CN117648882B - Establishment of dynamic model for acid fracturing in long open hole section of horizontal well and prediction method of fracture pressure - Google Patents
Establishment of dynamic model for acid fracturing in long open hole section of horizontal well and prediction method of fracture pressure Download PDFInfo
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Abstract
本发明提供了一种水平井长裸眼井段酸压动态模型建立和破裂压力预测方法，模型建立方法包括：建立水平井长裸眼井段物理模型和沿井筒分布的地质模型并进行网格划分，根据测井资料确认对应深度的特征参数和力学参数；根据上述参数建立井筒内流体压力模型和基质内流体压力模型；根据上述压力模型建立井筒内的基于注酸口位置的酸液流动速度模型；根据酸液流动速度模型、井筒内流体压力模型和基质内流体压力模型建立酸压动态模型。预测方法包括根据上述的酸压动态模型和岩石破坏准则确认破裂压力。本发明考虑酸液对储层的力学、物性特征的影响，简单准确的计算不同注酸参数、注酸口位置、储层条件下的动态破裂压力，为后续作业的优选提供了理论依据。
The present invention provides a method for establishing a dynamic model of acid fracturing and predicting fracture pressure of a long open hole section of a horizontal well. The model establishment method includes: establishing a physical model of a long open hole section of a horizontal well and a geological model distributed along the wellbore and performing grid division, confirming characteristic parameters and mechanical parameters of the corresponding depth according to logging data; establishing a fluid pressure model in the wellbore and a fluid pressure model in the matrix according to the above parameters; establishing an acid flow velocity model based on the acid injection port position in the wellbore according to the above pressure model; and establishing an acid fracturing dynamic model according to the acid flow velocity model, the fluid pressure model in the wellbore and the fluid pressure model in the matrix. The prediction method includes confirming the fracture pressure according to the above acid fracturing dynamic model and the rock failure criterion. The present invention takes into account the influence of acid on the mechanical and physical properties of the reservoir, and simply and accurately calculates the dynamic fracture pressure under different acid injection parameters, acid injection port positions, and reservoir conditions, providing a theoretical basis for the optimization of subsequent operations.
Description
Technical Field
The invention relates to the technical field of petroleum engineering, in particular to a method for establishing a dynamic model of acid pressure of a long open hole section of a horizontal well and a method for predicting dynamic fracture pressure of the acid pressure of the long open hole section of the horizontal well.
Background
Carbonate reservoirs are the main sites for the development of natural gas at present and in the future in China, acid fracturing transformation is one of the main means for realizing the efficient development of the reservoirs, and in order to realize the efficient transformation of the reservoirs, acid liquid needs to be injected under the condition of being higher than the fracture pressure of the reservoirs to form artificial cracks, so that the seepage channel and the flowing capacity of oil gas in the reservoirs are increased. Along with development of exploration and development theory and accumulation of field practice experience, a long horizontal well has become one of main well types for efficiently developing carbonate reservoirs, and segmented acid fracturing is an important modification and development process of carbonate of the long open hole horizontal well. However, because the carbonate reservoir has extremely strong heterogeneity and long open hole section of the horizontal well, the acid absorption conditions of the reservoir section are greatly different, and the physical properties and mechanical characteristics of the reservoir are affected by chemical reaction in the acid liquid injection process, so that the dynamic condition of acid pressure and the dynamic fracture pressure of the acid pressure of the long open hole section of the horizontal well are difficult to predict.
Currently, relatively complete numerical models have been constructed for horizontal well fracture pressure prediction. However, such models are developed aiming at hydraulic fracturing, for example, the invention patent with publication number of CN111219175A discloses a method for optimizing the matching property of the acid fracturing fracture of fractured carbonate rock by considering stress sensitivity, in the method, the initial effective closing stress of a stratum and the flow conductivity distribution of the acid fracturing fracture and the natural fracture calculated based on an N-K model are assigned to corresponding position grids in a reservoir model by inputting the etching widths of the natural fracture and the hydraulic fracture, so that the permeability of the corresponding grids is obtained, a fixed outlet simulated production well is arranged in the reservoir model, the pressure distribution of the reservoir fluid at the end of each time step is calculated, and further the simulation and evaluation of the production process are completed. However, the method is simple for acid liquor etching, takes the crack etching data in the case of minimum acid injection amount and acid injection discharge amount in all construction parameter cases as a reference etching form, and does not sufficiently consider the influence of acid liquor chemical reaction on physical properties and mechanical characteristics of a reservoir. The existing acid fracturing pressure prediction model does not consider the coupling of acid liquor in a shaft and a flowing model in a reservoir, and the invention patent with the publication number of CN110094196A discloses a carbonate open hole horizontal well subsection acid fracturing effect evaluation method. The dynamic and static rock mechanical parameter conversion coefficient is obtained mainly through fitting of indoor rock mechanical data and rock mechanical data calculated by well logging, and the influence of reservoir heterogeneity on the fracture pressure and the fracture starting position is not well considered. Therefore, a direct and simple method for calculating the acid fracturing dynamic fracture pressure of the long open hole section of the horizontal well is lacking at present, and reliable basis is provided for the design and construction optimization of the acid fracturing of the long horizontal well.
Disclosure of Invention
The present invention aims to address at least one of the above-mentioned deficiencies of the prior art. For example, one of the purposes of the invention is to provide a method for establishing a dynamic model of acid fracturing of a long open hole section of a horizontal well, which can fully consider the influence of acid liquor chemical reaction on physical properties and mechanical characteristics of a reservoir, the influence of the flow of acid liquor in a shaft and the reservoir on the whole of the heterogeneity of the reservoir and the fracture pressure and the fracture starting position of the reservoir, and can also utilize the dynamic model of acid fracturing to realize the prediction of different acid injection parameters, acid injection port positions and dynamic fracture pressure of the acid fracturing of the long open hole section of the horizontal well under the reservoir condition, thereby providing more accurate support for the optimization of the acid fracturing design and construction of the long open hole section of the carbonate horizontal well.
In order to achieve the purpose, the invention provides a method for establishing a dynamic model of acid pressure of a long open hole section of a horizontal well.
The method for establishing the acid fracturing dynamic model of the long open hole section of the horizontal well comprises the following steps:
s1, establishing a horizontal well long open hole section physical model and a geological model distributed along a well bore, and confirming characteristic parameters and mechanical parameters of corresponding depths according to logging data, the horizontal well long open hole section physical model subjected to grid division and the geological model distributed along the well bore.
S2, establishing a fluid pressure model in the shaft and a fluid pressure model in the matrix according to the characteristic parameters and the mechanical parameters.
S3, establishing an acid liquid flow speed model based on the acid injection port position in the shaft according to the shaft fluid pressure model and the matrix fluid pressure model.
S4, establishing an acid pressure dynamic model according to the acid liquid flow speed model, the fluid pressure model in the well bore and the fluid pressure model in the matrix.
In an exemplary embodiment of the method for creating a dynamic model of acid fracturing of a long open hole section of a horizontal well of the present invention, the wellbore fluid internal pressure model may include:
Formula 1:
Formula 2:
Formula 3:
Wherein n is the nth time step, is dimensionless, and is At bottom hole pressure Pa at the n+1th time stepThe pressure is Pa, the delta P n is the pressure change caused by the compressibility of fluid in a shaft at the nth time step, the delta P is the pressure change caused by the compressibility of fluid in the shaft, the delta V acid is the volume increment of acid liquid in the shaft at the nth time step, m 3, the V well is the volume of the shaft, m 3, the c 1 is the fluid compressibility, pa -1, the delta t is the time step, s, and the delta V acid is the volume increment of acid liquid in the shaft at the nth time stepThe acid liquid flow rate of the well bore is m 3/min in the nth time step, and the acid liquid flow rate is m 3/minFor the nth time step, the acid liquid flow out of the shaft, m 3/min, and when n=1, theThe Deltax and Deltay are respectively the lengths of the unit cell in the directions of the x axis and the y axis, m, the k y is the permeability of the unit cell in the direction of the y axis, m 2, the r is the radius of a shaft, m, the mu is the viscosity of fluid, pa.s, and theThe reservoir fluid pressure, pa, is the nth time step within the first grid in the y-axis direction.
In an exemplary embodiment of the method for establishing the acid fracturing dynamic model of the long open hole section of the horizontal well, the time step Δt can be confirmed according to the average permeability k m of the reservoir matrix, and specifically the method can comprise the steps of enabling the time step Δt to be 1s when the value range of k m is k m<10-15m2, enabling the time step Δt to be 1-10 s when the value range of k m is 10 -15m2≤km≤10-14m2, and enabling the time step Δt to be 10s when the value range of k m is 10 -14m2≤km.
In an exemplary embodiment of the method for creating a dynamic model of acid fracturing of a long open hole section of a horizontal well of the present invention, the intra-matrix fluid pressure model may include:
Formula 4:
Wherein ρ is fluid density, kg/m 3, k x、ky is permeability of unit cell in x-axis and y-axis directions, m 2, μ is fluid viscosity, pa.s, P is reservoir fluid pressure, pa, φ is reservoir porosity, dimensionless, c 1 is fluid compression coefficient, pa -1, t is acid injection time, s.
In an exemplary embodiment of the method for establishing the dynamic model of the acid pressure of the long open hole section of the horizontal well, the acid flow velocity model may include an upstream acid flow velocity model and a downstream acid flow velocity model, and each may include:
Formula 5:
Formula 6:
The method comprises the steps of (1) setting u i Upper part as the flow rate of upstream acid in a shaft, m/s, u i Lower part(s) as the flow rate of downstream acid in the shaft, m/s, x in as the position of an acid injection port, no dimension, i as the position of cells in the x-axis direction, no dimension, m as the total number of cells in the x-axis direction of an acid flow velocity model, no dimension, x m as the position of the m-th cell in the x-axis direction, Δx and Δy as the lengths of the cells in the x-axis and y-axis directions respectively, m, P well,i as the fluid pressure in the shaft in the x-axis direction, pa, P r,i as the fluid pressure in the stratum in the x-axis direction, pa, k y,i as the permeability in the y-axis direction of the reservoir, m 2 as the fluid viscosity, pa.s, and D Well as the diameter.
In an exemplary embodiment of the method for establishing the acid fracturing dynamic model of the long open hole section of the horizontal well, the acid fracturing dynamic model may include an acid liquor concentration distribution model, and the acid liquor concentration distribution model may include:
Formula 7:
Equation 8:v l,i＝Qout,i/(πD Well Δx).
The method comprises the steps of setting a length of a unit cell in an x-axis direction, wherein Deltax is m, D Well is the diameter of a well hole, m, C is the concentration of acid liquor, mol/m 3, t is the time of acid liquor injection, s, u is the flow rate of acid liquor in a well hole, m/s, k c acid-rock reaction rate, m/s, v l is the flow rate of acid liquor flowing into a reservoir from the well hole, m/s, i is the position of the unit cell in the x-axis direction, dimensionless, v l,i is the flow rate of acid liquor flowing into the reservoir from the well hole in the i-axis direction, m/s, Q out,i is the flow rate of acid liquor flowing out of the well hole in the i-axis direction in unit time, and m 3/min.
In an exemplary embodiment of the method for establishing the acid fracturing dynamic model of the long open hole section of the horizontal well, the acid fracturing dynamic model can comprise a porosity model and a permeability model after acid liquor corrosion, and the porosity model and the permeability model can respectively comprise:
formula 9:
formula 10:
Wherein, phi n is the porosity of the nth time step, phi is the porosity of the reservoir, delta x and delta y are the lengths of the unit cells in the directions of the x axis and the y axis, M, D Well is the diameter of the well bore, M, n is the nth time step, t is the time of acid injection, s, tau is the corresponding time step number of the acid liquid front reaching the unit cells at different positions in the well bore for the first time, delta V is the rock volume eroded by the acid liquid, M 3, beta is the dissolution capacity of the acid liquid to the rock mineral, kg/kg, M is the molar mass of the acid liquid, kg/mol, k c acid rock reaction rate, M/s, C is the acid liquid concentration, mol/M 3, rho S is the rock density, kg/M 3, k n is the permeability after corrosion, M 2, k is the initial permeability, M 2, beta is the dissolution capacity of the acid liquid to the rock mineral, and the structural parameter is SG.
In an exemplary embodiment of the method for establishing the acid fracturing dynamic model of the long open hole section of the horizontal well, the acid fracturing dynamic model can comprise a well wall tangential stress model, and the well wall tangential stress model can comprise:
Formula 11:
ν=5.89e[-(t-τ)/6.47]-6.23,
The method comprises the steps of setting a standard well wall tangential stress, setting sigma θ as well wall tangential stress, setting sigma H、σh and sigma ν as maximum horizontal main stress, minimum horizontal main stress and vertical stress, setting sigma z as well wall tangential stress, setting theta and theta' as well inclination angles and angles from the axial clockwise rotation of a well bore to the tangential stress direction of the bottom of the well bore on the well wall, setting P well as well bore fluid pressure, setting P as reservoir fluid pressure, setting MPa, setting alpha as Biot coefficient, setting gamma as Poisson ratio, setting omega as acid damage variable, setting phi as reservoir porosity, setting phi as zero factor, setting phi n as porosity of nth time step, setting t as acid injection time, setting t as corresponding time step number of the acid fluid front reaches different position cells in the well bore for the first time.
In an exemplary embodiment of the method for establishing the acid fracturing dynamic model of the long open hole section of the horizontal well, when the acid liquid concentration of the cell position in the well shaft is more than or equal to 301-903 mol/m 3, the leading edge of the acid liquid can be judged to reach the cell position for the first time.
The invention also provides a method for predicting the acid fracturing dynamic fracture pressure of the long open hole section of the horizontal well, which can comprise the step of confirming whether the difference of reservoir fluid pressure minus wall tangential stress is greater than or equal to the rock tensile strength by the acid fracturing dynamic model in the method for establishing the acid fracturing dynamic model of the long open hole section of the horizontal well.
When the difference is equal to or greater than the rock tensile strength, the fracture location and fracture pressure can be identified.
And when the difference is smaller than the rock tensile strength, the characteristic parameters and the mechanical parameters can be updated, and the steps S1-S4 are repeated until the difference is larger than or equal to the rock tensile strength.
When the process of injecting acid has been completed and the difference is less than the rock tensile strength, the construction parameters can be redesigned.
Compared with the prior art, the invention has the beneficial effects that at least one of the following contents is included:
(1) According to the method for establishing the acid fracturing dynamic model, provided by the invention, the mechanical characteristics and physical characteristic changes caused by the acid liquor chemical reaction on reservoir segments with different physical parameters in the acid fracturing process of the long open hole of the horizontal well are considered, the influences of reservoir heterogeneity on fracture pressure and fracture starting positions as a whole are considered, and the coupling is carried out on the acid liquor and the flow model in the shaft and the reservoir, so that the dynamic flow and the reaction process of the acid liquor in the shaft and the reservoir can be calculated and reflected in real time more accurately.
(2) The method for predicting the acid fracturing pressure dynamically can more accurately predict the acid fracturing pressure of the long open hole section of the horizontal well under different acid injection parameters, acid injection port positions and reservoir conditions by using the acid fracturing dynamic model.
(3) The acid fracturing dynamic model provided by the invention has the advantages that the calculation process is simple, no iteration is needed for a plurality of times, the calculation result is accurate, reliable support can be provided for the optimization and construction of the acid fracturing of the long open hole section of the carbonate horizontal well, and the well completion efficiency is improved.
Drawings
The foregoing and other objects and/or features of the invention will become more apparent from the following description taken in conjunction with the accompanying drawings in which:
FIG. 1 illustrates a schematic flow diagram of an exemplary embodiment of a method of dynamic modeling of acid fracturing of a long open hole section of a horizontal well of the present invention.
FIG. 2 is a schematic diagram showing the calculation of fluid pressure in a reservoir of an example of the method for predicting acid fracturing dynamic fracture pressure in a horizontal well long open hole section of the present invention.
Fig. 3 is a schematic diagram showing the calculation result of the flow velocity distribution of the acid in the well bore of an example of the method for predicting the acid fracturing pressure of the long open hole section of the horizontal well.
Fig. 4 is a schematic diagram showing the calculation result of the acid concentration distribution in the well bore of an example of the method for predicting the acid fracturing dynamic fracture pressure of the long open hole section of the horizontal well.
Fig. 5 is a schematic diagram showing a fracture pressure judgment result of an example of the method for predicting the acid fracturing dynamic fracture pressure of a long open hole section of a horizontal well according to the present invention.
Detailed Description
Hereinafter, the horizontal well long open hole acid fracturing dynamic model building and fracture pressure prediction method of the present invention will be described in detail with reference to exemplary embodiments. Wherein the burst pressure is also referred to as the cracking pressure.
It should be noted that the terms "S1", "S2", "S3", and the like are used herein to distinguish similar objects and are not necessarily used to describe a particular order or sequence. "upper", "lower", etc. are for convenience only in describing and constructing relative orientations or positional relationships and do not indicate or imply that the components in question must have that particular orientation or position.
Acidizing fracturing (acid fracturing for short) refers to the extrusion of acid into a reservoir at a pressure above the fracture pressure of the reservoir, creating hydraulic fractures in the reservoir. Meanwhile, the acid liquor and the rock on the wall surface of the crack are subjected to chemical reaction, the rock on the wall surface of the crack is etched unevenly to form a groove-shaped or rugged etching form, so that the hydraulic crack is not completely closed after construction is finished to finally form an acid etching crack with a certain geometric dimension and flow conductivity, and the yield of the oil and gas well is increased, so that the dynamic flowing and reaction processes of the acid liquor in the acid fracturing in a shaft and a reservoir layer and the prediction result of dynamic fracture pressure can influence the design of an acid fracturing scheme. The acid liquor can not only generate the change of mechanical characteristics and physical characteristics of reservoir sections with different physical parameters due to chemical reaction, but also flow in a well bore and the reservoir to cause the change of stress in the well bore. However, none of the current models can simultaneously take the above mentioned variations into account.
Aiming at the problems, the inventor provides a method for establishing a dynamic model of the acid pressure of the long open hole section of the horizontal well and a method for predicting the fracture pressure, and can accurately and simply calculate and reflect the dynamic state of the acid pressure of the long open hole section of the horizontal well under different acid injection parameters, acid injection port positions and reservoir conditions.
In order to achieve the purpose, the invention provides a method for establishing a dynamic model of acid pressure of a long open hole section of a horizontal well.
In an exemplary embodiment of the method for establishing a dynamic model of acid fracturing of a long open hole section of a horizontal well of the present invention, as shown in fig. 1, the method for establishing a dynamic model of acid fracturing of a long open hole section of a horizontal well comprises the following steps:
S1, establishing a horizontal well long open hole section physical model and geologic models distributed along a well bore, setting the horizontal well long open hole section physical model and the geologic models distributed along the well bore as an x-axis along the well bore direction, setting the depth increasing direction as an x-axis positive direction, setting the vertical well bore direction as a y-axis, setting the direction away from the well bore as a y-axis positive direction, and confirming characteristic parameters and mechanical parameters of corresponding depth according to logging data, the horizontal well long open hole section physical model subjected to grid division and the geologic models distributed along the well bore.
In this embodiment, the wellbore fluid pressure model may include:
Formula 1:
Formula 2:
Formula 3:
Wherein n is the nth time step, dimensionless; the bottom hole pressure at the n+1th time step, pa; The pressure is Pa, delta P n is pressure change caused by compressibility of fluid in a shaft in the nth time step, delta P is pressure change caused by compressibility of fluid in the shaft, delta V acid is volume increment of acid liquid in the shaft, m 3;Vwell is shaft volume, m 3;c1 is fluid compressibility coefficient, pa -1, delta t is time step s; the acid liquid flow rate of the well bore is m 3/min for the nth time step; The acid liquid flow rate flowing out of the shaft in the nth time step, m 3/min, and when n=1, Δx and Δy are the lengths of the unit cell in the x-axis and y-axis directions, m, k y is the permeability of the unit cell in the y-axis direction, m 2, r is the radius of the well bore, m, mu is the viscosity of the fluid, pa.s; the reservoir fluid pressure, pa, is the nth time step within the first grid in the y-axis direction.
In this embodiment, the time step Δt can be determined according to the average permeability k m of the reservoir matrix, and specifically includes time step Δt=1s when k m has a value range of k m<10-15m2, time step Δt=1 to 10s when k m has a value range of 10 -15m2≤km≤10-14m2, and time step Δt=10s when k m has a value range of 10 -14m2≤km.
S2, establishing a fluid pressure model in the shaft and a fluid pressure model in the matrix according to the characteristic parameters and the mechanical parameters.
In this embodiment, the fluid pressure model in the matrix may include:
Formula 4:
Wherein ρ is the fluid density, kg/m 3;kx、ky is the permeability of the unit cell in the x-axis and y-axis directions, m 2, μ is the fluid viscosity, pa.s, P is the reservoir fluid pressure, pa, φ is the reservoir porosity, dimensionless, c 1 is the fluid compression coefficient, pa -1, and t is the acid injection time, s.
S3, establishing an acid liquid flow speed model based on the acid injection port position in the shaft according to the fluid pressure model in the shaft and the fluid pressure model in the matrix.
In this embodiment, the acid flow rate model may include an upstream acid flow rate model and a downstream acid flow rate model, and may include:
Formula 5:
Formula 6:
Wherein u i Upper part is the flow velocity of the upstream acid in the shaft, m/s, u i Lower part(s) is the flow velocity of the downstream acid in the shaft, m/s, x in is the position of the acid injection port, i is the position of the cells in the x-axis direction, m is the total number of the cells in the x-axis direction of the acid flow velocity model, x m is the position of the m-th cell in the x-axis direction, no dimension, deltax and Deltay are the lengths of the cells in the x-axis direction and the y-axis direction respectively, m, P well,i is the fluid pressure in the shaft in the i-axis direction, pa, P r,i is the fluid pressure in the stratum in the i-axis direction, pa, k y,i is the permeability in the y-axis direction, m 2, mu is the fluid viscosity, pa·s, and D Well is the diameter of the shaft, m.
S4, establishing an acid pressure dynamic model according to the acid liquid flow speed model, the fluid pressure model in the well bore and the fluid pressure model in the matrix.
In this embodiment, the acid pressure dynamic model may include an acid solution concentration distribution model, and the acid solution concentration distribution model may include:
Formula 7:
Equation 8:v l,i＝Qout,i/(πD Well Δx).
Wherein Deltax is the length of the unit cell in the x-axis direction, m, D Well is the diameter of a well bore, m, C is the concentration of acid liquor, mol/m 3, t is the time of acid liquor injection, s, u is the flow rate of acid liquor in the well bore, m/s, k c is the acid liquor reaction rate, m/s, v l is the acid liquor flow rate flowing into a reservoir from the well bore, m/s, i is the position of the unit cell in the x-axis direction, v l,i is the acid liquor flow rate flowing into the reservoir from the well bore in the i-axis direction, m/s, Q out,i is the acid liquor flow rate flowing out of the well bore in the i-axis direction per unit time, and m 3/min.
In this embodiment, the acid fracturing dynamic model may include a porosity model and a permeability model after acid solution corrosion, and the porosity model and the permeability model may include:
formula 9:
formula 10:
Wherein phi n is the porosity of the nth time step, phi is the porosity of the reservoir, delta x and delta y are the lengths of the unit cells in the directions of the x axis and the y axis respectively, M is the diameter of a well bore, M is the nth time step, n is dimensionless, t is the time of acid injection, s is the corresponding time step number of the acid liquid leading edge reaching the unit cells at different positions in a shaft for the first time, tau is the rock volume eroded by the acid liquid, M 3 is the dissolution capacity of the acid liquid to the rock mineral, kg/kg is the molar mass of the acid liquid, kg/mol is the reaction rate of k c acid rock, M/s is the acid liquid concentration, mol/M 3 is the rock density, kg/M 3;kn is the permeability after erosion, M 2 is the initial permeability, and M 2;βSG is the pore structure parameter, and is dimensionless.
In this embodiment, the acid fracturing dynamic model may include a well wall tangential stress model, which may include:
Formula 11:
ν=5.89e[-(t-τ)/6.47]-6.23,
Wherein, sigma θ is the tangential stress of the well wall, MPa, sigma H、σh and sigma ν are the maximum horizontal main stress, the minimum horizontal main stress and the vertical stress respectively, MPa, sigma z is the tangential stress of the well wall, MPa, theta and theta' are the well inclination angle, the angle of the tangential stress direction from the axial clockwise rotation of the well bore to the bottom of the hole on the well wall, DEG, P well is the fluid pressure in the well bore, MPa, P is the reservoir fluid pressure, MPa, alpha is the Biot coefficient, dimensionless, v is the rock poisson ratio, dimensionless, omega is the acid damage variable, dimensionless, phi is the porosity of the reservoir, dimensionless, phi n is the porosity of the nth time step, dimensionless, t is the time of acid injection, s, and tau is the corresponding time step of the leading edge of the acid first reaching different position cells in the well bore.
In this embodiment, when the acid concentration at the cell position in the wellbore is greater than or equal to 301-903 mol/m 3, for example, 301, 602, 903mol/m 3, it may be determined that the acid front first reaches the cell position. The acid liquid concentration can be confirmed according to the initial concentration of the injected acid liquid, usually 10% -20% of the initial concentration can be taken, and the specific selection value can be confirmed according to the field condition of the oil field.
The invention also provides a method for predicting the acid fracturing dynamic fracture pressure of the long open hole section of the horizontal well.
In one exemplary embodiment of the horizontal well long open hole acid fracturing pressure prediction method of the present invention, the horizontal well long open hole acid fracturing pressure prediction method comprises the step of determining whether the difference of reservoir fluid pressure minus wall tangential stress is equal to or greater than rock tensile strength by the acid fracturing dynamic model in the horizontal well long open hole acid fracturing dynamic model building method of any one of the above.
When the difference is equal to or greater than the rock tensile strength, the fracture location and fracture pressure can be confirmed.
And when the difference is smaller than the rock tensile strength, the characteristic parameters and the mechanical parameters can be updated, and the steps S1-S4 are repeated until the difference is larger than or equal to the rock tensile strength.
When the process of injecting acid liquid is completed and the difference is less than the rock tensile strength, the construction parameters can be redesigned.
For a better understanding of the above-described exemplary embodiments of the present invention, reference will now be made to the following description, taken in conjunction with the accompanying drawings, by way of illustration, and not limitation.
Example 1
In this example, the method for establishing the acid fracturing dynamic model of the long open hole section of the horizontal well can be realized by the following steps:
S1, establishing a horizontal well long open hole section physical model and geologic models distributed along a well bore, setting the vertical well bore direction as a vertical direction, setting the vertical direction as a vertical direction, and confirming characteristic parameters and mechanical parameters of corresponding depth according to well logging data, the horizontal well long open hole section physical model subjected to grid division and the geologic models distributed along the well bore.
S11, establishing a geological model distributed along a shaft, wherein the number of cells of the geological model in the length direction is m, and assigning characteristic parameters such as reservoir porosity, permeability, formation pressure and the like of corresponding depths to each cell according to logging data.
S12, calculating a mechanical parameter profile distributed along the well bore according to logging data and an indoor experimental result, wherein the mechanical parameter profile comprises mechanical parameters of maximum horizontal main stress, minimum horizontal main stress, vertical main stress, young modulus, poisson' S ratio and the like of a reservoir layer, wherein the mechanical parameters are assigned to corresponding depths in each unit cell.
S2, establishing a fluid pressure model in the shaft and a fluid pressure model in the matrix according to the characteristic parameters and the mechanical parameters.
S21, calculating fluid pressure P well in a shaft according to parameters such as the volume V well of the shaft of the reconstruction section, the fluid pressure P of the reservoir, the injection quantity Q in and the like, wherein the fluid pressure P well in the shaft is represented by the following formulas 1-3:
Formula 1:
Formula 2:
Formula 3:
in the above formula, n is the nth time step, and is dimensionless; the bottom hole pressure at the n+1th time step, pa; The pressure is Pa, delta P n is pressure change caused by compressibility of fluid in a shaft in the nth time step, delta P is pressure change caused by compressibility of fluid in the shaft, delta V acid is volume increment of acid liquid in the shaft, m 3;Vwell is shaft volume, m 3;c1 is fluid compressibility coefficient, pa -1, delta t is time step s; the acid liquid flow rate of the well bore is m 3/min for the nth time step; The acid liquid flow rate flowing out of the shaft in the nth time step, m 3/min, and when n=1, Δx and Δy are the lengths of the unit cell in the x-axis and y-axis directions, m, k y is the permeability of the unit cell in the y-axis direction, m 2, r is the radius of the well bore, m, mu is the viscosity of the fluid, pa.s; the reservoir fluid pressure, pa, is the nth time step within the first grid in the y-axis direction.
S22, confirming a time step according to the average permeability of the reservoir matrix, wherein the method specifically comprises the following steps of:
When the value range of k m is k m<10-15m2, the time step Δt=1s.
When the value range of k m is 10 -15m2≤km≤10-14m2, the time step Δt=1 to 10s.
When the value range of k m is 10 -14m2≤km, the time step Δt=10s.
S23, calculating the fluid pressure in the matrix according to the fluid pressure P well in the time step shaft obtained in the step S21, wherein the fluid pressure is shown in the following formula:
Formula 4:
Wherein ρ is the fluid density, kg/m 3;kx、ky is the permeability of the unit cell in the x-axis and y-axis directions, m 2, μ is the fluid viscosity, pa.s, P is the reservoir fluid pressure, pa, φ is the porosity in the unit cell, dimensionless, c 1 is the fluid compression coefficient, pa -1, and t is the acid injection time, s.
S3, establishing an acid liquid flow speed model based on the acid injection port position in the shaft according to the fluid pressure model in the shaft and the fluid pressure model in the matrix.
S31, taking the position x in of the cell where the acid injection port is located as a reference, taking the positive direction of the x coordinate axis as the downstream, and taking the negative direction of the x coordinate axis as the upstream, and respectively calculating the acid flow speeds of different positions in the shaft according to the distinction of the acid injection port.
Wherein, the upstream acid flow velocity u i Upper part and the downstream acid flow velocity u i Lower part(s) can be confirmed by the following formula 5 and formula 6, respectively, calculation.
Formula 5:
Formula 6:
Wherein u i Upper part is the flow velocity of the upstream acid in the shaft, m/s, u i Lower part(s) is the flow velocity of the downstream acid in the shaft, m/s, x in is the position of the acid injection port, i is the position of the cells in the x-axis direction, m is the total number of the cells in the x-axis direction of the acid flow velocity model, x m is the position of the m-th cell in the x-axis direction, no dimension, deltax and Deltay are the lengths of the cells in the x-axis direction and the y-axis direction respectively, m, P well,i is the fluid pressure in the shaft in the i-axis direction, pa, P r,i is the fluid pressure in the stratum in the i-axis direction, pa, k y,i is the permeability in the y-axis direction, m 2, mu is the fluid viscosity, pa·s, and D Well is the diameter of the shaft, m.
S4, establishing an acid pressure dynamic model according to the acid liquid flow speed model, the fluid pressure model in the well bore and the fluid pressure model in the matrix.
S41, calculating the concentration distribution of the acid liquid in the shaft according to the flow speed of the acid liquid in the shaft, wherein the concentration distribution is shown in the following formulas 7 and 8.
Formula 7:
Equation 8:v l,i＝Qout,i/(πD Well Δx).
Wherein Deltax is the length of the unit cell in the x-axis direction, m, D Well is the diameter of a well bore, m, C is the concentration of acid liquor, mol/m 3, t is the time of acid liquor injection, s, u is the flow rate of acid liquor in the well bore, m/s, k c is the acid rock reaction rate, m/s, v l is the flow rate of acid liquor flowing into a reservoir from the well bore, m/s, i is the position of the unit cell in the x-axis direction, v l is the flow rate of acid liquor flowing into the reservoir from the well bore in the i position in the x-axis direction, m/s, Q out is the flow rate of acid liquor flowing out of the well bore from the well bore in the unit time of the i position in the x-axis direction, and m 3/min.
S42, judging that the front edge of the acid liquor reaches the position of the cell for the first time according to the acid liquor concentration of the position of the cell in the shaft being more than or equal to 301-903 mol/m 3.
S43, calculating the porosity and permeability of the acid solution after corrosion according to the acid solution concentration distribution in the shaft and the acid solution flow rate of the shaft to the reservoir from the position where the front edge of the acid solution reaches the corresponding position in the shaft for the first time.
Wherein, the calculation of the porosity after the acid solution is eroded is shown in the following formula 9.
Formula 9:
the calculation of permeability after erosion is shown in the following formula 10.
Formula 10:
In the above formula, phi n is the porosity of the nth time step, zero dimension, phi is the porosity of the reservoir, zero dimension, delta x and delta y are the lengths of the unit cells in the directions of the x axis and the y axis respectively, M is the diameter of a well bore, M is the nth time step, no dimension, t is the time of acid injection, s is tau is the corresponding time step number of the acid liquid leading edge reaching the unit cells at different positions in the well bore for the first time, delta V is the rock volume eroded by the acid liquid, M 3, beta is the dissolution capacity of the acid liquid to the rock mineral, kg/kg, M is the molar mass of the acid liquid, kg/mol, k c acid rock reaction rate, M/s, C is the acid liquid concentration, mol/M 3;ρS is the rock density, kg/M 3;kn is the permeability after erosion, M 2, k is the initial permeability, and M 2;βSG is the pore structure parameter, and no dimension.
S44, calculating tangential stress distribution along the well bore according to the well bore porosity phi n, reservoir fluid pressure P, bottom hole fluid pressure P well and other parameters and the well Zhou Yingli model. The fracture location and fracture pressure may be determined based on the calculated tangential stress distribution along the wellbore.
Wherein the well Zhou Yingli model can be represented by the following formula 11:
Formula 11:
ν=5.89e[-(t-τ)/6.47]-6.23,
Wherein, sigma θ is the tangential stress of the well wall, MPa, sigma H、σh and sigma ν are the maximum horizontal main stress, the minimum horizontal main stress and the vertical stress respectively, MPa, sigma z is the tangential stress of the well wall, MPa, theta and theta' are the well inclination angle, the angle of the tangential stress direction from the axial clockwise rotation of the well bore to the bottom of the hole on the well wall, DEG, P well is the fluid pressure in the well bore, MPa, P is the reservoir fluid pressure, MPa, alpha is the Biot coefficient, dimensionless, v is the rock poisson ratio, dimensionless, omega is the acid damage variable, dimensionless, phi is the porosity of the reservoir, dimensionless, phi n is the porosity of the nth time step, dimensionless, t is the time of acid injection, s, and tau is the corresponding time step of the leading edge of the acid first reaching different position cells in the well bore.
Example 2
In the example, a method for predicting the dynamic fracture pressure of the acid pressure of the long open hole section of the horizontal well is provided, and whether each position in the well bore reaches the fracture pressure can be judged in sequence according to a selected rock breaking criterion. It should be noted that the fracture pressure calculation model that may be used herein may select a corresponding fracture pressure model according to different well types, well completion modes, and reservoir characteristics. For example, when a well is perforated for casing, a computational model is selected that takes into account the perforated well.
Wherein the rock failure criteria may be represented by the following equation 12:
Formula 12P-sigma θ≥σt.
Wherein P is reservoir fluid pressure, MPa, sigma θ is well wall tangential stress, MPa, sigma t is rock tensile strength, and MPa. The tangential stress of the well wall can be obtained by the method for establishing the acid fracturing dynamic model of the long open hole section of the horizontal well in example 1, and the tensile strength sigma t of the rock can also be obtained by an indoor test.
Further, if the condition satisfies the above formula 12, the calculation is stopped, and the crack initiation position and the crack initiation pressure are obtained. If the cracking condition is not met, the reservoir permeability, the porosity, the fluid pressure in the shaft, the reservoir fluid pressure and the acid fluid concentration distribution are updated, and the steps S1-S4 in the example are repeated, so that the cracking position and the cracking pressure calculation can be obtained. If the acid injection process is finished and the cracking condition is not met, judging that the stratum cannot be cracked to form acid fracturing cracks under the corresponding acid injection condition, and redesigning construction parameters.
Example 3
In the example, a method for predicting the dynamic fracture pressure of the acid fracturing of the long open hole section of the horizontal well is provided, and the method is realized through the following steps:
S1, establishing a horizontal well long open hole section calculation physical model (comprising the horizontal well long open hole section physical model and a geological model distributed along a well bore in the example 1), and assigning parameters as shown in the following table 1.
Table 1 parameter assignment table
S2, selecting a proper time step according to parameters such as the volume of the well bore of the reconstruction section, the pressure of the reservoir fluid, the injection quantity and the like, and calculating the pressure of the fluid in the well bore according to the formulas 1-3 in the example 1.
S3, calculating the fluid distribution in the reservoir in time according to the formula 4 in the example 1, wherein the fluid distribution in the reservoir is shown in figure 2 based on parameters such as fluid pressure in the well bore, fluid pressure in the reservoir in time step, permeability of the reservoir, porosity and the like, and the calculation result of the fluid pressure in the reservoir is shown in figure 2, and it can be seen from figure 2 that the variation of the fluid pressure in the vicinity of the well bore presents stronger heterogeneity due to the heterogeneity of the physical property of the reservoir, so that a foundation can be provided for the calculation of heterogeneous fluid loss and heterogeneous flow of acid liquid in the well bore.
S4, calculating the flow rate of the acid liquid in the shaft according to the formulas 5-6 in the example 1 based on the calculated fluid pressure in the reservoir, wherein the flow rate of the acid liquid in the shaft is shown in fig. 3, the flow rate distribution calculation result of the acid liquid in the shaft is shown in fig. 3, the abscissa of fig. 3 shows the well section, the unit is m, the ordinate shows the flow rate in the shaft, the unit is m/S, and the broken lines in the figure show the flow rates in the shafts at different well section positions.
S5, according to the fluid pressure in the reservoir obtained by calculation in the S3, according to the acid concentration distribution in the well bore in the current time step of the formula 7-8 in the example 1, as shown in FIG. 4, FIG. 4 shows the calculation result of the acid concentration distribution in the well bore, the abscissa of FIG. 4 shows the orientation of the well bore unit cell, the ordinate shows the HCL acid concentration, the unit shows the HCL acid concentration in different well bore unit cell orientations, and the broken line in the figure shows the HCL acid concentration in different well bore unit cell orientations.
And taking whether the acid liquor concentration of the cell position in the current shaft is more than or equal to 602mol/m 3 as a judgment standard, and recording the moment when the acid liquor front reaches the cell at different positions in the shaft for the first time when the standard is met.
S6, calculating the porosity after acid corrosion and the permeability after corrosion according to the formulas 9-10 in the example 1 according to the acid concentration distribution of the acid in the shaft and the acid flow rate of the shaft to the reservoir from the leading edge of the acid to the corresponding position in the shaft for the first time.
S7, calculating tangential stress distribution along the well according to parameters such as porosity of the well along the well, reservoir fluid pressure, bottom hole fluid pressure and the like, according to a formula 11 in example 1, further judging whether each position in the well reaches fracture pressure according to a formula 12 in example 2 in turn, as shown in FIG. 5, wherein the judgment result of the fracture pressure is shown in FIG. 5, the abscissa of FIG. 5 shows time in terms of S, the ordinate shows pressure magnitude in terms of MPa, a broken line a in the figure shows tangential stress magnitude of the well at different times, a broken line b in the figure shows the reservoir pore pressure magnitude at different times, and a broken line c in the figure shows bottom hole flow pressure magnitude at different times. From fig. 5 it can be seen that the fluid pressure in the wellbore is always greater than the reservoir fluid pressure due to the summarized pressure loss of fluid in the wellbore to the reservoir flow process, and as the fluid is injected, the reservoir fluid pressure is at 413s at the sum of tangential stress and tensile strength of the wellbore, at which point the initiation condition is reached.
And S8, if the situation that the cracking condition is met at any position along the shaft is judged in S7, stopping calculating, and obtaining the cracking position and the cracking pressure. If the cracking condition is not met, the permeability, the porosity, the fluid pressure in the shaft, the reservoir fluid pressure and the acid liquid concentration distribution of the reservoir are updated, and the steps S1-S7 are repeated, so that the cracking position and the cracking pressure calculation can be obtained. If the acid injection process is finished and the cracking condition is not met, judging that the stratum cannot be cracked to form acid fracturing cracks under the corresponding acid injection condition, and redesigning construction parameters.
In summary, the method has the beneficial effects that the dynamic flow and reaction process of the acid liquor in the shaft and the reservoir are calculated in real time, and the dynamic fracture pressure prediction in the acid fracturing process is realized by considering the mechanical characteristics and physical characteristic changes of the acid liquor chemical reaction on reservoir sections with different physical parameters. The model calculation process is simple, iteration is not needed, the acid pressure dynamic fracture pressure of the long open hole well of the horizontal well under different acid injection parameters, acid injection port positions and reservoir conditions can be accurately and simply calculated, and theoretical basis is provided for the optimization of the acid pressure process type, process parameters, matched liquid and tools.
Although the present invention has been described above with reference to the exemplary embodiments and the accompanying drawings, it should be apparent to those of ordinary skill in the art that various modifications can be made to the above-described embodiments without departing from the spirit and scope of the claims.
Claims (7)
1. The method for establishing the acid fracturing dynamic model of the long open hole section of the horizontal well is characterized by comprising the following steps of:
S1, establishing a horizontal well long open hole section physical model and a geological model distributed along a well bore, and confirming characteristic parameters and mechanical parameters of corresponding depths according to logging data, the horizontal well long open hole section physical model subjected to grid division and the geological model distributed along the well bore;
s2, establishing a fluid pressure model in the shaft and a fluid pressure model in the matrix according to the characteristic parameters and the mechanical parameters;
S3, establishing an acid liquid flow speed model based on the acid injection port position in the shaft according to the shaft fluid pressure model and the matrix fluid pressure model;
s4, establishing an acid pressure dynamic model according to the acid flow speed model, the fluid pressure model in the well bore and the fluid pressure model in the matrix;
wherein the wellbore fluid pressure model comprises:
Formula 1:
Formula 2:
Formula 3:
Wherein n is the nth time step, is dimensionless, and is At bottom hole pressure Pa at the n+1th time stepThe pressure is Pa, the delta P n is the pressure change caused by the compressibility of fluid in a shaft at the nth time step, the delta P is the pressure change caused by the compressibility of fluid in the shaft, the delta V acid is the volume increment of acid liquid in the shaft at the nth time step, m 3, the V well is the volume of the shaft, m 3, the c 1 is the fluid compressibility, pa -1, the delta t is the time step, s, and the delta V acid is the volume increment of acid liquid in the shaft at the nth time stepThe acid liquid flow rate of the well bore is m 3/min in the nth time step, and the acid liquid flow rate is m 3/minFor the nth time step, the acid liquid flow out of the shaft, m 3/min, and when n=1, theThe Deltax and Deltay are respectively the lengths of the unit cell in the directions of the x axis and the y axis, m, the k y is the permeability of the unit cell in the direction of the y axis, m 2, the r is the radius of a shaft, m, the mu is the viscosity of fluid, pa.s, and theThe reservoir fluid pressure Pa is the nth time step in the first grid in the y-axis direction;
The fluid pressure model in the matrix comprises:
Formula 4:
Wherein ρ is fluid density, kg/m 3, k x、ky is permeability of unit cell in x-axis and y-axis directions, m 2, μ is fluid viscosity, pa.s, P is reservoir fluid pressure, pa, φ is reservoir porosity, dimensionless, c 1 is fluid compression coefficient, pa -1, t is acid injection time, s;
The acid liquid flow speed model comprises an upstream acid liquid flow speed model and a downstream acid liquid flow speed model, and the acid liquid flow speed model respectively comprises:
Formula 5:
Formula 6:
The method comprises the steps of (1) setting u i Upper part as the flow rate of upstream acid in a shaft, m/s, u i Lower part(s) as the flow rate of downstream acid in the shaft, m/s, x in as the position of an acid injection port, no dimension, i as the position of cells in the x-axis direction, no dimension, m as the total number of cells in the x-axis direction of an acid flow velocity model, no dimension, x m as the position of the m-th cell in the x-axis direction, Δx and Δy as the lengths of the cells in the x-axis and y-axis directions respectively, m, P well,i as the fluid pressure in the shaft in the x-axis direction, pa, P r,i as the fluid pressure in the stratum in the x-axis direction, pa, k y,i as the permeability in the y-axis direction of the reservoir, m 2 as the fluid viscosity, pa.s, and D Well as the diameter.
2. The method for establishing the acid fracturing dynamic model of the horizontal well long open hole section according to claim 1, wherein the time step delta t is confirmed according to the average permeability k m of a reservoir matrix, and specifically comprises the time step delta t=1s when the value range of k m is k m<10-15m2, the time step delta t=1-10s when the value range of k m is 10 -15m2≤km≤10-14m2, and the time step delta t=10s when the value range of k m is 10 -14m2≤km.
3. The method for building a dynamic model of acid pressure in a long open hole section of a horizontal well according to claim 1, wherein the dynamic model of acid pressure comprises an acid liquid concentration distribution model, and the acid liquid concentration distribution model comprises:
Formula 7:
Formula 8:v l,i＝Qout,i/(πD Well Δx);
The method comprises the steps of setting a length of a unit cell in an x-axis direction, wherein deltax is m, D Well is the diameter of a well hole, m, C is the concentration of acid liquor, mol/m 3, t is the time of acid liquor injection, s, u is the flow rate of acid liquor in a well hole, m/s, k c is the acid rock reaction rate, m/s, v l is the flow rate of acid liquor flowing into a reservoir from the well hole, m/s, i is the position of the unit cell in the x-axis direction, dimensionless, v l, i is the flow rate of acid liquor flowing into the reservoir from the well hole in the i-axis direction, m/s, Q out, i is the flow rate of acid liquor flowing out of the well hole in the i-axis direction in unit time, and m 3/min.
4. The method for building the acid fracturing dynamic model of the long open hole section of the horizontal well according to claim 1, wherein the acid fracturing dynamic model comprises a porosity model and a permeability model after acid liquor corrosion, and the porosity model and the permeability model respectively comprise:
formula 9:
formula 10:
Wherein, phi n is the porosity of the nth time step, phi is the porosity of the reservoir, delta x and delta y are the lengths of the unit cells in the directions of the x axis and the y axis, M, D Well is the diameter of the well bore, M, n is the nth time step, t is the time of acid injection, s, tau is the corresponding time step number of the acid liquid front reaching the unit cells at different positions in the well bore for the first time, delta V is the rock volume eroded by the acid liquid, M 3, beta is the dissolution capacity of the acid liquid to the rock mineral, kg/kg, M is the molar mass of the acid liquid, kg/mol, k c acid rock reaction rate, M/s, C is the acid liquid concentration, mol/M 3, rho S is the rock density, kg/M 3, k n is the permeability after corrosion, M 2, k is the initial permeability, M 2, beta is the dissolution capacity of the acid liquid to the rock mineral, and the structural parameter is SG.
5. The method for building the acid fracturing dynamic model of the long open hole section of the horizontal well according to claim 1, wherein the acid fracturing dynamic model comprises a well wall tangential stress model, and the well wall tangential stress model comprises:
Formula 11:
The method comprises the steps of setting a standard well wall tangential stress, setting sigma θ as well wall tangential stress, setting sigma H、σh and sigma ν as maximum horizontal main stress, minimum horizontal main stress and vertical stress, setting sigma z as well wall tangential stress, setting theta and theta' as well inclination angles and angles from the axial clockwise rotation of a well bore to the tangential stress direction of the bottom of the well bore on the well wall, setting P well as well bore fluid pressure, setting P as reservoir fluid pressure, setting MPa, setting alpha as Biot coefficient, setting gamma as Poisson ratio, setting omega as acid damage variable, setting phi as reservoir porosity, setting phi as zero factor, setting phi n as porosity of nth time step, setting t as acid injection time, setting t as corresponding time step number of the acid fluid front reaches different position cells in the well bore for the first time.
6. The method for establishing the acid fracturing dynamic model of the long open hole section of the horizontal well according to claim 1, wherein when the acid concentration of the cell position in the well shaft is more than or equal to 301-903 mol/m 3, the leading edge of the acid is judged to reach the cell position for the first time.
7. The method for predicting the acid fracturing dynamic fracture pressure of the long open hole section of the horizontal well is characterized by comprising the steps of determining whether the difference value of reservoir fluid pressure minus wall tangential stress is larger than or equal to the rock tensile strength according to the acid fracturing dynamic model in the method for establishing the acid fracturing dynamic model of the long open hole section of the horizontal well according to any one of claims 1-6;
When the difference is greater than or equal to the rock tensile strength, confirming the fracture position and the fracture pressure;
When the difference is smaller than the rock tensile strength, updating the characteristic parameters and the mechanical parameters, and repeating the steps S1-S4 until the difference is larger than or equal to the rock tensile strength;
When the process of injecting acid liquid is completed and the difference is smaller than the rock tensile strength, the construction parameters are redesigned.
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