CN111950111A - Dynamic analysis method for carbonate reservoir suitable for bottom opening - Google Patents
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Abstract
The invention provides a dynamic analysis method suitable for a carbonate reservoir with an open bottom, and belongs to the field of petroleum exploration and development. The method comprises the following steps: step 1, establishing a carbonate reservoir well testing mathematical model with an open bottom; the carbonate reservoir with the open bottom comprises n karsts, and the stratum at an infinite depth in the vertical direction can still provide fluid for the karsts; n is a natural number greater than or equal to 1; when n is greater than 1, the karst caves are connected through the crack regions; step 2, carrying out dimensionless transformation on the carbonate reservoir well testing mathematical model with the open bottom, and solving to obtain the pressure in n +1 fracture areas; step 3, obtaining dimensionless bottom hole pressure according to the pressure in the first fracture area; step 4, carrying out inversion on the dimensionless bottom hole pressure to obtain a bottom hole pressure solution in a real space; step 5, drawing a double logarithmic curve of a pressure curve and a pressure derivative curve according to the bottom hole pressure solution in the real space; and 6, carrying out dynamic analysis.
Description
Technical Field
The invention belongs to the field of petroleum exploration and development, and particularly relates to a dynamic analysis method suitable for a carbonate reservoir with an open bottom.
Background
Carbonate oil reserves occupy an important position in oil reservoirs found in the world, and in 256 large oil fields in the world, the number of carbonate oil fields is 115 and accounts for 45 percent, and the reserves and the yields of the carbonate oil reservoirs found account for 50 percent and 65 percent of the total amount of the world and always occupy an important position in oil field development. Foreign carbonate reservoirs are mainly distributed in the middle east and america.
The discovery of the Tahe oil field in China is a new important breakthrough of carbonate reservoirs, and a new stage of carbonate reservoir exploration and development in China is uncovered. The main body of the Tahe oil field is an Ordovician carbonate fracture-cave type oil reservoir, the main reservoir type is a fracture-cave type reservoir which is the result of multi-stage karst transformation, the reservoir space mainly comprises karst caves, holes, cracks and the like, the karst caves, the crack-hole type, the crack type and the cave type reservoir bodies are formed by combining the reservoir spaces with obviously different characteristics, and the boundary forms of the reservoir bodies distributed in the three-dimensional space are extremely irregular; the storage space distribution is discontinuous, the porosity change is huge, the regularity is poor, and the heterogeneity is very serious. The storage space of the cave-type reservoir is large-scale cave and crack, the storage space of the cave (including big hole and big hole) is huge, and the crack plays a role in communicating the cave and improving seepage performance, so that a favorable reservoir type with huge storage space and excellent seepage storage capacity is formed. The well testing analysis can obtain key information such as karst cave volume, connectivity, reserves and the like of the fracture-cave reservoir through inversion, and has important significance for determining the reserves of the carbonate fracture-cave reservoir and guiding the carbonate reservoir.
At present, fracture-cavity oil reservoirs mainly have two types of well testing analysis models: the first type is a continuous medium model which mainly comprises a double medium model, a triple medium model or an equivalent triple medium model and a double composite model, such as models disclosed in documents of 'triple medium oil reservoir well testing interpretation method research of variable well bore storage', 'carbonate karst cave type reservoir well testing interpretation new model', 'fracture cave type oil reservoir well testing model with well drilled in large-scale karst cave', and the like. The second type is a discrete medium model well testing model, such as a model disclosed in "new technology application for well testing interpretation of Tahe carbonate rock oil reservoir", "numerical well testing model of fracture-cave type oil reservoir with well drilled outside karst cave", and "well testing interpretation method for calculating karst cave volume" in Chinese patent publication CN 106599449A.
But the existing models and methods are only applicable to carbonate reservoirs with radial distribution of cavern and fracture planes. And many carbonate reservoirs are bead-string type karst caves which are communicated by vertical cracks, and the flow is mainly in the vertical direction. Therefore, the existing well testing analysis method is poor in applicability to vertically flowing fracture-cavity reservoirs (such as bead string type karst caves). At present, no related well testing analysis method is available for performing characteristic parameter description and pressure dynamic analysis of a fracture-cavity reservoir in which fluid flows in a vertical fracture-cavity.
Disclosure of Invention
The invention aims to solve the problems in the prior art and provides a dynamic analysis method for a carbonate reservoir with an open bottom, which is used for forming a well test analysis method for a vertical liquid supply type fracture-cavity carbonate reservoir with 1 or more karst caves from a deep bottom, namely, 1 or more karst caves are arranged in the reservoir, the karst caves supply liquid to a shaft through vertical cracks or high permeability zones at the upper part of the karst caves, and the reservoir at the lower part of the karst caves also supplies liquid to the karst caves through vertical cracks or high permeability zones. Starting from the geological characteristics of karst caves, cracks and bedrocks in the fractured-vuggy carbonate reservoir, a well testing analysis model for coupling vertical flow of the karst caves and the cracks is established, a basis is provided for determining accurate and reliable karst caves volume, high-permeability or fractured-zone flow capacity and geological reserves for the fractured-vuggy carbonate reservoir, basic information is provided for dynamic evaluation of the reservoir, and the method has important effects on guaranteeing high-efficiency development of the fractured-vuggy carbonate reservoir and improving economic benefits.
The invention is realized by the following technical scheme:
and 6, carrying out dynamic analysis by using the double logarithmic curves of the pressure curve and the pressure derivative curve.
And the n +1 fracture regions are all high permeability strips, and are the only flow channels between the karst caves and the shaft, between the karst caves and between the stratum and the karst caves.
The open-bottom multi-karst-cave carbonate reservoir well testing mathematical model established in the step 1 is as follows:
p(z,t＝0)＝pi (2)
p(z→∞,t)＝pi (3)
wherein p is pressure, Pa;
piis the pressure in the ith fracture zone, i ═ 1,2,.., n +1, Pa; the first crack area, the second crack area … … and the (n + 1) th crack area are arranged from top to bottom in sequence;
z is a vertical coordinate position, and the z axis is a one-dimensional coordinate axis which is established downwards by taking the circle center of the bottom end face of the shaft as an origin;
rho is the fluid density, kg/m3；
g is the acceleration of gravity, m/s2；
cfIs the fluid compression coefficient, 1/Pa;
phi is porosity and is dimensionless;
μ is the fluid viscosity, pas;
Ctis the comprehensive compression coefficient, 1/Pa;
k is the permeability, md;
t is time, s.
piIs the original formation pressure, Pa;
H2n-1the position m of the upper boundary of the nth karst cave from the origin;
h2nthe position of the lower boundary of the nth karst cave from the origin;
pvnis the pressure in the nth cavern, Pa;
rfis the radius of the karst cave, m;
Cvnis the reservoir coefficient of the nth cavern, m3/Pa；
q is daily yield, m3/s；
And B is the volume coefficient of the fluid.
The operation of carrying out dimensionless operation on the open-bottom multi-karst-cave carbonate reservoir well testing mathematical model in the step 2 comprises the following steps:
the non-dimensionalized models are obtained by non-dimensionalizing equations (1) to (6) using the following non-dimensionalized parameters:
dimensionless pressure pD：
Dimensionless time tD：
Dimensionless distance zD：
Dimensionless wellbore coefficient CD：
Dimensionless karst cave storage coefficient CvD：
Dimensionless gravity coefficient GD：
GD＝2ρgcf·rf。
The operation of solving in step 2 to obtain the pressures in the n +1 fracture zones comprises:
performing Laplace transformation on the dimensionless model to obtain a dimensionless seepage control equation in n +1 crack regions on a Laplace space;
and solving the dimensionless seepage control equation in the n +1 fracture regions on the Laplace space to obtain the dimensionless pressure in the n +1 fracture regions on the Laplace space.
The operation of step 3 comprises:
at ZDWhen the pressure is equal to 0, the pressure in the dimensionless first fracture area in the Laplace space is the dimensionless bottom hole pressure in the pull space.
The operation of step 4 comprises:
and inverting the dimensionless bottom hole pressure on the pull-type space by adopting a Stehfest numerical inversion algorithm to obtain a bottom hole pressure solution under a real space, namely the relationship between the bottom hole pressure and time.
The operation of step 6 comprises:
judging whether a karst cave exists in the reservoir: if a transition flow section and a karst cave storage section exist in the log-log curves of the pressure curve and the pressure derivative curve, judging that the karst cave exists in the reservoir, otherwise, judging that the karst cave does not exist in the reservoir;
if n >1, the operations of step 6 further comprise obtaining the number of vugs in the reservoir: counting the times of occurrence of a transition flow section and a karst cave storage section in a log-log curve of a pressure curve and a pressure derivative curve, wherein the counted times are the number of the karst caves;
the transition flow section refers to a part of a sudden drop in the pressure derivative curve;
the cavern storage section refers to a part of the pressure derivative curve, which is connected with the transition flow section and has a slope of 1.
The operation of step 6 comprises:
judging whether the deep reservoir below the karst cave supplies liquid vertically or not: if the double logarithmic curves of the pressure curve and the pressure derivative curve have boundary flow sections, judging that the deep reservoir below the karst cave supplies liquid vertically, otherwise, judging that the deep reservoir below the karst cave does not supply liquid vertically;
the boundary flow segment refers to the portion where the slope of both the pressure curve and the pressure derivative curve tend to 1/2.
The operation of step 6 comprises: carrying out history fitting according to the simulation data and the measured data to obtain the size of the cavern and the conductivity parameter of the hypertonic zone; the simulation data are pressure and pressure derivatives obtained by using bottom hole pressure solution in the real space, and the actual measurement data are pressure and pressure derivatives actually measured in a pressure recovery test.
Compared with the prior art, the invention has the beneficial effects that: the invention provides a well testing analysis method for fluid flow of a reservoir stratum with n karst caves to n vertical liquid supply type fracture-cavity carbonate reservoirs, wherein n karst caves are arranged in the reservoir stratum, liquid is supplied to a shaft through vertical cracks (or high permeability zones) at the upper part of the karst caves, and liquid is supplied to the karst caves through vertical cracks (or high permeability zones) at the reservoir stratum at the infinite depth at the lower part of the karst caves. Starting from the geological characteristics of karst caves, cracks and bedrocks in the carbonate fracture-cave reservoir, a well testing analysis model for coupling vertical flow of the karst caves and the cracks is established. The method can judge whether the karst caves exist or not and the number of the karst caves through the transition flow section and the karst cave storage section, and provides a technical means for qualitatively judging the existence of the karst caves; the gravity influence in the vertical flow is considered, and the liquid supply characteristics of the reservoir stratum at the deep bottom can be more accurately reflected; for a reservoir stratum with 1 karst cave, 6 complete flow states presented by a carbonate oil well which supplies liquid to the karst cave from a reservoir stratum in the depth bottom can be reflected, for a reservoir stratum with a plurality of karst caves, 9 complete flow states presented by a carbonate oil well which supplies liquid to the karst cave from a reservoir stratum in the depth bottom can be reflected, and the whole flowing processes of shaft storage, liquid supply to a shaft from the karst cave, flowing in the karst cave, liquid supply to the karst cave from a bottom stratum and the like are effectively reflected, so that the method has good adaptability to the carbonate oil well with liquid supply from the bottom and can be used for quantitatively determining key parameters such as the volume of the karst cave of the. Therefore, the method reflects the vertical fluid flow and the vertical liquid supply characteristics of the deep stratum in the karst cave and carries out fracture-cavity type carbonate reservoir flow dynamic analysis of the vertical distribution of the fracture and the karst cave. The method can quantitatively judge whether the karst caves exist and the number of the karst caves, qualitatively judge whether a deep reservoir below the karst caves supplies liquid vertically, reflect the flow characteristics of the carbonate oil well supplying liquid to the karst caves from the reservoir deep at the bottom, provide a basis for determining the accurate and reliable karst cave volume, the high-permeability zone flow capacity and the geological reserve of the fracture-cavity type carbonate reservoir, provide basic information for dynamic evaluation of the reservoir, and play an important role in ensuring the high-efficiency development of the fracture-cavity type carbonate reservoir and improving the economic benefit.
Drawings
FIG. 1 is a schematic diagram of a vertical liquid supply type fracture-cavity carbonate reservoir model of a bottom open reservoir to n karst caves; when n is 1, only the hypertonic region 1, the cavern and the hypertonic region 2 are shown in fig. 1.
2-1 n is 1, obtaining a log-log curve of the pressure curve and the pressure derivative curve;
2-2 n >1, obtaining a log-log curve of the pressure curve and the pressure derivative curve;
FIG. 3 is a block diagram of the steps of the method of the present invention.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
the invention relates to a novel method for testing, analyzing and dynamically evaluating a fracture-cavity type carbonate reservoir, in particular to a method for testing and evaluating a fracture-cavity type carbonate reservoir by vertically supplying liquid to 1 or more karst caves from a reservoir stratum deep at the bottom. The model takes into account gravitational effects, flow in the hypertonic zones, flow in the caverns, etc. Required dimensionless parameters are defined, a solution of the model is obtained through Laplace transformation and numerical inversion, a fracture-cavity carbonate reservoir well testing analysis method is formed, a basis is provided for determining accurate and reliable karst cave volume and geological reserve of a fracture-cavity carbonate reservoir, basic information is provided for dynamic evaluation of the reservoir, and the method plays an important role in guaranteeing high-efficiency development of the fracture-cavity carbonate reservoir and improving economic benefits.
Physical assumption of vertical liquid supply type fracture-cavity carbonate reservoir well test model from bottom deep to n karst caves
As shown in fig. 1, the present invention employs the following assumptions:
1. when n is greater than 1, the karst caves are connected through cracks, and the properties of the karst caves are kept unchanged;
2. the solution cavity is a cylinder with radius rfThe upper boundary of the karst cave is h2n-1The lower boundary is h2n；
3. The pressure at the karst cave is equal everywhere;
4. the high permeability zone is represented by a fracture zone, the fracture zone is a fracture with limited conductivity, the matrix permeability can be neglected compared with the fracture permeability, and the fracture zone is the only flow channel between the karst cave and the shaft, between the karst cave and the karst cave, and between the stratum and the karst cave;
5. simplifying a fracture system between the karst caves into a cylindrical area, wherein the permeability in the area is equivalent to the permeability of the fracture in the area;
6. the oil reservoir temperature is unchanged, and the original formation pressure is equal everywhere;
7. the properties within each region remain unchanged;
8. the fluid in the formation is a single phase fluid;
9. the fluid and the rock are both micro-compressible, and the compression coefficients are both constants;
10. very deep vertically (near infinite depth) still provides fluid to the cavern:
11. well reserves, skin and gravitational effects are considered.
Based on the above assumptions, the flow in the model can be reduced to a one-dimensional vertical flow.
(II) vertical liquid supply type fracture-cave carbonate reservoir well testing mathematical model from bottom deep part to karst cave
Under a one-dimensional rectangular coordinate system, considering the influence of gravity, and according to the mass conservation law, obtaining seepage control equations in n +1 fracture zones (i.e. n +1 high-seepage zones in fig. 1) as follows:
in the formula:
p is pressure, Pa;
piis the pressure in the ith fracture zone, i ═ 1,2,.., n +1, Pa; the first crack area, the second crack area … … and the (n + 1) th crack area are arranged from top to bottom in sequence;
z is a vertical coordinate position, and the z axis is a one-dimensional coordinate axis which is established downwards by taking the circle center of the bottom end face of the shaft as an origin;
rho is the fluid density, kg/m3；
g is the acceleration of gravity, m/s2；
cfIs the fluid compression coefficient, 1/Pa;
phi is porosity and is dimensionless;
μ is the fluid viscosity, pas;
Ctis the comprehensive compression coefficient, 1/Pa;
k is the permeability, md;
t is time, s.
The initial conditions were:
p(z,t＝0)＝pi (2)
in the formula: p is a radical ofiIs the original formation pressure, Pa;
outer boundary conditions: assuming that fluid is still provided to the cavern at very depths (near infinite depth) vertically:
p(z→∞,t)＝pi (3)
assuming that the pressure in each cavern is equal everywhere, there are:
in the formula:
H2n-1the position m of the upper boundary of the nth karst cave from the origin;
h2nthe position of the lower boundary of the nth karst cave from the origin;
pvnis the pressure in the nth cavern, Pa;
let the storage coefficient of the cavern be CvThen according to the law of conservation of mass, the flow at the upper and lower boundaries of the karst cave is obtainedQuantitative relationship:
in the formula:
rfis the radius of the karst cave, m;
Cvnis the reservoir coefficient of the nth cavern, m3/Pa；
According to the conservation of mass and Darcy's law, the flow relation at the intersection of the fracture region 1 and the wellbore is obtained as follows:
in the formula:
q is daily yield, m3/s；
And B is the volume coefficient of the fluid.
Formulas (1) to (6) are mathematical models of well testing of the vertical liquid supply type fracture-cavity carbonate reservoir from the bottom deep part to the karst cave.
(III) dimensionless parameter definition
Dimensionless parameters are defined as follows:
dimensionless pressure:
dimensionless time:
dimensionless distance:
dimensionless wellbore coefficient:
dimensionless cavern storage coefficient:
in the formula: c is a wellbore storage constant, m3/Pa。
Dimensionless gravity coefficient:
GD＝2ρgcf·rf
(IV) dimensionless equation and model Laplace transformation and solution
Through the defined dimensionless variables, the well testing model is subjected to dimensionless transformation, and then Laplace transformation is carried out, so that dimensionless seepage control equations in n +1 fracture regions on the Laplace space are obtained.
And solving the dimensionless seepage control equation in the n +1 fracture regions on the Laplace space to obtain the dimensionless pressure in the n +1 fracture regions on the Laplace space.
Since the bottom hole position (i.e., the bottom face of the wellbore, the top face of the first fracture zone) is used as the origin of coordinates in the physical modeling, when taking ZDWhen the pressure is equal to 0, the pressure in the dimensionless first fracture area in the Laplace space is dimensionless bottom hole pressure in the pull space.
(V) solving the model in real space
And inverting the dimensionless bottom hole pressure on the pull-type space by adopting a Stehfest numerical inversion algorithm to obtain a bottom hole pressure solution under a real space, namely the relationship between the bottom hole pressure and time. Based on the bottom hole pressure solution in real space, a model curve may be drawn, including a pressure curve and a pressure derivative curve.
The method of the invention is shown in figure 3 and comprises the following steps:
and 6, carrying out dynamic analysis by using the log-log curves of the pressure curve and the pressure derivative curve, including whether the karst cave exists or not, the number of the karst caves and whether the reservoir at the bottom supplies liquid vertically or not, and fitting the actually measured data of the pressure recovery test with the model data to obtain the characteristic parameters of the karst cave size, the high-permeability zone flow conductivity and the like.
The examples of the invention are as follows:
example 1:
taking a well in a carbonate reservoir as an example, a karst cave is arranged at a position 50 meters away from the bottom of the well, the karst cave supplies liquid to the well through a high-permeability strip, a reservoir layer below the karst cave also supplies liquid to the karst cave through the high-permeability strip, and the permeability of the high-permeability strip is 1000 md. The well pressure recovery is simulated to obtain a log-log curve of the pressure and pressure derivative during the pressure recovery process, i.e. the pressure curve and pressure derivative curve are plotted according to the bottom hole pressure solution, as shown in fig. 2-1. The flow dynamic analysis can be realized through the obtained log-log curves of the pressure curve and the pressure derivative curve shown in figure 2-1, and as can be seen from the log-log curves, the carbonate rock oil well with the bottom reservoir supplying liquid to the karst cave presents 6 flow regime sections which are a pure shaft storage section, a skin effect section, a linear flow section, a transition flow section, a karst cave storage section and a boundary flow section respectively. The flow state 1 corresponds to a pure shaft storage section and is characterized in that the slopes of a pressure curve and a pressure derivative curve are both 1; the flow state 2 corresponds to the skin effect section and is characterized in that a derivative curve has a peak, and the larger the skin is, the larger the peak value is; flow regime 3 corresponds to a linear flow segment, representing flow in a hypertonic strip, characterized by a pressure derivative curve with a slope of 1/2; flow regime 4 corresponds to the transition flow segment, representing the transition from a hypertonic strip to a cavern flow, with a sudden change in flow path resulting in a dip in the pressure derivative curve; the flow state 5 corresponds to a cavern storage section and represents the flow in the cavern, and the slope of a pressure derivative curve is 1; the slope of the pressure curve and the pressure derivative curve of the boundary flow section corresponding to the flow state 6 tends to 1/2, and reflects the characteristic that the bottom reservoir continuously supplies liquid to the karst cave through a high-permeability strip. The flow states 4 and 5 are caused by the existence of the karst cave, so that whether the karst cave exists can be judged by the existence of the flow states 4 and 5.
Through the judgment of the 6 flow states, the flow characteristics of shaft storage, solution cavity liquid supply to the shaft, solution cavity flow, bottom stratum liquid supply to the solution cavity and the like are effectively reflected, therefore, the method provided by the invention can be used for carrying out flow dynamic analysis on bottom liquid supply solution cavity type carbonate rock, and the size of the solution cavity can be obtained through fitting of pressure recovery test measured data and model data (namely, historical fitting is carried out according to simulation data and measured data, specifically, pressure and pressure derivative of the measured data are used for respectively fitting the pressure and pressure derivative curve of the model data, when a good fitting effect is obtained, the size of the solution cavity given by the model is considered to be the size of the actual solution cavity), characteristic parameters such as high permeability zone flow conductivity and the like (similar to the method for obtaining the size of the solution cavity and also obtained through historical fitting), and further, the method can be used for judging the storage size and can also be used for the characteristic yield of the carbonate oil-gas well in the production process, And (5) performing pressure characteristic prediction analysis.
Example 2:
taking a well in a carbonate reservoir as an example, the well is vertically communicated with 2 karst caves at positions 10 meters and 50 meters away from the bottom of the well respectively. The caverns feed the well via the hypertonic strips, while reservoirs very far below the caverns also feed the caverns via the hypertonic strips, the permeability of which is 1000 md. The well pressure recovery is simulated to obtain a log-log curve of the pressure and the pressure derivative in the pressure recovery process, i.e. a log-log curve of the pressure curve and the pressure derivative curve drawn according to a bottom hole pressure solution in real space, as shown in fig. 2-2. As can be seen from fig. 2-2, the carbonate oil well whose bottom deep reservoir supplies liquid to the karst cave exhibits 9 flow states, which respectively correspond to the shaft storage section, the skin effect section, the first linear flow section, the first transition flow section, the first karst cave storage section, the second linear flow section, the second transition flow section, the second karst cave storage section and the boundary flow section. The flow state 1 corresponds to a pure shaft storage section and is characterized in that the slopes of a pressure curve and a pressure derivative curve are both 1; the flow state 2 corresponds to the skin effect section and is characterized in that a derivative curve has a peak, and the larger the skin is, the larger the peak value is; flow regime 3 corresponds to the first linear flow segment, representing flow in the hypertonic strip 1, and is characterized by a pressure derivative curve slope of 1/2; flow regime 4 corresponds to the first transition flow segment, representing the transition from the hypertonic strip 1 to the cavern 1 flow, with a sudden change in flow path leading to a dip in the derivative curve; the flow state 5 corresponds to a first karst cave storage section and represents the flow in the karst cave I, and the slope of a pressure derivative curve is 1; flow regime 6 corresponds to the second linear flow segment, representing flow in the hypertonic strip 2; the flow state 7 corresponds to a second transition flow section and represents the transition of the flow from the hypertonic strip 2 to the karst cave 2; the flow state 8 corresponds to a second karst cave storage section, namely the flow reaches the karst cave 2; the slope of the pressure curve and the slope of the pressure derivative curve of the boundary flow section corresponding to the flow state 9 are both 1/2, and the characteristic that the bottom reservoir continuously supplies liquid to the karst cave through a high-permeability strip is reflected.
The flow states 4 and 5 are caused by the existence of the karst cave 1, and the flow states 7 and 8 are caused by the existence of the karst cave 2, so that whether the karst cave exists or not and the existence of a plurality of karst caves can be judged through the flow states. Specifically, only if 2 flow states of the transition flow section and the karst cave storage section appear in sequence, a karst cave can be judged to appear. And (4) counting the occurrence times of 2 flow states of the transition flow section and the karst cave storage section to obtain the number of the karst caves. And in statistics, if the excessive flow section and the karst cave storage section appear for the first time, adding one to the number of times, and if the excessive flow section and the karst cave storage section appear for the second time, adding one to the number of times, and so on.
Through the judgment of the 9 flow states, the flow characteristics of shaft storage, solution cavity liquid supply to the shaft, solution cavity flow, bottom stratum liquid supply to the solution cavity and the like are effectively reflected, therefore, the method provided by the invention can carry out flow dynamic analysis (realized through analysis of the 9 flow states) on the bottom liquid supply solution cavity type carbonate rock, can obtain the size of the solution cavity through fitting of pressure recovery test measured data and model data (historical fitting is carried out according to simulation data and measured data, specifically, pressure and pressure derivative curves of the model data are respectively fitted by using the pressure and pressure derivative in the measured data, when a good fitting effect is obtained, the size of the solution cavity given by the model is considered to be the size of the actual cavity), characteristic parameters of high permeability zone flow conductivity and the like (similar to the method for obtaining the size of the solution cavity, obtained by adopting historical fitting), and further judge the storage capacity, the method can also be used for predicting and analyzing the yield characteristics and the pressure characteristics of the carbonate oil-gas well in the production process.
After the embodiment is implemented, the following effects are achieved: (1) whether the karst caves exist or not and the number of the karst caves can be judged through the transition flow section and the karst cave storage section, and a technical means is provided for qualitatively judging the existence of the karst caves; (2) the gravity influence in the vertical flow is considered, and the liquid supply characteristics of the reservoir stratum at the deep bottom can be more accurately reflected; (3) the method can reflect 9 complete flow states presented by the carbonate rock oil well supplying liquid to the karst cave from the reservoir stratum in the deep bottom, and effectively reflects the whole flowing processes of shaft storage, karst cave liquid supply to the shaft, flow in the karst cave, bottom stratum liquid supply to the karst cave and the like, so the method has good adaptability to the carbonate rock oil well of the bottom liquid supply type and can be used for quantitatively determining key parameters of the karst cave volume of the reservoir stratum and the like.
The above-described embodiment is only one embodiment of the present invention, and it will be apparent to those skilled in the art that various modifications and variations can be easily made based on the application and principle of the present invention disclosed in the present application, and the present invention is not limited to the method described in the above-described embodiment of the present invention, so that the above-described embodiment is only preferred, and not restrictive.
Claims (10)
1. A dynamic analysis method for a carbonate reservoir with an open bottom is characterized by comprising the following steps: the method comprises the following steps:
step 1, establishing a carbonate reservoir well testing mathematical model with an open bottom; the carbonate reservoir with the open bottom comprises n karsts, and the stratum at an infinite depth in the vertical direction can still provide fluid for the karsts; n is a natural number greater than or equal to 1; when n is greater than 1, the karst caves are connected through the crack regions;
step 2, carrying out dimensionless transformation on the carbonate reservoir well testing mathematical model with the open bottom, and solving to obtain the pressure in n +1 fracture areas;
step 3, obtaining dimensionless bottom hole pressure according to the pressure in the first fracture area;
step 4, carrying out inversion on the dimensionless bottom hole pressure to obtain a bottom hole pressure solution in a real space;
step 5, drawing a double logarithmic curve of a pressure curve and a pressure derivative curve according to the bottom hole pressure solution in the real space;
and 6, carrying out dynamic analysis by using the double logarithmic curves of the pressure curve and the pressure derivative curve.
2. The dynamic analysis method for carbonate reservoirs with open bottoms according to claim 1, characterized in that: and the n +1 fracture regions are all high permeability strips, and are the only flow channels between the karst caves and the shaft, between the karst caves and between the stratum and the karst caves.
3. The dynamic analysis method for carbonate reservoirs with open bottoms according to claim 1, characterized in that: the open-bottom multi-karst-cave carbonate reservoir well testing mathematical model established in the step 1 is as follows:
p(z,t＝0)＝pi (2)
p(z→∞,t)＝pi (3)
wherein p is pressure, Pa;
piis the pressure in the ith fracture zone, i ═ 1,2,.., n +1, Pa; the first crack area, the second crack area … … and the (n + 1) th crack area are arranged from top to bottom in sequence;
z is a vertical coordinate position, and the z axis is a one-dimensional coordinate axis which is established downwards by taking the circle center of the bottom end face of the shaft as an origin;
rho is the fluid density, kg/m3；
g is the acceleration of gravity, m/s2；
cfIs the fluid compression coefficient, 1/Pa;
phi is porosity and is dimensionless;
μ is the fluid viscosity, pas;
Ctis the comprehensive compression coefficient, 1/Pa;
k is the permeability, md;
t is time, s;
piis the original formation pressure, Pa;
H2n-1the position m of the upper boundary of the nth karst cave from the origin;
h2nthe position of the lower boundary of the nth karst cave from the origin;
pvnis the pressure in the nth cavern, Pa;
rfis the radius of the karst cave, m;
Cvnis the reservoir coefficient of the nth cavern, m3/Pa；
q is daily yield, m3/s；
And B is the volume coefficient of the fluid.
4. The dynamic analysis method for carbonate reservoirs with open bottoms according to claim 3, characterized in that: the operation of carrying out dimensionless operation on the open-bottom multi-karst-cave carbonate reservoir well testing mathematical model in the step 2 comprises the following steps:
the non-dimensionalized models are obtained by non-dimensionalizing equations (1) to (6) using the following non-dimensionalized parameters:
dimensionless pressure pD：
Dimensionless time tD：
Dimensionless distance zD：
Dimensionless wellbore coefficient CD：
Dimensionless karst cave storage coefficient CvD：
Dimensionless gravity coefficient GD：
GD＝2ρgcf·rf。
5. The dynamic analysis method for carbonate reservoirs with open bottoms according to claim 4, characterized in that: the operation of solving in step 2 to obtain the pressures in the n +1 fracture zones comprises:
performing Laplace transformation on the dimensionless model to obtain a dimensionless seepage control equation in n +1 crack regions on a Laplace space;
and solving the dimensionless seepage control equation in the n +1 fracture regions on the Laplace space to obtain the dimensionless pressure in the n +1 fracture regions on the Laplace space.
6. The dynamic analysis method for carbonate reservoirs with open bottoms according to claim 5, characterized in that: the operation of step 3 comprises:
at ZDWhen the pressure is equal to 0, the pressure in the dimensionless first fracture area in the Laplace space is the dimensionless bottom hole pressure in the pull space.
7. The dynamic analysis method for carbonate reservoirs with open bottoms according to claim 6, characterized in that: the operation of step 4 comprises:
and inverting the dimensionless bottom hole pressure on the pull-type space by adopting a Stehfest numerical inversion algorithm to obtain a bottom hole pressure solution under a real space, namely the relationship between the bottom hole pressure and time.
8. The dynamic analysis method for carbonate reservoirs with open bottoms according to claim 1, characterized in that: the operation of step 6 comprises:
judging whether a karst cave exists in the reservoir: if a transition flow section and a karst cave storage section exist in the log-log curves of the pressure curve and the pressure derivative curve, judging that the karst cave exists in the reservoir, otherwise, judging that the karst cave does not exist in the reservoir;
if n >1, the operations of step 6 further comprise obtaining the number of vugs in the reservoir: counting the times of occurrence of a transition flow section and a karst cave storage section in a log-log curve of a pressure curve and a pressure derivative curve, wherein the counted times are the number of the karst caves;
the transition flow section refers to a part of a sudden drop in the pressure derivative curve;
the cavern storage section refers to a part of the pressure derivative curve, which is connected with the transition flow section and has a slope of 1.
9. The dynamic analysis method for carbonate reservoirs with open bottoms according to claim 1, characterized in that: the operation of step 6 comprises:
judging whether the deep reservoir below the karst cave supplies liquid vertically or not: if the double logarithmic curves of the pressure curve and the pressure derivative curve have boundary flow sections, judging that the deep reservoir below the karst cave supplies liquid vertically, otherwise, judging that the deep reservoir below the karst cave does not supply liquid vertically;
the boundary flow segment refers to the portion where the slope of both the pressure curve and the pressure derivative curve tend to 1/2.
10. The dynamic analysis method for carbonate reservoirs with open bottoms according to claim 1, characterized in that: the operation of step 6 comprises: carrying out history fitting according to the simulation data and the measured data to obtain the size of the cavern and the conductivity parameter of the hypertonic zone; the simulation data are pressure and pressure derivatives obtained by using bottom hole pressure solution in the real space, and the actual measurement data are pressure and pressure derivatives actually measured in a pressure recovery test.
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