Academic Journal of Science and Technology ISSN: 2771-3032 | Vol. 14, No. 2, 2025 1 Analysis of Factors Affecting the Production Capacity of Diamond‐shaped Anti‐Nine‐point Fracturing Well Network in Chang 8 Reservoir of Heshui Oilfield Liyan Zou1, 2, Ke Wang1, * 1School of Earth Sciences and Engineering, Xi'an Shiyou University, Xi'an 710065, China 2China Changqing Oilfield Branch No. 12 Oil Production Plant, China *Corresponding Author: WANG Ke Abstract: The Chang 8 ultra-low permeability reservoir in Heshui Oilfield has a typical “three low” characteristics. The reservoir economic development needs to use fracturing to increase the productivity of single well. Based on the theory of multiphase seepage, the author is based on the Heshui Oilfield. The seepage characteristics of the rhombohedral anti-nine-point fracturing well pattern in low-permeability reservoirs were studied in a zoning study, and an oil-water two-phase seepage model considering non-Darcy matrix seepage zone, elliptical radial flow zone and pressure crack control zone was established. The results show that in the initial stage of vertical well fracturing well pattern development, the smaller the well spacing, the higher the oil production, but the faster the water content rises. In the initial stage of small row spacing, the vertical well fracturing well spacing has little effect on the accumulated yield, but the water cut in the small row is faster. The row spacing should be optimized reasonably. The larger the crack length, the higher the yield and the water content. The faster the ascending speed is, the larger the flow capacity of the pressure crack is, the larger the accumulated capacity is. As the fracture conductivity increases, the increase of the cumulative yield becomes smaller, and the water content increases faster. The direction of the injection well and the main crack The angle of the pair is small for the output. Keywords: Ultra-low permeability reservoir; diamond-shaped anti-nine-point well pattern; conductivity; crack length. 1. Introduction Chang 8 reservoir of Heshui Oilfield in Ordos Basin is a typical ultra-low permeability reservoir with "low pressure, low yield and low permeability" as its typical characteristics, which needs to be transformed by hydraulic fracturing to obtain economic productivity. The Chang8 reservoir in Heshui Oilfield is a set of braided river delta deposits developed under the background of lake basin expansion and high steep slope, and the main NE30° micro-fractures are obviously developed. The average porosity of the reservoir is 10.09%, the average permeability is 0.46mD, the physical property of the reservoir is poor, the oil-water two-phase flow area is small, the bound water and the residual oil saturation are 37.33% and 34.23%, respectively, and the oil displacement efficiency is poor. The development practice of ultra-low permeability reservoir shows that the well spacing adjustment of rhomboid reverse nine-point development pattern can adapt to different types of low permeability reservoirs. However, in the rhomboid-reverse nine-point development well pattern with fracturing, the seepage law becomes complicated and the distribution of remaining oil in the well pattern changes[1-2]. Therefore, it is of guiding significance[3] to study the construction parameters of the corner well fracturing in the rhombic reverse nine-point well pattern to improve the displacement efficiency in the well pattern. 2. Physical Model Theory Ultra-low permeability reservoir adopts fracturing mining mode, the seepage flow in the fracturing area is different from the conventional unmodified area, and the diamond-shaped reverse nine-point well pattern is divided into three seepage zones: the first zone is the high-speed seepage zone controlled by pressure fracture, the second zone is the elliptical seepage zone within the fracture range, and the third zone is the matrix seepage zone[4-6] far from the pressure fracture control. 3. Two-phase Percolation Model in The Three Zones Assumed conditions: (1) The oil-water phase is incompressible and the formation temperature is constant. (2) the influence of gravity and capillary force is not considered; (3) the reservoir is homogeneous. Considering the symmetry characteristic of the rhomboidal inverse nine-point well pattern, the representative unit in the well pattern is selected and the seepage law of the well pattern is obtained by the superposition principle. Figure 1. Diamond-shaped anti-nine point well network diagram 2 3.1. Zone 1: high speed seepage zone in crack The experiment of porous media seepage mechanics shows that in Darcy flow process, as the seepage velocity increases, the linear relationship between it and pressure gradient will not exist. In the transition zone, it is called "nonlinear seepage", and there are two kinds of resistance, namely viscous force and inertial force.[7-10]        2vv kdx dp  (1) Where, p is the oil reservoir pressure, MPa; μ is fluid viscosity, mpa·s; k is reservoir permeability, mD; v fluid flow velocity, m/s; β is the nonlinear flow coefficient; ρ is the fluid density g/cm³. 3.2. Zone 2: Elliptical seepage in the crack range Within the control range of pressure fracture transformation, the pressure wave is transmitted in an almost ellipsoidal way, and the flow in zone 2 is ellipsoidal seepage. Based on the concept of ellipsoidal percolation, the varying rectangular cluster is used to describe the isobaric elliptic cluster[11-13]. coshfxx  ，      sinh 2 sin 2 f 2 0 x dny   (2) Where: xf is the length of pressure crack, m; n is the row distance, m. Then the partial differential equation of the seepage flow of the ellipse in the second zone is: t S G y pkk y o o ro                      (3)   t S G y pkk y o w rw                    1  (4) Where: kro is the relative permeability of oil phase; krw is the water phase relative permeability; G is the starting pressure gradient, Mpa/m; So is oil saturation; μo is the oil phase viscosity, mpa·s; μw is the oil phase viscosity, mpa·s. The flow rate formula is:                 G y pkk xQ w rw   cossinh8 2 f (5) Where: ξ is the outer boundary of the ellipse. The elliptic flow rate in the well pattern unit area is a part of the elliptic seepage flow, namely: M M Q Q m tt  (6) Where: Mt is the area of the ellipse falling in the well pattern unit area; Qt is the elliptic flow rate in the well pattern unit area; M is the area of the ellipse. The corner well on the long diagonal in the rhomboid anti- nine-point pattern unit, where m is   /49/3cos 22 nmm lllarm  (7) Short diagonal corner Wells are:   /369/6cos 22 nmn lllarm  (8) Side well on the long diagonal:    /4/cos 22  nmm lllarm (9) Side well on the short diagonal:    /4/4cos 22  nmn lllarm (10) 3.3. Zone 3: Far away from the pressure fracture control matrix seepage zone The fluid flow in the third zone is the plane radial non- Darcy flow law, which is simplified to the relationship[14-17] between the independent variables r and t. The partial differential equation of percolation can be written as: t S q r pkk r o o o ro                       (11)   t S q r pkk r o w w rw                     1   (12) Where: q is the source and sink term, which can be written as:      mmwo yyxxf ah q q  1 (13)      nnww yyxxf bh q q  1Ⅰ (14) Where: q and qⅠ are the flow rate of injection well and production well respectively, δ is the Dirac function, f is the waterw cut, %. Considering that the flow rate of the injection well and the production well is only a part of the flow rate of the well, according to the flow line distribution, the flow rate in the flow line control area should be divided by the corresponding coefficients a and b, for the diamond-shaped inverse nine-point well pattern, a=8, b=16. 3.4. Condition of definite solution Initial conditions              wcw wa ow ss ptlrp ptrrp 0 0, 0, ， (15) 3 Where: po is the bottom hole flow pressure of the oil well, MPa; pw is the bottom-hole flow pressure of the well, MPa; rw is wellbore radius, m; swc is the original water saturation, %. The inner boundary conditions are Kh q r p r o rr o w   2     (16) Kh q r p r w rr w w   2     (17) The outer boundary conditions are: 0   Cn p (18) The interface conditions for Zone 2 and Zone 3 are:     rf ppxpp 32021 ， (19) In the formula:, M, N are respectively the short and short semi-axes of the ellipse,, and are the inner boundaries of the ellipse.  2222 sincos NMr  coshfxM  sinhfxN  0 3.5. Reservoir matrix-fracture coupling flow equation     w s s ro w rw w t I ro w rwf o x ff f f f oow ds kk f dt c q nbk q d kk q kx q dx hw q hw qx k Gx rrGpp wf w f                            00 0 0 2 0 2 0 0 4 2             sinhsinh sinhsinh '' (20) 4. Analysis of Influencing Factors of Fracturing Data of rhomboid-reverse nine-point development zone of an ultra-low permeability reservoir in Ordos Basin: Well spacing is 540m, row spacing is 130m, reservoir depth is 1834m, effective oil thickness is 16.0m, average porosity is 0.11, oil saturation is 0.45, average oil permeability is 0.70mD, injection and production pressure difference is 13.6MPa, fracture half-length is 96m, fracture conductivity is 0.2μm2·m, fracture width is 0.002m. 4.1. Diamond inverse nine-spot well spacing (2a) (2b) Figure 2. The relationship between yield and water content of different well spacings with time production time（103d） production time（103d） m oi st ur e co nt en t( % ) A cc um ul at ed p ro du ct io n( 10 3 m ³） 4 As can be seen from FIG. 2, the smaller the well spacing of vertical well fracturing pattern in the early stage of development, the higher the cumulative oil production, but the greater the increase of water cut. The water cut growth rate of the inverted nine points of the diamond well spacing is lower, and its cumulative oil production exceeds that of the small well spacing near 800 days. 4.2. Rhomboid reverse nine-point spacing As can be seen from FIG. 3, in the early stage of development, vertical well fracturing pattern spacing has little influence on cumulative production, but water cut increases faster in small row spacing. At around 1600d, the cumulative production of different row spacing increased slightly and basically approached a straight line. (3a) (3b) Figure 3. The relationship between different row spacing yield and water content with time 4.3. Press the crack half length As can be seen from FIG. 4, the cumulative production increases rapidly within 800d, and the corresponding water content changes rapidly from 0 to 50%. The main production period of ultra-low permeability reservoir is concentrated in the middle and low water cut section. The longer the fracture, the higher the production, but the faster the water cut rises. 4.4. Pressure crack conductivity As can be seen from Figure 5, the greater the conductivity of pressure fractures in vertical Wells, the higher the cumulative oil production and the greater the increase in water content. It can be seen that the validity period of fracturing well pattern development is concentrated in the early and middle stages of development. production time（103d） production time（103d） m oi st ur e co nt en t( % ) A cc um ul at ed p ro du ct io n( 10 3 m ³） 5 (4a) (4b) Figure 4. The relationship between half-length yield and water content of different cracks with time (5a) (5b) Figure 5. The relationship between yield and water content of different fracture conductivity production time（103d） production time（103d） production time（103d） production time（103d） m oi st ur e co nt en t( % ) m oi st ur e co nt en t( % ) A cc um ul at ed p ro du ct io n( 10 3 m ³） A cc um ul at ed p ro du ct io n( 10 3 m ³） 6 4.5. Angle between the connecting direction of the well and the main fracture As can be seen from Figure 6, for the same water content of Angle Wells, the smaller the Angle, the higher the cumulative production. With the increase of water cut, under the same water cut, the greater the Angle, the higher the degree of production. On the whole, the Angle between the connection direction of water injection well and the main fracture has little effect on production. (6a) (6b) Figure 6. The relationship between yield and water content with time under different fracture conductivity 5. Conclusion (1) Based on the theoretical characteristics of percolation, the characteristics of percolation in the rdiamond-shaped reverse nine-point fracturing pattern were studied in different zones, and a three-zone two-phase fracturing model was established considering the matrix non-Darcy percolation, elliptical radial flow and linear fracture flow of starting pressure gradient. (2) In the initial stage of small row spacing, the vertical fracturing pattern row spacing has little influence on the cumulative production, but the water cut rising rate of small row spacing is faster, so the row spacing should be optimized reasonably; The larger the fracture length, the higher the cumulative production and the faster the water cut increase; The smaller the fracture conductivity, the lower the cumulative yield. With the increase of fracture conductivity, the increase of cumulative yield becomes smaller, and the increase of water content is faster. 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