Method and device for determining bottom water breakthrough time of horizontal well in multi-medium bottom water gas reservoir

Abstract

The present disclosure provides a method and device for determining the bottom water breakthrough time of a horizontal well in a multi-media bottom water gas reservoir, and belongs to the field of oil and gas exploitation. The method includes establishing a potential distribution model of the formation; establishing a formation potential gradient model and a horizontal well production model based on the potential distribution model; determining the vertical seepage velocity of the bottom water based on the formation potential gradient model; determining the critical production of the gas well based on the horizontal well production model; and determining the bottom water breakthrough time based on the seepage velocity and the critical production. The vertical seepage velocity affects the time of the bottom water breakthrough. When the production of the gas well reaches or exceeds the critical production, the horizontal well may see water. The seepage velocity and the critical production are both related to the permeability of the formation. The determined seepage velocity and the critical production reflect the influence of the permeability of different regions of the formation. Based on the critical production and the seepage velocity, a relatively accurate bottom water breakthrough time of the horizontal well in the multi-media bottom water gas reservoir can be determined.

Description

Technical Field

[0001] The present invention relates to the field of oil and gas exploitation, and in particular to a method and device for determining bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir. Background Art

[0002] A horizontal well is a special well with a maximum well inclination angle reaching or approaching 90° (generally not less than 86°) and maintaining a certain length of horizontal section in the target layer.

[0003] The pressure distribution of the horizontal section of a horizontal well is of great significance for the exploitation of a gas reservoir. For a horizontal well in a homogeneous bottom water gas reservoir, the bottom water generally breaks through at the end of the horizontal section of the horizontal well, and the time is easy to determine. However, for a horizontal well in a multi-media bottom water gas reservoir, the formation environment is more complex, and the bottom water often does not break through at the end of the horizontal section, making it difficult to determine the bottom water breakthrough time. Summary of the invention

[0004] The disclosed embodiment provides a method and device for determining the bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir, which can facilitate determining the bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir. The technical solution is as follows:

[0005] In a first aspect, an embodiment of the present disclosure provides a method for determining bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir, the method comprising:

[0006] Establishing the potential distribution model of the formation;

[0007] Establishing a formation potential gradient model and a horizontal well production model based on the potential distribution model;

[0008] Determining the vertical seepage velocity of bottom water based on the formation potential gradient model;

[0009] Determining the critical production of the gas well based on the horizontal well production model;

[0010] The bottom water breakthrough time is determined based on the seepage velocity and the critical production.

[0011] Optionally, establishing a potential distribution model of the formation includes:

[0012] Establishing a three-dimensional coordinate system, wherein the origin of the three-dimensional coordinate system is located at the original bottom water boundary, the X-axis of the three-dimensional coordinate system is parallel to the horizontal section of the horizontal well, the Z-axis of the three-dimensional coordinate system extends in the vertical direction, and the Y-axis of the three-dimensional coordinate system is perpendicular to the X-axis and the Z-axis;

[0013] Based on the three-dimensional coordinate system, the following potential distribution model is established:

[0014]

[0015] Among them, Φ(y, z) is the potential of the point in the yz plane, Φ e is the potential at the bottom water boundary, q is the horizontal well production, h is the production layer thickness, z w It is the vertical distance between the central axis of the horizontal section of the horizontal well and the bottom water boundary.

[0016] Optionally, establishing a formation potential gradient model and a horizontal well production model based on the potential distribution model includes:

[0017] The potential distribution model is derived to establish the following formation potential gradient model:

[0018]

[0019] determining the potential at the lower wellbore wall based on the potential distribution model;

[0020] Based on the difference between the potential at the bottom water boundary and the potential at the lower well wall, the following horizontal well production model is established:

[0021]

[0022] Where L is the length of the horizontal section of the horizontal well, Φ w is the potential at the lower well wall, r w is the radius of the horizontal section of the horizontal well, K H is the horizontal permeability of the formation, K V is the vertical permeability of the formation, p e is the outer boundary pressure at the top of the gas reservoir, p wf is the wellbore flowing pressure, μ g is the viscosity of natural gas under formation conditions, B g is the volume coefficient of natural gas.

[0023] Optionally, determining the vertical seepage velocity of bottom water based on the formation potential gradient model includes:

[0024] According to the following relationship

[0025]

[0026] Combined with the formation potential gradient model, the seepage velocity is determined

[0027]

[0028] Among them, V z is the vertical seepage velocity of bottom water.

[0029] Optionally, determining the critical production of the gas well based on the horizontal well production model includes:

[0030] Based on the distribution of fractures and caves, the horizontal section of the horizontal well is divided into n sections from the heel end to the toe end, where n is not less than 2 and is an integer;

[0031] Based on the horizontal well production model, determine the production of a single section

[0032]

[0033] β 2 =K H / K V

[0034] Among them, q i is the output of the i-th segment, i is a positive integer not exceeding n, K Hi is the horizontal permeability of the formation in the i-th section, K Vi is the vertical permeability of the formation in the i-th section, β is the anisotropy ratio of the gas layer;

[0035] Determine critical production differential pressure;

[0036] Determine the critical production rate of the gas well based on the production rate of a single section at the critical production pressure difference

[0037]

[0038] Among them, Q crit is the critical production of the gas well, p r is the formation pressure, p wf (τ) is the wellbore flowing pressure at a distance τ from the toe end in the horizontal section, and S is the skin coefficient of the gas well.

[0039] Optionally, determining the bottom water breakthrough time based on the seepage velocity and the critical production includes:

[0040] The water breakthrough time of the i-th section at the critical production is determined according to the following relationship:

[0041]

[0042] Among them, T i is the water breakthrough time of the i-th section, φ is the formation porosity;

[0043] The shortest water breakthrough time among the n segments is determined as the bottom water breakthrough time.

[0044] In a second aspect, the disclosed embodiment further provides a device for determining bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir, the device comprising:

[0045] A model building module, used to build a potential distribution model of the formation, and to build a formation potential gradient model and a horizontal well production model based on the potential distribution model;

[0046] A first determination module is used to determine the vertical seepage velocity of bottom water based on the formation potential gradient model;

[0047] A second determination module is used to determine the critical production of the gas well based on the horizontal well production model;

[0048] The third determination module is used to determine the bottom water breakthrough time based on the seepage velocity and the critical production.

[0049] Optionally, the model building module is used to establish a three-dimensional coordinate system, the origin of the three-dimensional coordinate system is located at the original bottom water boundary, the X-axis of the three-dimensional coordinate system is parallel to the horizontal section of the horizontal well, the Z-axis of the three-dimensional coordinate system extends in the vertical direction, and the Y-axis of the three-dimensional coordinate system is perpendicular to the X-axis and the Z-axis;

[0050] Based on the three-dimensional coordinate system, the following potential distribution model is established:

[0051]

[0052] Among them, Φ(y, z) is the potential of the point in the yz plane, Φ e is the potential at the bottom water boundary, q is the horizontal well production, h is the production layer thickness, z w It is the vertical distance between the central axis of the horizontal section of the horizontal well and the bottom water boundary.

[0053] Optionally, the model building module is used to derive the potential distribution model to establish the following formation potential gradient model:

[0054]

[0055] determining the potential at the lower wellbore wall based on the potential distribution model;

[0056] Based on the difference between the potential at the bottom water boundary and the potential at the lower well wall, the following horizontal well production model is established:

[0057]

[0058] Where L is the length of the horizontal section of the horizontal well, Φ w is the potential at the lower well wall, r w is the radius of the horizontal section of the horizontal well, K H is the horizontal permeability of the formation, K V is the vertical permeability of the formation, p e is the outer boundary pressure at the top of the gas reservoir, p wf is the wellbore flowing pressure, μ g is the viscosity of natural gas under formation conditions, B g is the volume coefficient of natural gas.

[0059] Optionally, the first determining module is used to determine the following relationship:

[0060]

[0061] Combined with the formation potential gradient model, the seepage velocity is determined

[0062]

[0063] Among them, V z is the vertical seepage velocity of bottom water.

[0064] Optionally, the second determination module is used to divide the horizontal section of the horizontal well from the heel end to the toe end into n sections based on the distribution of fractures and holes, where n is not less than 2 and is an integer;

[0065] Based on the horizontal well production model, determine the production of a single section

[0066]

[0067] β 2 =K H / K V

[0068] Among them, q i is the output of the i-th segment, i is a positive integer not exceeding n, K Hi is the horizontal permeability of the formation in the i-th section, K Vi is the vertical permeability of the formation in the i-th section, β is the anisotropy ratio of the gas layer;

[0069] Determine critical production differential pressure;

[0070] Determine the critical production rate of the gas well based on the production rate of a single section at the critical production pressure difference

[0071]

[0072] Among them, Q crit is the critical production of the gas well, p r is the formation pressure, p wf (τ) is the wellbore flowing pressure at a distance τ from the toe end in the horizontal section, and S is the skin coefficient of the gas well.

[0073] Optionally, the third determination module is used to determine the water breakthrough time of the i-th section at the critical production according to the following relationship:

[0074]

[0075] Among them, T i is the water breakthrough time of the i-th section, φ is the formation porosity;

[0076] The shortest water breakthrough time among the n segments is determined as the bottom water breakthrough time.

[0077] In a third aspect, the disclosed embodiment further provides a device for determining bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir, comprising:

[0078] processor;

[0079] a memory for storing instructions executable by a processor;

[0080] The processor is configured to execute the method for determining the bottom water breakthrough time of a horizontal well in a multi-media bottom water gas reservoir as described in the first aspect.

[0081] In a fourth aspect, an embodiment of the present disclosure further provides a computer-readable storage medium, wherein the storage medium stores at least one instruction, and the instruction is loaded and executed by a processor to implement the method for determining the bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir as described in the first aspect above.

[0082] The beneficial effects brought by the technical solution provided by the embodiments of the present disclosure include at least:

[0083] By establishing a potential distribution model of the formation, a formation potential gradient model and a horizontal well production model are established based on the potential distribution model, and then the bottom water seepage velocity in the vertical direction is determined based on the formation potential gradient model, and the critical production of the gas well is determined based on the horizontal well production model. The vertical seepage velocity affects the time of bottom water breakthrough. When the production of the gas well reaches or exceeds the critical production, the horizontal well may see water. The seepage velocity and critical production are both related to the permeability of the formation. The determined seepage velocity and critical production reflect the influence of the permeability of different regions of the formation. Based on the critical production and seepage velocity, the bottom water breakthrough time of the horizontal well in the multi-media bottom water gas reservoir can be determined more accurately. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] In order to more clearly illustrate the technical solutions in the embodiments of the present disclosure, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present disclosure. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0085] Figure 1 It is a flow chart of a method for determining bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir provided by an embodiment of the present disclosure;

[0086] Figure 2 It is a flow chart of another method for determining bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir provided by an embodiment of the present disclosure;

[0087] Figure 3 Schematic diagram of a horizontal section of a horizontal well provided in an embodiment of the present disclosure. The figure shows a horizontal section with a length of L;

[0088] Figure 4 is a yield curve provided by an embodiment of the present disclosure;

[0089] Figure 5 is a schematic diagram of the structure of a horizontal well provided by an embodiment of the present disclosure;

[0090] Figure 6 This is the distribution diagram of water emergence time when the high permeability zone is located in the first zone;

[0091] Figure 7 This is the distribution diagram of water emergence time when the hypertonic zone is located in the II zone;

[0092] Figure 8 This is the distribution diagram of water emergence time when the hypertonic zone is located in the third zone;

[0093] Fig. 9 is a flow chart of establishing a wellbore pressure distribution model provided by an embodiment of the present disclosure;

[0094] Fig.10 is a schematic diagram of a horizontal well provided by an embodiment of the present disclosure;

[0095] Fig.11 It is a structural block diagram of a device for determining bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir provided by an embodiment of the present disclosure;

[0096] Fig.12 It is a structural block diagram of a device for determining bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir provided by an embodiment of the present disclosure. DETAILED DESCRIPTION

[0097] In order to make the objectives, technical solutions and advantages of the present disclosure more clear, the embodiments of the present disclosure will be further described in detail below with reference to the accompanying drawings.

[0098] Figure 1 The present invention provides a method for determining the bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir. Figure 1 As shown, the method includes:

[0099] S11: Establish a potential distribution model of the formation.

[0100] S12: Establish formation potential gradient model and horizontal well production model based on the potential distribution model.

[0101] S13: Determine the vertical seepage velocity of bottom water based on the formation potential gradient model.

[0102] S14: Determine the critical production of the gas well based on the horizontal well production model.

[0103] S15: Determine the bottom water breakthrough time based on the seepage velocity and critical production.

[0104] By establishing a potential distribution model of the formation, a formation potential gradient model and a horizontal well production model are established based on the potential distribution model, and then the bottom water seepage velocity in the vertical direction is determined based on the formation potential gradient model, and the critical production of the gas well is determined based on the horizontal well production model. The vertical seepage velocity affects the time of bottom water breakthrough. When the production of the gas well reaches or exceeds the critical production, the horizontal well may see water. The seepage velocity and critical production are both related to the permeability of the formation. The determined seepage velocity and critical production reflect the influence of the permeability of different areas of the formation. Based on the critical production and seepage velocity, the bottom water breakthrough time of the horizontal well in the multi-media bottom water gas reservoir can be determined more accurately.

[0105] Figure 2 This is another flow chart of a method for determining bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir provided by an embodiment of the present disclosure. It is used to determine the bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir. The method includes:

[0106] S21: Establish a three-dimensional coordinate system.

[0107] Figure 3 Schematic diagram of a horizontal section of a horizontal well provided in an embodiment of the present disclosure. The figure shows a horizontal section with a length of L. Figure 3 As shown, the origin of the three-dimensional coordinate system is located at the original bottom water boundary, that is, the bottom water boundary when the horizontal well has not been put into production and the bottom water has not risen. The X-axis of the three-dimensional coordinate system is parallel to the horizontal section of the horizontal well, the Z-axis of the three-dimensional coordinate system extends in the vertical direction, and the Y-axis of the three-dimensional coordinate system is perpendicular to the X-axis and the Z-axis.

[0108] S22: Establish a potential distribution model based on a three-dimensional coordinate system.

[0109] According to the mirror reflection principle, the horizontal well can be reflected in the yz plane as a straight line well row with two sinks and two sources arranged alternately in infinite space. There are two positions of the sink wells, namely [0, 2(2n+1)hz w ] and [0,4nh+z w ], where h is the pay zone thickness in meters; z w It is the vertical distance between the central axis of the horizontal section of the horizontal well and the bottom water boundary (also called the horizontal well water avoidance height), in meters; n is not less than 2 and is an integer, indicating the number of sections into which the horizontal section is divided from the heel end to the toe end, see the subsequent step S25.

[0110] According to the principle of potential superposition, the potential distribution of any point in the yz plane stratum is:

[0111]

[0112] Where Φ(y, z) is the potential of a point in the yz plane, q is the horizontal well production, h is the gas layer thickness, and z w is the water avoidance height of the horizontal well, C is the pressure drop coefficient of the horizontal well, n is not less than 2 and is an integer.

[0113] Using Besset's formula

[0114]

[0115] By simplifying equation (1), we can get the following equation:

[0116]

[0117] At the bottom water boundary, y = 0, z = 0, and according to equation (3), it can be concluded that Φ(0, 0) = C = Φ e , where Φ e is the potential at the bottom water boundary, dimensionless, so the relationship (3) is transformed to establish the following potential distribution model:

[0118]

[0119] S23: Determine the potential at the lower wellbore wall based on the potential distribution model.

[0120] At the lower wall, y = 0, z = z w -r w , Φ w =Φ(0, z w -r w ), where r w is the radius of the horizontal section of the horizontal well, Φ w It is the potential at the lower well wall.

[0121] The difference between the potential at the bottom water boundary and the potential at the lower well wall can be expressed as follows:

[0122]

[0123] Since the radius r of the horizontal segment w Much smaller than the vertical distance z w , the radius of the horizontal segment r w is much smaller than the pay zone thickness h, so equation (5) can be simplified to the following equation:

[0124]

[0125] Combined with the trigonometric function relationship 1-cos(2α)=2sin 2 α, 1 + cos(2α) = 2cos 2 α, transform the relation (6) to obtain the following relation:

[0126]

[0127] S24: Establish a horizontal well production model based on the difference between the potential at the bottom water boundary and the potential at the lower well wall.

[0128] By transforming equation (7), the following horizontal well production model is established:

[0129]

[0130] Where L is the length of the horizontal section of the horizontal well, K H is the horizontal permeability of the formation, K V is the vertical permeability of the formation, p e is the formation pressure at the bottom water boundary, p wf is the wellbore flowing pressure, μ g is the viscosity of natural gas under formation conditions, and Bg is the volume coefficient of natural gas.

[0131] S25: Based on the distribution of fractures and cavities, the horizontal section of the horizontal well is divided into n sections from the heel end to the toe end.

[0132] Wherein, n is not less than 2 and is an integer. Step S25 may also be performed before step S22. In step S22, n in relational equation (1) is the same as n in step S25, and both represent the number of segments into which the horizontal section of the horizontal well is divided from the heel end to the toe end.

[0133] Figure 3 In the horizontal well, the end of the horizontal section close to the Z axis is the heel end, and the end away from the Z axis is the toe end. In the embodiment of the present disclosure, the horizontal section is exemplarily divided into 8 sections. In the water of the multi-medium bottom water gas reservoir, the distribution of fractures and holes in the formation is uneven. The fractures and holes are densely distributed in some areas and sparsely distributed in some areas. Based on the distribution of fractures and holes, the horizontal section of the horizontal well is segmented so that the density of the fracture and hole distribution in different areas of each section does not exceed a certain threshold, so that the fractures and holes in each section are regarded as uniformly distributed, and the reservoir properties in the same section are regarded as consistent, so as to achieve the purpose of simplification.

[0134] S26: Determine the production of a single section based on the horizontal well production model.

[0135] Based on the horizontal well production model shown in equation (8), the following equation is determined:

[0136]

[0137] β 2 =K H / K V (10)

[0138] Among them, q i is the output of the i-th segment, i is a positive integer not exceeding n, K Hi is the horizontal permeability of the formation in the i-th section, K Vi is the vertical permeability of the formation in the i-th section, and β is the anisotropy ratio of the gas layer.

[0139] According to equation (9), the output of any section can be determined.

[0140] S27: Determine the critical production pressure difference.

[0141] After a horizontal well is put into production at a certain bottom flow pressure, the bottom water will rise to a certain height under the corresponding production pressure difference. Figure 3 The height indicated by the center line A, Figure 3 The figure schematically shows a section of air column and a section of water column, wherein the rectangle below line A represents the water column with a height of z, and the rectangle above line A represents the air column with a height of z. w -z. During the rising process of bottom water, the force analysis of the gas-water column is carried out. If the production pressure difference is greater than the gravity pressure difference of the gas-water column, the bottom water will rise. Therefore, the bottom water will not continue to rise if the following relationship is satisfied:

[0142] p e -p wf (τ)≤ρ g g(z w -z)+ρ w gz (11)

[0143] Among them, p e is the formation pressure at the bottom water boundary, p wf (τ) is the wellbore flow pressure at the distance τ from the toe end in the horizontal section, ρ g is the density of natural gas under bottom hole pressure, g is the acceleration due to gravity, ρ w is the density of the bottom water, and z is the height to which the bottom water rises, that is, the Z-axis coordinate corresponding to the bottom water rising in the three-dimensional coordinate system.

[0144] Since the production pressure difference is the largest at the end of the horizontal section of the horizontal well, if the production pressure difference at the end is less than the gravity pressure difference of the water column ρ w gz w , then the bottom water will always be difficult to rise to the horizontal section of the wellbore. Therefore, the critical production pressure difference of the gas well is defined as the production pressure difference when water can just be seen at the bottom end of the horizontal well, that is,

[0145] p dH =ρ w gz w (12)

[0146] Among them, p dH is the critical production pressure difference of the gas well.

[0147] S28: Determine the critical production rate of the gas well based on the production rate of a single section under the critical production pressure difference.

[0148] According to equation (9), the critical production of the gas well is determined as:

[0149]

[0150] Among them, Q crit is the critical production of the gas well, K H (τ) is the horizontal permeability of the formation at a distance τ from the toe end in the horizontal section, K V (τ) is the vertical permeability of the formation at a distance τ from the toe end in the horizontal section, p r is the formation pressure, p wf (τ) is the wellbore flowing pressure at a distance τ from the toe end in the horizontal section, and S is the skin coefficient of the gas well.

[0151] S29: Derivative the potential distribution model and establish the formation potential gradient model.

[0152] By taking the derivative of the above relationship (4), the following formation potential gradient model is established:

[0153]

[0154] S30: Determine the vertical seepage velocity of the bottom water.

[0155] The vertical seepage velocity of bottom water and the formation potential gradient have the following relationship:

[0156]

[0157] Among them, V z is the vertical seepage velocity of bottom water.

[0158] According to equations (14) and (15), it is determined that the vertical seepage velocity of bottom water satisfies the following equation:

[0159]

[0160] S31: Determine bottom water breakthrough time.

[0161] Since the seepage velocity of bottom water and the actual flow velocity of bottom water in the pores have the following relationship:

[0162]

[0163] Where φ is the formation porosity.

[0164] By transforming equation (17), we get the following equation:

[0165]

[0166] Therefore, the water breakthrough time of the i-th section can be determined according to the following relationship:

[0167]

[0168] Among them, T i is the water breakthrough time of the ith section.

[0169] Combining equation (16) and equation (19), it can be obtained that the water breakthrough time of the i-th segment satisfies the following relationship:

[0170]

[0171] If the production of the gas well is equal to or lower than the critical production, the bottom water may rise fastest along the fracture-cavity development zone in the local area, but the bottom water rises to a certain height along the fracture-cavity development zone (not exceeding the horizontal well water avoidance height z w ) will no longer continue to rise, and at the heel end of the horizontal well, although the bottom water may rise slowly due to the low permeability of the formation, the bottom water will eventually rise to the maximum height at the heel end. If the production of the gas well is greater than the critical production, the production pressure difference in the fracture-cavity development zone may be greater than the critical production pressure difference, resulting in the bottom water being able to rise along the fracture-cavity development zone to the water avoidance height of the horizontal well under the action of the production pressure difference. Since the fracture-cavity zone has a high permeability and a fast bottom water rise rate, water will appear in the fracture-cavity development zone before the heel end in the horizontal section. Combined with equation (9), according to the mirror reflection method and the principle of potential superposition, it is determined that under the critical production, the water appearance time of the i-th section satisfies the following relationship:

[0172]

[0173] Among them, J g (τ) is the specific capacity index at a distance τ from the toe end in the horizontal section.

[0174] Specific capacity index J g (τ) satisfies the following relationship

[0175]

[0176] K H (τ) is the horizontal permeability of the formation at a distance τ from the toe end in the horizontal section, K V(τ) is the vertical permeability of the formation at a distance τ from the toe end in the horizontal section, μ g is the viscosity of natural gas under formation conditions, β is the anisotropy ratio of the gas layer, h is the thickness of the pay zone, D is the wellbore diameter of the horizontal section, z w is the water avoidance height, and S is the skin coefficient of the gas well.

[0177] The shortest water breakthrough time among the n sections is determined as the bottom water breakthrough time. The water breakthrough time of each section can be determined by equation (21), and the bottom water breakthrough time is the time when the bottom water first enters the horizontal section of the horizontal well. Therefore, the shortest water breakthrough time among the n sections is the bottom water breakthrough time. In addition, in the process of comparing the water breakthrough time of each section and determining the bottom water breakthrough time, it is also known which section first sees water, thereby simultaneously determining the position of the bottom water breakthrough.

[0178] For a certain gas reservoir, its reservoir properties and fluid parameters will not change significantly over a considerable period of time. Therefore, the position of the horizontal section of the horizontal well in the reservoir has a greater impact on the development indicators of the horizontal well. Figure 4 is a yield curve provided by the embodiment of the present disclosure. Figure 4 As shown in the figure, the farther the horizontal section of the horizontal well is from the gas-water boundary, that is, the greater the water avoidance height, the higher the critical production pressure difference of the horizontal well, and the closer the horizontal section of the horizontal well is to the top of the gas reservoir, the greater the seepage resistance and the smaller the oil leakage area, which will reduce the production of the horizontal well. When the production pressure difference and the anisotropy ratio of the gas layer are constant, when the dimensionless position (z w / h) is less than a certain value (for example, 0.9), as z w As z increases, the critical production of the horizontal well increases. When the dimensionless position is greater than this value, w As the horizontal section of the horizontal well increases, the critical production of the horizontal well continues to decrease. Therefore, there is a more reasonable position for the horizontal section of the horizontal well, which makes the horizontal well production high and the water breakthrough time long. The formation permeability also affects the critical production of the horizontal well. Under the condition of constant production pressure difference and the horizontal section position of the horizontal well, as the formation permeability increases, the gas layer's ability to replenish the wellbore becomes stronger, and the critical production of the horizontal well increases. By determining the bottom water breakthrough time and position, it is helpful to guide the layout of the horizontal well, so that the horizontal section can see water evenly, thereby increasing the production of the gas well.

[0179] Figure 5 Schematic diagram of a horizontal well structure provided by an embodiment of the present disclosure. When arranging the horizontal well, different areas of the horizontal section are located in the high permeability area of ​​the formation, and the water breakthrough time at different positions in the horizontal section is also different. Figure 6 This is the distribution diagram of water breakthrough time when the hypertonic zone is located in the first zone. The horizontal axis "position" refers to the distance from the end of the horizontal segment, for example Figure 6In the figure, the time corresponding to the horizontal axis 150m represents the time when water appears at a point 150m away from the bottom end of the horizontal section. Figure 6 It can be seen that the farther the area is from the root end, the longer it takes for water to appear, and the time it takes for water to appear in different areas varies greatly. Figure 7 This is the distribution diagram of water emergence time when the hypertonic zone is located in the second zone. Figure 7 It can be seen that the water breakthrough time near the toe end is quite different from that in other areas. Figure 8 This is the distribution diagram of water emergence time when the hypertonic zone is located in the third zone. Figure 8 It can be seen that the differences in water breakthrough time in the entire horizontal section are relatively small and close.

[0180] according to Figure 6 to Figure 8 It can be seen that due to the variable mass flow effect, the production pressure difference from the toe end to the heel end gradually increases. Arranging the toe end in the high permeability area is beneficial to the wellbore pressure drop effect of the horizontal section, so as to suppress the production pressure difference in the high permeability area and increase the production pressure difference in the low permeability area, thereby making the water seepage in the horizontal section relatively uniform.

[0181] The disclosed embodiment also provides a process for establishing a wellbore pressure distribution model. Figure 1 or Figure 2 The method shown was previously established to determine the pressure distribution in the horizontal section of a horizontal well. Fig. 9 : is a flow chart of establishing a wellbore pressure distribution model provided by an embodiment of the present disclosure. Fig. 9 As shown, the method includes:

[0182] S201: Establish an inflow distribution model.

[0183] Fig.10 Schematic diagram of a horizontal well provided by an embodiment of the present disclosure. Fig.10 As shown in the figure, based on the steady seepage theory, the following inflow distribution model is established:

[0184] dQ g (τ) = J g (τ)[p r -p wf (τ)]dτ (23)

[0185] Among them, dQ g (τ) is the inflow rate on the wellbore wall at the micro-element section dτ away from the toe end in the horizontal section, J g (τ) is the specific capacity index at the distance τ from the toe end in the horizontal section, p r is the formation pressure, p wf (τ) is the wellbore flow pressure at the distance τ from the toe end in the horizontal section, and the specific productivity index J g (τ) Refer to the aforementioned relationship (22).

[0186] The unit of distance τ is m; the specific capacity index J g The unit of (τ) is m 3 / (d·MPa·m); formation pressure at the bottom water boundary p e , critical production pressure difference p dH , formation pressure p r 、Wellbore flow pressure p wf The unit of (τ) is MPa; the critical yield Q crit Unit: m 3 / d; water seepage time T i The unit is d; the horizontal permeability of the formation is K H (τ), vertical permeability of the formation K V The unit of (τ) is mD; the viscosity of natural gas under formation conditions is μ g The unit is mPa·s; the thickness of the production layer h, the length of the horizontal section L, the diameter of the wellbore D and the water avoidance height z w The unit of is m; the potential function Φ, gas well skin coefficient S and gas layer anisotropy ratio β are dimensionless; among them, the gas layer anisotropy ratio β is related to the horizontal permeability K of the formation. H (τ) and the vertical permeability of the formation K V (τ) has the following relationship:

[0187] β 2 =K H (τ) / K V (τ) (24)

[0188] Substituting equation (22) into equation (23), the inflow at any distance from the toe end in the horizontal section can be obtained.

[0189] S202: Establish a flow velocity distribution model.

[0190] The above relationship (23) is integrated to establish the following velocity distribution model:

[0191]

[0192] Wherein, v(τ) is the flow velocity at a distance τ from the toe end in the horizontal section, and the unit of flow velocity v(τ) is m / d.

[0193] According to the above relationship (25), the average flow velocity at any distance from the toe end in the horizontal section can be accurately determined.

[0194] S203: Establish a flow friction pressure drop model.

[0195] Specifically, the following flow friction pressure drop model is established based on the flow velocity distribution model:

[0196]

[0197] Among them, -dp wf (τ) is the flow friction pressure drop on the micro-element segment dτ away from the toe end in the horizontal segment, f is the friction coefficient, ρ g is the density of natural gas under bottom hole pressure.

[0198] Flow friction pressure drop-dp wf The unit of (τ) is MPa, and the natural gas density under bottom hole pressure is ρ g The unit is g / cm 3 , the friction coefficient f is dimensionless.

[0199] S204: Establish a wellbore pressure distribution model.

[0200] Specifically, the following wellbore pressure distribution model is established based on the flow velocity distribution model and the flow friction pressure drop model:

[0201]

[0202] Among them, p d (τ) is the pressure at a distance τ from the toe end in the horizontal section, p dH is the production pressure difference at the heel end, and C is the pressure drop coefficient.

[0203] Pressure d The unit of (τ) and the production pressure difference p at the end dH The unit is MPa.

[0204] When establishing the wellbore pressure distribution model, the flow state in the horizontal wellbore is considered to be turbulent. The above equations (25) and (26) are combined, and τ is derived to obtain the following equation:

[0205]

[0206] in,

[0207]

[0208] p d (τ) = p r -p wf (τ) (30)

[0209] Then determine the boundary conditions of equation (28). Since when the production pressure difference is 0, the derivative at any position in the horizontal wellbore should be equal to 0, the following first boundary condition can be obtained:

[0210]

[0211] According to the definition of the heel-end pressure difference of a horizontal well, the following relationship can be obtained:

[0212] p d (τ)| τ＝0 =p dH =p r -p wH (32)

[0213] Among them, p wH is the pressure at the bottom of the horizontal well. That is, the second boundary adjustment of equation (28) is obtained.

[0214] By integrating and solving equation (28), we can obtain equation (27), that is, the wellbore pressure distribution model.

[0215] Fig.11 The structure diagram of a device for determining bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir provided by an embodiment of the present disclosure is shown in FIG. The device for determining bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir is used to execute Figure 1 or Figure 2 The method for determining the bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir is shown in FIG. Fig.11 As shown, the determination device includes a model building module 10 , a first determination module 20 , a second determination module 30 and a third determination module 40 .

[0216] The model building module 10 is used to build a potential distribution model of the formation, and to build a formation potential gradient model and a horizontal well production model based on the potential distribution model. The model building module 10 can be used to execute the aforementioned steps S11 and S12.

[0217] The first determination module 20 is used to determine the vertical seepage velocity of bottom water based on the formation potential gradient model. The first determination module 20 can be used to execute the aforementioned step S13.

[0218] The second determination module 30 is used to determine the critical production of the gas well based on the horizontal well production model. The second determination module 30 can be used to execute the aforementioned step S14.

[0219] The third determination module 40 is used to determine the bottom water breakthrough time based on the seepage velocity and the critical production. The third determination module 40 can be used to execute the aforementioned step S15.

[0220] By establishing a potential distribution model of the formation, a formation potential gradient model and a horizontal well production model are established based on the potential distribution model, and then the bottom water seepage velocity in the vertical direction is determined based on the formation potential gradient model, and the critical production of the gas well is determined based on the horizontal well production model. The vertical seepage velocity affects the time of bottom water breakthrough. When the production of the gas well reaches or exceeds the critical production, the horizontal well may see water. The seepage velocity and critical production are both related to the permeability of the formation. The determined seepage velocity and critical production reflect the influence of the permeability of different areas of the formation. Based on the critical production and seepage velocity, the bottom water breakthrough time of the horizontal well in the multi-media bottom water gas reservoir can be determined more accurately.

[0221] Optionally, the model building module 10 is used to establish a potential distribution model as shown in equation (4), to establish a horizontal well production model as shown in equation (8), and to establish a formation potential gradient model as shown in equation (14).

[0222] The process of establishing the potential distribution model by the model building module 10 refers to the aforementioned steps S21 to S22, the process of establishing the horizontal well production model refers to the aforementioned steps S23 to S24, and the process of establishing the formation potential gradient model refers to the aforementioned step S29, which will not be described in detail here.

[0223] Optionally, the process of the first determining module 20 determining the vertical seepage velocity of the bottom water refers to the aforementioned step S30, which will not be described in detail here.

[0224] Optionally, the process of the second determination module 30 determining the critical production of the gas well refers to the aforementioned steps S25 to S28, which will not be described in detail here.

[0225] Optionally, the process of determining the bottom water breakthrough time by the third determination module 40 refers to the aforementioned step S31, which will not be described in detail here.

[0226] Fig.12 FIG. 1 is a block diagram showing a device for determining bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir provided by an exemplary embodiment of the present disclosure. Fig.12 As shown, the determining device 300 includes a central processing unit (CPU) 301, a system memory 304 including a random access memory (RAM) 302 and a read-only memory (ROM) 303, and a system bus 305 connecting the system memory 304 and the central processing unit 301. The determining device 300 also includes a basic input / output system (I / O system) 306 that helps to transmit information between various components in the computer, and a large-capacity storage device 307 for storing an operating system 313, application programs 314 and other program modules 315.

[0227] The basic input / output system 306 includes a display 308 for displaying information and an input device 309 such as a mouse and a keyboard for user inputting information. The display 308 and the input device 309 are connected to the central processing unit 301 through an input / output controller 310 connected to the system bus 305. The basic input / output system 306 may also include an input / output controller 310 for receiving and processing inputs from a plurality of other devices such as a keyboard, a mouse, or an electronic stylus. Similarly, the input / output controller 310 also provides output to a display screen, a printer, or other types of output devices.

[0228] The mass storage device 307 is connected to the central processing unit 301 through a mass storage controller (not shown) connected to the system bus 305. The mass storage device 307 and its associated computer readable medium provide non-volatile storage for the determination device 300. That is, the mass storage device 307 may include a computer readable medium (not shown) such as a hard disk or a CD-ROM drive.

[0229] Without loss of generality, computer readable media may include computer storage media and communication media. Computer storage media include volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information such as computer readable instructions, data structures, program modules or other data. Computer storage media include RAM, ROM, EPROM, EEPROM, flash memory or other solid-state storage technologies, CD-ROM, DVD or other optical storage, cassettes, magnetic tapes, disk storage or other magnetic storage devices. Of course, those skilled in the art will appreciate that computer storage media are not limited to the above. The above-mentioned system memory 304 and mass storage device 307 can be collectively referred to as memory.

[0230] According to various embodiments of the present disclosure, the determining device 300 can also be connected to a remote computer on the network through a network such as the Internet. That is, the determining device 300 can be connected to the network 312 through the network interface unit 311 connected to the system bus 305, or the network interface unit 311 can also be used to connect to other types of networks or remote computer systems (not shown).

[0231] The memory also includes one or more programs, which are stored in the memory and configured to be executed by the CPU. The one or more programs include instructions for performing the method for establishing the wellbore pressure distribution model as described above provided in the embodiment of the present disclosure.

[0232] The present disclosure also provides a non-transitory computer-readable storage medium, wherein the storage medium stores at least one instruction, which is loaded and executed by a processor to implement Figures 1-2 A method for determining bottom water breakthrough time of a horizontal well in a multi-media bottom water gas reservoir provided by any one of the items.

[0233] A computer program product containing instructions that, when executed on a computer, causes the computer to perform Figure 1-2 Any one of the items provides a method for determining bottom water breakthrough time in a horizontal well of a multi-media bottom water gas reservoir.

[0234] It should be noted that: the device for determining the bottom water breakthrough time of a horizontal well in a multi-media bottom water gas reservoir provided in the above embodiment only uses the division of the above functional modules as an example when determining the bottom water breakthrough time of a horizontal well in a multi-media bottom water gas reservoir. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. In addition, the device for determining the bottom water breakthrough time of a horizontal well in a multi-media bottom water gas reservoir provided in the above embodiment and the method for determining the bottom water breakthrough time of a horizontal well in a multi-media bottom water gas reservoir belong to the same concept. The specific implementation process is detailed in the method embodiment and will not be repeated here.

[0235] A person skilled in the art will understand that all or part of the steps to implement the above embodiments may be accomplished by hardware or by instructing related hardware through a program, and the program may be stored in a computer-readable storage medium, and the above-mentioned storage medium may be a read-only memory, a disk or an optical disk, etc.

[0236] The above description is only an optional embodiment of the present disclosure and is not intended to limit the present disclosure. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present disclosure shall be included in the protection scope of the present disclosure.

Claims

1. A method for determining bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir, characterized in that: The method comprises: Establishing the potential distribution model of the formation; Establishing a formation potential gradient model and a horizontal well production model based on the potential distribution model; Determining the vertical seepage velocity of bottom water based on the formation potential gradient model; Based on the distribution of fractures and holes, the horizontal section of the horizontal well is divided into n sections from the heel end to the toe end, so that the density of fracture and hole distribution in different areas of each section does not exceed a certain threshold, n is not less than 2 and is an integer; Based on the horizontal well production model, determine the production of a single section b 2 =K H / K V Among them, q i is the output of the i-th segment, i is a positive integer not exceeding n, K Hi is the horizontal permeability of the formation in the i-th section, K Vi is the vertical permeability of the formation in the i-th section, h is the thickness of the production layer, L is the length of the horizontal section of the horizontal well, and p e is the formation pressure at the bottom water boundary, p wf is the wellbore flowing pressure, μ g is the viscosity of natural gas under formation conditions, B g is the natural gas volume coefficient, β is the anisotropy ratio of the gas layer, r w is the radius of the horizontal section of the horizontal well, z w K is the vertical distance between the central axis of the horizontal section of the horizontal well and the bottom water boundary, H is the horizontal permeability of the formation, K V is the vertical permeability of the formation; Determine a critical production pressure difference, wherein the critical production pressure difference is the production pressure difference when water can be seen at the bottom end of the horizontal well; Determine the critical production rate of the gas well based on the production rate of a single section at the critical production pressure difference Among them, Q crit is the critical production of the gas well, K H (τ) is the horizontal permeability of the formation at a distance τ from the toe end in the horizontal section, K v (τ) is the vertical permeability of the formation at a distance τ from the toe end in the horizontal section, p r is the formation pressure, p wf (τ) is the wellbore flow pressure at a distance τ from the toe end in the horizontal section, S is the gas well skin factor, and D is the wellbore diameter of the horizontal section; The water breakthrough time of the i-th section at the critical production is determined according to the following relationship: Among them, T i is the water breakthrough time of the i-th segment, is the formation porosity, J g (τ) is the specific capacity index at a distance τ from the toe end in the horizontal section; The shortest water breakthrough time among the n segments is determined as the bottom water breakthrough time.

2. The determination method according to claim 1, characterized in that: The step of establishing a potential distribution model of a stratum comprises: Establishing a three-dimensional coordinate system, wherein the origin of the three-dimensional coordinate system is located at the original bottom water boundary, the X-axis of the three-dimensional coordinate system is parallel to the horizontal section of the horizontal well, the Z-axis of the three-dimensional coordinate system extends in the vertical direction, and the Y-axis of the three-dimensional coordinate system is perpendicular to the X-axis and the Z-axis; Based on the three-dimensional coordinate system, the following potential distribution model is established: Among them, Φ(y, z) is the potential of the point in the yz plane, Φ e is the potential at the bottom water boundary, q is the horizontal well production, h is the production layer thickness, z w It is the vertical distance between the central axis of the horizontal section of the horizontal well and the bottom water boundary.

3. The determination method according to claim 2, characterized in that: The step of establishing a formation potential gradient model and a horizontal well production model based on the potential distribution model includes: The potential distribution model is derived to establish the following formation potential gradient model: determining the potential at the lower wellbore wall based on the potential distribution model; Based on the difference between the potential at the bottom water boundary and the potential at the lower well wall, the following horizontal well production model is established: Where L is the length of the horizontal section of the horizontal well, Φ w is the potential at the lower well wall, r w is the radius of the horizontal section of the horizontal well, K H is the horizontal permeability of the formation, K V is the vertical permeability of the formation, p e is the formation pressure at the bottom water boundary, p wf is the wellbore flowing pressure, μ g is the viscosity of natural gas under formation conditions, B g is the volume coefficient of natural gas.

4. The determination method according to claim 3, characterized in that: Determining the vertical seepage velocity of bottom water based on the formation potential gradient model includes: According to the following relationship Combined with the formation potential gradient model, the seepage velocity is determined Among them, V z is the vertical seepage velocity of bottom water.

5. A device for determining bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir, characterized in that: The determining device comprises: A model building module, used to build a potential distribution model of the formation, and to build a formation potential gradient model and a horizontal well production model based on the potential distribution model; A first determination module is used to determine the vertical seepage velocity of bottom water based on the formation potential gradient model; The second determination module is used to divide the horizontal section of the horizontal well from the heel end to the toe end into n sections based on the distribution of fractures and holes, so that the density of the distribution of fractures and holes in different areas of each section does not exceed a certain threshold, and n is not less than 2 and is an integer; Based on the horizontal well production model, determine the production of a single section b 2 =K H / K V Among them, q i is the output of the i-th segment, i is a positive integer not exceeding n, K Hi is the horizontal permeability of the formation in the i-th section, K Vi is the vertical permeability of the formation in the i-th section, h is the thickness of the production layer, L is the length of the horizontal section of the horizontal well, and p e is the formation pressure at the bottom water boundary, p wf is the wellbore flowing pressure, μ g is the viscosity of natural gas under formation conditions, B g is the natural gas volume coefficient, β is the anisotropy ratio of the gas layer, r w is the radius of the horizontal section of the horizontal well, z w K is the vertical distance between the central axis of the horizontal section of the horizontal well and the bottom water boundary, H is the horizontal permeability of the formation, K V is the vertical permeability of the formation; Determine a critical production pressure difference, wherein the critical production pressure difference is the production pressure difference when water can be seen at the bottom end of the horizontal well; Determine the critical production rate of the gas well based on the production rate of a single section at the critical production pressure difference Among them, Q crit is the critical production of the gas well, K H (τ) is the horizontal permeability of the formation at a distance τ from the toe end in the horizontal section, K v (τ) is the vertical permeability of the formation at a distance τ from the toe end in the horizontal section, p r is the formation pressure, p wf (τ) is the wellbore flow pressure at a distance τ from the toe end in the horizontal section, S is the gas well skin factor, and D is the wellbore diameter of the horizontal section; The third determination module is used to determine the water breakthrough time of the i-th section under the critical production according to the following relationship: Among them, T i is the water breakthrough time of the i-th segment, is the formation porosity, J g (τ) is the specific capacity index at a distance τ from the toe end in the horizontal section; The shortest water breakthrough time among the n segments is determined as the bottom water breakthrough time.

6. The determination device according to claim 5, characterized in that: The model building module is used to establish a three-dimensional coordinate system, the origin of the three-dimensional coordinate system is located at the original bottom water boundary, the X-axis of the three-dimensional coordinate system is parallel to the horizontal section of the horizontal well, the Z-axis of the three-dimensional coordinate system extends in the vertical direction, and the Y-axis of the three-dimensional coordinate system is perpendicular to the X-axis and the Z-axis; Based on the three-dimensional coordinate system, the following potential distribution model is established: Among them, Φ(y, z) is the potential of the point in the yz plane, Φ e is the potential at the bottom water boundary, q is the horizontal well production, h is the production layer thickness, z w It is the vertical distance between the central axis of the horizontal section of the horizontal well and the bottom water boundary.

7. The determination device according to claim 6, characterized in that: The model building module is used to derive the potential distribution model and establish the following formation potential gradient model: determining the potential at the lower wellbore wall based on the potential distribution model; Based on the difference between the potential at the bottom water boundary and the potential at the lower well wall, the following horizontal well production model is established: Where L is the length of the horizontal section of the horizontal well, Φ w is the potential at the lower well wall, r w is the radius of the horizontal section of the horizontal well, K H is the horizontal permeability of the formation, K V is the vertical permeability of the formation, p e is the formation pressure at the bottom water boundary, p wf is the wellbore flowing pressure, μ g is the viscosity of natural gas under formation conditions, B g is the volume coefficient of natural gas.

8. The determination device according to claim 7, characterized in that: The first determination module is used to determine the following relationship Combined with the formation potential gradient model, the seepage velocity is determined Among them, V z is the vertical seepage velocity of bottom water.

9. A device for determining bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir, characterized in that: include: processor; a memory for storing instructions executable by a processor; The processor is configured to execute the method for determining the bottom water breakthrough time of a horizontal well in a multi-media bottom water gas reservoir according to any one of claims 1 to 4.

10. A computer-readable storage medium, characterized in that: The storage medium stores at least one instruction, which is loaded and executed by the processor to implement the method for determining the bottom water breakthrough time of a horizontal well in a multi-medium bottom water gas reservoir as described in any one of claims 1 to 4.

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