CN116776556B - Method, device, equipment and medium for determining equivalent porosity of propping agent laid fracture - Google Patents
Method, device, equipment and medium for determining equivalent porosity of propping agent laid fracture Download PDFInfo
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Abstract
The invention provides a method, a device, equipment and a medium for determining equivalent porosity of a propping agent laying crack, and relates to the technical field of petroleum and natural gas development. In the embodiment of the invention, the porosity of the supporting belt is determined by adopting the following steps:based on the method, it was determined that the porosity of the support belt increased with increasing proppant placement concentration and inter-particulate distance coefficient, but when the placement concentration was not less than 13kg/m 2 When the laying concentration is increased, the improvement of the crack flow conductivity is mainly reflected by increasing the crack width, and the porosity of the supporting belt is hardly influenced. In addition, by adopting the method for determining the equivalent porosity of the propping agent laid fracture provided by the embodiment of the invention, the equivalent porosity of the propping agent laid fracture can be determined on the basis of considering the non-compact laying characteristic of the propping agent, so that the basis is provided for the follow-up research of the permeability of the propping belt after elastoplastic embedding.
Description
Technical Field
The embodiment of the invention relates to the technical field of petroleum and natural gas exploitation, in particular to a method, a device, equipment and a medium for determining equivalent porosity of a propping agent laid fracture.
Background
Compared with the middle shallow shale reservoir, the deep shale gas in China has high initial yield in the well test, but has fast pressure drop and lower long-term yield, and one of the main reasons is as follows: the sand laying difficulty is high, the net-sewing supporting effect is not ideal, and the flow conductivity is fast reduced.
Keeping the fracture and the permeate channel open is one of the key technologies to ensure economic development of hydrocarbon resources, while propped fracture formed by proppant pack is the main channel for hydrocarbon seepage. The penetration capacity of the cracks is rapidly reduced due to the embedding, deformation, crushing, dissolution, blocking and the like of the proppants; proppant breakage/dissolution can be generally avoided by a mode of selection, the randomness of the muddy blockage is strong, and the elucidation is difficult; while proppant placement/deformation problems are generally unavoidable, while proppant placement has negligible impact on fracture conductivity in locations such as the wellbore periphery where the proppant placement concentration is high, proppant placement will have a significant impact on conductivity in some areas where the proppant placement concentration is low. In the transformation process of the deep shale reservoir, the initial seam width of each stage of cracks is narrow, propping agents are difficult to lay, and the propping agents in the deep shale reservoir coexist in a plurality of laying characteristics such as multilayer, single-layer, sparse and the like; therefore, aiming at deep shale gas development, the proppant embedding behavior is deeply known, and the method has important significance for exploring the evolution rule of the support type fracture seepage channel and ensuring the efficient development of the reservoir.
Deep shale gas reservoirs in China often show five-high characteristics, namely high formation temperature, high overburden pressure, high horizontal ground stress difference, high cracking pressure and high closing pressure; in the high-temperature and high-pressure environment, the shale plastic-delaying property of the reservoir shale is enhanced, in addition, a larger volume of fracturing fluid is injected into the reservoir during the fracturing process, the water-shale interaction is more remarkable, and the shale is hydrated and softened. On the other hand, under the action of high closing pressure, the load born by the propping agent is increased, the phenomenon that the propping agent is embedded into the shale wall surface is obviously enhanced, and for example, a core propping agent embedding test of 3800-4000 m of the burial depth of a certain reservoir in Chuan south shows that the average embedding depth can reach 0.611mm. Meanwhile, in the process of deep reservoir fracturing transformation, in order to reduce sand blocking risk, the small-particle-size propping agent ratio needs to be greatly improved, and related technology indicates that critical yield load is in a proportional relation with the square of the particle size of the propping agent, namely that the smaller the particle size of the propping agent is, the easier elastoplastic embedding behavior occurs.
Therefore, when the deep shale gas seepage channel is constructed artificially, a series of deep features such as high closing pressure, remarkable shale ductility characteristic, small propping agent particle size and the like are necessarily faced. Therefore, when the propping agent interacts with the shale wall surface, the elastic embedding behavior of the middle shallow layer is gradually converted into the elastic-plastic or full-plastic embedding behavior of the deep part; if the middle-shallow elastic embedding depth model is directly applied to deep shale gas development engineering, the embedding depth of the propping agent is inevitably underestimated, and the fracture conductivity is overestimated; this can have adverse effects on proppant type selection during reservoir development and design, as well as on post production operation management. Therefore, aiming at the shale plasticity characteristics in the deep in-situ environment, the interaction mechanism of the propping agent and the shale and the influence rule of the interaction mechanism on the crack seepage capability are explored, and important theoretical support and technical guarantee can be provided for deep shale gas development in China.
Thus, there is a need for a proppant placement fracture equivalent porosity determination method for shale.
Disclosure of Invention
The embodiment of the invention provides a method, a device, equipment and a medium for determining equivalent porosity of a propping agent laid fracture, which are used for at least partially solving the problems in the related art.
An embodiment of the present invention provides a method for determining equivalent porosity of a proppant placement fracture, the method comprising:
the porosity of the support band was determined using the following:
wherein D is the particle size of the propping agent and n i To propping agent layer number m in the length direction of the crack i To support the number of layers in the fracture height direction, L F Represents the crack length, H F Represents the crack height, W F Represents the width of the crack, w i The number of layers laid in the fracture width direction is shown, and δ represents the proppant insertion depth.
Alternatively, n is calculated using the formula i ：
Wherein,the representation function takes an integer down, K being the distance coefficient.
Alternatively, m is calculated using the formula i ：
Wherein,the representation function takes an integer down, K being the distance coefficient.
Alternatively, w is calculated using the formula i ：
Wherein,the representation function takes an integer down, K being the distance coefficient.
A second aspect of an embodiment of the present invention provides a proppant placement fracture equivalent porosity determination device, the device comprising:
a determination module for determining the porosity of the support band using the formula:
wherein D is the particle size of the propping agent and n i To propping agent layer number m in the length direction of the crack i To support the number of layers in the fracture height direction, L F Represents the crack length, H F Represents the crack height, W F Represents the width of the crack, w i The number of layers laid in the fracture width direction is shown, and δ represents the proppant insertion depth.
Alternatively, n is calculated using the formula i ：
Wherein,the representation function takes an integer down, K being the distance coefficient.
Alternatively, m is calculated using the formula i ：
Wherein,the representation function takes an integer down, K being the distance coefficient.
Alternatively, w is calculated using the formula i ：
Wherein,the representation function takes an integer down, K being the distance coefficient.
A third aspect of the embodiments of the present invention provides an electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, which when executed implements the steps in the proppant placement fracture equivalent porosity determination method according to the first aspect of the present invention.
A fourth aspect of the embodiments of the present invention provides a computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps in a proppant placement fracture equivalent porosity determination method according to the first aspect of the present invention.
In the embodiment of the invention, a method for determining the equivalent porosity of a propping agent laying crack is provided, based on the method, the porosity of a supporting belt can be determined to be increased along with the increase of the laying concentration of the propping agent and the inter-grain distance coefficient, but when the laying concentration is not lower than 13kg/m 2 When the laying concentration is increased, the improvement of the crack flow conductivity is mainly reflected by increasing the crack width, and the porosity of the supporting belt is hardly influenced. In addition, by adopting the method for determining the equivalent porosity of the propping agent laid fracture provided by the embodiment of the invention, the equivalent porosity of the propping agent laid fracture can be determined on the basis of considering the non-compact laying characteristic of the propping agent, thereby providing a basis for accurately describing the flow conductivity of the propping agent laid fracture and further providing a basis for propping agent type selection and design during fracturing design.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments of the present invention will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a schematic representation of proppant-shale interactions involved in an embodiment of the present invention, wherein part (a) shows a proppant-shale interaction schematic and part b shows a single proppant intercalation process schematic;
FIG. 2 is a schematic illustration of proppant mono-layer/sparse lay-up involved in an embodiment of the present invention;
FIG. 3 is a schematic diagram of a proppant placement scenario involved in an embodiment of the present invention, wherein (a) shows a multi-layered proppant placement schematic in section and (b) shows a geometric topology in section;
FIG. 4 is a graph showing the porosity of the support tape according to the distance coefficient without considering the variation of the support tape porosity with the number of layers of the support tape when the proppant is embedded in the embodiment of the present invention;
FIG. 5 is the effect of depth of embedment on relative porosity when a proppant monolayer is laid down in an embodiment of the present invention;
FIG. 6 is a graph showing the relative porosity as a function of depth of embedment for 10 layers of proppant in an embodiment of the present invention.
Detailed Description
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to the appended drawings and appended detailed description.
For ease of understanding, a proppant-shale interaction mechanics model is first explained:
after hydraulic fracturing, proppant-shale interactions are shown in fig. 1, which shows a schematic diagram of proppant-shale interactions involved in embodiments of the invention, wherein part (a) shows a schematic diagram of proppant-shale interactions and part b shows a schematic diagram of a single proppant intercalation process; since the model shown in part (a) of fig. 1 is directly used for research, and is difficult to accurately describe, most students abstract one proppant particle, and the proppant is similar to a sphere in morphology, so that the interaction behavior of the proppant and shale can be simplified into the problem of contact between single spherical particles and an infinite flat plate, as shown in part (b) of fig. 1. In order to solve the contact problem, the precondition is to accurately acquire various physical and mechanical parameters of shale, so as to effectively describe the physical and mechanical behaviors of the shale; and then combining with a nonlinear contact mechanics theory, the single spherical particle elastoplastic embedded depth model can be constructed. However, since the proppant-shale system in actual situations is shown in part (a) of fig. 1, the pore volume evolution of the support zone, the relationship between the closing pressure and the contact force, and the like are all affected by the proppant placement situation, the application of the single spherical particle elastoplastic embedded depth model to actual situations must take into account the placement characteristics of the proppant in the fracture and the inter-particle interference problem.
Proppant interactions with shale remain essentially contact problems, which, from a mechanical standpoint, are largely comprised of two aspects: (1) Mechanical properties of the contact material (shale) itself, such as its elastic, yielding, strengthening, etc., necessarily affect the deformation behavior during proppant-shale contact; (2) How the mechanical behavior of shale affects the elastoplastic embedding process of proppants.
The propped fracture conductivity is generally determined by the permeability (K) of the propped band f ) Width of the supporting seam (W) F ) After the proppant is embedded in the formation, the fracture width is reduced resulting in a decrease in conductivity. However, after the proppant is embedded, not only the width of the fracture is reduced, but also the pore structure formed by the proppant and the fracture wall is changed, so that the porosity of the supporting belt is affected, and the permeability of the supporting belt is reduced. Thus, there is a need for a more accurate and rational method of determining the porosity of a support belt.
The propping type cracks formed by propping agent filling are main channels for oil and gas resource seepage, and under the action of closing pressure, propping agent particles are embedded into shale wall surfaces to reduce the width of the cracks and the evolution of pore structures of the propping bands are one of main factors for reducing the diversion capacity of the propping type cracks.
In an actual crack, a plurality of propping agents are moved and piled up to form sparse, single-layer, multi-layer and other laying modes, pore structures formed by different laying modes are different, and the contact force caused by the pore structures is different, so that the permeability of the supporting belt is affected. Although proppants generally have certain grain size distribution in actual engineering, if the influence of embedding on permeation is discussed according to actual conditions, great difficulties are faced in mathematics, so that the scholars still use an equal grain size model to discuss the problem of embedding the proppants, and the embodiment of the invention still adopts an equal grain size assumption.
The arrangement of particles of equal particle size can be generally divided into: cubic, body centered cubic, wedge tetrahedron, hexagonal close packing, etc. arrangement modes; wherein the cubic packing coordination number (the number of points of contact of each particle with other surrounding particles) is 6, the porosity is about 48%, the hexagonal close packing coordination number is 12, and the porosity is about 26%. Under the natural accumulation condition, the particles are generally in a composite arrangement mode, the porosity is about 36%, under the stress disturbance effect, the particles at the bottom layer of the container tend to be arranged in a hexagonal compact mode, and the particles at the top layer of the container are arranged in a random mode; this also shows that the hexagonal close-packed mode is the most stable one of the many alignment modes, and other alignment modes have a tendency to evolve towards hexagonal close-packing under stress disturbance. In the fracturing process, when the fracturing fluid carries propping agent to fill a crack, the migration of the fluid causes the propping agent to be in a disturbed condition, in addition, after the reservoir is fractured, the reservoir is in an unstable state, and the reservoir stress adjustment causes the crack to slip, dislocate and the like, so that the disturbance rearrangement of the propping agent can be caused. The porosity of the supporting belt under the conditions of different types of propping agents and different laying concentrations is measured through an indoor test in the related art, and the porosity is about 28% -44% and is more than 26% of the porosity of the hexagonal close arrangement; thus, embodiments of the present invention contemplate that proppants should be deployed in the fracture in a manner that will predominate in the hexagonal close-packed mode and the other modes of alignment coexist.
In order to describe the state of the propping agent in the crack more accurately and avoid the mathematical problems caused by researching the problems of propping agent laying, embedding and the like in a mixed arrangement mode, the embodiment of the invention introduces the distance coefficient K, namely the propping agent is considered to be still arranged in a hexagonal compact mode, and the mixed laying problem is equivalent to: the particles are not closely together but are present at a distance, and for mathematical simplicity, it is assumed that the spacing between any adjacent particles in the same plane is uniform, thus solving the problem of greater porosity in practical situations.
Specifically, assuming that the spacing between adjacent proppants is the same, when the spacing between proppants changes, the change rule of each pair is consistent, so thatThe spacing between adjacent proppants is KD (K is a distance coefficient, and D is the particle size of proppants); at the crack length L F The number of layers of proppants is n i From the geometrical relationship in FIG. 2 (showing proppant monolayer/sparse lay-up schematic)
Wherein:in the embodiment of the invention, the finger function takes an integer downwards.
At crack height H F The number of layers of proppants is m i Then the same principle can be obtained
When a double rhombohedra stacking system is adopted, the adjacent layers are affected by the regular boundary, and the particle numbers of the adjacent layers are different by 1, as shown in FIG. 2H F In the direction, if the difference between the numbers of particles in adjacent layers is ignored, the total number of proppant particles is
N i ＝m i n i (3)
This will result in an increase in the statistical particle count by m i 2 particles;
alternatively, as shown in FIG. 2, a dashed box can be used as a cell where the total number of proppant particles is
At this time, if m i In the case of even numbers, the use of equation (4) does not mathematically cause any error, whereas when m i When odd, equation (4) will reduce the particle count by n i -1 or n i Granulating;
the maximum errors caused by the formulas (3) and (4) in the topological relation are respectively as follows:
and->
It can be noted that even when larger particle proppants are used, such as 20 mesh, the particle size is about 0.84mm assuming a fracture length or height of 10mm, error 1 And error 2 The values of (2) were 4.7% and 8%, respectively. In most cases, the proppant particle size is often less than 20 mesh, while the fracture length/height is also much greater than 10mm; thus, the use of formula (3) or (4) does not have a significant impact, and in view of the simplicity of the form, the total number of proppant particles can be calculated using formula (3) in embodiments of the present invention.
For the single layer lay-up mode, the propped fracture initiation porosity, i.e., regardless of the propped band porosity at proppant insertion, can be given by formula (5)
When the propping agent is embedded into the shale wall surface under the action of closing stress, the embedding depth is delta, the deformation influence generated outside the contact area in the process of embedding the propping agent is ignored, at the moment, the sphere (propping agent) is a sphere defect in the crack, and if the deformation of the propping agent is not considered, the volume in the crack after embedding is
Thus, when considering proppant insertion effects, the support band porosity is
In the embodiment of the invention, the following elastoplastic model considering the shale strengthening limit can be adopted to analyze the elastoplastic embedding depth of the propping agent of shale:
when the embedding depth is smaller than the critical embedding depth (delta is smaller than or equal to delta) y )，
When the depth of the embedment is greater than the critical embedment depth, but less than the shale ultimate strength depth (delta y ≤δ≤δ pp )，
When the depth of embedment is greater than the shale ultimate strength depth (delta pp ≤δ)，
Wherein,
f represents a contact force; r represents the radius of the proppant particle; delta represents the depth of embedding, delta y Representing a critical embedding depth; delta pp Represents the shale ultimate strength depth, a represents the radius of the contact circle of shale and proppant particles, E * V is poisson's ratio, which is the integrated elastic modulus; p is p py As a matter of the strength limit of the material,p mc the contact pressure of the proppant particles with the shale contact center point when the rock just yields, Y is the material constant of the D-P yield criterion.
Specifically, in the embodiment of the invention, the plastic characteristics can be described by using a stress strain curve obtained by a conventional triaxial compression test.
Shale typical threeThe axial compressive stress strain curve can be generally obtained from 4 key points (crack closing point sigma cc Crack initiation point sigma ci Injury starting point sigma cd Peak stress point sigma p ) It is divided into 5 phases: a crack closing stage, an elastic deformation stage, a crack stable expansion stage, a crack unstable expansion stage and a post-peak deformation stage.
First stage (0)<σ≤σ cc ): the micro-defect closing section gradually closes initial defects such as micro-cracks, pores and the like in the shale under the action of compressive stress, and a stress-axial strain curve protrudes to a strain axis; the axial deformation is far higher than the lateral deformation under the unit stress increment at the stage, namely the Poisson ratio calculated at the stage is close to 0.
Second stage (sigma) cc <σ≤σ ci ): in the elastic stage, shale primary micro-defects are compacted, new micro-defects are not generated, the linear elastic characteristic is a main expression form of the stage, and externally provided energy is completely converted into elastic strain energy to be stored in the rock.
Third stage (sigma) ci <σ≤σ cd ): crack initiation and stable propagation stage when the stress continues to increase beyond the crack initiation point (sigma ci ) After that, the inside of shale starts to randomly initiate microcracks, the external energy is partially converted into elastic strain energy, and a small amount of energy is converted into surface energy of newly generated microcracks, acoustic emission and the like; the stress-strain curve starts to deviate from a straight line into a nonlinear section, and the lateral deformation gradually increases under the increment of unit stress.
Fourth stage (sigma) cd <σ≤σ p ): in the unstable expansion stage of the crack, the microcracks are further expanded and converged under the action of stress, and the nonlinear characteristics are more remarkable; the development of cracks causes the rock volume deformation to change from compression to expansion.
Fifth stage (sigma) p <Sigma): at the post-peak stage, when the stress reaches the peak strength, microcracks in the shale are mutually converged and communicated to form macrocracks, the elastic strain energy stored in the shale is gradually released, the energy consumed by the macrocracks is insufficient to consume the release energy of the elastic strain energy of the shale, and the shale is laterally added withIn the strain control mode, the equipment is continuously unloaded and loaded to ensure the continuation of the experiment, so that a complex post-peak class II stress-strain curve is formed.
In general, among the 4 key points, the peak stress point (σ p ) As a parameter for distinguishing the integral instability of the rock, the point is taken as a distinguishing point before and after the peak to be consensus; for hard rock with high density and low porosity such as shale, the crack closing stage is not obvious, and the stage is not directly related to the characteristics of damage, plasticity, strength and the like, so the crack closing point (sigma) can be ignored in shale cc ) Is a function of (a) and (b). The inflection point of the volume change is used as a critical point for the transition of the microcrack from stable expansion to unstable expansion, and therefore, the point can be used as a damage starting point (sigma cd ). Crack initiation point (sigma) ci ) There is no significant feature on the stress-strain curve, precisely, σ ci Almost impossible, but sigma ci As the end point of the linear elastic phase, the end point of the linear segment is generally regarded as the initial yield point in the plastic mechanics, so that although the crack start point and the initial yield point have a certain difference in physical sense, both values reflect the state of the rock material converted from the linear elastic phase to the nonlinear phase, and the values are significant for constructing the strength criterion of the rock, engineering design and the like.
In the deformation and destruction process of the rock, if the influence of an external heat source is not considered, the work of the rock by the external force is converted into elastic strain energy, plastic deformation energy, surface energy and the like. From the first law of thermodynamics, it is known that:
U＝U d +U e
wherein U is the density of the external input strain energy, U d Dissipation energy density, energy dissipation mainly due to plastic deformation and damage, U e Is the elastic strain energy density.
The external input strain energy density is given by:
elastic strain energy density U e From generalized hooke's law:
defining an energy dissipation ratio U r To dissipate energy density U d And the ratio of the input total strain energy density U.
When the energy dissipation ratio reaches a minimum value, the crack starting point of the material is:
in the micro-defect closing stage, part of the work done by the external force is converted into elastic strain energy to be stored in the rock sample, part of the elastic strain energy is dissipated due to the micro-defect closing, and the elastic strain energy and the dissipation energy are synchronously increased, but the elastic strain energy is mainly increased. In the elastic stage, the existing microdefect of the rock sample is basically closed, the new microdefect is not generated, the work done by the external force is completely converted into elastic strain energy, the change characteristic of the dissipation energy along with the axial strain in the stage is a straight line approximately parallel to the coordinate axis, and the energy dissipation ratio is continuously reduced; when the elastic phase is finished, new micro defects start to be generated, part of work done by external force is dissipated in the forms of plastic deformation energy, surface energy and the like, namely, the dissipation energy starts to be newly increased, and along with the increase of stress, the increase speed of the dissipation energy is gradually increased until the dissipation energy is destroyed, and at the end point of the elastic phase, the energy dissipation ratio reaches a minimum value.
No matter how the rock deforms and the energy evolves, the energy dissipation caused by plastic deformation, damage and the like is basically the initiation and evolution of the microdefect, namely the evolution of the microdefect determines the trend of the dissipation energy, and thus, the embodiment of the inventionTaking the end point of the dissipation energy straight section as a crack starting point; since the end point of the dissipation energy flat section is still affected by human factors, the minimum point of the energy dissipation ratio is used as the crack starting point (sigma ci ). In the embodiment of the invention, the crack initiation point (sigma ci ) The determined fracture initiation strength is taken as the initial yield point of the shale.
In the embodiment of the invention, through the triaxial compression test of shale,
will initially yield point sigma 1 、σ 3 Conversion to I 1 、J 2 The D-P straight line fitting indication of the shale initial yield points with different bedding inclination angles can be obtained. Furthermore, according to the invention, the alpha of shale with 0 degree, 30 degree, 60 degree and 90 degree is 0.1096, 0.0817, 0.1527 and 0.114 respectively, and Y is 37.44MPa, 43.33MPa, 28.52MPa and 48.06MPa respectively.
Therefore, in the embodiment of the invention, the embedding depth of the propping agent can be calculated.
When the number of layers of the propping agent is large, a single-layer paving model can be still adopted for the contact layer with the shale wall surface, and the propping agent is still stacked in a similar manner to a single-layer paving rule in the width direction of the crack, a schematic diagram of the propping agent paving condition is shown in fig. 3, the propping agent paving characteristics and the geometric topological relation of the propping agent paving characteristics are shown in fig. 3 in the section perpendicular to the wall surface of the crack, wherein part (a) shows the schematic diagram of the propping agent multi-layer paving, and part (b) shows the geometric topological relation. The length of OD, i.e., h, can be obtained i Is that
Similarly, the number of layers w of the propping agent laid in the width direction of the crack i Is that
For multilayer paving, the range of the distance coefficient should be 1.ltoreq.K.ltoreq.1.5 whenWhen the gaps between adjacent particles are increased, the particles in the middle layer are inevitably moved to a contact layer with the wall surface of the crack, and then the particles are degenerated into a single-layer or sparse arrangement mode; when->During the time, the proppant penetration phenomenon, namely 2h, will occur i <D, which is not possible in practice.
Similarly, ignoring the differences in proppant particles from layer to layer, the total number of proppant particles can be given by formula (10)
N i ＝m i n i w i (10)
For multilayer laying applications, the support belt pores are formed by wall contact layer pores and intermediate layer pores, the contact layer pores have a volume similar to that of a single layer, e.g
The pore volume of the intermediate layer is
When proppant intercalation occurs, the intermediate layer pore volume does not change with increasing intercalation depth, and the intercalation behavior only affects the contact layer pore volume V c0 The method comprises the steps of carrying out a first treatment on the surface of the When the proppant embedding depth is delta, the contact layer pore volume is reduced to
From this, the porosity of the support band was found to be
It can be found that when w i When =1, i.e. when the proppant is laid in a single layer, formula (14) is degenerated to formula (7), so single layer laying is a special case when multi-layer laying, but it should be noted that the distance coefficient K cannot be greater than 1.5 when multi-layer laying, while there is no restriction on this condition when single layer laying.
In the embodiment of the invention, the values of the porosity models (7) and (14) are also assigned so as to more intuitively obtain the influence of the laying characteristics on the pore structure. Assuming a sphere particle diameter of 0.63mm, the fracture geometry L F 、H F 23mm and 45mm, respectively, and the crack width (w i -1)h i +D，h i Obtained from equation (8).
When the number of layers of the support agent is different, the change rule of the initial porosity of the support belt (the porosity when the embedding depth is 0) along with the distance coefficient is shown in fig. 4, and fig. 4 shows the change rule of the initial porosity of the support belt along with the distance coefficient without considering the number of layers of the support belt when the support agent is embedded. As can be seen from fig. 4, the number of layers and the distance coefficient of the laying layer have a great influence on the porosity of the supporting belt, the porosity of the supporting belt tends to decrease as the number of layers increases, but the influence thereof decreases as the number of layers increases, when the number of layers is not less than 10 layers, the porosity hardly changes as the number of layers changes, and the permeability generally has a positive correlation with the porosity, that is, when the number of layers is not less than 10 layers, the influence of the number of layers on the flow conductivity is mainly reflected by changing the width of the crack. For the compact arrangement (k=1.0) the maximum porosity achieved when the single layer is laid up is about 40.7%; when the number of layers of the propping agent is more than or equal to 15, the porosity gradually reaches the minimum value, about 28 percent, and less than 70 percent when the propping agent is arranged in a single layer. On the other hand, the porosity of the support belt increases monotonically with increasing distance coefficient, and when k=1.5, the porosity is about 1.8 to 1.9 times that when k=1.0, and the porosity increases significantly.
To quantitatively discuss the effect of embedding depth on porosity, a relative porosity is defined as the ratio of the support band porosity at embedding depth δ to the porosity at δ=0, as shown in equation (15). When propping agent is arranged in a single layer or sparsely in the crack, the change rule of the relative porosity of the propping belt along with the embedding depth under the condition of different distance coefficients is shown in fig. 5, and fig. 5 shows the influence of the embedding depth on the relative porosity when the propping agent is laid in a single layer. As can be seen from fig. 5, the smaller the distance coefficient, the greater the effect of the proppant embedding depth on the relative porosity, and after the distance coefficient exceeds 1.3, the effect of the embedding depth on the relative porosity no longer changes with the change of the distance coefficient. And when K is less than or equal to 1.3, the relative porosity is reduced in an approximately exponential manner along with the embedding depth, and when K is more than 1.3, the relative porosity is attenuated in a linear manner along with the embedding depth. When δ=0.2 mm (about 31.7% of particle size), the minimum relative porosity is about 13.5% (k=1.0) and the maximum relative porosity is about 32.5% (k=1.7), it can be seen that for single or sparse arrangements, proppant intercalation will result in a sharp decrease in support band porosity.
When the proppants are laid in multiple layers (taking 10 layers as an example), the change rule of the relative porosity with the embedded depth is shown in fig. 6, and fig. 6 shows the change rule of the relative porosity with the embedded depth when the proppants are laid in 10 layers. As can be seen from fig. 6, the effect of proppant insertion depth on porosity is significantly reduced when the layers are laid up, with a minimum relative porosity of 82.2% still when δ=0.2 mm. And when K=1.1, 1.2 and 1.3, the three have no obvious difference along with the change rule of the embedding depth. Further, unlike in the case of single-layer laying, when δ is 0.1mm (about 15.9% of the particle diameter), the close arrangement is most affected by the embedding depth, and then the arrangement at a distance coefficient of 1.5 is most affected by the arrangement at k=1.3. When delta is more than or equal to 0.1mm, the arrangement condition is the arrangement condition when K=1.5, and the arrangement condition is the tight arrangement condition; this is mainly due to the fact that when the distance coefficient is large, a large number of voids exist between the propping agent and the shale wall surface contact layer, the contact layer void volume occupies the whole supporting belt void volume proportion to rise, the embedding depth is increased, the voids are rapidly reduced, and accordingly the relative porosity is obviously reduced.
In the embodiment of the invention, the change condition of the porosity after the propping agent with different layers is embedded can be analyzed according to the porosity parameter of the propping belt, so as to analyze and discuss relevant factors.
In the embodiment of the invention, based on the method for determining the equivalent porosity of the propping agent laying crack, the method can be used for further analysis and determination: the porosity of the support belt increases with the increase of the proppant laying concentration and the inter-grain distance coefficient, but when the laying concentration is not lower than 13kg/m 2 When the laying concentration is increased, the improvement of the crack flow conductivity is mainly reflected by increasing the crack width, and the porosity of the supporting belt is hardly influenced.
In the embodiment of the invention, after the equivalent porosity of the propping agent laying crack is determined, a crack diversion capacity model considering the propping agent laying characteristics and elastoplastic embedding behavior can be established based on a C-K permeation model and by introducing a Comiti-Renaud tortuosity model.
Further, the embodiment of the invention can determine that when the closing stress of the reservoir is low, the optimal proppant laying concentration exists in the fracture conductivity; when the closing stress is higher, the increase of the laying concentration of the propping agent (the increase of the laying layers) is beneficial to reducing the influence of the embedding of the propping agent, so that the crack keeps higher diversion capacity, and therefore, the use proportion of the propping agent with the large and small particle sizes is increased in the development process of the ultra-deep shale gas, so that the laying layers of the propping agent are increased, and the diversion capacity of the propping type crack is increased. In addition, properly increasing the distance between the proppant particles helps to increase the conductivity of the fracture.
Based on the above exploration, the embodiment of the invention provides a method for determining equivalent porosity of a propping agent laid fracture, which comprises the following steps:
the porosity of the support band was determined using the following:
wherein D is the particle size of the propping agent and n i To propping agent layer number m in the length direction of the crack i To be at the height of the crackTo the number of proppant layers, L F Represents the crack length, H F Represents the crack height, W F Represents the width of the crack, w i The number of layers laid in the fracture width direction is shown, and δ represents the proppant insertion depth.
Alternatively, n is calculated using the formula i ：
Wherein,the representation function takes an integer down, K being the distance coefficient.
Alternatively, m is calculated using the formula i ：
Wherein,the representation function takes an integer down, K being the distance coefficient.
Alternatively, w is calculated using the formula i ：
Wherein,the representation function takes an integer down, K being the distance coefficient.
Based on the same inventive concept, the embodiment of the invention also provides a proppant placement fracture equivalent porosity determination device, which comprises:
a determination module for determining the porosity of the support band using the formula:
wherein D is the particle size of the propping agent and n i To propping agent layer number m in the length direction of the crack i To support the number of layers in the fracture height direction, L F Represents the crack length, H F Represents the crack height, W F Represents the width of the crack, w i The number of layers laid in the fracture width direction is shown, and δ represents the proppant insertion depth.
Alternatively, n is calculated using the formula i ：
Wherein,the representation function takes an integer down, K being the distance coefficient.
Alternatively, m is calculated using the formula i ：
Wherein,the representation function takes an integer down, K being the distance coefficient.
Alternatively, w is calculated using the formula i ：
Wherein,the representation function takes an integer down, K being the distance coefficient.
Based on the same inventive concept, an embodiment of the present invention provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor implements the steps in the proppant placement fracture equivalent porosity determination method described in any one of the embodiments above when executing the computer program.
Based on the same inventive concept, embodiments of the present invention provide a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps in the proppant placement fracture equivalent porosity determination method described in any of the above embodiments.
In this specification, each embodiment is described in a progressive manner, and each embodiment is mainly described by differences from other embodiments, and identical and similar parts between the embodiments are all enough to be referred to each other.
It will be apparent to those skilled in the art that embodiments of the present invention may be provided as a method, apparatus, or computer program product. Accordingly, embodiments of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, embodiments of the invention may take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) having computer-usable program code embodied therein.
Embodiments of the present invention are described with reference to flowchart illustrations and/or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations 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 passive device oriented electromagnetic response optimizing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable passive device oriented electromagnetic response optimizing terminal device, 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 passive device-oriented electromagnetic response optimization terminal device 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 passive device-oriented electromagnetic response optimization terminal device to cause a series of operational steps to be performed on the computer or other programmable terminal device to produce a computer implemented process such that the instructions which execute on the computer or other programmable terminal device provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
While preferred embodiments of the present invention have been described, additional variations and modifications in those embodiments may occur to those skilled in the art once they learn of the basic inventive concepts. It is therefore intended that the following claims be interpreted as including the preferred embodiment and all such alterations and modifications as fall within the scope of the embodiments of the invention.
Finally, it is further noted that relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or terminal that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or terminal. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article or terminal device comprising the element.
The method, the device, the equipment and the medium for determining the equivalent porosity of the propping agent laid fracture are described in detail, and specific examples are applied to illustrate the principle and the implementation mode of the propping agent laid fracture, and the description of the examples is only used for helping to understand the method and the core idea of the propping agent laid fracture; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present invention, the present description should not be construed as limiting the present invention in view of the above.
Claims (4)
1. A method for determining equivalent porosity of a proppant placement fracture, the method comprising:
the porosity of the support band was determined using the following:
wherein D is the particle size of the propping agent and n i To propping agent layer number m in the length direction of the crack i To support the number of layers in the fracture height direction, L F Represents the crack length, H F Represents the crack height, W F Represents the width of the crack, w i The number of layers laid in the width direction of the fracture, and delta represents the proppant embedding depth;
calculating n using i ：
Wherein,representing the function down integer, K is distanceCoefficients;
calculating m using i ：
Wherein,the expression function is an integer downwards, K is a distance coefficient;
calculate h using i ：
Calculating w by using i ：
Wherein,the representation function takes an integer down, K being the distance coefficient.
2. A proppant placement fracture equivalent porosity determination device, the device comprising:
a determination module for determining the porosity of the support band using the formula:
wherein D is the particle size of the propping agent and n i To propping agent layer number m in the length direction of the crack i To support the number of layers in the fracture height direction, L F Represents the crack length, H F Represents the crack height, W F Representation ofCrack width, w i The number of layers laid in the width direction of the fracture, and delta represents the proppant embedding depth;
calculating n using i ：
Wherein,the expression function is an integer downwards, K is a distance coefficient;
calculating m using i ：
Wherein,the expression function is an integer downwards, K is a distance coefficient;
calculate h using i ：
Calculating w by using i ：
Wherein,the representation function takes an integer down, K being the distance coefficient.
3. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein the processor performs the steps of the proppant placement fracture equivalent porosity determination method of claim 1 when the computer program is executed.
4. A computer readable storage medium having stored thereon a computer program, characterized in that the computer program when executed by a processor realizes the steps of the proppant placement fracture equivalent porosity determination method of claim 1.
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