior in the reservoir is described by the following equation:

[0099] In the formula, q i (z,t) represents the volumetric flow rate of phase i at depth z and time t, i∈[o,w], where o represents the oil phase and w represents the water phase; h(z) represents the mesh segment thickness at depth z; P e (z) represents the drain boundary pressure at depth z; S represents the total skin coefficient.

[0100] By substituting the corresponding boundary conditions into the multiphase flow model, the screen-reservoir coupled seepage model can be obtained, which can reflect the influence of screen-reservoir seepage coupling. The screen-reservoir coupled seepage model is shown in the following equation:

[0101] In the formula, q s i (z,t) represents the screen tube-reservoir exchange volumetric flow rate density; r w The wellbore radius is represented by k(z); the absolute permeability at depth z is represented by k. ri (z,t) represents the relative permeability of phase i at depth z and time t; ​ i This represents the hydrodynamic viscosity of phase i; P r ( r w , z , t ) indicates that the radius at depth z is r w The reservoir pressure at time t at the outer edge of the wellbore; P s ( z , t () represents the pressure inside the screen tube at depth z at time t; r e Indicates the oil drain radius; S s (t) represents the time-varying sieve skin coefficient at time t;

[0102] This expression reflects the effect of screen performance on flow rate suppression and ensures physical continuity between normal flux and pressure distribution. As screen performance degrades over time... S s (t) increases, thus decreasing P s ( z , t This enables dynamic feedback of the influence of the screen tube.

[0103] By superimposing the above four sand-producing mechanisms, the sand-producing behavior of the formation under different conditions can be comprehensively characterized, taking into account both instantaneous factors (pressure difference, flow velocity) and slow-varying factors (water content, fatigue), laying the foundation for subsequent seepage coupling and screen performance degradation. Then, the obtained total sand-producing rate model, screen-reservoir coupled seepage model, and multiphase flow model are coupled into a dynamic physical model. When calculating subsequent variables using the dynamic physical model, the results of the above models are calculated separately.

[0104] Step S3: Combining mechanical damage, hydraulic performance degradation, and chemical corrosion factors, construct an evolution model of the overall integrity of the screen tube and calculate the relationship between the overall integrity of the screen tube and time.

[0105] The evolution model of the overall integrity of the sieve tube is shown in the following equation:

[0106] In the formula, I i ( z , t () represents the overall integrity of the sieve tube at depth z at time t; I m ( z , t () represents the mechanical integrity at depth z at time t; I h ( z , t () represents the hydraulic integrity at depth z at time t; I c ( z , t () represents the chemical integrity at depth z at time t;

[0107] Among them, the mechanical integrity at depth z at time t I m ( z , t The calculation method for ) is shown in the following formula:

[0108] In the formula, M c ( z , t() represents the cumulative sand volume at time t at depth z; M cr ( z () represents the critical sand quantity at depth z where the screen fails; when the cumulative sand quantity M c ( z , t Reaching or exceeding the critical sand quantity M cr ( z When the mechanical integrity reaches zero, it indicates that the mechanical structure of the screen tube has completely failed. The critical sand quantity at which the screen tube fails is... M cr ( z It can be calibrated on-site by combining the material and geometry of the sieve tube.

[0109] Cumulative sand volume at depth z at time t M c ( z , t The calculation method for ) is shown in the following formula:

[0110] In the formula, Δ t Indicates the step size for rolling calculation; M c ( z , t- Δ t () represents the cumulative sand volume at depth z at the previous step size;

[0111] Hydraulic integrity at depth z at time t I h ( z , t The calculation method for ) is shown in the following formula:

[0112] In the formula, α This represents the hydraulic attenuation coefficient, which ranges from 2.0 to 2.5, and is usually taken as 2.0 depending on the actual situation.

[0113] Chemical integrity at depth z at time t I c ( z , t The calculation method for ) is shown in the following formula:

[0114] In the formula, - k cor ( z () represents the basic corrosion rate at depth z; t p ( t ) indicates from production to tThe number of calendar days that have elapsed since the beginning of the moment; f WC ( ​ () represents the water content correction factor; f T ( ​ () indicates the temperature correction factor; f pH ( ​ () indicates the pH correction factor;

[0115] Among them, the water content correction factor f WC ( ​ The calculation method for ) is shown in the following formula:

[0116] In the formula, β w This represents the slope affected by water content, and its value ranges from 2.0 to 2.5, with 2.0 usually being chosen based on actual conditions.

[0117] Temperature correction factor f T ( ​ The calculation method for ) is shown in the following formula:

[0118] In the formula, E a The activation energy of the corrosion system is represented by a value of 75000 J / mol. R Represents the ideal gas constant; T ref This indicates room temperature, with a value of 25℃. T (z,t) represents the temperature at depth z at time t;

[0119] pH correction factor f pH ( ​ The calculation method for ) is shown in the following formula:

[0120] In the formula, ​ ( ​ () represents the pH value at depth z at time t;

[0121] Time-varying sieve skin coefficient at time t S s The calculation method for (t) is shown in the following formula:

[0122] In the formula, k d This represents the epidermal damage coefficient, which ranges from 0.01 to 0.1, and is usually set to 0.05 depending on the actual situation.

[0123] Step S4: Combine the dynamic physical model and the screen tube integrity evolution model to calculate the comprehensive model prediction values ​​of oil, water, sand yields and screen tube integrity at any time point.

[0124] The dynamic physical model obtained in step S2 can be used to calculate the yields of oil, water, and sand, while the screen tube integrity evolution model can directly yield the overall integrity of the screen tubes. Combining the two allows for the calculation of the comprehensive model prediction value at any given time point. The calculation method for sand yield is shown in the following formula:

[0125] In the formula, Q s ( z , t () represents the sand production rate per meter of well section at depth z at time t; h ( z () indicates the thickness of the grid segment;

[0126] The calculation methods for water and oil yields are shown in the following formulas:

[0127] In the formula, Q i ( z , t ) represents the yield of the i-th phase per meter interval at time t at depth z, where i∈[o,w], o represents the oil phase and w represents the water phase; q s i (z,t) represents the volumetric flow rate of phase i at time t at depth z, i∈[o,w]; h(z) represents the mesh segment thickness at depth z;

[0128] The calculation method for the flow capacity of water and oil is shown in the following formula:

[0129] In the formula, ​ i ( z , t Let ) represent the flow capacity of the i-th phase at time t at depth z, where i∈[o,w], where o represents the oil phase and w represents the water phase; ​ i Denotes the hydrodynamic viscosity of phase i, i∈[o,w]; k ri (z,t) represents the relative permeability of phase i at time t at depth z, where i∈[o,w].

[0130] Step S5: Based on the calculation results of the dynamic physical model and the screen pipe integrated integrity evolution model, as well as well logging data and historical production data, construct feature vectors and train a machine learning regression model.

[0131] The feature vectors used for training mainly include the calculation results of the dynamic physical model and the screen pipe integrated integrity evolution model in the aforementioned steps, as well as the logging data and historical production data obtained in step S1. The main feature vectors include: corrected reservoir porosity, corrected reservoir permeability, water saturation, and depth.

[0132] Oil-water ratio change rate, water content rise acceleration, production stage;

[0133] Water saturation, relative permeability of water phase, relative permeability of oil phase, oil Reynolds number, water Reynolds number, oil flow velocity, and water flow velocity at any point;

[0134] Oil flowability, water flowability, water softening coefficient, oil-water flow competition index, and water softening strength;

[0135] Oil yield, water yield, sand yield, and overall integrity of the screen tube.

[0136] The calculation method for the water softening coefficient is shown in the following formula:

[0137] In the formula, f soft ( z , t () represents the water softening coefficient at depth z at time t; F soft This indicates the calibration water softening coefficient, taken as 0.65; S w ( ​ () represents the water saturation at depth z at time t; S wi ( z () represents the initial water saturation at depth z;

[0138] The calculation method for the oil-water flow competition index is shown in the following formula:

[0139] In the formula, I comp ( z , t This indicates the oil-water flow competition index; ​ o ( z , t () represents the flowability of the oil phase at depth z at time t; ​ w ( z , t () represents the flow capacity of the water phase at depth z at time t;

[0140] The calculation method for water-bearing softening strength is shown in the following formula:

[0141] In the formula, I soft ( z , t () indicates the water softening strength; f soft ( z , t () represents the water softening coefficient at depth z at time t; S w ( ​ () represents the water saturation at depth z at time t.

[0142] The trained machine learning regression model adopts a voting fusion structure of random forest and gradient boosting regression. The specific method for outputting the prediction result is as follows: the feature vector is concatenated and input into the random forest model and the gradient boosting regression model respectively for training, and then the prediction result is output by weighting the random forest model and the gradient boosting regression model with a weight of 0.4:0.6.

[0143] In the random forest model, the number of weak learners is 300, and the maximum depth of the decision tree is 20. In the gradient boosting regression model, the number of weak learners is 300, and the learning rate is 0.05. The well logging data and historical production data used for training can be within 10 years, and usually about 5 years of data is sufficient.

[0144] S6: Using a machine learning regression model, the oil, water, and sand yields and the overall integrity of the screen tube are iteratively predicted at a set time step to obtain the machine learning prediction value at any time point.

[0145] The prediction time step of the machine learning regression model is 30 days. During the iterative prediction process, the prediction result of the previous step is used as the base value of the subsequent step, thereby calculating the predicted value at any time point.

[0146] S7: The two types of predicted values ​​obtained in steps S4 and S6 are weighted and fused, and then rolled correction is performed using Kalman filtering combined with measured production data to obtain the final predicted results of oil, water, and sand yields and screen tube integrity at each time point.

[0147] In the weighted fusion, the weight of the comprehensive model prediction is 0.6, and the weight of the machine learning prediction is 0.4.

[0148] The method of rolling correction of model error by combining Kalman filtering with measured production data is as follows: Kalman filtering is used to perform rolling correction on the data at each time step until a set time limit is reached. This invention can achieve high accuracy prediction within a 20-year range. Based on this, the remaining lifespan of the screen tube can be characterized by the overall integrity of the screen tube. When the overall integrity of the screen tube is <0.1, the lifespan is 0, and the screen tube can be considered to have failed. When the overall integrity of the screen tube is ≥0.1, the remaining lifespan of the screen tube satisfies the following formula, and linear extrapolation can be performed based on this formula:

[0149] Remaining life of the screen tube = (1 - overall integrity of the screen tube / 0.9) × years.

[0150] The state vector for Kalman filter correction includes oil yield, water yield, sand yield, overall integrity of screen tube, internal pressure of screen tube, time-varying screen tube skin coefficient, and cumulative sand quantity. Example

[0151] Production data from a well in a marine oilfield in northern China for the past five years were selected and calculated using the method described above. This well began production in 2003 and has been in production for 21 years as of 2024. The calculation results were used for model training and validation. During training, the training set consisted of data from the first four years (70%), the validation set consisted of data from the first half of the fifth year (15%), and the test set consisted of data from the second half of the fifth year (15%). The output oil, water, and sand production were compared with the predicted and measured values, as shown in Tables 1 and 2, respectively.

[0152] Table 1 Comparison of predicted and measured oil and water production results

[0153]

[0154] Table 2 Comparison of Cumulative Sand Production Forecast and Measured Values

[0155]

[0156] Meanwhile, the sieve tube integrity prediction results on a 20-year timescale are output using the above method, as shown in Table 3.

[0157] Table 3. Prediction of Screen Tube Integrity

[0158]

[0159] In summary, as shown in Tables 1 and 2, the error between the method in this invention and the measured values ​​can be controlled within 10% on a 20-year timescale. This demonstrates that the prediction method in this invention has high accuracy on a longer timescale, effectively improving the accuracy and robustness of long-term predictions while maintaining physical interpretability.

[0160] Furthermore, based on the prediction results in Table 3, and ​ By comparing the condition of the screen pipes during actual well bottom maintenance, it was found that the screen pipes were damaged, proving that the screen pipe integrity prediction method in this invention can be used to accurately predict the condition of the screen pipes.

[0161] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the embodiments of the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims. denoted as represents the drain boundary pressure at depth z.

Claims

1. A method for predicting production and sand output of offshore wells in loose sandstone considering the influence of screens, characterized in that, Includes the following steps: S1: Obtain logging data and historical production data of the target well, combine water-bearing softening effect and Biot coefficient to correct the stress path coefficient and porosity changes caused by compaction, update reservoir permeability, and obtain corrected porosity, permeability, stress path coefficient and relative permeability parameters. S2: Considering the influence of flow field disturbance near the screen tube and the sand control efficiency of the screen tube on sand production, a dynamic physical model integrating sand production effect, multiphase flow model and screen tube-reservoir seepage coupling effect is established. S3: Combining mechanical damage, hydraulic performance degradation and chemical corrosion factors, construct an evolution model of the overall integrity of the screen tube and calculate the relationship between the overall integrity of the screen tube and time. S4: Combine the dynamic physical model and the screen tube integrity evolution model to calculate the comprehensive model prediction value of oil, water, sand production and screen tube integrity at any time point; S5: Based on the calculation results of the dynamic physical model and the screen pipe integrated integrity evolution model, as well as well logging data and historical production data, feature vectors are constructed to train a machine learning regression model; S6: Using a machine learning regression model, the oil, water, and sand yields and the overall integrity of the screen tube are iteratively predicted at a set time step to obtain the machine learning prediction value at any time point. S7: The two types of predicted values ​​obtained in steps S4 and S6 are weighted and fused, and rolling correction is performed by combining Kalman filtering with measured production data to obtain the final predicted results of oil, water, and sand yields and screen tube integrity at each time point. In step S2, the sand production effect is a multi-mechanism coupled sand production. The sand production mechanisms include pressure-driven sand production, water softening and interfacial tension-driven sand production, fluid shear spalling-driven sand production, and fatigue accumulation-driven sand production. First, the original formation sand production rate is calculated, and then corrected according to the interception efficiency of the screen pipe to obtain the net sand production rate entering the wellbore. The original formation sand production rate model is shown in the following formula: In the formula, R t (z,t) This represents the total sand output rate at depth z at time t; R p (z,t) This represents the sand output rate at depth z at time t due to the pressure-driven effect. R w (z,t) The sand discharge rate at time t at depth z is represented by the effect of water softening and interfacial tension. R s (z, t) The sand discharge rate at depth z and time t is represented by the effect of fluid shear spalling. R f (z,t) The sand output rate at time t represents the cumulative effect of fatigue at depth z. The evolution model of the overall integrity of the sieve tubes mentioned in step S3 is shown in the following formula: In the formula, I i ( z , t () represents the overall integrity of the sieve tube at depth z at time t; I m ( z , t () represents the mechanical integrity at depth z at time t; I h ( z , t () represents the hydraulic integrity at depth z at time t; I c ( z , t ) represents the chemical integrity at depth z at time t.

2. The method for predicting production and sand output of offshore wells in loose sandstone considering the influence of screens, as described in claim 1, is characterized in that: The logging data of the target well includes reservoir porosity, reservoir permeability, water saturation, and depth; Historical production data includes the rate of change in oil-water ratio, the acceleration of water cut increase, and the production stage.

3. The method for predicting production and sand output of offshore wells in loose sandstone considering the influence of screens, as described in claim 1, is characterized in that: The method for obtaining the corrected porosity, permeability, stress path coefficient, and relative permeability parameters in step S1 is as follows: Corrected reservoir porosity φ(z,t) The calculation method is shown in the following formula: In the formula, φ(z,t) This indicates the updated reservoir porosity; φ 0 (z) Indicates initial porosity; Δ φ(z,t) Indicates changes in porosity; Corrected reservoir permeability k(z,t) The calculation method is shown in the following formula: In the formula, k(z,t) This represents the corrected reservoir permeability; k 0 (z) Indicates the initial reservoir permeability; fw(z,t) Indicates the water content effect factor; Among them, water content effect factor fw(z,t) The calculation method is shown in the following formula: In the formula, S w ( z , t () represents the water saturation at depth z at time t; Porosity change Δ φ(z,t) The calculation method is shown in the following formula: In the formula, λ por To calibrate the influence coefficient of water softening on porosity; ΔP 2 (z,t) This represents the formation pressure difference at depth z at time t; ε(z,t) This represents the compaction factor at depth z at time t. Corrected Biot coefficient α ef (z,t) The calculation method is shown in the following formula: In the formula, α(z) This represents the initial Biot coefficient at depth z; For elastic modulus based on water softening effect E ef (z,t) The calculation method is shown in the following formula: In the formula, E(z) Indicates the basic elastic modulus of the rock skeleton; F soft Indicates the calibrated water softening coefficient; S w ( z,t () represents the water saturation at depth z at time t; S wi ( z () represents the initial water saturation at depth z; Considering the effect of water softening on the skeleton Poisson's ratio v ef (z,t) The revised calculation method is shown in the following formula: In the formula, v fr (z) This represents the initial Poisson's ratio of the skeleton at depth z; For horizontal stress path coefficient γ h (z,t) The calculation method is shown in the following formula: Vertical stress path coefficient γ v (z,t) The calculation method is shown in the following formula: In the formula, e This indicates the longitudinal and transverse aspect ratio of the oil reservoir.

4. The method for predicting production and sand output of offshore wells in loose sandstone considering the influence of screens, as described in claim 3, is characterized in that: The sand production rate at depth z and time t in the original formation sand production rate model is influenced by pressure drive. R p (z, t) The calculation method is shown in the following formula: In the formula, k p Indicates the pressure sand output coefficient; Δ P ( z , t ) represents the pressure difference between the reservoir and the screen at time t at depth z; Δ P c ( z , t () represents the critical sand discharge pressure difference at depth z at time t; The effect of water softening and interfacial tension on sand production rate at depth z and time t R w (z,t) The calculation method is shown in the following formula: In the formula, S w ( z,t () represents the water saturation at depth z at time t; S wi ( z () represents the initial water saturation at depth z; k in Indicates the interfacial tension coefficient; The effect of fluid shear spalling on sand production rate at depth z at time t R s (z,t) The calculation method is shown in the following formula: In the formula, k s Indicates the shear sand production coefficient; Re ( z , t () represents the pore Reynolds number at depth z at time t; Re c Indicates the critical Reynolds number; The effect of fatigue accumulation on sand production rate at time t at depth z R f (z,t) The calculation method is shown in the following formula: In the formula, k f Indicates the fatigue coefficient; t p ( t ) indicates from production to t The number of calendar days that have elapsed since the beginning of the moment; f h ( z ) represents the heterogeneity factor at depth z, ranging from 0.5 to 1.5; The overall sand control efficiency of the screen tube η s (z,t) Its interception efficiency is determined by its size, flow rate capture efficiency, and its own integrity. In the formula, η 1 indicates size interception efficiency; η 2 indicates flow rate capture efficiency; η 3 indicates its own integrity, which is numerically equal to the overall integrity of the sieve tube; The sieve tube η The calculation method for size interception efficiency is shown in the following formula: In the formula, ds This refers to the sieve tube slot width or aperture. f(d) This is the grain size distribution function of the formation sand particles; d The particle size of the stratum gravel; The sieve tube η 2 (z,t) The calculation method for flow velocity capture efficiency is shown in the following formula: In the formula, v c The critical flow velocity required to lift or wash away sand particles of a specific size; The sieve tube η 3 (z,t) Its integrity directly depends on the current overall integrity of the screen tube; After considering the sand control efficiency of the screen tube, the final net sand discharge rate entering the screen tube-annular system is... R t,net (z,t) The calculation method is shown in the following formula: In the formula, R ss (z,t) The rate of particle shedding due to erosion and corrosion of the screen tube itself cannot be ignored in the later stages of production.

5. The method for predicting production and sand output of offshore wells in loose sandstone considering the influence of screens, as described in claim 4, is characterized in that: The screen-reservoir flow coupling effect mentioned in step S2 is reflected by the screen-reservoir coupled flow model, as shown in the following equation: In the formula, q s i (z,t) represents the screen tube-reservoir exchange volumetric flow rate density; r w The wellbore radius is represented by k(z); the absolute permeability at depth z is represented by k. ri (z,t) represents the relative permeability of phase i at depth z and time t; μ i This represents the hydrodynamic viscosity of phase i; P r ( r w , z , t ) indicates that the radius at depth z is r w The reservoir pressure at time t at the outer edge of the wellbore; P s ( z , t () represents the pressure inside the screen tube at depth z at time t; r e Indicates the oil drain radius; S s (t) represents the time-varying sieve skin coefficient at time t; The pressure difference Δ between the reservoir and the screen at time t at depth z P ( z , t The calculation method for ) is shown in the following formula: In the formula, P e (z) This represents the reservoir pressure at depth z, obtained from well logging data; P s (z,t) This represents the pressure inside the screen tube at depth z at time t; The method for calculating the pressure inside the screen tube is shown in the following formula: In the formula, P wh Indicates wellhead pressure; ρ mix This indicates the mixed density of the oil and water phases; z wh Indicates the wellhead depth; z Indicates the current depth; f s Indicates the coefficient of friction of the sieve tube; Q t ( z , t () represents the total fluid flow rate at depth z at time t; D s This indicates the inner diameter of the sieve tube.

6. The method for predicting production and sand output of offshore wells in loose sandstone considering the influence of screens, as described in claim 5, is characterized in that: The mechanical integrity at depth z at time t in the screen tube integrity evolution model described in step S3 I m ( z , t The calculation method for ) is shown in the following formula: In the formula, M c ( z , t () represents the cumulative sand volume at time t at depth z; M cr ( z () represents the critical amount of sand required for screen failure at depth z; Cumulative sand volume at depth z at time t M c ( z , t The calculation method for ) is shown in the following formula: In the formula, Δ t Indicates the step size for rolling calculation; M c ( z , t- Δ t () represents the cumulative sand volume at depth z at the previous step size; Hydraulic integrity at depth z at time t I h ( z , t The calculation method for ) is shown in the following formula: In the formula, α Indicates the hydraulic attenuation coefficient; Chemical integrity at depth z at time t I c ( z , t The calculation method for ) is shown in the following formula: In the formula, - k cor ( z () represents the basic corrosion rate at depth z; t p ( t ) indicates from production to t The number of calendar days that have elapsed since the beginning of the moment; f WC ( z,t () represents the water content correction factor; f T ( z,t () indicates the temperature correction factor; f pH ( z,t () indicates the pH correction factor; Among them, the water content correction factor f WC ( z,t The calculation method for ) is shown in the following formula: In the formula, β w This indicates the slope affected by water content, and its value ranges from 2.0 to 2.

5. Water content correction factor f T ( z,t The calculation method for ) is shown in the following formula: In the formula, E a The activation energy of the corrosion system is represented by a value of 75000 J / mol. R Represents the ideal gas constant; T ref This indicates room temperature, with a value of 25℃. T (z,t) represents the temperature at depth z at time t; pH correction factor f pH ( z,t The calculation method for ) is shown in the following formula: In the formula, pH ( z,t () represents the pH value at depth z at time t; Time-varying sieve skin coefficient at time t S s The calculation method for (t) is shown in the following formula: In the formula, k d This represents the epidermal damage coefficient, which ranges from 0.01 to 0.

1.

7. The method for predicting production and sand output of offshore wells in loose sandstone considering the influence of screens, as described in claim 6, is characterized in that: The feature vector mentioned in step S5 includes: Corrected reservoir porosity, corrected reservoir permeability, water saturation, and depth; Oil-water ratio change rate, water content rise acceleration, production stage; Water saturation, relative permeability of water phase, relative permeability of oil phase, oil Reynolds number, water Reynolds number, oil flow velocity, and water flow velocity at any point; Oil flowability, water flowability, water softening coefficient, oil-water flow competition index, and water softening strength; Oil yield, water yield, sand yield, and overall integrity of the screen tube.

8. The method for predicting production and sand output of offshore wells in loose sandstone considering the influence of screens, as described in claim 7, is characterized in that: The method for calculating the sand yield is shown in the following formula: In the formula, Q s ( z , t () represents the sand production rate per meter of well section at depth z at time t; h ( z () indicates the thickness of the grid segment; The calculation methods for water and oil yields are shown in the following formulas: In the formula, Q i ( z , t ) represents the yield of the i-th phase per meter interval at time t at depth z, where i∈[o,w], o represents the oil phase and w represents the water phase; q s i (z,t) represents the volumetric flow rate of phase i at time t at depth z, i∈[o,w]; h(z) represents the mesh segment thickness at depth z; The calculation method for the flow capacity of water and oil is shown in the following formula: In the formula, λ i ( z , t Let ) represent the flow capacity of the i-th phase at time t at depth z, where i∈[o,w], where o represents the oil phase and w represents the water phase; μ i Let k represent the hydrodynamic viscosity of phase i, where i∈[o,w,]. ri (z,t) represents the relative permeability of phase i at time t at depth z, i∈[o,w]; The calculation method for the water softening coefficient is shown in the following formula: In the formula, f soft ( z , t () represents the water softening coefficient at depth z at time t; F soft This indicates the calibration water softening coefficient, taken as 0.65; S w ( z,t () represents the water saturation at depth z at time t; S wi ( z () represents the initial water saturation at depth z; The calculation method for the oil-water flow competition index is shown in the following formula: In the formula, I comp ( z , t This indicates the oil-water flow competition index; λ o ( z , t () represents the flowability of the oil phase at depth z at time t; λ w ( z , t () represents the flow capacity of the water phase at depth z at time t; The calculation method for water-bearing softening strength is shown in the following formula: In the formula, I soft ( z , t () indicates the water softening strength; f soft ( z , t () represents the water softening coefficient at depth z at time t; S w ( z,t () represents the water saturation at depth z at time t.

9. The method for predicting production and sand output of offshore wells in loose sandstone considering the influence of screens, as described in claim 1, is characterized in that: The machine learning regression model described in step S5 adopts a voting fusion structure of random forest and gradient boosting regression. The specific method for outputting the prediction result is as follows: the feature vector is concatenated and input into the random forest model and the gradient boosting regression model for training, and then the prediction result is output by weighting the random forest model and the gradient boosting regression model with a weight of 0.4:0.

6. In the random forest model, the number of weak learners is 300, and the maximum depth of the decision tree is 20; in the gradient boosting regression model, the number of weak learners is 300, and the learning rate is 0.

05. In step S6, the prediction time step of the machine learning regression model is 30 days. During the iterative prediction process, the prediction result of the previous step is used as the base value of the subsequent step, thereby calculating the predicted value at any time point. In the weighted fusion described in step S7, the weight of the comprehensive model prediction is 0.6, and the weight of the machine learning prediction is 0.

4.

10. The method for predicting production and sand output of offshore wells in loose sandstone considering the influence of screens, as described in claim 1, is characterized in that: The method of rolling correction by combining Kalman filtering with measured production data is as follows: rolling correction is performed on the data of each time step by Kalman filtering until the set time limit is reached; The state vector for Kalman filter correction is oil yield, water yield, sand yield, overall integrity of screen tube, internal pressure of screen tube, time-varying screen tube skin coefficient, and cumulative sand quantity.

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