Multiporosity and Multiscale Flow Characteristics of a Stimulated Reservoir Volume ( SRV )-Fractured Horizontal Well in a Tight Oil Reservoir

There are multiporosity media in tight oil reservoirs after stimulated reservoir volume (SRV) fracturing. Moreover, multiscale flowing states exist throughout the development process. The fluid flowing characteristic is different from that of conventional reservoirs. In terms of those attributes of tight oil reservoirs, considering the flowing feature of the dual-porosity property and the fracture network system based on the discrete-fracture model (DFM), a mathematical flow model of an SRV-fractured horizontal well with multiporosity and multipermeability media was established. The numerical solution was solved by the finite element method and verified by a comparison with the analytical solution and field data. The differences of flow regimes between triple-porosity, dual-permeability (TPDP) and triple-porosity, triple-permeability (TPTP) models were identified. Moreover, the productivity contribution degree of multimedium was analyzed. The results showed that for the multiporosity flowing states, the well bottomhole pressure drop became slower, the linear flow no longer arose, and the pressure wave arrived quickly at the closed reservoir boundary. The contribution ratio of the matrix system, natural fracture system, and network fracture system during SRV-fractured horizontal well production were 7.85%, 43.67%, and 48.48%, respectively in the first year, 14.60%, 49.23%, and 36.17%, respectively in the fifth year, and 20.49%, 46.79%, and 32.72%, respectively in the 10th year. This study provides a theoretical contribution to a better understanding of multiscale flow mechanisms in unconventional reservoirs.

The research methods of the flow characteristics of SRV-fractured horizontal wells in a tight oil reservoir have been mainly focused on analytical, semi-analytical, and numerical methods.The analytical or semianalytical solution is mainly represented by the three linear flow model proposed by Brown [24], the five-zone model raised by Stalgorova [25], and the compound flow model presented by Su [26].However, those models have relatively strict assumptions.Generally, the models need to idealize the complex fracture network to regular fracture network forms composed of orthogonal primary and secondary fractures and simplify the complex flow processes to specific flow regimes such as elliptic or linear flow regimes [27][28][29].In terms of numerical models, Yao [30] and Fan [31] used the finite element method to carry out dynamic analysis of a horizontal well with a complex fractured continuous medium system, but those models did not consider the development degree of the natural fractures in tight oil reservoirs or the existence of the threshold pressure gradient in the matrix system.Therefore, it is a challenge to use these models to accurately describe the complex structures of actual network fractures and reveal the multiporosity and multiscale flow characteristics of an SRV-fractured horizontal well in tight oil reservoirs.
The objective of this work was to study the multiporosity and multiscale flow characteristics of SRV-fractured horizontal wells.Moreover, the innovation of this paper was to reveal the contribution of multiple porous media to horizontal well productivity by establishing a multiscale flow model.Enlightened by previous studies, a mathematical flow model was built to reflect the multiscale attributes of tight oil reservoirs based on the dual-porosity model (DPM) and discrete-fracture model (DFM), which were divided into three kinds of media systems.A reasonable solution of this numerical model was obtained and verified by the finite element method.Additionally, the flow mechanisms of an SRV-fractured horizontal well with the consideration of the multiporosity and multiscale effect were revealed, which were different to that of a conventional multifractured horizontal well without an SRV system.The findings of this research provide effective theoretical and methodological support for the prediction of the production performance prediction of unconventional hydrocarbon resources.

Physical Model and Assumed Conditions
SRV fracturing of a horizontal well in tight oil reservoirs with natural fractures has often induced complex fracture network growth, as revealed by microseismic monitoring [32][33][34][35].Moreover, the complex fracture network divides the reservoir into multiple porous media systems.Furthermore, the physical properties and fluid flow rules of each system are different.Based on the network fracture propagation process and the final form in the tight oil reservoir, a physical model of an SRV fractured horizontal well was built that considered the structure characteristics of multiple porous media, as shown in Figure 1, where ∆y f is the interval between fracturing segments (m); and a and b are the band width and band length of single fracture network, respectively (m).
Complex fracture networks composed of primary and secondary fractures formed by SRV fracturing are integrated into both the natural fracture system and matrix system.A reservoir that has been subjected to SRV fracturing treatment can be represented by a combination of a complex fracture network system, a natural fracture system, and a matrix system.Assumptions of the physical model were made as follows: (1) the study area was a three-dimensional, box-shaped closed, and isotropic body with natural fractures; (2) the rock and fluid were slightly compressible bodies, and the nonlinear flow in the matrix system, Darcy flow in the fracture system, and pseudosteady crossflow between the matrix system and fracture system are also found in the multiple media; and (3) the simulated production process was a single-phase fluid flow in porous and isothermal media without considering the influence of gravity.Complex fracture networks composed of primary and secondary fractures formed by SRV fracturing are integrated into both the natural fracture system and matrix system.A reservoir that has been subjected to SRV fracturing treatment can be represented by a combination of a complex fracture network system, a natural fracture system, and a matrix system.Assumptions of the physical model were made as follows: (1) the study area was a three-dimensional, box-shaped closed, and isotropic body with natural fractures; (2) the rock and fluid were slightly compressible bodies, and the nonlinear flow in the matrix system, Darcy flow in the fracture system, and pseudosteady crossflow between the matrix system and fracture system are also found in the multiple media; and (3) the simulated production process was a single-phase fluid flow in porous and isothermal media without considering the influence of gravity.

Nonlinear Flow in the Matrix System
The nonlinear flow equation in the matrix system can be given as [36,37] ( ) where vm is the flow velocity vector of fluid (10 −3 m/s); Km is the permeability tensor of the matrix (D); μ is the viscosity of fluids (mPa•s); ▽ is the Hamiltonian; pm is the pore pressure in the matrix system (MPa); χ is the threshold pressure gradient tensor (MPa/m) and can be defined as χ = χE, where χ is the threshold pressure gradient of matrix (MPa/m), and E is the unit matrix.
Via a combination of the state equation and continuity equation, the surface source in the 3D space is equivalent to the superposition of line sources in the 2D space, and the mathematical flow model for the matrix system can be derived [38] as where α is the shape factor of matrix; pn is the pressure of natural fracture (MPa); CL is the compression coefficient of fluid (MPa −1 ); and Cm is the comprehensive compression coefficient of matrix system (MPa −1 ).

Nonlinear Flow in the Matrix System
The nonlinear flow equation in the matrix system can be given as [36,37] where v m is the flow velocity vector of fluid (10 −3 m/s); K m is the permeability tensor of the matrix (D); µ is the viscosity of fluids (mPa•s); is the Hamiltonian; p m is the pore pressure in the matrix system (MPa); χ is the threshold pressure gradient tensor (MPa/m) and can be defined as χ = χE, where χ is the threshold pressure gradient of matrix (MPa/m), and E is the unit matrix.
Via a combination of the state equation and continuity equation, the surface source in the 3D space is equivalent to the superposition of line sources in the 2D space, and the mathematical flow model for the matrix system can be derived [38] as where α is the shape factor of matrix; p n is the pressure of natural fracture (MPa); C L is the compression coefficient of fluid (MPa −1 ); and C m is the comprehensive compression coefficient of matrix system (MPa −1 ).
Since [39], φ m << 1 and C mf = φ m C p , the comprehensive compressibility of the matrix system is defined as where φ m is the porosity of the matrix; C mf represents the compression coefficient of the matrix rock (MPa −1 ); and C p is the compression coefficient of the pore (MPa −1 ).The dimensionless pressure is defined as where j represents m, n, or f ; p i is the initial formation pressure (MPa); p j is the pressure of each system (MPa); K n is the permeability of natural fracture (D); and q j is the volume flow of each system (s −1 ).
Energies 2018, 11, 2724 4 of 14 The dimensionless permeability of the matrix is defined as The dimensionless threshold pressure gradient is The crossflow coefficient between the matrix system and natural fracture system is defined as The elastic storativity ratio of the natural fracture system is where φ n is the porosity of the natural fracture; and C n is the comprehensive compression coefficient of the natural fracture system (MPa −1 ).The dimensionless production time is Then, the dimensionless flow equation can be obtained [38] as Accordingly, the initial and boundary condition for fluid flow in the matrix system are given by

Darcy Flow in the Natural Fracture System
Assuming that there exists fluid crossflow between the matrix system and natural fracture system in the formation as well only the natural fracture system instead of the matrix system for fluid exchange to the network fracture system [40], the dimensionless variables are defined as follows: the dimensionless distances are M D = M/L, M eD = M e /L (M = x, y, z), a D = a/L, b D = b/L, where the length, width, and height of the study area are x e , y e , and h e , respectively (m); the horizontal well length is L (m); the dimensionless production rate is q kD = q k /q t , where k represents n or f ; and q t is the total volume flow (s −1 ).
Therefore, the dimensionless Darcy flow equation in the matrix system can be given [31] as where δ(M − M ) is the Dirac delta function.
The initial and boundary conditions for fluid flow are given by Energies 2018, 11, 2724 5 of 14

Darcy Flow in the Network Fracture System
The discrete-fracture model (DFM) is used to characterize the fracture network stimulated system [41,42].According to the fracture flow model of parallel plate openings (cubic law), the permeability of the network fracture is defined as , where a f is the fracture opening (mm).The dimensionless permeability of the network fracture is defined as K fD = K f /K n ; the elastic storativity ratio of the network fracture system is defined as , where φ f is the porosity of the network fracture; and C f is the comprehensive compression coefficient of the network fracture system (MPa −1 ).
Similarly, the dimensionless Darcy flow equation in the network fracture system can be given [31] by The initial and boundary conditions for fluid flow in the natural fracture system are given by All of the above flow equations and the fixed solution conditions of the matrix, natural fracture, and network fracture systems together constitute the multiporosity and multiscale flow mathematical model for an SRV-fractured horizontal well in tight oil reservoir.

Finite Element Method Meshing
The finite element integral equation is established by using Galerkin's weighted residual method and the continuous solving unit with an infinite degree of freedom is discretized into the finite element unit.The horizontal well, network fracture, and reservoir unit are described by a line, triangle, and tetrahedron, respectively.The dimensionless parameters of horizontal wells and hydraulic fractures in a box-shaped closed reservoir are the length of horizontal well L D = 1; the reservoir domain x eD = 6, y eD = 6, and h eD = 0.1; the coordinate of five fracturing sections in the x-direction (−0.4,0.2, 0, 0.2, 0.4).It is assumed that all fractures are vertical, the mesh generation of the whole model is based on triangle forward algorithm, and local grid refinement (LGR) is performed at the horizontal well and network fracture.The three-dimensional gridding division of an SRV-fractured horizontal well can be obtained as shown in Figure 2.

Finite Element Solution
Assuming that the study area node number is Np, the node pressure of matrix system and natural fracture system can be written by Pm = [Pm,1, Pm,2,..., Pm,N p ] T and Pn = [Pn,1, Pn,2,..., Pn,N p ] T .The equivalent integral transformation for control Equations ( 10), (12), and ( 14) is carried out by using the

Finite Element Solution
Assuming that the study area node number is N p , the node pressure of matrix system and natural fracture system can be written by P m = [P m,1 , P m,2 ,..., P m,Np ] T and P n = [P n,1 , P n,2 ,..., P n,Np ] T .The equivalent integral transformation for control Equations ( 10), (12), and ( 14) is carried out by using the equilibrium condition and variation principle, and the characteristic matrix equation of the system element can be obtained.The element characteristic matrix of the network fracture system can be expressed [38] as where a fD is the dimensionless opening of the 2D fracture surface; P e,f is the pressure matrix of the node in the network fracture system; Ω e,f is the flow area of the network fracture located at the node; and N e,f = [N 1 , N 2 , N 3 ] represents the shape function of two-dimensional triangular elements.Finally, based on the element characteristic matrix of the matrix system and natural fracture system, the equilibrium equation of the reservoir system can be derived [38] as where the expression of the coefficient matrix is Assuming that the fluid flows from the natural fracture system to the network fracture system in the initial time, by using the implicit backward difference method concerning time for the equilibrium Equation ( 18) of the natural fracture system, the governing equation of the finite element method corresponding to the (k + 1)th time of the fracture system can be obtained [38] by Energies 2018, 11, 2724 7 of 14 According to the Equation ( 17), the pressure of the matrix system at (k + 1)th time step can be calculated as When the coefficient matrix A m = 0, the model represents the triple-porosity, dual-permeability (TPDP) media.When A m = 0, the abovementioned represents the triple-porosity, triple-permeability (TPTP) model.Using the abovementioned dominating Equations ( 12) and ( 13), the transient pressure and production performance of an SRV-fractured horizontal well under the conditions of constant productivity rate and stable bottomhole pressure can be calculated respectively.

Multiscale Flow Characteristics of SRV-Fractured Horizontal Well
In recent years, SRV fracturing technology has been widely used in the tight oil reservoirs of the Longdong oilfield, Ordos Basin, China.The Chang-7 oil reservoir in the mining area, which has an average depth of 1705 m, is a typical lithologically controlled oil reservoir characterized by tight pores, low pressure, and well-developed natural fractures.Therefore, complex fracture networks with multiple pores are easily developed in the formation after fracturing.According to the actual geological parameters and microseismic monitoring data of a ZP1 horizontal well with SRV fracturing of tight oil reservoirs in the Longdong oilfield, the basic parameters were determined (Table 1).The dimensionless variables used for the analysis and discussion of the results can be calculated, as shown in Table 2.The above parameters were substituted into the dominating Equations ( 12) and ( 13) to verify the finite element solution of the proposed model.Furthermore, the flow regimes and production performance of an SRV-fractured horizontal well with multiporosity media were analyzed.

Accuracy Verification of the Numerical Solution
To verify the accuracy of the numerical solution of our model, on the one hand, it was considered that the reservoir was a dual-porosity and single-permeability medium without threshold pressure.Moreover, only primary fractures exist in the reservoir after fracturing.The numerical solution of the finite element model was compared with the analytical solution of the Zerzar et al. 2004 model [43] for a conventional multistage fractured horizontal well, and the comparative curve of the pressure and pressure derivative behaviors were obtained, as shown in Figure 3. On the other hand, according to the actual geological parameters and fracturing parameters of a ZP1 well with 33 months of production history in the Longdong oilfield, the oil production rate and cumulative oil production of the ZP1 well with SRV fracturing could be calculated using the numerical model proposed in this paper, and the comparison curves are shown in Figure 4.

Accuracy Verification of the Numerical Solution
To verify the accuracy of the numerical solution of our model, on the one hand, it was considered that the reservoir was a dual-porosity and single-permeability medium without threshold pressure.Moreover, only primary fractures exist in the reservoir after fracturing.The numerical solution of the finite element model was compared with the analytical solution of the Zerzar et al. 2004 model [43] for a conventional multistage fractured horizontal well, and the comparative curve of the pressure and pressure derivative behaviors were obtained, as shown in Figure 3. On the other hand, according to the actual geological parameters and fracturing parameters of a ZP1 well with 33 months of production history in the Longdong oilfield, the oil production rate and cumulative oil production of the ZP1 well with SRV fracturing could be calculated using the numerical model proposed in this paper, and the comparison curves are shown in Figure 4.   Matrix permeability, KmD 0.001 Network fracture permeability, KfD 2.08 × 10 6 Threshold pressure gradient, χD 0.001 Elastic storativity ratio of the natural fracture system, ωn 0.78 Elastic storativity ratio of network fracture system, ωf 0.92 Crossflow coefficient, λ 60

Accuracy Verification of the Numerical Solution
To verify the accuracy of the numerical solution of our model, on the one hand, it was considered that the reservoir was a dual-porosity and single-permeability medium without threshold pressure.Moreover, only primary fractures exist in the reservoir after fracturing.The numerical solution of the finite element model was compared with the analytical solution of the Zerzar et al. 2004 model [43] for a conventional multistage fractured horizontal well, and the comparative curve of the pressure and pressure derivative behaviors were obtained, as shown in Figure 3. On the other hand, according to the actual geological parameters and fracturing parameters of a ZP1 well with 33 months of production history in the Longdong oilfield, the oil production rate and cumulative oil production of the ZP1 well with SRV fracturing could be calculated using the numerical model proposed in this paper, and the comparison curves are shown in Figure 4.   Figure 3 shows that the pressure and pressure derivative behaviors of a multistage fractured horizontal well calculated by the two models were basically consistent.Figure 4 shows that the theoretical model had good degree of fit with the actual well production Therefore, the model established in this paper could not only be simplified as the Zerzar analytical solution model, but could also be used to accurately predict the production performance of an SRV-fractured well in tight oil reservoirs.

Flow Regimes Division during Well Production
Considering the effect of natural fractures inherent in tight formation and network fracture systems produced by SRV fracturing on the productivity of the horizontal well and using the TPDP and TPTP models to simulate the production performance of a horizontal well under the conditions of constant productivity rate, the pressure, and pressure derivative behaviors (type-curves of well testing) [44] for an SRV-fractured horizontal well in a tight oil reservoir could be obtained, as shown in Figure 5.
Figure 3 shows that the pressure and pressure derivative behaviors of a multistage fractured horizontal well calculated by the two models were basically consistent.Figure 4 shows that the theoretical model had good degree of fit with the actual well production data.Therefore, the model established in this paper could not only be simplified as the Zerzar analytical solution model, but could also be used to accurately predict the production performance of an SRV-fractured well in tight oil reservoirs.

Flow Regimes Division during Well Production
Considering the effect of natural fractures inherent in tight formation and network fracture systems produced by SRV fracturing on the productivity of the horizontal well and using the TPDP and TPTP models to simulate the production performance of a horizontal well under the conditions of constant productivity rate, the pressure, and pressure derivative behaviors (type-curves of well testing) [44] for an SRV-fractured horizontal well in a tight oil reservoir could be obtained, as shown in Figure 5.For the TPDP model, the matrix system exhibited only the fluid crossflow phenomenon with the natural fracture system, but was not involved in the fluid flow process to the network fracture system.Under the assumption that the stimulated area was composed of triple-porosity media and the unstimulated area was composed of dual-porosity media, based on the pressure derivative curve, the TPDP model flow regimes during SRV-fractured horizontal well production in a tight oil reservoir could be divided into seven flow periods, as shown in Figure 6, where k is the slope of the pressure derivative curve; and both m and n are constants.For the TPDP model, the matrix system exhibited only the fluid crossflow phenomenon with the natural fracture system, but was not involved in the fluid flow process to the network fracture system.Under the assumption that the stimulated area was composed of triple-porosity media and the unstimulated area was composed of dual-porosity media, based on the pressure derivative curve, the TPDP model flow regimes during SRV-fractured horizontal well production in a tight oil reservoir could be divided into seven flow periods, as shown in Figure 6, where k is the slope of the pressure derivative curve; and both m and n are constants.
The TPDP model flow regimes can be divided into the following periods.Stage A: The initial pseudosteady flow around primary fractures; this stage mainly reflects the linear flow inside the primary fractures and the radial flow around the primary fractures, and the combination of the two causes the pressure derivative behavior to show a straight line with unit slope.Stage B: Linear flow inside the network fracture system; this stage reflects the linear flow from the secondary fractures to the primary fracture, and the pressure derivative behavior shows an oblique line with a near unit slope.Stage C: Pseudosteady crossflow between the matrix and natural fracture systems; as the pressure drop of the natural fracture system is greater than that of the matrix system, this stage mainly reflects the pseudosteady flow process from the matrix system into the natural fracture system, which leads to a concave part of the pressure derivative behavior.Stage D: Formation linear flow; this stage represents the linear flow around the network fracture, and the pressure derivative curve shows a straight line with a 1/2 slope.Stage E: Pseudosteady flow in the stimulated area; when the pressure wave propagates to the boundary of the stimulated area, the effective distance of fluid flow in the unstimulated area increases continuously, resulting in the formation of a moving sealed boundary with time changing around the stimulated areas.The pressure derivative behavior shows an oblique line with a near unit slope.Stage F: Pseudo radial flow near the SRV-fractured horizontal well; the flow characteristics at this stage are expressed as a pseudo radial flow centered on the horizontal well with the network fracture system, and the pressure derivative behavior is shown as a horizontal straight line.Stage G: Pseudosteady flow in the whole reservoir; the influence of the closed outer boundary is observed during the later stage of well production, i.e., when the pressure wave propagates to the reservoir boundary, the bottomhole pressure drops rapidly and pressure derivative behavior is shown as a straight line with unit slope.The TPDP model flow regimes can be divided into the following periods.Stage A: The initial pseudosteady flow around primary fractures; this stage mainly reflects the linear flow inside the primary fractures and the radial flow around the primary fractures, and the combination of the two causes the pressure derivative behavior to show a straight line with unit slope.Stage B: Linear flow inside the network fracture system; this stage reflects the linear flow from the secondary fractures to the primary fracture, and the pressure derivative behavior shows an oblique line with a near unit slope.Stage C: Pseudosteady crossflow between the matrix and natural fracture systems; as the pressure drop of the natural fracture system is greater than that of the matrix system, this stage mainly reflects the pseudosteady flow process from the matrix system into the natural fracture system, which leads to a concave part of the pressure derivative behavior.For the TPTP model, the fluid in the matrix system is involved in the flow to the network fracture system.Therefore, comparing with the TPDP model flow regimes, the bottomhole pressure drop of the horizontal well with the TPTP model becomes slower in the B', C', E', and F' stages.The linear flow in the formation (D) no longer arises and is covered by the pseudosteady crossflow (C'), which quickly changes the pseudosteady flow (E').Then, the pressure wave propagates quickly to the closed reservoir boundary, and the bottomhole pressure drop increases rapidly during the pseudosteady flow in the whole reservoir (G'), which is consistent with the pressure and pressure derivative behaviors of the TPDP model gradually.According to the development experience of tight oil reservoirs, the TPTP model is more reasonable for tight oil reservoir simulation.

Productivity Contribution Degree of Multiporosity Systems
To further quantitatively analyze the contribution degree of multiporosity systems to well productivity, the TPTP model was used to simulate the production process of the SRV-fractured horizontal well (800 m in length and fracturing with 10 segments) under the following three cases: (1) there was only the matrix system in the reservoir; (2) there were only the matrix and natural fracture systems in reservoirs; (3) there were the matrix, natural fracture, and network fracture systems in the reservoirs.The productivity (including the daily production and cumulative production) contribution curves for the three systems (including the matrix, natural fracture, and network fracture systems) during SRV-fractured horizontal well production in tight oil reservoirs can be calculated respectively, as shown in Figure 7.Moreover, the daily production contribution ratio (DPCR) cumulative production contribution ratio (CPCR) of the three systems to SRV-fractured horizontal well productivity can be obtained statistically, as shown in Table 3.
systems in the reservoirs.The productivity (including the daily production and cumulative production) contribution curves for the three systems (including the matrix, natural fracture, and network fracture systems) during SRV-fractured horizontal well production in tight oil reservoirs can be calculated respectively, as shown in Figure 7.Moreover, the daily production contribution ratio (DPCR) and cumulative production contribution ratio (CPCR) of the three systems to SRV-fractured horizontal well productivity can be obtained statistically, as shown in Table 3.  1 DPCR is the daily production contribution ratio; 2 CPCR is the cumulative production contribution ratio.
The simulation results indicated that the proportion of productivity contribution for tripleporosity media systems during SRV-fractured horizontal well production varied at different stages of reservoir development.In the early stage of tight oil reservoir development, the productivity of the SRV-fractured horizontal well was mainly contributed to by natural fracture and network fracture systems with high conductivity.The daily production rate was large, but declined rapidly.After that stage, due to the fracture failure, the DPCR of the natural fracture and network fracture systems gradually decreased, and the latter was more serious; on the contrary, the DPCR of matrix system increased rapidly.In the late stage of reservoir development, the daily production of the horizontal well was maintained at a lower level, and the DPCR of the matrix system was more than half.The CPCR of the matrix system, natural fracture system, and network fracture system during SRV-  1 DPCR is the daily production contribution ratio; 2 CPCR is the cumulative production contribution ratio.
The simulation results indicated that the proportion of productivity contribution for triple-porosity media systems during SRV-fractured horizontal well production varied at different stages of reservoir development.In the early stage of tight oil reservoir development, the productivity of the SRV-fractured horizontal well was mainly contributed to by natural fracture and network fracture systems with high conductivity.The daily production rate was large, but declined rapidly.After that stage, due to the fracture failure, the DPCR of the natural fracture and network fracture systems gradually decreased, and the latter was more serious; on the contrary, the DPCR of matrix system increased rapidly.In the late stage of reservoir development, the daily production of the horizontal well was maintained at a lower level, and the DPCR of the matrix system was more than half.The CPCR of the matrix system, natural fracture system, and network fracture system during SRV-fractured horizontal well production were 7.85%, 43.67%, and 48.48%, respectively in the 1st year; 14.60%, 49.23%, and 36.17%,respectively in the 5th year; and 20.49%, 46.79%, and 32.72%, respectively in the 10th year.

Conclusions
During the development of a tight oil reservoir after SRV fracturing, the flow characteristics are different from those of conventional reservoirs.This paper investigated the multiporosity and multiscale flow characteristics of an SRV-fractured horizontal well in a tight oil reservoir.Based on the dual-media theory and discrete-fracture network models, a mathematical flow model of an SRV-fractured horizontal well with multiporosity and multipermeability media was built, solved, and verified.It has been found that there exist different flow regimes and productivity characteristics in SRV-fractured horizontal wells.The TPDP model flow regimes during SRV-fractured horizontal well production in tight oil reservoirs could be divided into seven flow periods, which include the initial pseudosteady flow around the primary fractures, linear flow inside the network fracture system, pseudosteady crossflow, formation linear flow, pseudosteady flow in the stimulated area, pseudoradial flow near horizontal well, and pseudosteady flow in the whole reservoir.For the multiporosity and multiscale flowing states, the well bottomhole pressure drop became slower, the linear flow in the formation no longer arose, and the pressure wave arrived quickly at the closed reservoir boundary.The initial production rate of the SRV-fractured horizontal well was large but declined rapidly.The contribution ratio of the matrix system, natural fracture system, and network fracture system during SRV-fractured horizontal well production were 7.85%, 43.67%, and 48.48%, respectively in the 1st year; 14.60%, 49.23%, and 36.17%,respectively in the 5th year; and 20.49%, 46.79%, and 32.72%, respectively in the 10th year.The proposed research may provide valuable insight into understanding the multiporosity and multiscale flow mechanisms and unconventional hydrocarbon recovery maximization.For the actual oilfield, the change of the dynamic energy of the formation system can be predicted by the change of well productivity, which could guide managers in carrying out the development of regime adjustment and improvements in the management system in a timely manner.

Figure 1 .
Figure 1.Physical model diagram of the SRV-fractured horizontal well with multi-porosity media.

Figure 1 .
Figure 1.Physical model diagram of the SRV-fractured horizontal well with multi-porosity media.

Figure 3 .Figure 4 .
Figure 3. Pressure and pressure derivative behaviors in a multi-stage fractured horizontal well intercepted by the numerical solution and Zerzar [43] analytical solution.

Figure 3 .
Figure 3. Pressure and pressure derivative behaviors in a multi-stage fractured horizontal well intercepted by the numerical solution and Zerzar [43] analytical solution.

Figure 3 .Figure 4 .
Figure 3. Pressure and pressure derivative behaviors in a multi-stage fractured horizontal well intercepted by the numerical solution and Zerzar [43] analytical solution.

Figure 4 .
Figure 4. Comparison curve of the ZP1 well production data and theoretical calculation data.(a) Oil production rate.(b) Cumulative oil production.

Figure 5 .
Figure 5. Type-curves of well testing for an SRV-fractured horizontal well with the TPDP and TPTP models.

Figure 5 .
Figure 5. Type-curves of well testing for an SRV-fractured horizontal well with the TPDP and TPTP models.

Figure 6 .
Figure 6.Flow regimes division during SRV-fractured horizontal well production in tight oil reservoir.

Figure 7 .
Figure 7. Productivity contribution curves of three systems during SRV-fractured horizontal well production in a tight oil reservoir.(a) Oil production rate.(b) Cumulative oil production.

Figure 7 .
Figure 7. Productivity contribution curves of three systems during SRV-fractured horizontal well production in a tight oil reservoir.(a) Oil production rate.(b) Cumulative oil production.

Table 1 .
Geological and engineering parameters of the ZP1 well in the Longdong oilfield.

Table 2 .
Dimensionless variables used for the analysis and discussion of the results.

Table 3 .
DPCR and CPCR of three systems to SRV-fractured horizontal well productivity in different development stages of tight oil reservoir

Table 3 .
DPCR and CPCR of three systems to SRV-fractured horizontal well productivity in different development stages of tight oil reservoir