CN115559714A - Method and system for determining fracture-cavity parameters of multi-branch fractured-solution reservoir - Google Patents
Method and system for determining fracture-cavity parameters of multi-branch fractured-solution reservoir Download PDFInfo
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Abstract
The invention discloses a method and a system for determining fracture-cavity parameters of a multi-branch solution reservoir, wherein the method comprises the following steps: acquiring actual measurement data of the bottom pressure of the test well changing along with time after the well is shut in; determining initial parameters of a pre-constructed mathematical model of the bottom hole pressure of the multi-branch solution commingled production reservoir according to basic geological data of fracture holes of the multi-branch solution commingled production reservoir, taking the initial parameters as initial values of fitting parameters, and solving to obtain a bottom hole pressure solution of the multi-branch solution commingled production reservoir; calculating a difference value between the pressure of the measured data and a pressure solution obtained by solving; if the difference is smaller than the preset fitting error, taking the initial parameter as a final fitting parameter; and if the difference is larger than or equal to the preset fitting error, correcting the fitting parameters until the difference is smaller than the preset fitting error, and obtaining the final fitting parameters. The method can determine the spatial distribution of the multi-branch fractured oil reservoir fracture-cave only by acquiring pressure data once.
Description
Technical Field
The invention relates to a method and a system for determining fracture-cavity parameters of a multi-branch solution reservoir, and belongs to the technical field of oil and gas field development.
Background
The dissolved-fluid reservoir is a special strong-heterogeneity strong-discrete type slit-type carbonate reservoir, its longitudinal large-scale dissolved cave is formed along the deep large main fracture and secondary fracture, and is made into the form of string bead, and its cross-section possesses the dendritic structural characteristics (Roxinshu, huwen, wang, etc.. Tahe area carbonate reservoir characteristics and development practice [ J ] oil and natural gas geology 2015,36 (03): 347-355.). The fractured-solution reservoir space has a tree-shaped multi-branch structure, and fracture-cavity reservoirs are mainly distributed along branch fractures. The phenomenon of slurry compaction when the drill meets a fracture body frequently occurs in the field drilling process, the normal drilling process is seriously hindered, and the potential danger of drill bit empty drilling is faced (often few inches, fazenda, dunxing beam, and the like. The high-efficiency well prediction method and the application effect of the fractured solution reservoir [ J ] petroleum geophysical exploration, 2017,52 (S1): 199-206.). Therefore, the method is vital to timely and accurately obtain the information such as the number of fracture-cavity branches of the solution reservoir, the space structure and the like.
At present, a means for acquiring reservoir information on site is a well closing unstable well testing test, but the existing technology is mainly established on a single fractured fracture body drilled in a vertical well based on a seepage theory, does not consider the connectivity of different branched fracture bodies, and is not suitable for a commingled production horizontal well of a multi-branched fractured solution reservoir.
Chinese patent publication No. CN 113294147A: a single-hole type solution reservoir well test interpretation method considering the influence of gravity factors is provided, a single-hole type solution reservoir well test interpretation method based on the combination of an energy conservation law and solution cavity fluctuation is provided, the influence of gravity factors is considered at the same time, single-hole type solution reservoir well test interpretation parameters are obtained through pressure recovery well test curve interpretation, and sensitivity analysis of gravity coefficients is carried out. However, the method only considers the condition that one straight well drill meets a vertical fracture-cave reservoir stratum, still belongs to a single-branch fracture-cave body reservoir stratum seepage model, and is not suitable for a multi-branch fracture-solution communicating reservoir stratum.
Chinese patent publication No. CN 113919111A: a method for reservoir well test curve interpretation of an immiscible fluid, comprising: acquiring pressure recovery well testing data of a target object, performing type analysis on a pressure recovery well testing curve, determining a seam/hole combination model to which the target object belongs according to the curve type, and performing key parameter adjustment fitting by combining the pressure recovery well testing curve to obtain key parameters of the target object; and carrying out inversion based on the key parameters and an inversion formula to obtain application parameters representing reservoir characteristics so as to explain the reservoir characteristics of the target object. Although the technology considers the situation of the large-inclination well drilling meeting the fracture-cave, only a single-branch fracture-cave reservoir stratum is considered, and the problem of the seepage of the co-production well of the multi-branch fractured-solution reservoir stratum is still not solved.
Constructing a theoretical physical model of the well cave according to the karst cave characteristics of the fractured-fluid oil reservoir; introducing a fluctuation coefficient and a damping coefficient to construct a mathematical model (with the publication number of CN 113626969A) by combining the actual flow characteristics of the fluid, obtaining a dimensionless calculation formula of the fluctuation coefficient and the damping coefficient, and obtaining a radius (with the publication number of CN 113918866A) and a karst cave height (with the publication number of CN 113919110A) representing the characteristics of the karst cave; and performing fitting calculation according to the radius and the height to obtain the volume characteristic of the karst cave. The model established by the method only considers the condition that the vertical well drilling meets a large karst cave, and does not meet the communication characteristic of the actual complex multi-branch fractured-solution reservoir.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, provides a method and a system for determining fracture-cavity parameters of a multi-branch fractured-solution reservoir, overcomes the current situation that the existing seepage model is built on a single fractured-cavity body drilled in a straight well, does not consider the connectivity of different branch fracture-cavities and is not suitable for a horizontal well of the multi-branch fractured-solution reservoir, and expands the existing seepage theory and a well testing model. In order to achieve the purpose, the invention is realized by adopting the following technical scheme:
in a first aspect, the invention provides a method for determining parameters of a multi-branch solution reservoir fracture hole, which comprises the following steps:
acquiring actual measurement data of the bottom pressure of the test well changing along with time after the well is shut in;
determining initial parameters of a pre-constructed mathematical model of the bottom hole pressure of the multi-branch solution commingled production reservoir according to basic geological data of fracture holes of the multi-branch solution commingled production reservoir, taking the initial parameters as initial values of fitting parameters, and solving to obtain a bottom hole pressure solution of the multi-branch solution commingled production reservoir;
calculating a difference value between the pressure of the measured data and a pressure solution obtained by solving; if the difference value is smaller than the preset fitting error, taking the initial parameter as a final fitting parameter; if the difference is larger than or equal to the preset fitting error, correcting the fitting parameters until the difference is smaller than the preset fitting error, and taking the finally corrected fitting parameters as final fitting parameters; and the final fitting parameters are parameters of the multi-branch fractured-solution reservoir fracture-cavern.
With reference to the first aspect, further, the initial parameters of the pre-constructed mathematical model of bottom hole pressure of the multi-branch solution commingled production reservoir include: number j of branch reservoirs and original formation pressure p i Reservoir permeability k j Porosity of the resin composition
Integrated compression factor c tj 。
With reference to the first aspect, further, the initial values of the fitting parameters are M 0 (d j0 ,A fj0 ,h j0 ) Showing that d is the reservoir distance of the branch well, h is the depth of the karst cave region, A f Is the seepage area.
With reference to the first aspect, further, the pre-constructed bottom hole pressure mathematical model of the multi-branch solution commingled production reservoir is constructed by considering initial conditions and boundary conditions of the fracture cavity according to characteristics of horizontal pipe flow, linear seepage flow of the fracture region and storage and collection flow of the solution cavity region of a horizontal shaft;
wherein, according to the characteristics of the horizontal pipe flow of the horizontal wellbore: the relationship between the flow rate of the horizontal well stable full pipe laminar flow and the driving pressure difference is represented by the following mathematical model:
in the formula (1), Δ p w The pressure difference is Pa corresponding to the length of the shaft; q. q.s w Is the flow rate of the wellbore region, m 3 S; μ is viscosity, pas; d is the length of the shaft, m; r is w Is the wellbore radius, m;
the mathematical differential equation for describing the fluid seepage is as follows according to the linear seepage characteristic of the fracture area:
in the formula (2), k is the permeability of the crack region, m 2 (ii) a μ is viscosity, pas; p is a radical of f Pressure in the fracture area, pa; h is depth, m; rho is fluid density kg/m 3 (ii) a g is gravitational acceleration of 9.8m/s 2 ；c l Is a coefficient of compression of the fluid, pa -1 ；
Porosity,%; c. C t Is the reservoir comprehensive compression coefficient, pa -1 (ii) a t is time, s;
the flow rate in the fractured zone of the reservoir is obtained from the pressure change:
in the formula (3), q f For flow in the fracture zone，m 3 /s；A f Is the seepage area of the fracture area, m 2 (ii) a k is the permeability of the crack region, m 2 ；p f Pressure in the fracture area, pa; t is time, s;
the mathematical equation for describing the relationship between the net flow of the karst cave fluid and the change of the karst cave pressure according to the characteristics of the storage flow of the karst cave region is as follows:
in the formula (4), q v Is the flow rate of the karst cave region, m 3 /s；C v Is the karst cave storage coefficient, m 3 /Pa；p v Is the pressure in the karst cave area, pa; t is time, s;
wherein, the initial condition of the fracture hole is that the pressure of each part of the reservoir is the same and equal to the original pressure of the reservoir before well opening and production, and then the mathematical model expression of the initial pressure is as follows:
p tf (h,0)＝p v (0)＝p bf (h,0)＝p i (5)
in the formula (5), p tf The pressure of the upper crack area of the karst cave is Pa; p is a radical of v Is the pressure in the karst cave area, pa; p is a radical of formula bf The pressure of a crack area at the lower part of the karst cave is Pa; p is a radical of formula i Reservoir original pressure, pa; h is depth, m;
wherein, the boundary conditions of the slot and the hole comprise:
inner boundary conditions:
wellbore production equals the sum of the flows in the upper fracture zone of the karst cave:
the bottom hole pressure is equal to the sum of the pressure of the reservoir of the branch near the well and the pressure difference of the horizontal section near the well:
p w (t)＝Δp w1 +p tf1 (t) (7)
in the formulas (6) and (7), Q is the bottom hole flow rate, m 3 /s；q tf Is a karst caveUpper fracture zone flow rate, m 3 /s；p w Bottom hole pressure, pa; delta p w1 The pressure difference is the pressure difference corresponding to the near wellbore section length, pa; t is time, s;
interface connection conditions:
the fluid flows from the fracture system at the lower part of the karst cave to the fracture area at the upper part of the karst cave through the karst cave area; at the interface of the cavern with the upper and lower fracture zones, the flow is the same:
at the interface of the cavern with the upper and lower fracture zones, the pressure is the same:
p tf (h tv ,t)＝p v (t)＝p bf (h bv ,t) (9)
in the formulae (8), (9), C v Is the karst cave storage coefficient, m 3 /Pa；h tv The depth of the top surface of the karst cave is m; h is bv The depth of the bottom surface of the karst cave is m;
outer boundary conditions:
the outer boundary of the reservoir is a closed boundary without fluid flow.
In the formula: h is a total of fb M is the bottom degree of the lower fracture area of the karst cave.
With reference to the first aspect, further, the calculating the solved data of the change of the bottom hole pressure with time includes:
carrying out non-dimensionalization on parameters in the mathematical model to obtain: dimensionless pressure
Dimensionless time
Dimensionless flow
Dimensionless reservoir coefficient
Dimensionless depth
Dimensionless gravity coefficient
Dimensionless offset reservoir distance
Dimensionless flow coefficient ratio
Ratio of dimensionless pressure transmission coefficient
After dimensionless and laplace space transformation, the pressure of the upper part crack and the lower part crack of the arbitrary j branch karst cave is as follows:
the flow equation of the upper cracks of the arbitrary j-branch karst cave is as follows:
the arbitrary j-branch karst cave flow equation is:
the flow equation for any j sections of the wellbore is:
the flow rate conditions of the well bore are as follows:
the pressure conditions of the well bore are as follows:
any j branches of lower cracks-karst caves-upper cracks are adopted, and the flow conditions are as follows:
arbitrary j branches of lower cracks-karst caves-upper cracks, and the pressure conditions are as follows:
and if the outer boundary of the reservoir is a sealed edge boundary, the flow is 0:
equation (11) corresponds to a solution of the form:
in the formula (20), c is a coefficient to be solved, r is a conjugate characteristic root, and the expression form is as follows:
substituting equation (20) into the inner boundary conditions (15-16), the interface connection conditions (17-18), the outer boundary conditions (19) yields a linear system of equations for the coefficient c to be solved:
the matrix D is 4n × 4n elements, and is 0 except for the following elements.
The first row elements are:
the elements in rows 2 to n are:
the n + 1-2 n elements are:
elements in rows 2n +1 to 3n are:
the elements of the row 3n + 1-4 n are:
for the two-branch model, D is specifically:
for a single branch, D specifically is:
solving the system of equations (22) to obtain all the coefficients to be solved c t1 Then the bottom hole pressure can be solved as
Inverting Laplace space dimensionless bottom hole pressure (23) by a Stehfest numerical integration algorithm to obtain solved data p of dimensionless bottom hole pressure changing along with time under real space wD 。
With reference to the first aspect, further, the modifying the fitting parameters includes: reservoir distance d of each branch well j Depth h of each solution cavity area j Seepage area A of each branch reservoir fj 。
In a second aspect, the present invention provides a system for determining fracture-cavity parameters of a multi-branch solution reservoir, comprising:
an acquisition module: the method comprises the steps of obtaining measured data of bottom hole pressure of a test well changing along with time after shut-in;
a calculation module: the method comprises the steps of determining initial parameters of a pre-constructed mathematical model of the bottom hole pressure of the multi-branch solution commingled production reservoir according to basic geological data of fracture holes of the multi-branch solution commingled production reservoir, and solving to obtain a bottom hole pressure solution of the multi-branch solution commingled production reservoir by taking the initial parameters as initial values of fitting parameters;
an output module: the pressure calculation device is used for calculating the difference between the pressure of the measured data and the pressure solution obtained by solving; if the difference is smaller than the preset fitting error, taking the initial parameter as a final fitting parameter; if the difference is larger than or equal to the preset fitting error, correcting the fitting parameters until the difference is smaller than the preset fitting error, and taking the finally corrected fitting parameters as final fitting parameters; and the final fitting parameters are parameters of the multi-branch fractured-solution reservoir fracture-cavern.
In a third aspect, the present invention provides a computing device comprising a processor and a storage medium;
the storage medium is used for storing instructions;
the processor is configured to operate in accordance with the instructions to perform the steps of the method of the first aspect.
In a fourth aspect, the invention provides a computer-readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of the method of the first aspect.
Compared with the prior art, the method and the system for determining the fracture-cave parameters of the multi-branch fractured-solution reservoir provided by the embodiment of the invention have the beneficial effects that:
the method comprises the steps of obtaining actual measurement data of bottom hole pressure of a test well changing along with time after the well is shut in; determining initial parameters of a pre-constructed bottom-hole pressure mathematical model of the multi-branch solution commingled production reservoir according to basic geological data of fracture holes of the multi-branch solution commingled production reservoir, taking the initial parameters as initial values of fitting parameters, and solving to obtain a bottom-hole pressure solution of the multi-branch solution commingled production reservoir; the pre-constructed bottom hole pressure mathematical model of the multi-branch fractured-solution commingled production reservoir considers the commingled production working conditions of a plurality of branch fracture-hole reservoirs, and no multi-branch reservoir fractured-solution commingled production model exists at present; a horizontal well is introduced into a well bore part in a pre-constructed multi-branch fractured-solution commingled oil reservoir bottom hole pressure mathematical model, the factors of horizontal flow of fluid in the horizontal well bore and flowing pressure loss are considered, and a seepage model of a fractured-solution reservoir horizontal well does not exist at present. The invention considers the pressure and flow coupling between reservoir seepage, karst cave storage flow and well bore pipe flow. The existing single-branch reservoir seepage model is expanded, and the unstable seepage theory of the existing fracture-cave carbonate reservoir is enriched.
The invention calculates the difference between the pressure of the measured data and the pressure of the solved data; if the difference is smaller than the preset fitting error, taking the initial parameter as a final fitting parameter; if the difference is larger than or equal to the preset fitting error, correcting the fitting parameters until the difference is smaller than the preset fitting error, and taking the finally corrected fitting parameters as final fitting parameters; and the final fitting parameters are parameters of the multi-branch fractured-solution reservoir fracture-cavern. The method determines the number of the fracture-cave branches of the multi-branch solution reservoir through the bottom hole pressure measurement data, considers the mutual connectivity of the multi-branch reservoir of the solution reservoir, and better accords with the real working condition of the actual solution reservoir.
The invention obtains the number of the fracture-cavity branches of the whole reservoir layer only by one-time pressure data, reduces the operation cost of the layered test, improves the test efficiency and greatly shortens the time of the well shut-in test. The invention is especially suitable for multi-branch solution reservoirs which adopt horizontal wells, highly deviated wells and even vertical wells for production and exploitation, and is also suitable for fracture-solution-cave type reservoirs, solution-cave type reservoirs and fracture type oil and gas reservoirs.
Drawings
FIG. 1 is a flow chart of a method for determining fracture-cavity parameters of a multi-branch solution reservoir according to an embodiment;
FIG. 2 is the fitting effect and the explanation result of the measured pressure of the single-branch slot in the second embodiment of the present invention;
FIG. 3 shows the fitting effect and the explanation result of the measured pressure of the present invention and the double-branch slit hole in the second embodiment.
Detailed Description
The invention is further described below with reference to the accompanying drawings. The following examples are only for illustrating the technical solutions of the present invention more clearly, and the protection scope of the present invention is not limited thereby.
The first embodiment is as follows:
as shown in fig. 1, an embodiment of the present invention provides a method for determining a fracture-cavity parameter of a multi-branch fractured-solution reservoir, including:
acquiring actual measurement data of the bottom pressure of the test well changing along with time after the well is shut in;
determining initial parameters of a pre-constructed mathematical model of the bottom hole pressure of the multi-branch solution commingled production reservoir according to basic geological data of fracture holes of the multi-branch solution commingled production reservoir, taking the initial parameters as initial values of fitting parameters, and solving to obtain a bottom hole pressure solution of the multi-branch solution commingled production reservoir;
calculating a difference value between the pressure of the measured data and a pressure solution obtained by solving; if the difference value is smaller than the preset fitting error, taking the initial parameter as a final fitting parameter; if the difference is larger than or equal to the preset fitting error, correcting the fitting parameters until the difference is smaller than the preset fitting error, and taking the finally corrected fitting parameters as final fitting parameters; and the final fitting parameters are parameters of the multi-branch fractured-solution reservoir fracture-cavern.
The method comprises the following specific steps:
step 1: obtaining measured data (t, P) of the time variation of the bottom pressure of the test well after shut-in t0 )。
And 2, step: determining an initial parameter M of a pre-constructed bottom hole pressure mathematical model of the multi-branch solution commingled production reservoir according to basic geological data of fracture holes of the multi-branch solution commingled production reservoir 0 And taking the initial parameters as initial values of the fitting parameters.
The initial parameters of the pre-constructed mathematical model of the bottom hole pressure of the multi-branch solution commingled production reservoir comprise: number j of branch reservoir and original formation pressure p i Reservoir permeability k j Porosity, degree of porosity
Integrated compression factor c tj 。
M for initial values of fitting parameters 0 (d j0 ,A fj0 ,h j0 ) Showing that d is the reservoir distance of the branch well, h is the depth of the karst cave area, A f Is the seepage area.
The pre-constructed bottom hole pressure mathematical model of the multi-branch fractured-solution commingled production reservoir is constructed by considering fracture-cave initial conditions and boundary conditions according to the characteristics of horizontal pipe flow of a horizontal shaft, linear seepage flow of a fracture area and storage and collection flow of a solution-cave area. The method specifically comprises the following steps:
according to the characteristics of the horizontal pipe flow of the horizontal wellbore: after fluid in a reservoir enters a shaft, flowing from a far end to a bottom horizontal well of a near well along the horizontal section of the shaft, and the relationship between the flow of a stable full pipe laminar flow and the driving pressure difference is characterized by the following mathematical model:
in the formula (1), Δ p w The pressure difference is Pa corresponding to the length of the shaft; q. q.s w Is the flow rate of the wellbore region, m 3 S; μ is viscosity, pas; d is the length of the shaft, m; r is w Is the wellbore radius, m.
In a reservoir fracture zone, reservoir fluids are primarily infiltrated through the fracture system, according to the characteristics of the linear seepage in the fracture zone. The mathematical differential equation describing fluid seepage is:
in the formula (2), k is the permeability of the crack region, m 2 (ii) a μ is viscosity, pas; p is a radical of f Pressure in the fracture area, pa; h is depth, m; rho is fluid density kg/m 3 (ii) a g is the acceleration of gravity, 9.8m/s 2 ；c l Is a coefficient of compression of the fluid, pa -1 ；
Porosity,%; c. C t Is the comprehensive compression coefficient of the reservoir, pa -1 (ii) a t is time, s;
the flow rate in the fractured zone of the reservoir is obtained from the pressure change:
in the formula (3), q f Is the flow rate of the fracture zone, m 3 /s；A f Is the seepage area of the fracture area, m 2 (ii) a k is the permeability of the crack region, m 2 ；p f Pressure in the fracture area, pa; t is time, s.
According to the characteristics of the storage flow in the karst cave region, the fluid in the karst cave can be elastically compressed or expanded under the change of the reservoir pressure. The mathematical equation describing the relationship between the net flow of the cavern fluid and the change in the cavern pressure is:
in the formula (4), q v Is the flow rate of the karst cave region, m 3 /s；C v Is the karst cave storage coefficient, m 3 /Pa；p v Pa is the pressure of a karst cave area; t is time, s.
The initial conditions of the fracture and the hole are that the pressure of all parts of the reservoir before well opening production is the same and equal to the original pressure of the reservoir, and then the mathematical model of the initial pressure is expressed as follows:
p tf (h,0)＝p v (0)＝p bf (h,0)＝p i (5)
in formula (5), p tf The pressure of the upper crack area of the karst cave is Pa; p is a radical of formula v Is the pressure in the karst cave area, pa; p is a radical of formula bf The pressure of a crack area at the lower part of the karst cave is Pa; p is a radical of i Is the reservoir original pressure, pa; h is depth, m.
The seam hole boundary conditions include: an inner boundary condition, an interface connection condition, and an outer boundary condition.
Inner boundary conditions:
wellbore production equals the sum of the flows in the upper fracture zone of the karst cave:
the bottom hole pressure is equal to the sum of the pressure of the near well branch reservoir and the pressure difference of the near well horizontal segment:
p w (t)＝Δp w1 +p tf1 (t) (7)
in the formulas (6) and (7), Q is the bottom hole flow rate, m 3 /s；q tf M is the flow rate of the upper fracture area of the karst cave 3 /s；p w Bottom hole pressure, pa; delta p w1 The pressure difference is Pa corresponding to the length of a near wellbore section; t is time, s.
Interface connection conditions:
the fluid flows from the fracture system at the lower part of the karst cave to the fracture area at the upper part of the karst cave through the karst cave area; at the interface of the cavern with the upper and lower fracture zones, the flow is the same:
at the interface of the cavern with the upper and lower fracture zones, the pressure is the same:
p tf (h tv ,t)＝p v (t)＝p bf (h bv ,t) (9)
in the formulae (8), (9), C v Is the karst cave storage coefficient, m 3 /Pa；h tv The depth of the top surface of the karst cave is m; h is a total of bv Is the depth of the bottom surface of the karst cave, m.
Outer boundary conditions:
the outer boundary of the reservoir is a closed boundary without fluid flow.
In the formula: h is fb The bottom degree m of the lower crack region of the karst cave.
The pre-constructed bottom hole pressure mathematical model of the multi-branch fractured-solution commingled production reservoir considers the commingled production working condition of a plurality of branch fracture-cavity reservoirs, and no multi-branch reservoir fractured-solution commingled production model exists at present; a horizontal well is introduced into a well bore part in a pre-constructed multi-branch fractured-solution commingled oil reservoir bottom hole pressure mathematical model, the factors of horizontal flow of fluid in the horizontal well bore and flowing pressure loss are considered, and a seepage model of a fractured-solution reservoir horizontal well does not exist at present. The invention considers the pressure and flow coupling between reservoir seepage, karst cave storage flow and well bore pipe flow. The existing single-branch reservoir seepage model is expanded, and the unstable seepage theory of the existing fracture-cave carbonate rock oil and gas reservoir is enriched.
And step 3: according to the initial value M of the fitting parameter 0 Solving a pre-constructed mathematical model of the bottom hole pressure of the multi-branch-fracture solution commingled production reservoir to obtain the multi-branch fractureAnd (4) solving the bottom hole pressure of the solution commingled oil reservoir.
And solving the established mathematical model through the processes of parameter dimensionless, laplace space transformation, numerical inversion and the like.
Specifically, the method comprises the following steps:
carrying out dimensionless operation on parameters in the mathematical model to obtain: dimensionless pressure
Dimensionless time
Dimensionless flow
Dimensionless reservoir coefficient
Dimensionless depth
Dimensionless gravity coefficient
Dimensionless offset reservoir distance
Dimensionless flow coefficient ratio
Ratio of dimensionless pressure transmission coefficient
After dimensionless and laplace space transformation, the pressure of the upper fracture and the lower fracture of the arbitrary j-branch karst cave is as follows:
the flow equation of the upper cracks of the arbitrary j branch karst caves is as follows:
the arbitrary j-branch karst cave flow equation is:
the flow equation for any j sections of the wellbore is:
the flow rate conditions of the well bore are as follows:
the wellbore pressure conditions were:
arbitrary j branches of lower cracks-karst caves-upper cracks, and the flow conditions are as follows:
arbitrary j branches of lower cracks-karst caves-upper cracks, and the pressure conditions are as follows:
the outer boundary of the reservoir is a sealed edge boundary, and the flow is 0:
equation (11) corresponds to a solution of the form:
in the formula (20), c is the coefficient to be solved, r is the conjugate characteristic root, and the expression form is:
substituting equation (20) into the inner boundary conditions (15-16), the interface connection conditions (17-18), the outer boundary conditions (19) yields a linear system of equations for the coefficient c to be solved:
the matrix D is 4n × 4n elements, except the following elements, which are all 0.
The first row of elements is:
the elements in rows 2 to n are:
the n + 1-2 n elements are:
elements in rows 2n +1 to 3n are:
the elements of the row 3n + 1-4 n are:
for the two-branch model, D is specifically:
for a single branch, D specifically is:
solving the system of equations (22) to obtain all the coefficients to be solved c t1 Then the bottom hole pressure can be solved as
Inverting Laplace space dimensionless bottom hole pressure (23) by a Stehfest numerical integration algorithm to obtain solved data p of dimensionless bottom hole pressure changing along with time under real space wD 。
And 4, step 4: calculating the pressure P of the measured data to And the pressure solution P obtained by solving t Difference | P between t -P to L, |; if the difference is smaller than the preset fitting error e, the initial parameter M is set 0 As final fitting parameter M; if the difference is larger than or equal to the preset fitting error e, correcting the fitting parameters until the difference is smaller than the preset fitting error, and taking the finally corrected fitting parameter M as a final fitting parameter; and the final fitting parameters are the parameters of the multi-branch fractured solution reservoir fracture-vugs.
The method determines the number of the fracture-cave branches of the multi-branch solution reservoir through the bottom hole pressure measurement data, considers the mutual connectivity of the multi-branch reservoirs of the solution reservoir, and better accords with the real working condition of the actual solution reservoir.
The invention obtains the number of the fracture-cavity branches of the whole reservoir layer only by one-time pressure data, reduces the operation cost of the layered test, improves the test efficiency and greatly shortens the time of the well shut-in test. The invention is especially suitable for multi-branch solution reservoirs which adopt horizontal wells, highly deviated wells and even vertical wells for production and exploitation, and is also suitable for fracture-solution-cave type reservoirs, solution-cave type reservoirs and fracture type oil and gas reservoirs.
Example two:
in this embodiment, the method for determining parameters of a fracture hole of a multi-branch solution reservoir described in the first embodiment is used for determining the parameters.
The method for determining parameters of the multi-branch solution reservoir fracture hole is adopted to determine parameters of a single-branch fracture hole (figure 2, right drawing). The left graph of FIG. 2 shows the fitting result of the single-branch model, the distance d between the fracture-cave branch and the well heel end 1 =135m, cavern depth h 1 =50m, karst cave volume V 1 ＝350m 3 。
The method for determining parameters of the fracture-vug of the multi-branch fractured-solution reservoir described in the first embodiment is adopted to determine parameters of the double-branch fracture-vug (the right diagram of fig. 3). As shown in the left diagram of fig. 3, the fitting result of the two-branch model is that the distance d1=35m from the fracture-cave branch 1 to the well heel end, the depth h1=10m of the karst cave 1, and the volume V1=280m of the karst cave 1 3 The distance d2=50m between the fracture-cave branch 2 and the well heel end, the depth h2=15m of the karst cave 2, and the volume V2=560m of the karst cave 2 3 。
The result shows that the method for determining the fracture-cavity parameters of the multi-branch fractured-solution reservoir can quickly and accurately determine the fracture-cavity parameters of the multi-branch fractured-solution reservoir and determine the quantity and the space structure of the fracture-cavity branches of the multi-branch fractured-solution reservoir.
Example three:
the embodiment of the invention provides a system for determining parameters of a multi-branch solution reservoir fracture hole, which comprises:
an acquisition module: the device is used for acquiring the actual measurement data of the bottom pressure of the test well changing along with the time after the well is shut in;
a calculation module: the method comprises the steps of determining initial parameters of a pre-constructed mathematical model of the bottom hole pressure of the multi-branch solution commingled production reservoir according to basic geological data of fracture holes of the multi-branch solution commingled production reservoir, and solving to obtain a bottom hole pressure solution of the multi-branch solution commingled production reservoir by taking the initial parameters as initial values of fitting parameters;
an output module: the pressure calculation device is used for calculating the difference between the pressure of the measured data and the pressure solution obtained by solving; if the difference is smaller than the preset fitting error, taking the initial parameter as a final fitting parameter; if the difference is larger than or equal to the preset fitting error, correcting the fitting parameters until the difference is smaller than the preset fitting error, and taking the finally corrected fitting parameters as final fitting parameters; and the final fitting parameters are parameters of the multi-branch fractured-solution reservoir fracture-cavern.
Example four:
the embodiment of the invention provides a computing device, which comprises a processor and a storage medium;
the storage medium is used for storing instructions;
the processor is configured to operate in accordance with the instructions to perform the steps of the method of embodiment one.
Example five:
embodiments of the present invention further provide a computer-readable storage medium, on which a computer program is stored, where the computer program, when executed by a processor, implements the steps of the method of an embodiment.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.
Claims (9)
1. A method for determining parameters of a multi-branch solution reservoir fracture hole is characterized by comprising the following steps:
acquiring actual measurement data of the bottom pressure of the test well changing along with time after the well is shut in;
determining initial parameters of a pre-constructed bottom-hole pressure mathematical model of the multi-branch solution commingled production reservoir according to basic geological data of fracture holes of the multi-branch solution commingled production reservoir, taking the initial parameters as initial values of fitting parameters, and solving to obtain a bottom-hole pressure solution of the multi-branch solution commingled production reservoir;
calculating a difference value between the pressure of the measured data and a pressure solution obtained by solving; if the difference value is smaller than the preset fitting error, taking the initial parameter as a final fitting parameter; if the difference is larger than or equal to the preset fitting error, correcting the fitting parameters until the difference is smaller than the preset fitting error, and taking the finally corrected fitting parameters as final fitting parameters; and the final fitting parameters are parameters of the multi-branch fractured-solution reservoir fracture-cavern.
2. The method for determining the parameters of the fracture-vug of the multibranched solution reservoir according to claim 1, wherein the initial parameters of the pre-constructed mathematical model of the bottom-hole pressure of the multibranched solution reservoir comprise: number j of branch reservoirs and original formation pressure p i Reservoir permeability k, porosity
Integrated compression factor c t 。
3. The method of claim 2, wherein the initial value of the fitting parameter is M 0 (d j0 ,A fj0 ,h j0 ) Showing that d is the reservoir distance of the branch well, h is the depth of the karst cave region, A f Is the seepage area.
4. The method for determining parameters of the fracture-cavern of the multi-branch fractured-solution reservoir according to claim 1, wherein the pre-constructed mathematical model of the bottom hole pressure of the multi-branch fractured-solution reservoir is constructed by considering initial conditions and boundary conditions of the fracture-cavern according to the characteristics of horizontal pipe flow, linear seepage flow of a fracture region and storage and collection flow of a solution-cavern region of a horizontal shaft;
wherein, according to the characteristics of the horizontal pipe flow of the horizontal wellbore: the relationship between the flow rate and the driving pressure difference of the stable full pipe laminar flow of the horizontal well is represented by the following mathematical model:
in the formula (1), Δ p w The pressure difference is Pa corresponding to the length of the shaft; q. q.s w Is the flow rate of the wellbore region, m 3 S; μ is viscosity, pas; d is the length of the shaft, m; r is w Is the wellbore radius, m;
according to the characteristic of linear seepage in a fracture area, a mathematical differential equation for describing fluid seepage is as follows:
in the formula (2), k is the permeability of the crack region, m 2 (ii) a μ is viscosity, pas; p is a radical of f Pressure in the crack area, pa; h is depth, m; rho is fluid density kg/m 3 (ii) a g is gravitational acceleration of 9.8m/s 2 ；c l Is the coefficient of compression of the fluid, pa -1 ；
Porosity,%; c. C t Is the reservoir comprehensive compression coefficient, pa -1 (ii) a t is time, s;
the flow rate in the fractured zone of the reservoir is obtained from the pressure change:
in the formula (3), q f Is the flow rate of the fracture zone, m 3 /s；A f Is the seepage area of the fracture area, m 2 (ii) a k is the permeability of the crack region, m 2 ；p f Pressure in the crack area, pa;t is time, s;
the mathematical equation for describing the relationship between the net flow of the karst cave fluid and the change of the karst cave pressure according to the characteristics of the storage flow of the karst cave region is as follows:
in the formula (4), q v Is the flow rate of karst cave region, m 3 /s；C v Is the karst cave storage coefficient, m 3 /Pa；p v Is the pressure in the karst cave area, pa; t is time, s;
wherein, the initial condition of the fracture hole is that the pressure of each part of the reservoir is the same and equal to the original pressure of the reservoir before the well is opened and the production is carried out, and then the mathematical model expression of the initial pressure is as follows:
p tf (h,0)＝p v (0)＝p bf (h,0)＝p i (5)
in the formula (5), p tf The pressure of the upper crack area of the karst cave is Pa; p is a radical of formula v Is the pressure in the karst cave area, pa; p is a radical of bf The pressure of a crack area at the lower part of the karst cave is Pa; p is a radical of formula i Reservoir original pressure, pa; h is depth, m;
wherein, the boundary conditions of the slot and the hole comprise:
inner boundary conditions:
wellbore production equals the sum of the flows in the upper fracture zone of the cavern:
the bottom hole pressure is equal to the sum of the pressure of the reservoir of the branch near the well and the pressure difference of the horizontal section near the well:
p w (t)＝Δp w1 +p tf1 (t) (7)
in the formulas (6) and (7), Q is the bottom hole flow rate, m 3 /s；q tf Flow rate of upper fracture zone of karst cave, m 3 /s；p w Bottom hole pressure, pa; delta p w1 The pressure difference is Pa corresponding to the length of a near wellbore section;t is time, s;
interface connection conditions:
the fluid flows from the fracture system at the lower part of the karst cave to the fracture area at the upper part of the karst cave through the karst cave area; at the interfaces of the cavern with the upper and lower fracture zones, the flow rates are the same:
at the interface of the cavern with the upper and lower fracture zones, the pressure is the same:
p tf (h tv ,t)＝p v (t)＝p bf (h bv ,t) (9)
in the formulae (8) and (9), C v Is the karst cave storage coefficient, m 3 /Pa；h tv The depth of the top surface of the karst cave is m; h is a total of bv The depth of the bottom surface of the karst cave is m;
outer boundary conditions:
the outer boundary of the reservoir is a closed boundary without fluid flow.
In the formula: h is a total of fb M is the bottom degree of the lower fracture area of the karst cave.
5. The method for determining the parameters of the fracture-vug of the multi-branch fractured-solution reservoir according to claim 4, wherein the solving to obtain the bottom-hole pressure solution of the multi-branch fractured-solution commingled production reservoir comprises:
carrying out non-dimensionalization on parameters in the mathematical model to obtain: dimensionless pressure
Dimensionless time
Dimensionless flow
Dimensionless reservoir coefficient
Dimensionless depth
Dimensionless gravity coefficient
Dimensionless offset reservoir distance
Dimensionless ratio of flow coefficients
Ratio of dimensionless pressure conductance
After dimensionless and laplace space transformation, the pressure of the upper fracture and the lower fracture of the arbitrary j-branch karst cave is as follows:
the flow equation of the upper cracks of the arbitrary j branch karst caves is as follows:
the arbitrary j-branch karst cave flow equation is:
the flow equation for any j sections of the wellbore is:
the flow rate conditions of the well bore are as follows:
the wellbore pressure conditions were:
arbitrary j branches of lower cracks-karst caves-upper cracks, and the flow conditions are as follows:
any j branches of lower cracks-karst caves-upper cracks are adopted, and the pressure condition is as follows:
and if the outer boundary of the reservoir is a sealed edge boundary, the flow is 0:
equation (11) corresponds to a solution of the form:
in the formula (20), c is the coefficient to be solved, r is the conjugate characteristic root, and the expression form is:
substituting equation (20) into the inner boundary conditions (15-16), the interface connection conditions (17-18), the outer boundary conditions (19) yields a linear system of equations for the coefficient c to be solved:
the matrix D is 4n × 4n elements, and is 0 except for the following elements.
The first row elements are:
the elements in rows 2 to n are:
the n + 1-2 n elements are:
the elements of the 2n +1 to 3n are:
the row elements of 3n +1 to 4n are:
for the two-branch model, D is specifically:
for a single branch, D specifically is:
solving the system of equations (22) to obtain all the coefficients to be solved c t1 Then the bottom hole pressure can be solved as
Inverting Laplace space dimensionless bottom hole pressure (23) through a Stehfest numerical integration algorithm to obtain solved data p of dimensionless bottom hole pressure changing along with time in real space wD 。
6. The method for determining the parameters of the multi-branch fractured solution reservoir fracture hole according to claim 1, wherein the modifying the fitting parameters comprises: reservoir distance d of each branch well j Depth h of each solution cavity area j Seepage area A of each branch reservoir fj 。
7. A system for determining parameters of a multi-branch solution reservoir fracture hole is characterized by comprising:
an acquisition module: the method comprises the steps of obtaining measured data of bottom hole pressure of a test well changing along with time after shut-in;
a calculation module: the method comprises the steps of determining initial parameters of a pre-constructed mathematical model of the bottom hole pressure of the multi-branch solution commingled production reservoir according to basic geological data of fracture holes of the multi-branch solution commingled production reservoir, and solving to obtain a bottom hole pressure solution of the multi-branch solution commingled production reservoir by taking the initial parameters as initial values of fitting parameters;
an output module: the pressure calculation module is used for calculating the difference between the pressure of the measured data and the pressure solution obtained by solving; if the difference is smaller than the preset fitting error, taking the initial parameter as a final fitting parameter; if the difference is larger than or equal to the preset fitting error, correcting the fitting parameters until the difference is smaller than the preset fitting error, and taking the finally corrected fitting parameters as final fitting parameters; and the final fitting parameters are parameters of the multi-branch fractured-solution reservoir fracture-cavern.
8. A computing device comprising a processor and a storage medium;
the storage medium is to store instructions;
the processor is configured to operate in accordance with the instructions to perform the steps of the method of any one of claims 1 to 6.
9. Computer readable storage medium, on which a computer program is stored, which program, when being executed by a processor, is adapted to carry out the steps of the method of any one of claims 1 to 6.
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| CN117076956B (en) * | 2023-10-16 | 2024-01-26 | 西安石油大学 | Fracture-cavity oil reservoir physical model similarity criterion optimization method and device |
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