Well test analysis method, storage medium and computer equipment for multi-stage fractured horizontal wells in tight reservoirs

Abstract

The present invention discloses a well test analysis method, a storage medium and a computer device for a multi-stage fractured horizontal well in a tight reservoir. The method includes: establishing a physical model of the multi-stage fractured horizontal well; establishing mathematical models corresponding to the near-wellbore fracture network reconstruction area and the far-well secondary fracture affected area respectively, and solving the mathematical models; obtaining the measured well test curve of the multi-stage fractured horizontal well in the tight reservoir according to the collected well test data, and fitting the measured curve with the theoretical curve obtained by solving the mathematical models based on the initial values of the known well test reservoir and fracture parameters; dynamically adjusting the initial values of the well test reservoir and fracture parameters according to the fitting result between the measured curve and the theoretical curve, and when the fitting result meets the conditions, solving the mathematical models based on the current well test reservoir and fracture parameters to obtain the fracturing transformation parameters, which can effectively invert the relevant information of the reservoir and the wellbore by analyzing the unstable pressure response characteristics of the well.

Description

Technical Field

[0001] The present invention belongs to the technical field of oil and gas field development applications, and particularly relates to a well test analysis method, a storage medium, and a computer device for a multi-stage fractured horizontal well in a tight reservoir. Background Art

[0002] It is difficult to obtain economic production by means of natural exploitation of tight reservoirs. However, with the wide application of hydraulic fracturing technology, especially volume fracturing technology, the production of tight oil wells has been greatly improved. At the same time, more and more field practices have proved that the large-scale complex fracture network fracturing technology is the most effective means to improve the ultimate recovery rate of tight reservoirs.

[0003] At present, domestic and foreign scholars have carried out some relevant research on the seepage theory of multi-stage fractured horizontal wells. In 1998, scholars such as Mukherejee studied a simple seepage model to analyze the size and optimal number of vertical transverse fractures in horizontal wells. In the same year, scholars such as Soliman studied the dynamic characteristics of the bottom-hole pressure in horizontal wells, considering the existence of one-dimensional finite conductivity vertical fractures in horizontal wells, and assuming that the fluid flows linearly around the fracture surface. Through solution, an analytical solution in the Laplace space was obtained, and the production efficiency of vertical wells and horizontal wells with one-dimensional finite conductivity vertical fractures was compared. However, this comparison is only valid for the early linear flow. In 1995, scholars such as Home established a physical and mathematical seepage model for multi-stage fractured horizontal wells, solved the model using the superposition principle, analyzed the interference effect between multiple fractures, and divided the seepage flow stages of multi-stage fractured horizontal wells, mainly including four stages: 1: Fracture linear flow (the first linear flow), mainly reflected as the fluid in the artificial fracture flowing linearly into the horizontal wellbore and the fluid in the formation flowing linearly perpendicular to each artificial fracture; 2: Fracture radial flow (the first radial flow), mainly reflected as the fluid in the formation flowing pseudo-radially around each artificial fracture. When the fracture is short or the fracture spacing is large, the pseudo-radial flow section is more obvious. When the fracture is long or the fracture spacing is short, the pseudo-radial flow section cannot be reflected; 3: Formation linear flow (the second linear flow), mainly reflected as the formation fluid flowing linearly perpendicular to the wellbore around the horizontal well and fractures as a whole. This stage occurs in the later stage of flow; 4: Formation radial flow (the second radial flow). If the production time is long enough, the formation fluid far from the horizontal well will flow pseudo-radially around the horizontal well and fractures as a whole. In 2009, scholars such as Fan Dongyan established and solved a seepage model for multi-stage fractured horizontal wells in an infinite conductivity closed oil reservoir considering fracture dip angle based on the source function and Newman product principle, and drew the well test template curve. In 2013, scholars such as Chen Wei proposed an approximate treatment method considering the interference between fractures but not considering the flow rate distribution of fractures, obtained a fast calculation model for multi-stage fractured horizontal wells, and carried out an example application analysis. In 2014, scholars such as Su Yuliang studied the composite flow model of multi-stage fractured horizontal wells and analyzed the influence of each parameter on the production.

[0004] Therefore, the current modern well test analysis method lacks a macroscopic qualitative evaluation of the fracture geometry, and there is still a lack of a seepage model and effective solution method for fractured wells considering the unconventional reservoir and seepage characteristics of tight oil and gas reservoirs.

[0005] There is an urgent need for a well test analysis method, storage medium and computer equipment for multi-stage fractured horizontal wells in tight oil reservoirs. Summary of the Invention

[0006] In view of the above problems, the present invention provides a well test analysis method, a storage medium, and a computer device for multi-stage fractured horizontal wells in tight reservoirs.

[0007] In a first aspect, the present invention provides a well test analysis method for multi-stage fractured horizontal wells in tight reservoirs, comprising the following steps:

[0008] Establish a physical model of the multi-stage fractured horizontal well, wherein the physical model at least includes a near-wellbore fracture network reconstruction area and a far-well secondary fracture affected area;

[0009] Establish mathematical models corresponding to the near-wellbore fracture network reconstruction area and the far-well secondary fracture affected area respectively, and solve the mathematical models;

[0010] Obtain the actual well test curve of the multi-stage fractured horizontal well in the tight reservoir according to the collected well test data, and fit the actual curve with the theoretical curve obtained by solving the mathematical model based on the initial values of the known well test reservoir and fracture parameters;

[0011] Dynamically adjust the initial values of the well test reservoir and fracture parameters according to the fitting result between the actual curve and the theoretical curve, and when the fitting result meets the conditions, solve the mathematical model based on the current well test reservoir and fracture parameters to obtain the fracturing treatment parameters.

[0012] According to an embodiment of the present invention, preferably, the assumption conditions of the physical model include: the formation fluid within the near-wellbore fracture network reconstruction area and the far-well secondary fracture affected area flows vertically into the fracture in a one-dimensional manner; the fractures are the same throughout the formation height, equidistant between fractures, and perpendicular to the horizontal well; the flow within the fracture is in a one-dimensional flow form; the fluid within the fracture is incompressible and has infinite conductivity; the original reservoir permeability is low, and the fluid flow from the original reservoir to the secondary fracture area is ignored.

[0013] According to an embodiment of the present invention, preferably, the fluid flow mode of the physical model is:

[0014] The fluid in the far-well secondary fracture affected area linearly flows into the near-wellbore fracture network reconstruction area, the fluid in the matrix rock blocks in the near-wellbore fracture network reconstruction area channels into the secondary fracture network, linearly flows to the main fracture through the secondary fracture network, and flows into the wellbore through the main fracture.

[0015] According to an embodiment of the present invention, preferably, the establishment of the mathematical models corresponding to the near-wellbore fracture network reconstruction area and the far-well secondary fracture affected area respectively includes:

[0016] Establish a seepage mathematical model for the far-well secondary fracture affected area, a seepage mathematical model for the near-wellbore fracture network reconstruction area, and a fluid linear flow mathematical model from the far-well secondary fracture affected area to the near-wellbore fracture network reconstruction area,

[0017] Among them, the fluid control equation of the seepage mathematical model in the effective area of the far-well secondary fracture is as follows:

[0018]

[0019] The control conditions of the outer boundary of the seepage mathematical model in the effective area of the far-well secondary fracture are as follows:

[0020]

[0021] The initial condition of the seepage mathematical model in the effective area of the far-well secondary fracture is as follows:

[0022] P| (t＝0) = P i

[0023] The fluid control equation of the seepage mathematical model in the near-well fracture network reconstruction area is as follows:

[0024]

[0025] The control conditions of the inner and outer boundaries of the seepage mathematical model in the near-well fracture network reconstruction area are as follows:

[0026]

[0027] The connection surface condition of the seepage mathematical model in the near-well fracture network reconstruction area is as follows:

[0028]

[0029] The control equation of the linear fluid flow from the far-well secondary fracture area to the near-well fracture network reconstruction area is as follows:

[0030]

[0031] The control conditions of the boundary of the linear fluid flow are as follows:

[0032]

[0033] The initial condition of the linear fluid flow is as follows:

[0034] P| (t＝0) = P i

[0035] Among them, r is the well radius, m; p, p Γ1，2 and p F are the formation pressure, the pressure in the near-well fracture network reconstruction area, and the fracture pressure, respectively, MPa; φ is the effective porosity, dimensionless; μ is the fluid viscosity, mPa·s; C t is the comprehensive compressibility, MPa -1 ; t is the production time, h; P iis the initial reservoir pressure, MPa; q m , q sc and q F are the matrix flow rate, the fracture flow rate under standard conditions, and the fracture flow rate respectively, m 3 / d; ω is the fracture network volume ratio, dimensionless; Ω3 is the effective area of the far-well secondary fractures affected, Ω 1，2 is the near-well fracture network reconstruction area, h and h F are the reservoir thickness and the fracture thickness respectively, m; k and k F are the in-zone permeability and the fracture permeability respectively, μm 2 ; B is the volume coefficient, dimensionless; W F is the fracture width, m; y is the distance in the y direction, m; ω takes 1 when the matrix flow term in the near-well fracture network area does not consider the fracture network.

[0036] According to an embodiment of the present invention, preferably, the solving of the mathematical model includes:

[0037] Simplify each of the mathematical models using dimensionless variables to obtain a linearized mathematical model;

[0038] Solve the linearized mathematical model using the Laplace transform method to obtain the bottom-hole pressure solution;

[0039] Using the superposition principle, obtain the bottom-hole pressure solution considering the wellbore storage effect and the skin effect based on the bottom-hole pressure solution;

[0040] Using the Stehfest numerical inversion, transform the bottom-hole pressure considering the wellbore storage effect and the skin effect in the Laplace space to the bottom-hole pressure in the real space.

[0041] According to an embodiment of the present invention, preferably, the obtaining of the measured well test curve of the multi-stage fractured horizontal well in the tight oil reservoir based on the collected well test data and the fitting of the measured curve with the theoretical curve obtained by solving the mathematical model includes:

[0042] Obtain the measured curves of pressure and pressure derivative based on the collected well test data, and then analyze the actual fluid flow process according to the characteristics of the measured curves;

[0043] Divide the pressure and pressure derivative curves into the seepage flow stages of the multi-stage fractured horizontal well according to the actual fluid flow process respectively;

[0044] For each seepage flow stage of the multi-stage fractured horizontal well, select the theoretical curve obtained by solving the corresponding mathematical model based on the initial values of the known well test reservoir and fracture parameters for well test fitting.

[0045] According to an embodiment of the present invention, preferably, for each fracturing horizontal well seepage flow stage, selecting a theoretical curve obtained by solving the corresponding mathematical model based on the initial values of known well test reservoir and fracture parameters for well test fitting includes:

[0046] For each fracturing horizontal well seepage flow stage, perform the following steps:

[0047] According to the corresponding relationship between pressure and time in the current stage, obtain the measured double logarithmic curve, semi-logarithmic curve, and pressure history curve of the well test of the fracturing horizontal well;

[0048] Based on the initial values of known well test reservoir and fracture parameters, solve the mathematical model corresponding to the current stage to obtain the theoretical double logarithmic curve, semi-logarithmic curve, and pressure history curve of the well test of the fracturing horizontal well;

[0049] Respectively compare the fitting degrees between the measured double logarithmic curve and the theoretical double logarithmic curve, the measured semi-logarithmic curve and the theoretical semi-logarithmic curve, and the measured pressure history curve and the theoretical pressure history curve of the well test of the fracturing horizontal well.

[0050] According to an embodiment of the present invention, preferably, the method further includes:

[0051] Based on the production dynamic historical data, according to the current well test reservoir and fracture parameters, perform collaborative analysis on the collected well test data to verify the well test reservoir and fracture parameters.

[0052] In a second aspect, the present invention provides a storage medium on which a computer program is stored, and when the computer program is executed by a processor, the steps of the above-mentioned well test analysis method for multi-stage fractured horizontal wells in tight oil reservoirs are implemented.

[0053] In a third aspect, the present invention provides a computer device, which includes a memory and a processor, and a computer program is stored on the memory, and when the computer program is executed by the processor, the steps of the above-mentioned well test analysis method for multi-stage fractured horizontal wells in tight oil reservoirs are implemented.

[0054] Compared with the prior art, one or more of the above embodiments may have the following advantages or beneficial effects:

[0055] Applying the well test analysis method for multi-stage fractured horizontal wells in tight reservoirs of the present invention, a physical model of a multi-stage fractured horizontal well is established, wherein the physical model at least includes a near-wellbore fracture network reconstruction area and a far-well secondary fracture affected area; mathematical models corresponding to the near-wellbore fracture network reconstruction area and the far-well secondary fracture affected area are established respectively, and the mathematical models are solved; the actual well test curve of the multi-stage fractured horizontal well in the tight reservoir is obtained according to the collected well test data, and the actual curve is fitted with the theoretical curve obtained by solving the mathematical model based on the initial values of the known well test reservoir and fracture parameters; the initial values of the well test reservoir and fracture parameters are dynamically adjusted according to the fitting result between the actual curve and the theoretical curve, and when the fitting result meets the conditions, the fracture stimulation parameters are obtained by solving the mathematical model based on the current well test reservoir and fracture parameters, and the relevant information of the reservoir and the wellbore can be effectively inverted through the analysis of the unstable pressure response characteristics of the well, so as to better evaluate the fracture and dynamically monitor these complex fractured wells through the macroscopic qualitative evaluation of the fracture geometry.

[0056] Other features and advantages of the present invention will be described in the following specification, and will become apparent in part from the specification, or will be understood by implementing the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the structures specifically pointed out in the specification, claims and drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The drawings are used to provide a further understanding of the present invention, and constitute a part of the specification, and are used together with the embodiments of the present invention to explain the present invention, and do not constitute a limitation to the present invention. In the drawings:

[0058] Figure 1 The flowchart of the well test analysis method for multi-stage fractured horizontal wells in tight reservoirs according to Embodiment 1 of the present invention is shown;

[0059] Figure 2 The flowchart of the well test analysis method for multi-stage fractured horizontal wells in tight reservoirs according to Embodiment 2 of the present invention is shown;

[0060] Figure 3 The schematic diagram of the physical model of the multi-stage fractured horizontal well in tight oil reservoirs according to Embodiment 3 of the present invention is shown;

[0061] Figure 4 The schematic diagram of the regional division of the physical model of the multi-stage fractured horizontal well in tight oil reservoirs according to Embodiment 3 of the present invention is shown;

[0062] Figure 5 The theoretical pressure and pressure conductivity characteristic curves of the well test model of the multi-stage fractured horizontal well in tight reservoirs according to Embodiment 3 of the present invention are shown;

[0063] Figure 6Shows the schematic diagram of the influence of fracture length on the well test model morphology in the third embodiment of the present invention;

[0064] Figure 7 Shows the schematic diagram of the influence of fracture conductivity on the well test model morphology in the third embodiment of the present invention;

[0065] Figure 8 Shows the schematic diagram of the influence of fracture network volume ratio on the well test model morphology in the third embodiment of the present invention;

[0066] Figure 9 Shows the schematic diagram of the influence of matrix crossflow capacity coefficient on the well test model morphology in the third embodiment of the present invention;

[0067] Figure 10 Shows the double logarithm curve after fitting the measured curve and the theoretical curve of the multi-stage fractured horizontal well well test in the tight oil reservoir in the third embodiment of the present invention;

[0068] Figure 11 Shows the semi-logarithm curve after fitting the measured curve and the theoretical curve of the multi-stage fractured horizontal well well test in the tight oil reservoir in the third embodiment of the present invention;

[0069] Figure 12 Shows the pressure-production history curve after fitting the measured curve and the theoretical curve of the multi-stage fractured horizontal well well test in the tight oil reservoir in the third embodiment of the present invention. Detailed implementation manners

[0070] The following will combine the drawings and embodiments to detail the implementation manners of the present invention, so as to fully understand how the present invention uses technical means to solve technical problems and the implementation process of achieving technical effects and implement accordingly. It should be noted that as long as there is no conflict, the various embodiments in the present invention and the various features in each embodiment can be combined with each other, and the formed technical solutions are all within the protection scope of the present invention.

[0071] Example 1

[0072] To solve the above technical problems existing in the prior art, the embodiment of the present invention provides a well test analysis method for multi-stage fractured horizontal wells in tight oil reservoirs.

[0073] Refer to Figure 1 , the well test analysis method for multi-stage fractured horizontal wells in this embodiment includes the following steps:

[0074] S1, establish a physical model of a multi-stage fractured horizontal well, where the physical model includes at least a near-well fracture network reconstruction area and a far-well secondary fracture affected area;

[0075] S2. Establish mathematical models corresponding to the near-wellbore fracture network reconstruction area and the far-well secondary fracture affected area respectively, and solve the mathematical models.

[0076] S3. Obtain the actual measured well test curve of the multi-stage fractured horizontal well in the tight oil reservoir according to the collected well test data, and fit the actual measured curve with the theoretical curve obtained by solving the mathematical model based on the initial values of the known well test reservoir and fracture parameters.

[0077] S4. Dynamically adjust the initial values of the well test reservoir and fracture parameters according to the fitting result between the actual measured curve and the theoretical curve, and when the fitting result meets the conditions, solve the mathematical model based on the current well test reservoir and fracture parameters to obtain the fracturing reconstruction parameters.

[0078] In this embodiment, in step S1, the assumed conditions of the physical model include: the formation fluid in the near-wellbore fracture network reconstruction area and the far-well secondary fracture affected area flows vertically into the fracture in a one-dimensional manner; the fractures are the same throughout the formation height, equidistant between fractures, and perpendicular to the horizontal well; the flow in the fracture is in a one-dimensional flow form; the fluid in the fracture is incompressible and has infinite conductivity; the original reservoir permeability is low, and the fluid flow from the original reservoir to the secondary fracture area is ignored.

[0079] In this embodiment, in step S1, the fluid flow mode of the physical model is:

[0080] The fluid in the far-well secondary fracture affected area linearly flows into the near-wellbore fracture network reconstruction area. The fluid in the matrix rock block of the near-wellbore fracture network reconstruction area channels into the secondary fracture network, linearly flows to the main fracture through the secondary fracture network, and flows into the wellbore through the main fracture.

[0081] In this embodiment, the method further includes:

[0082] Based on the production dynamic historical data, perform collaborative analysis on the collected well test data according to the current well test reservoir and fracture parameters to verify the well test reservoir and fracture parameters.

[0083] Example 2

[0084] To solve the above technical problems existing in the prior art, the embodiment of the present invention provides a well test analysis method for a multi-stage fractured horizontal well in a tight oil reservoir based on Embodiment 1. Among them, the well test analysis method for a multi-stage fractured horizontal well in the embodiment of the present invention improves steps S2 and S3 in Embodiment 1.

[0085] Refer to Figure 2 , the method of this embodiment includes the following steps:

[0086] S1. Establish a physical model of a multi-stage fractured horizontal well, where the physical model at least includes a near-wellbore fracture network reconstruction area and a far-well secondary fracture affected area;

[0087] S21. Establish a seepage mathematical model for the far-well secondary fracture affected area, a seepage mathematical model for the near-wellbore fracture network reconstruction area, and a fluid linear flow mathematical model from the far-well secondary fracture affected area to the near-wellbore fracture network reconstruction area;

[0088] S22. Simplify each of the mathematical models using dimensionless variables to obtain the linearized mathematical models;

[0089] S23. Solve the linearized mathematical models using the Laplace transform method to obtain the bottom-hole pressure solution;

[0090] S24. Using the superposition principle, obtain the bottom-hole pressure solution considering the wellbore storage effect and skin effect based on the bottom-hole pressure solution;

[0091] S25. Using the Stehfest numerical inversion, transform the bottom-hole pressure considering the wellbore storage effect and skin effect in the Laplace space to the bottom-hole pressure in the real space;

[0092] S31. Obtain the measured curves of pressure and pressure derivative based on the collected well test data, and then analyze the actual fluid flow process according to the characteristics of the measured curves;

[0093] S32. Divide the pressure and pressure derivative curves into multi-stage fractured horizontal well seepage flow stages according to the actual fluid flow process;

[0094] S33. For each multi-stage fractured horizontal well seepage flow stage, select the theoretical curve obtained by solving the corresponding mathematical model based on the initial values of the known well test reservoir and fracture parameters for well test fitting;

[0095] S4. Dynamically adjust the initial values of the well test reservoir and fracture parameters according to the fitting results between the measured curves and the theoretical curves, and when the fitting results meet the conditions, solve the mathematical model based on the current well test reservoir and fracture parameters to obtain the fracturing treatment parameters.

[0096] In this embodiment, in step S21, the fluid control equation of the seepage mathematical model for the far-well secondary fracture affected area is:

[0097]

[0098] The control condition of the outer boundary of the seepage mathematical model for the far-well secondary fracture affected area is:

[0099]

[0100] The initial conditions of the seepage mathematical model for the far-well secondary fracture affected area are as follows:

[0101] P| (t＝0) = P i

[0102] The fluid control equation of the seepage mathematical model for the near-well fracture network reconstruction area is as follows:

[0103]

[0104] The control conditions for the internal and external boundaries of the seepage mathematical model for the near-well fracture network reconstruction area are as follows:

[0105]

[0106] The connection surface conditions of the seepage mathematical model for the near-well fracture network reconstruction area are as follows:

[0107]

[0108] The control equation of the fluid linear flow from the far-well secondary fracture area to the near-well fracture network reconstruction area is as follows:

[0109]

[0110] The control conditions for the boundaries of the fluid linear flow are as follows:

[0111]

[0112] The initial conditions of the fluid linear flow are as follows:

[0113] P| (t＝0) = P i

[0114] where r is the well radius, m; p, p Γ1，2 and p F are the formation pressure, the pressure in the near-well fracture network reconstruction area, and the fracture pressure, respectively, MPa; φ is the effective porosity, dimensionless; μ is the fluid viscosity, mPa·s; C t is the comprehensive compressibility, MPa -1 ; t is the production time, h; P i is the initial reservoir pressure, MPa; q m , q sc and q F are the matrix flow rate, the fracture flow rate under standard conditions, and the fracture flow rate, respectively, m 3 / d; ω is the fracture network volume ratio, dimensionless; Ω3 is the far-well secondary fracture affected area, Ω 1，2 is the near-well fracture network reconstruction area, h and h F are the reservoir thickness and the fracture thickness, respectively, m; k and k FThey are the in - zone permeability and the fracture permeability, respectively, in μm 2 ; B is the volume coefficient, dimensionless; W F is the fracture width, in m; y is the distance in the y - direction, in m; when the matrix flow term in the near - well fracture network area does not consider the fracture network, ω takes 1.

[0115] In this embodiment, in step S33, for each seepage flow stage of the fractured horizontal well, selecting the theoretical curves obtained by solving the corresponding mathematical model based on the initial values of the known well - test reservoir and fracture parameters for well - test fitting includes:

[0116] For each seepage flow stage of the fractured horizontal well, perform the following steps:

[0117] According to the corresponding relationship between the pressure and time in the current stage, obtain the measured double - logarithmic curve, semi - logarithmic curve, and pressure history curve of the well - test of the fractured horizontal well;

[0118] Based on the initial values of the known well - test reservoir and fracture parameters, solve the mathematical model corresponding to the current stage to obtain the theoretical double - logarithmic curve, semi - logarithmic curve, and pressure history curve of the well - test of the fractured horizontal well;

[0119] Compare the fitting degrees between the measured double - logarithmic curve and the theoretical double - logarithmic curve, the measured semi - logarithmic curve and the theoretical semi - logarithmic curve, and the measured pressure history curve and the theoretical pressure history curve of the well - test of the fractured horizontal well, respectively.

[0120] Example 3

[0121] To solve the above - mentioned technical problems existing in the prior art, the embodiment of the present invention provides an application example of the well - test analysis method for multi - stage fractured horizontal wells in tight oil reservoirs in Embodiment 2.

[0122] The well - test analysis method for multi - stage fractured horizontal wells in tight oil reservoirs in this embodiment includes the following steps:

[0123] The first step, establishing the physical model of the tight oil fracture network fractured horizontal well

[0124] After the horizontal well undergoes fracturing construction, fractures are generated in the near - well zone, and the fractures communicate with each other to form a complex fracture network. Therefore, the physical model not only considers the main fractures, but also considers the complex fracture network and high - permeability zones formed after formation fracturing, as Figure 3 and Figure 4 shown. The physical model includes: the main fracturing fractures, the near - well complex fracture network reconstruction area, the far - well secondary fracture affected area, and the original reservoir. In the affected area, the fluid linearly flows into the reconstruction area, the fluid in the matrix rock blocks in the reconstruction area channels into the secondary fracture network, linearly flows through the secondary fracture network to the main fracture, and flows into the wellbore through the main fracture. As Figure 3 shown.

[0125] Step 2: Establishment of the Unsteady Well Test Mathematical Model for Tight Oil Fracture Network Horizontal Wells

[0126] Introduce the following three parameters to describe the properties of the fractured area:

[0127] Fracture network volume ratio: Equivalent to the artificial fracture density.

[0128] Matrix crossflow capacity coefficient: Characterizes the speed of the detection pressure propagation.

[0129] Shape factor: Indicates the distribution of the fracture network in the reservoir matrix.

[0130] For the multi-stage fractured horizontal well model in tight oil reservoirs, establish its mathematical model. First, according to symmetry, establish the corresponding mathematical model for the main fractures and formation flow patterns.

[0131] (1) Seepage Mathematical Model for the Effective Area of the Remote Well Secondary Fractures

[0132] The control equation is:

[0133] The control conditions for the outer boundary are:

[0134] The initial condition is: P| (t＝0) = P i (3)

[0135] (2) Seepage Mathematical Model for the Near-Well Fracture Network Reformed Area

[0136] The control equation for the fluid is:

[0137] When the matrix flow term in the near-well fracture network area does not consider the fracture network, ω takes 1.

[0138] The control conditions for the inner and outer boundaries are:

[0139] The connection surface condition is:

[0140] (3) Linear Flow of Fluid from the Secondary Fracture Area to the Fracture Network Area

[0141] The control equation for the fluid is:

[0142] The control conditions for the boundary are:

[0143] The initial condition is: P| (t＝0) = P i (9)

[0144] Solve the well test analysis model of multi-stage fractured horizontal wells in tight reservoirs using the trilinear flow model. To facilitate the solution of the equations, first simplify the model using dimensionless variables:

[0145] (1) Dimensionless pressure:

[0146]

[0147]

[0148] (2) Sub-fracture network volume ratio and matrix inter-porosity flow coefficient:

[0149]

[0150] (3) Dimensionless time:

[0151]

[0152] (4) Dimensionless flow rate:

[0153]

[0154] (5) Dimensionless distance:

[0155]

[0156] (6) Dimensionless fracture conductivity:

[0157]

[0158] (7) Diffusion ratio:

[0159]

[0160] After the model is simplified, we get:

[0161] (1) Equation for the fracture-affected zone

[0162]

[0163] (2) Matrix equation for the fracture treatment zone

[0164]

[0165] (3) Sub-fracture network equation for the fracture treatment zone

[0166]

[0167] (4) Main fracture equation

[0168]

[0169] The Laplace transform method is used to solve the linearized well test mathematical model. The combined model can obtain the bottom hole pressure solution as follows:

[0170]

[0171] in:

[0172]

[0173] Furthermore, based on equation (22) and using the superposition principle, the bottom hole pressure solution considering the wellbore reservoir effect and the skin effect can be obtained:

[0174]

[0175] Using Stehfest numerical inversion, the bottom hole pressure in Laplace space can be transformed into the bottom hole pressure in real space:

[0176]

[0177] In the formula, p wD is the dimensionless bottom hole pressure; C FD is the dimensionless fracture conductivity; s is the Laplace spatial variable; S is the skin factor; C D is the dimensionless wellbore storage coefficient.

[0178] The third step is to establish the unstable well test curve chart of tight oil fracture network fracturing horizontal well

[0179] The mathematical model is solved and the theoretical pressure and pressure-conductivity characteristic curve of the well test model of multi-stage fractured horizontal wells in tight oil reservoirs are established to compare the well test model morphology with the well test curve morphology of the actual test well. The basic parameters required for solving the mathematical model are shown in Table 1.

[0180] Table 1

[0181]

[0182] The well test characteristic curves of multi-stage fractured horizontal wells in tight oil reservoirs are divided according to the flow stage

[0183] from Figure 5 It can be seen that the typical characteristic curve of the three-linear flow well test can be divided into 6 stages, namely:

[0184] In the first stage, the curve is the wellbore storage section. The curve features the overlap of the pressure curve and the pressure derivative curve and the straight line slope is 1, which is affected by the wellbore storage coefficient C.

[0185] In the second stage, the curve is the fracture bilinear flow stage, and the curve is characterized by the appearance of a bilinear 1 / 4 slope line segment;

[0186] In the third stage, the curve is in the stage of fracture linear flow. The curve feature is the appearance of a 1 / 2 slope segment of linear flow. Here, the 1 / 4 slope segment is masked by the wellbore effect due to the small half-length of the fracture and the very high fracture conductivity. This stage is affected by fracture parameters.

[0187] In the fourth stage, the curve is in the transition stage of crossflow from the matrix in the stimulated area to the natural fracture. The curve is concave downward with an inflection point. The transition time and the position of the inflection point are affected by the characteristic parameters λ and ω respectively.

[0188] In the fifth stage, the curve is in the stage of linear flow in the affected area before reaching the boundary (the second linear flow stage in the affected area), presenting a 1 / 2 slope line segment, which is affected by the reservoir permeability.

[0189] In the sixth stage, the curve is in the pseudo-steady state flow segment (boundary control stage) after detecting the boundary, presenting a straight line segment with a slope of 1, which is affected by the radius Xe of the reservoir affected area and the fracture spacing Ye.

[0190] In order to determine the adjustment parameters when dynamically adjusting the initial values of the well test reservoir and fracture parameters, an analysis of the influencing factors of the well test curve of the multi-stage fractured horizontal well well test model in a tight oil reservoir is carried out to determine the adjustment parameters according to the influencing factors.

[0191] Based on the theoretical model, sensitivity analysis of different parameters is carried out to obtain the influence of different fracture parameters on the characteristic curve, and an analysis of the influencing factors of the well test curve is carried out.

[0192] (1) Influence of fracture length on the morphology of the well test model

[0193] The fracture lengths are taken as 50 m, 100 m, 150 m, and 200 m respectively. It can be seen that the fracture length mainly affects the fracture bilinear flow stage and the fracture linear flow stage. With the increase of the fracture length, the duration of the linear flow stage decreases; with the increase of the fracture length, the duration of the bilinear flow stage increases. The increase of the fracture length leads to an increase in the network fracture area and an increase in the bilinear flow range; for a model with a constant outer boundary radius, when the fracture length increases, the secondary fracture affected area decreases and the supply capacity decreases. Figure 6

[0194] (2) Influence of fracture conductivity on the morphology of the well test model

[0195] The fracture conductivities are taken as 50 mD·m, 100 mD·m, 500 mD·m, 1000 mD·m, and 1500 mD·m respectively. It can be seen that the conductivity mainly affects the fracture bilinear flow stage and the fracture linear flow stage. With the increase of the conductivity, the duration of the bilinear flow stage becomes shorter; with the increase of the conductivity, the duration of the linear flow stage becomes shorter. Figure 7

[0196] ​​The fracture conductivity reflects the ability of the fracture to transport fluid. The stronger the fracture conductivity, the earlier the end of the bilinear and linear flow stages of the fracture.

[0197] (3) Influence of the fracture network volume ratio on the shape of the well test model

[0198] The fracture network volume ratios are taken as 0.01, 0.05, 0.1, 0.5, and 1 in sequence. From Figure 8 it can be seen that the fracture network volume ratio affects the early stage of the well test model shape and the stage of matrix flow into the fracture network. As ω decreases, the concave depth increases; the decrease in ω indicates that the matrix flow into the fracture network is more obvious, reflecting the oil supply capacity of the matrix to the fracture network.

[0199] (4) Influence of the matrix crossflow coefficient on the shape of the well test model

[0200] The matrix crossflow coefficients are respectively taken as 2.2×10-6, 2.2×10-7, 2.2×10-8, and 2.2×10-9. From Figure 9 it can be seen that the matrix crossflow coefficient mainly affects the time when the matrix flow into the fracture network stage appears. As the crossflow coefficient λ decreases, the time when the concave appears is later. As the crossflow coefficient decreases, the matrix flow into the fracture network stage appears later, reflecting the oil supply rate of the matrix to the fracture network.

[0201] Fourth step, construction of the interpretation process for the unstable well test data of tight oil fracture network fractured horizontal wells

[0202] The entire analysis process is completed through five steps: data collection, model setting, flow segment division, fitting analysis, and parameter evaluation and application.

[0203] Firstly, determine the input and output of the inversion parameters through the collected geological data, well test data, fracturing construction data, etc. Secondly, obtain the pressure and pressure derivative curves based on the well test data, then analyze the actual flow process according to the characteristic segments shown on the curves, divide the flow types of the well test data according to the actual flow process, select a suitable model for well test fitting, and couple the parameters obtained by fitting with pressure and production using production dynamic data to verify the reliability of the results. Finally, determine the fracturing treatment parameters and conduct evaluation and application.

[0204] Under the constraints of production performance history, the unstable well test data of typical wells were analyzed collaboratively to determine the reservoir and fracture parameters of the wells. By applying the established multi-stage fractured horizontal well test analysis model to analyze the well test data of different wells and different periods, parameters such as fracture half-length, fracture conductivity, proportion coefficient of fracture network volume, matrix-fracture crossflow capacity coefficient, matrix-fracture crossflow distance, permeability of fracture network area, single-well controlled radius, average formation pressure, etc. and their variation characteristics can be obtained. The specific influencing factors of each parameter are shown in Table 2.

[0205] Table 2

[0206]

[0207]

[0208] Taking the multi-stage fractured horizontal wells in the JM tight oil reservoir as an example, the interpretation of the unstable well test data of the fractured horizontal wells in the tight oil reservoir was carried out. Using the established well test analysis method for multi-stage fractured horizontal wells in the tight oil reservoir, the existing well in the JM tight oil reservoir was interpreted and analyzed. The pressure build-up test was carried out during the production stage of a certain well in 2017. This well was fractured in stages, with a total of 23 fracture stages, and 12130 m of fracturing fluid 3 , and a total of 887 m of sand added 3 . The pressure build-up test was carried out on this well in October 2017. As of September 2017, the cumulative production was 1262.6 days, and the cumulative oil production was 0.7284×104 t.

[0209] After fitting using the well test analysis model for multi-stage fractured horizontal wells in the tight oil reservoir, the fitted double logarithmic curve, semi-logarithmic curve, and pressure-production history curve were obtained respectively. From Figures 10 to 12 it can be seen that the fitting effect is good, and the fitting results are shown in Table 3.

[0210] Table 3

[0211] Parameter Unit Value Fracture half-length m 10 Fracture conductivity mD·m 22 Coefficient of fracture network volume ratio ％ 10 Coefficient of matrix-fracture crossflow capacity / <![CDATA[1×10 -6 > Matrix-fracture crossflow distance m 5 Permeability of fracture network reconstruction area mD 1 Single well control radius m 15 Average formation pressure MPa 19.36

[0212] The method for interpreting the unstable well test data of the fractured horizontal wells in the tight oil reservoir provided in this embodiment is based on seepage mechanics, modern interpretation theory, and numerical well test interpretation methods. Considering the complex seepage characteristics of the tight oil reservoir and the fracture morphology of the fracturing, a well test model and a mathematical model for multi-stage fractured horizontal wells in the tight oil reservoir are established, so as to establish a well test analysis method for multi-stage fractured horizontal wells in the tight oil reservoir, propose a reasonable well spacing optimization method for multi-stage fractured horizontal wells in the tight oil reservoir, propose a fracture cluster spacing optimization method for multi-stage fractured horizontal wells in the tight oil reservoir, and propose a reasonable shut-in time optimization method for multi-stage fractured horizontal wells in the tight oil reservoir. It can qualitatively evaluate the macroscopic geometry of the fractures, and finally form a set of research systems for the evaluation, optimization, and reservoir engineering design of fractured horizontal wells.

[0213] This embodiment provides an unstable pressure response model and dynamic inversion technology for multi-stage fractured horizontal wells in tight reservoirs, which can effectively invert relevant information of the reservoir and wellbore by analyzing the characteristics of the well's unstable pressure response, such as wellbore storage coefficient, skin factor, matrix permeability, fracture permeability, fracture crossflow capacity, fracture conductivity, effective fracture half-length, etc., and conduct a macroscopic qualitative evaluation of the fracture geometry, so as to better evaluate and dynamically monitor these complex fractured wells, thereby providing scientific and effective reservoir technical support for the development of oilfields.

[0214] Example 4

[0215] To solve the above technical problems existing in the prior art, the embodiment of the present invention also provides a storage medium.

[0216] The storage medium of this embodiment stores a computer program, and when the program is executed by a processor, it implements the steps of the method in the above embodiment.

[0217] Example 5

[0218] To solve the above technical problems existing in the prior art, the embodiment of the present invention also provides a controller.

[0219] The controller of this embodiment includes a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, it implements the steps of the above method.

[0220] Although the disclosed embodiments of the present invention are as above, the content described is only an embodiment adopted for the convenience of understanding the present invention and is not used to limit the present invention. Any person skilled in the art within the technical field to which the present invention pertains can make any modifications and changes in the form of implementation and details without departing from the spirit and scope disclosed by the present invention. However, the protection scope of the present invention shall still be subject to the scope defined by the appended claims.

Claims

1. A well test analysis method for multi-stage fractured horizontal wells in tight reservoirs, characterized in that, It includes the following steps: Establish a physical model of a multi-stage fractured horizontal well, where the physical model at least includes a near-wellbore fracture network reconstruction area and a far-well secondary fracture affected area; Establish mathematical models corresponding to the near-wellbore fracture network reconstruction area and the far-well secondary fracture affected area respectively, and solve the mathematical models; Obtain the actual measured curve of the well test of the multi-stage fractured horizontal well in the tight oil reservoir according to the collected well test data, and fit the actual measured curve with the theoretical curve obtained by solving the mathematical model based on the initial values of the known well test reservoir and fracture parameters; Dynamically adjust the initial values of the well test reservoir and fracture parameters according to the fitting result between the actual measured curve and the theoretical curve, and when the fitting result meets the conditions, solve the mathematical model based on the current well test reservoir and fracture parameters to obtain the fracturing reconstruction parameters; The establishment of the mathematical models corresponding to the near-wellbore fracture network reconstruction area and the far-well secondary fracture affected area respectively includes: Establish a seepage mathematical model for the far-well secondary fracture affected area, a seepage mathematical model for the near-wellbore fracture network reconstruction area, and a fluid linear flow mathematical model from the far-well secondary fracture affected area to the near-wellbore fracture network reconstruction area, where the fluid control equation of the seepage mathematical model for the far-well secondary fracture affected area is: The control condition of the outer boundary of the seepage mathematical model for the far-well secondary fracture affected area is: The initial condition of the seepage mathematical model for the far-well secondary fracture affected area is: The fluid control equation of the seepage mathematical model for the near-wellbore fracture network reconstruction area is: The control conditions of the inner and outer boundaries of the seepage mathematical model for the near-wellbore fracture network reconstruction area are: The connection surface condition of the seepage mathematical model for the near-wellbore fracture network reconstruction area is: The fluid control equation of the fluid linear flow from the far-well secondary fracture area to the near-wellbore fracture network reconstruction area is: The control condition of the boundary of the fluid linear flow is: The initial condition of the fluid linear flow is: where, r is the well radius, m; p, pΓ1,2 and pF are the formation pressure, the pressure in the near-well fracture network reconstruction area and the fracture pressure respectively, MPa; φ is the effective porosity, dimensionless; μ is the fluid viscosity, mPa·s; Ct is the comprehensive compressibility, MPa-1; t is the production time, h; Pi is the initial reservoir pressure, MPa; qm, qsc and qF are the matrix flow rate, the fracture flow rate under standard conditions and the fracture flow rate respectively, m3 / d; ω is the fracture network volume ratio, dimensionless; Ω3 is the effective area of the far-well secondary fracture, Ω1,2 is the near-well fracture network reconstruction area, h and hF are the reservoir thickness and the fracture thickness respectively, m; k and kF are the permeability in the area and the fracture permeability respectively, μm2; B is the volume coefficient, dimensionless; WF is the fracture width, m; y is the distance in the y direction, m; the matrix flow term in the near-well fracture network area does not consider the fracture network Take 1.

2. The method according to claim 1, characterized in that, The assumed conditions of the physical model include: the formation fluid in the near-wellbore fracture network reconstruction area and the far-well secondary fracture affected area flows vertically to the fracture in a one-dimensional manner; the fractures are the same throughout the formation height, equidistant between fractures, and perpendicular to the horizontal well; the flow in the fracture is in a one-dimensional flow form; the fluid in the fracture is incompressible and has infinite conductivity; the original reservoir permeability is low, and the fluid flow from the original reservoir to the secondary fracture area is ignored.

3. The method according to claim 1, characterized in that, The fluid flow mode of the physical model is: The fluid in the far-well secondary fracture affected area linearly flows into the near-wellbore fracture network reconstruction area, the fluid in the matrix rock blocks in the near-wellbore fracture network reconstruction area channels into the secondary fracture network, linearly flows to the main fracture through the secondary fracture network, and flows into the wellbore through the main fracture.

4. The method according to claim 1, characterized in that, The solution of the mathematical models includes: Simplify each of the mathematical models using dimensionless variables to obtain a linearized mathematical model; Solve the linearized mathematical model using the Laplace transform method to obtain the bottom-hole pressure solution; Using the superposition principle, obtain the bottom-hole pressure solution considering the wellbore storage effect and skin effect according to the bottom-hole pressure solution; Using the Stehfest numerical inversion, transform the bottom-hole pressure considering the wellbore storage effect and skin effect in the Laplace space to the bottom-hole pressure in the real space.

5. The method according to claim 1, characterized in that,Obtaining the measured well test curve of a multi-stage fractured horizontal well in a tight oil reservoir based on the collected well test data, and fitting the measured curve with the theoretical curve obtained by solving the mathematical model, includes: Obtaining the measured curves of pressure and pressure derivative based on the collected well test data, and analyzing the actual fluid flow process according to the characteristics of the measured curves; Dividing the pressure and pressure derivative curves into the seepage flow stages of the multi-stage fractured horizontal well respectively according to the actual fluid flow process; For each seepage flow stage of the multi-stage fractured horizontal well, selecting the theoretical curve obtained by solving the corresponding mathematical model based on the initial values of the known well test reservoir and fracture parameters for well test fitting.

6. The method according to claim 5, wherein, The step of, for each seepage flow stage of the multi-stage fractured horizontal well, selecting the theoretical curve obtained by solving the corresponding mathematical model based on the initial values of the known well test reservoir and fracture parameters for well test fitting, includes: For each seepage flow stage of the multi-stage fractured horizontal well, performing the following steps: Obtaining the measured double logarithm curve, semi-logarithm curve and pressure history curve of the well test of the fractured horizontal well according to the corresponding relationship between the pressure and time in the current stage; Based on the initial values of the known well test reservoir and fracture parameters, solving the mathematical model corresponding to the current stage to obtain the theoretical double logarithm curve, semi-logarithm curve and pressure history curve of the well test of the fractured horizontal well; Comparing the fitting degrees between the measured double logarithm curve and the theoretical double logarithm curve, the measured semi-logarithm curve and the theoretical semi-logarithm curve, and the measured pressure history curve and the theoretical pressure history curve of the well test of the fractured horizontal well respectively.

7. The method according to claim 1, wherein, The method further includes: Based on the production dynamic history data, co-analyzing the collected well test data according to the current well test reservoir and fracture parameters to test the well test reservoir and fracture parameters.

8. A storage medium, on which a computer program is stored, wherein, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 7.

9. A computer device, which comprises a memory and a processor, wherein, A computer program is stored on the memory, and when the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 7.

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