CN114922604B - Prediction method for stacking and laying morphology of propping agent in fracture - Google Patents
Prediction method for stacking and laying morphology of propping agent in fracture Download PDFInfo
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- CN114922604B CN114922604B CN202210714104.3A CN202210714104A CN114922604B CN 114922604 B CN114922604 B CN 114922604B CN 202210714104 A CN202210714104 A CN 202210714104A CN 114922604 B CN114922604 B CN 114922604B
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- E—FIXED CONSTRUCTIONS
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- E21B43/00—Methods or apparatus for obtaining oil, gas, water, soluble or meltable materials or a slurry of minerals from wells
- E21B43/25—Methods for stimulating production
- E21B43/26—Methods for stimulating production by forming crevices or fractures
- E21B43/267—Methods for stimulating production by forming crevices or fractures reinforcing fractures by propping
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Abstract
The invention relates to a method for predicting the stacking and laying morphology of propping agents in a fracture, which comprises the following steps: carrying out proppant laying experiments with different injection parameters until proppant sand dikes are completely piled up in cracks; dividing the proppant sand dike stacking process into two stages, wherein the first stage is that the sand dike does not reach the bottom perforation height, the stacking form is regarded as a right trapezoid, and the second stage is that the sand dike reaches the bottom perforation height, and the stacking form is regarded as a common trapezoid; the first stage sand pile is divided into an inlet sand pile and a tail sand pile, the second stage sand pile is divided into an inlet sand pile, a middle sand pile and a tail sand pile, and the characteristic parameters of the sand piles are used for representing the shapes of the sand piles of all parts; establishing an empirical relation between characteristic parameters and injection parameters of each sand pile in each stage and each part; a piecewise functional expression of the proppant sand stack morphology is established. The method is reliable in principle and simple and convenient to operate, can predict multi-parameter and large-range proppant stacking and laying forms, and provides theoretical basis for optimizing hydraulic fracturing proppant pumping parameters.
Description
Technical Field
The invention belongs to the field of proppant placement research in a hydraulic fracturing process, and particularly relates to a method for predicting the stacking and placement morphology of propping agents in cracks.
Background
Continuous and effective exploitation of oil gas resources is significant in guaranteeing energy safety of China, and the unconventional oil gas resources are huge in quantity, so that the effective exploitation of unconventional oil gas is a key for relieving the current energy safety situation. Because the physical property characteristics of unconventional reservoir low-pore hypotonic are that natural production cannot meet production requirements, hydraulic fracturing must be implemented to fully break up the reservoir, so that effective exploitation of oil and gas resources is realized. The hydraulic fracturing technology mainly comprises the steps of pumping high-pressure fluid from the ground to a target reservoir position in the underground, opening the reservoir by utilizing the energy of the fluid to form an artificial fracture, then continuously injecting sand-carrying fluid containing propping agent particles, carrying the propping agent particles into the underground fracture by the fluid, stopping pumping, and stopping the propping agent retained in the fracture to a certain extent to prevent the fracture from being completely closed, so that a high-speed channel for oil gas flow is formed, and the accumulation and laying form of the propping agent in the fracture is the key for influencing the flow guiding capability of the oil gas flow channel, so that the quality of the hydraulic fracturing effect is determined, and therefore, the accumulation and laying form of the propping agent in the fracture is significant.
At present, the research on the stacking and laying form of propping agent in a crack is mainly to simulate the proppant conveying process by establishing an experimental device or a numerical model close to the actual crack form and characteristics, so that the stacking and laying form of propping agent in the crack is obtained, but no matter in an experimental mode or a digital-analog mode, the proppant stacking and laying form under a certain condition can be obtained only once, after the injection condition is changed, the experiment or the numerical simulation is needed to be carried out again, so that the proppant stacking and laying form under the condition can be obtained, the labor, material and financial resources are consumed greatly, the research range is limited, and the efficiency is low. The reason for this is that the placement form of the proppant clusters in the fracture cannot be predicted simply and accurately due to the lack of an empirical expression of the proppant stacking form in the fracture.
Disclosure of Invention
The invention aims to provide a method for predicting the stacking and laying morphology of propping agents in cracks, which is reliable in principle and simple and convenient to operate, and obtains the change relation between characteristic parameters and time of proppant sand piles under different conditions by carrying out a small amount of proppant conveying experiments, so that the stacking and laying morphology of propping agents with multiple parameters and a large range is predicted, and a theoretical basis is provided for optimizing pumping parameters of hydraulic fracturing propping agents.
In order to achieve the technical purpose, the invention adopts the following technical scheme.
The method for predicting the stacking and laying morphology of the propping agent in the fracture sequentially comprises the following steps:
step one, carrying out proppant laying experiments with different injection parameters, simulating the process of injecting sand-carrying fluid into a crack until the proppant sand dike is completely piled up in the crack, wherein the injection parameters comprise the crack size and single-crack sand-carrying fluid discharge Q1 (the unit is m 3 Per second), carrier fluid injection rate V0 (in m/s), proppant concentration Sn (in kg/m) 3 ) And branchPropping agent particle size, wherein the crack size comprises a crack length X0, a height Y0 and a width W0 (the units are m);
simplifying the stacking form of the propping agent sand dike to be formed by combining straight line segments with different angles, and dividing propping agent sand piles in cracks according to the stacking form, wherein the process is as follows: dividing the proppant sand dike stacking process into two stages according to time sequence, wherein the first stage is that the sand dike does not reach the bottom perforation height H0, the stacking form is regarded as a right trapezoid, and the second stage is that the sand dike reaches the bottom perforation height H0, and the stacking form is regarded as a common trapezoid;
step three, the sand pile in the stage one is divided into two parts, namely an inlet sand pile and a tail sand pile; the second stage sand pile is divided into three parts, namely an inlet sand pile, a middle sand pile and a tail sand pile, and the shape of each part of sand pile is represented by the characteristic parameters of the sand pile;
step four, establishing an empirical relation between characteristic parameters and injection parameters of each stage and each part of sand pile according to proppant laying experiments of different injection parameters;
and fifthly, establishing a piecewise function expression of the complete proppant sand pile morphology (wherein the expression of the stage one consists of a straight line segment and an inclined line segment with a negative slope, and the expression of the stage two consists of an inclined line segment with a positive slope, a straight line segment and an inclined line segment with a negative slope), so as to realize the prediction of the proppant pile laying morphology.
Further, in the second step, the bottom perforation height is the distance (in m) from the bottom of the crack to the first perforation hole arranged at the top of the crack along the height direction of the crack.
Further, in the third step, the sand pile characteristic parameters are used for representing the shape of each part of the sand pile, and the process is as follows: setting the length direction of the crack as the x axis, the height direction as the y axis, the crack inlet as the origin, establishing a coordinate axis, and setting the section of the sand pile at stage one, wherein the section of the sand pile at the inlet is a rectangle with the length L1 and the height y1, and the section of the sand pile at the tail is a right triangle with the side length (x 1-L1), the height y1 and the slope of the bevel edge K1; in the second stage, the section of the sand pile at the inlet is a right trapezoid with the height L1 and the side lengths H0 and y3, the section of the sand pile at the middle part is a rectangle with the length (x 2-L1) and the height y3, and the section of the sand pile at the tail part is a right triangle with the side length (x 3-x 2), the height y3 and the slope of the bevel edge K2.
In the fourth step, an empirical relation between characteristic parameters and injection parameters of each sand pile at each stage and each part is established, and the formula is as follows:
L1＝Q1×480 (1)
k1 is equal to the slope of the tail sand pile settling ramp angle α, k1= - (tan (α)), and the empirical relationship of α and V0 is:
α＝-324×V0 2 +39.6×V0+24.85 (2)
x2 is the sum of the inlet sand pile and the length of the middle sand pile, and the growth rate V1 of the length direction of the middle sand pile is related to the injection time t:
x2＝L1+V1×t (3)
and V1 is a function related to V0, which has the empirical relationship:
V1＝(1.6152×V0+0.4126)/100 (4)
according to the obtained empirical relationship, the remaining unknown parameters x1, y1, x3, y3 can be all obtained based on proppant volume conservation:
x1＝(-2×V p / K1+L1 2 ) 0.5 (5)
y1＝K1×(L1-x1) (6)
y3＝K2×(x2-x3) (8)
k1 and K2 are in agreement with each other in empirical relationship, vp being the bulk of the proppant within the fracture.
Further, in step five, a piecewise function expression of the complete proppant sand pack morphology is established, as follows:
when the bank stack height Y1< H0,
when the pile height Y1 of the sand dike is more than or equal to H0,
wherein X (X) and Y (X) are the length and height, m, of the proppant sand pack morphology in the fracture, respectively.
Compared with the prior art, the invention has the following beneficial effects:
according to the method, the growth characteristics of the proppant sand pile and the change characteristics of the characteristic parameters are obtained through a small amount of proppant conveying experiments, an empirical relation between the injection parameters and the sand pile characteristic parameters is established based on the growth characteristics and the change characteristics of the characteristic parameters, and finally, a prediction relation of the proppant sand pile laying morphology in the crack is obtained.
Drawings
FIG. 1 is a schematic diagram of crack size.
Figure 2 is a schematic diagram of a proppant dike stacking and laying process.
Fig. 3 (a) and 3 (b) are schematic diagrams of the morphology division and the characteristic parameter determination of the proppant sand stack in the stage 1 and the stage 2 respectively.
Fig. 4 is an experimental scatter plot of inlet sand pack length L1 and carrier fluid displacement Q1.
Fig. 5 is an experimental scatter plot of the sedimentation ramp angle α and the carrier fluid injection velocity V0.
Fig. 6 is an experimental scatter plot of the middle dyke growth rate V1 and the carrier fluid injection rate V0.
Detailed Description
The present invention is further described below with reference to the accompanying drawings to facilitate understanding of the present invention by those skilled in the art. It should be understood that the invention is not limited to the precise embodiments, and that various changes may be effected therein by one of ordinary skill in the art without departing from the spirit or scope of the invention as defined and determined by the appended claims.
See fig. 1, 2, 3, 4, 5, 6.
A method for predicting the stacking and laying morphology of propping agents in a fracture, comprising the following steps:
step one: and simulating the process of injecting the sand-carrying fluid into the crack by using the proppant conveying experimental device, respectively carrying out proppant conveying experiments for changing parameters such as the size of the crack, the single-crack sand-carrying fluid discharge capacity Q1, the sand-carrying fluid injection speed V0, the proppant concentration, the proppant particle size and the like, ending the experiment until the proppant sand dike is completely piled up in the crack, and recording videos of the whole experimental process by adopting a camera.
As shown in FIG. 1, the length of the crack was X0, the height of the crack was Y0, the width of the crack was W0, the height of the bottom perforation was H0, the viscosity of the fluid was 2.5 mPas, and a 40/70 mesh ceramic was used as the proppant.
Step two: the process of piling up the propping agent sand dikes is divided into two stages according to the time t, as shown in fig. 2, wherein stage one is that the sand dikes do not reach the bottom perforation height H0, and the piling up form is similar to a right trapezoid; the second stage is to reach the bottom perforation height H0, and the stacking form is similar to a common trapezoid.
Step three: dividing a propping agent sand pile in the crack according to the shape of the sand pile, wherein the sand pile in the stage one is divided into two parts, namely an inlet sand pile and a tail sand pile, the section of the inlet sand pile in the stage one is a rectangle with a length L1 and a height y1, and the section of the tail sand pile is a right triangle with a side length (x 1-L1), a height y1 and a bevel slope K1; in the second stage, the section of the sand pile at the inlet is a right trapezoid with the height L1 and the side lengths H0 and y3, the section of the sand pile at the middle part is a rectangle with the length (x 2-L1) and the height y3, and the section of the sand pile at the tail part is a right triangle with the side length (x 3-x 2), the height y3 and the slope of the bevel edge K2.
Step four: the experimental relation between the injection parameters and the characteristic parameters is obtained, experimental relation between the characteristic parameters of each stage and each part of sand pile and the injection conditions is established according to proppant laying experiments of different injection parameters, and the experimental relation is obtained by the experiments that L1, K2 and x2 are all related to single crack sand carrying fluid discharge Q1 and sand carrying fluid velocity V0 (V0 = Q1/Y0/W0), wherein the experimental relation is as follows:
see fig. 4, the empirical relationship of L1 and Q1 is:
L1＝Q1×480 (1)
k1 is equal to the slope of the tail sand pile settling ramp angle α, k1= - (tan (α)), see fig. 5, empirical relationship of α to V0 is:
α＝-324×V0 2 +39.6×V0+24.85 (2)
x2 is the sum of the inlet sand pile and the length of the middle sand pile, and the growth rate V1 of the length direction of the middle sand pile is related to the injection time t:
x2＝L1+V1×t (3)
and V1 is a function related to V0, see FIG. 6, with empirical relationships:
V1＝(1.6152×V0+0.4126)/100 (4)
from the empirical relationship obtained, the remaining unknown parameters x1, y1, x3, y3 can all be calculated based on the back-calculation of the conservation of proppant volume (the injected volume of proppant is equal to the volume filled in the fracture):
x1＝(-2×V p / K1+L1 2 ) 0.5 (5)
y1＝K1×(L1-x1) (6)
y3＝K2×(x2-x3) (8)
k1 and K2 are in agreement, vp being the bulk volume of the proppant within the fracture.
Step five: establishing a piecewise function expression of the complete sand pile form, wherein the expression of the stage one consists of a straight line segment and an oblique line segment with a negative slope, and the expression of the stage two consists of an oblique line segment with a positive slope, a straight line segment and an oblique line segment with a negative slope, and the mathematical expression of the complete sand pile in fig. 3 is as follows:
when the bank stack height Y1< H0,
when the pile height Y1 of the sand dike is more than or equal to H0,
wherein X (X) and Y (X) are respectively the length and the height of the form of the proppant sand stack in the fracture, and m.
The mathematical expression can be used for predicting the sand bank stacking forms at different stages.
Claims (3)
1. The method for predicting the stacking and laying morphology of the propping agent in the fracture sequentially comprises the following steps:
step one, carrying out proppant laying experiments with different injection parameters, simulating a process of injecting sand-carrying fluid into a crack until a proppant sand dike is completely piled up in the crack, wherein the injection parameters comprise a crack size, single crack sand-carrying fluid discharge Q1, sand-carrying fluid injection speed V0, proppant concentration and particle size, and the crack size comprises a crack length X0, a height Y0 and a width W0;
simplifying the stacking form of the propping agent sand dike to be formed by combining straight line segments with different angles, and dividing propping agent sand piles in cracks according to the stacking form, wherein the process is as follows: dividing the proppant sand dike stacking process into two stages according to time sequence, wherein the first stage is that the sand dike does not reach the bottom perforation height H0, the stacking form is regarded as a right trapezoid, and the second stage is that the sand dike reaches the bottom perforation height H0, and the stacking form is regarded as a common trapezoid;
step three, the sand pile in the stage one is divided into two parts, namely an inlet sand pile and a tail sand pile; the second stage sand pile is divided into three parts, namely an inlet sand pile, a middle sand pile and a tail sand pile, and the sand pile characteristic parameters are used for representing the shape of each part of the sand pile, and the process is as follows: setting the length direction of the crack as the x axis, the height direction as the y axis, the crack inlet as the origin, establishing a coordinate axis, and setting the section of the sand pile at stage one, wherein the section of the sand pile at the inlet is a rectangle with the length L1 and the height y1, and the section of the sand pile at the tail is a right triangle with the side length (x 1-L1), the height y1 and the slope of the bevel edge K1; the section of the sand pile at the second stage is a right trapezoid with the height L1 and the side lengths H0 and y3, the section of the sand pile at the middle part is a rectangle with the length (x 2-L1) and the height y3, and the section of the sand pile at the tail part is a right triangle with the side length (x 3-x 2), the height y3 and the slope of the bevel edge K2;
step four, establishing an empirical relation between characteristic parameters and injection parameters of each stage and each part of sand pile according to proppant laying experiments with different injection parameters:
L1＝Q1×480
K1＝-(tan(α))
α＝-324×V0 2 +39.6×V0+24.85
x2＝L1+V1×t
V1＝(1.6152×V0+0.4126)/100
x1＝(-2×V p /K1+L1 2 ) 0.5
y1＝K1×(L1-x1)
y3＝K2×(x2-x3)
wherein alpha is the settling slope angle of the tail sand pile, y1 is the section height of the stage one sand pile, x1 is the total length of the section of the stage one sand pile, L1 is the section length of the stage one inlet sand pile, K1 is the slope of the settling slope angle of the stage one tail sand pile, y3 is the section height of the stage two sand piles, x3 is the total length of the section of the stage two sand piles, x2 is the sum of the section length of the stage two inlet sand piles and the section length of the middle sand pile, K2 is the slope of the settling slope angle of the stage two tail sand piles, V1 is the growth speed of the length direction of the middle sand pile, and Vp is the accumulation volume of propping agent in a crack;
and fifthly, establishing a piecewise function expression of the complete proppant sand pile morphology, and realizing prediction of the proppant pile laying morphology.
2. The method of claim 1, wherein the bottom perforation height is a distance from the bottom of the fracture along the height of the fracture to the top of the fracture.
3. A method of predicting a proppant pack placement configuration in a fracture according to claim 1 or claim 2, wherein establishing a piecewise functional expression of the complete proppant sand pack configuration is performed as follows:
when the bank stack height Y1< H0,
when the pile height Y1 of the sand dike is more than or equal to H0,
wherein X (X) and Y (X) are the length and height of the proppant sand pack morphology in the fracture, respectively.
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