Search

Fracturing fluids will carry an amount of proppant flowing back to the wellbore due to the inappropriate flowback schedule, which causes some parts of fractures to be closed without support. The appearance of closed fracture sections without support (pinch point) has a serious negative effect on well performance and is also a potential signal of refracturing. A four-region model considering fracture closure is developed to detect pinch points by analyzing production data in material equilibrium time. Therefore, a novel four-region flow model is proposed to study the influence of pinch points on well dynamics performance in the initial stage of production and to diagnose the pinch point. In this model, the fluid flow to the wellbore is regarded as three parts: matrix, fracture, and pinch points. The position of the pinch point on the fracture (near wellbore) is considered. The existence of pinch points makes the fracture conductivity segmented, and the partial closure of fracture can be simulated by setting different fracture lengths, widths, and permeability. The flow in each region is treated as the linear flow and is coupled through boundary conditions and flux supply. Thereby, the mathematical model of flow containing pinch points is established. This paper analyzes the production data of oil well, draws the logarithmic curve of RNP and its derivative RNP’ versus the material balance time (MBT), and conducts rate transient analysis to determine the occurrence of pinch points. In the case of the near-wellbore pinch point, the slope of the first half of RNP curves is relatively small, while the slope of the back section is about 1/2. Compared with RNP curves, the early slope of RNP’ curves is relatively large and gradually changes into the linear flow stage with a slope of 1/2. Different properties of pinch points mainly affect the slope of the left and right ends of RNP and RNP’ curves. The new analysis method can be used to analyze the influence of fracture closure position and degree of fracture closure on well productivity. Finally, the novel four-region flow analysis model was applied to the analysis of oil production data from a typical well in Ordos Basin. The length, width, and permeability of the near-wellbore fracture closure section can be obtained by fitting the proposed chart. The novel four-region flow model method and its curve characteristics provided in this article can be used as an important reference for judging whether there is a pinch point in fracture. It has a certain guiding significance for the formulation of fracturing schemes for new wells and whether old wells need refracturing in actual production.

Sandstone oil reservoirs with huge bottom water and high permeability are generally developed with high flow rate. After long-term water flooding (LTWF), the water flooding characteristics are quite different from that of original reservoir. In this paper, the effects of the PV number, viscosity, and displacement rate during LTWF are studied through experiments. The mechanism is analyzed based on analysis of changes in oil composition, rock mineral composition and wettability. The oil-water relative permeability curves, oil recovery and wettability were obtained with new experiments methods, which avoids the oil metering error by measuring oil and water separately. The research indicates that when the viscosity increases, the water phase permeability decreases, the residual oil saturation increases, and the water content rate increases earlier. A higher water flooding rate results in a higher ultimate recovery. A higher asphaltene content results in a higher viscosity and more oil-wet reservoir conditions. After LTWF, the wettability tends to water-wet, which is more favorable for heavy oil recovery. Moreover, LTWF reduces the clay content, which creates a more water-wet surface and a larger reservoir pore throat environment. This research provides insightful characteristics of offshore sandstone oil reservoirs, which can be used to enhance oil recovery.

Imbibition is an important recovery mechanism for tight oil reservoirs, which occurs during hydraulic fracturing and development. Due to the massive distribution of micro‐nano scale pore throats and the existence of a boundary layer in tight formation, agreement consensus has not been reached on the imbibition mechanism. Based on the effect of the boundary layer, experiments were conducted to study the imbibition in tight sandstone, and NMR was used to determine the efficiency of imbibition. The results reveal that the imbibition rate is related to the connection area of the matrix‐fracture, throat connection, and radius. Then, the effective capillary pressure was modified by describing the thickness of the boundary layer in the micro‐nano pore throats. The calculation results show that the existence of boundary layer in micro‐nano throats makes the capillary pressure much larger than those of reservoirs without boundary layer. And the boundary layer reduces the effective flow radius, which dramatically decreases the imbibition quantity. The final result of existence of a boundary layer dramatically weakens the imbibition ability of a tight oil reservoir, and thus, the existence of a boundary layer cannot be ignored. Finally, the effective throat radius limit was analyzed during imbibition in a water‐oil‐rock system of a tight oil reservoir. Without a boundary layer, the effective radius of the pore throats in the water‐oil‐rock system during imbibition is greater than 200 nm, which is due to the advantages of the large capillary force and pore throats that are not too small. With a boundary layer, the main radius of the pore throats used for the water‐oil‐rock imbibition is approximately 400 nm. Thus, the imbibition occurs in the pore throats larger than 200 nm in the water‐oil‐rock system, and a surfactant could reduce the limit of the throat radius during imbibition in tight oil reservoirs.

The mismatching between the multi-scale feature of complex fracture networks (CFNs) in unconventional reservoirs and their current numerical approaches is a conspicuous problem to be solved. In this paper, the CFNs are divided into hydraulic macro-fractures, induced fractures, and natural micro-fractures according to their mode of origin. A hybrid model coupling various numerical approaches is proposed to match the three-dimensional multi-scale fracture networks. The macro-fractures with high-conductivity and wide-aperture are explicitly characterized by a mimetic Green element method-based hierarchical fracture model. The induced fractures and natural micro-fractures that have features of low-conductivity and small-openings are upscaled to the dual-medium grid and enhanced matrix grid through the equivalent continuum-medium method, respectively. Subsequently, some benchmark cases are implemented to confirm the high-precision and high-robustness of the proposed hybrid model that indeed accomplishes accurate modeling of fluid flow in multi-scale CFNs by comparing with commercial software tNavigator®. Furthermore, an integrated workflow of simulation modeling for multiscale CFNs combined with a field example in Sichuan from China is used to analyzing the production information of fractured horizontal wells in shale gas reservoirs. Compared with the field production data from this typical well, it can be proved that the hybrid model has strong reliability and practicability.

In this paper, an efficient three-dimensional (3D) embedded discrete fracture model (EDFM) for production simulation of multistage fractured horizontal well is developed. The proposed model can be adaptive to vertical and inclined fractures with arbitrary shapes in any position of 3D reservoirs. The boundary integral equations of transient flow equations are handled to approximate the transfer flux between matrix gridblocks and their containing fracture cells, and this approximation has a higher accuracy than that in original 3D EDFM. Meanwhile, corresponding methods of fracture-shape characterization and calculating the multiple singular integrals on arbitrary polygonal fracture cells are introduced. Three examples are implemented to confirm the proposed 3D EDFM is valid and indeed accomplishes a more accurate modeling of transient effects compared with original 3D EDFM. Furthermore, two cases of natural depletion with a complex fracture network, water flooding with inclined elliptic fractures are implemented to demonstrate the performance and applicability of the proposed 3D EDFM to production simulation of multi-stage fractured horizontal well.

Fluid flow in tight formations deviates significantly from that in conventional reservoirs due to the micro/nano pores and high confining pressure; non-linear flow occurs at low displacement pressure gradients. The effects of boundary layer and media deformation on fluid flow cannot be ignored. In this paper, a stochastic network model with anisotropic topology is firstly constructed to represent the complex structures of tight formations. Subsequently, a series of network models with different physical scales are generated to obtain the representative elementary volume (REV). Based on the representative network model, a pore network flow model coupling the boundary layer effect with media deformation is developed. Iterative methods are proposed to solve the strong nonlinear mathematical model. Microtube experiments with different radii and three corresponding representative networks with different distributions of throat radii are employed to verify the accuracy and reliability of the numerical results. After the validation, pore scale flow regularity considering the boundary layer effect and media deformation of tight formations is obtained. Furthermore, the factors influencing pore scale flow, such as the effective stress, aspect ratio, coordination number and fluid viscosity, are studied. The results show that pore scale flow velocity considering the boundary layer effect and media deformation is smaller than that without considering the two mechanisms. Nonlinear flow occurs at low displacement pressure gradients because of the boundary layer effect, and media deformation aggravates the nonlinear phenomenon. Similarly, the absolute permeability also decreases when the two mechanisms are considered. It is no longer constant when boundary layer effect is taken into consideration, which increases with increasing displacement pressure gradient and reaches a plateau when the displacement pressure gradient is large enough. The effects of different factors on pore scale flow considering boundary layer effect and media deformation differ from their roles in conventional flow network models. Although the absolute permeability increases with decreasing aspect ratio and increasing coordination number, the value is far smaller than that without considering the two mechanisms because they result in the compression of the effective flow space. Additionally, the absolute permeability no longer remains unchanged when the variation of fluid viscosity is included. This indicates that the absolute permeability considering the boundary layer effect is not only affected by the pore structures but also the fluid viscosity. The methodology developed in this work provides a novel way to study the effects of boundary layer and media deformation on pore scale flow. The results provide new insights into fluid flow in tight formations.

Application of multi-fractured horizontal wells has led to significant progress in the development of tight oil reservoirs. However, oil production rapidly decreases and the estimated ultimate recovery is still low when the well is in production and approaching depletion. Water huff-n-puff is regarded as a useful measure to improve oil recovery due to oil-water imbibition and drainage. Additionally, complex fracture networks consisting of natural fractures (NF) and hydraulic fractures can significantly enhance oil recovery in the process of water huff-n-puff after multi-stage hydraulic fracturing. However, there is a non-flowing thin film on the solid-liquid wall surface in the pore-throats of the matrix, and the so-called boundary layer effect (BLE) is quite significant at the nano-scale. This effect reduces the effective flow space and effective permeability of the reservoir, leading to production damage. To date, few numerical simulation studies have considered the impact of the BLE and complex fracture networks in water huff-n-puff process simulation studies. In this study, the process of water huff-n-puff is evaluated considering complex fracture networks and formation damage in a matrix. The embedded discrete fracture model (EDMF), validated by local grid refinement (LGR), is applied to describe the distribution of hydraulic fractures and NF. The well performance considering the BLE is analyzed by a vectorization programming. The results show that the BLE reduces production and accelerates the production decline, so the BLE should be considered in reservoir simulations and productivity evaluations of water huff-n-puff processes. A certain degree of natural fracture development is conducive to improving the sweep efficiency of the water huff-n-puff, which could significantly improve oil recovery compared to depletion. By considering the impact of the BLE in water huff-n-puff simulations in tight oil reservoirs, it is possible to accurately evaluate the well performance and provide a theoretical basis for the optimization of water huff-n-puff.

This paper firstly proposes a novel three-dimensional (3D) Green element method (GEM). We have proven it by theoretical error analysis that, the novel GEM with the third-order accuracy, has good convergence and stability, which are the advantages that previous GEMs do not have. This novel method is used to numerically simulate 3D core's counter-current imbibition process with gravity effect, and 1D, 2D and 3D models are implemented to depict good convergence and accuracy of proposed method. Compared with finite difference method (FDM) used by many previous studies, the novel method has the same advantage as previous GEMs, that it requires less elements to achieve a good agreement between simulation results and experiment data. Moreover, specific gravity effect is analyzed, and three typical stages of gravity effect are divided. In summary, the novel 3D GEM and corresponding 3D simulator are effective to simulate counter-current imbibition of the real 3D core considering the effect of gravity.

Based on mimetic Green element method (GEM), which synthesizes some typical advantages of boundary element method (BEM), finite element method (FEM) and mimetic finite difference method (mimetic FDM), This paper study the application of mimetic GEM in the system of partial differential equations (PDEs) of oil-water two-phase flow in porous media. It is the first time to apply GEM to solve numerically the system of PDEs, which is one of novelties in this paper. For numerical simulation of oil-water two-phase flow in porous media, this paper provides a novel numerical method based on mimetic GEM, which is the other novelty of this work.

In this study, we present an embedded discrete fracture model (EDFM) for an in-house reservoir simulator that incorporates the effect of each fracture with arbitrary orientations, lengths and fracture conductivities. Instead of using the linear flow approximation for the EDFM, the interflows between local matrix grids and fracture elements are derived using boundary element method, which considers the effect of local grid geometry and boundary pressure on the flow into the fracture. The implementation is generally compatible with existing finite-difference reservoir simulators, and the accuracy of the EDFM is validated by comparing the results of analytical/semi-analytical models for fracture flow, LGR modules for fracture flow in commercial reservoir simulators and complex fracture flow in discrete fracture network using finite element method. A grid-sensitivity study is conducted to show the convergence of the new method. Moreover, the cases of multiple bi-wing fractures and complex fracture systems are presented to demonstrate the robustness, applicability and computational convenience of the novice approach for simulating the fracture flow in anisotropic reservoir.

Green element method (GEM) is a numerical approach that combines boundary element method (BEM) and finite element method (FEM), which is effective to solve many physical problems, such as diffusion equation, heat transfer equation, etc. This paper proposes a novel GEM named mimetic GEM, which utilizes discrete flux operator derived from mimetic FDM to approximate boundary integral of the product of fundamental solution and edge-normal flux in GEM. Proposed mimetic GEM is indeed a novel numerical method mixing the ideas of BEM, FEM, and mimetic FDM, which The method synthesizes some typical advantages of traditional numerical methods, that has a semi-analytical accuracy same as BEM. The method can be adaptive to unstructured grid same as FEM, and has a good convergence same as FDM.

In this study, we present a hybrid model coupled with two-set nodes Green element method (GEM) and embedded discrete fracture model (EDFM) for capturing the effect of transient flow in inhomogeneous fractured porous media. GEM is an excellent advanced algorithm, which can solve nonlinear problems in heterogeneous media. That is also an obvious advantage of GEM against the original boundary element method (BEM). The novel GEM has double nodes of pressure and flux and it is an improvement of classical GEM, which has a second-order precision and fits for triangle structured grids. In the place of adopting the linear flow approximation for original EDFM, the interflows between local triangle matrix grids and fracture elements are derived using the novel GEM, which has higher accuracy than those in previous EDFMs. Consequently, the modified hybrid model can indeed calculate the pressure and flux distribution of transient flow in multifracture porous media. Three numerical cases are presented to show the practicability of our novel model which include (i) multistage fractured horizontal well, (ii) heterogeneous fractured porous media, and (iii) complex fracture networks (CFNs) in an unconventional reservoir.

Most of the mature oilfields are on the verge of being abandoned. Drilling infill wells or chemical displacement is a standard method to improve mature oilfield performance. But these methods are not economical. For the sustainable and economic development of mature oilfields, large displacement natural water flooding was applied for improving mature oilfield performance. After high-intensity water flooding, most of the mature oilfields are in high water-cut and high recovery stages, and it is difficult for performance prediction. In this study, the displacement flux (P.A.), was applied to characterize the scouring intensity. Two types of relative permeability curves were obtained through high-intensity waterflooding (HIWF) experiments, including one type of continuous relative permeability curve of different displacement fluxes and the second type of multiple relative permeability curves of different displacement fluxes under re-saturated conditions. In addition, a two-dimensional five-point pattern model was established to compare the calculation results. Finally, a numerical model of a real reservoir in a mature oilfield was generated to test the method. The results demonstrate that using the type I relative permeability curve is fast and accurate to characterize the performance of the high water cut stage for sustainable development.

In recent years, greenhouse gases have increased in the atmosphere, and climate change concerns have triggered global efforts to find solutions for CO2 capture, separation, transport, and storage. Geological sequestration in the depleted unconventional reservoir is an effective measure to reduce the atmosphere’s CO2 content. The exact evaluation of the CO2 storage capacity can verify the feasibility of storing carbon dioxide and parameter optimization. A reasonable boundary element method to estimating the CO2 storage capacity of depleted shale gas reservoirs considering arbitrarily shaped boundaries is introduced. Firstly, the physical model with fracture networks is built based on the microseismic data. Then, the flow equation including the matrix and fracture can be obtained considering adsorption, and the star-delta transformation is used to deal with interconnected fracture segments. The point source function with an infinite boundary can be obtained after the Laplace transform method. Finally, the semianalytical flow solution is obtained by using the boundary element method in the Laplace region. Moreover, the results have a high agreement with commercial software for the regular boundary. The sensitivity of relevant parameters is analyzed by this method, and the importance of considering the boundary shape is emphasized. This method can evaluate the CO2 storage capacity of formation with the irregular boundary and is regarded as the guide of parameter optimization in CO2 storage.

This paper pointed out that the simulation accuracy of original embedded discrete fracture model (EDFM) during early-time production of multi-stage fractured horizontal well is low due to the linear pressure distribution assumption in matrix cells containing fracture cells. To resolve the above limitation of original EDFM, a modified EDFM is presented by adding multi-layer virtual cells adjacent and parallel to fracture cells and changing the connections between cells. This modified EDFM can make the same function like LGR technique, and does not bring any complexity to pre-processing algorithm of EDFM, especially for its 3D implementations. A test case and an application example for complex fracture network are implemented to verify that this modified EDFM can significantly improve the early-time simulation accuracy to greatly eliminate the errors of the original EDFM.

As an important technology in improving oil recovery, CO2 miscible flooding has achieved great success in many oil fields. However, studies on CO2 transport in porous media are mostly based on equilibrium adsorption in one-dimensional displacement where rate-controlled adsorption is not taken into consideration. In this work, we develop a radial convection–dispersion model, which simultaneously combines rate-controlled adsorption, convection, and dispersion. Based on this model, four dimensionless groups representing CO2 dispersion, adsorption capacity, flow rate, and kinetic rate groups are proposed for the first time. Subsequently, the Barakat–Clark forward and backward difference methods are combined to solve the mathematical model. CO2 concentration and adsorption at different positions in the porous media (including the effluent concentration and adsorption histories) are then calculated. Furthermore, the effects of the parameters on CO2 transport behavior are studied in detail. The results reveal that CO2 gradually moves forward with the increase in the CO2 injection volume. Once CO2 reaches a certain position, its concentration there increases and an S-shaped curve is formed. Moreover, the adsorption capacity at this position also increases significantly, and the changing rate is much higher than CO2 concentration. CO2 effluent concentration grows more uniform, and the breakthrough occurs earlier with increased dispersion velocity and CO2 injection rate and decreased adsorption capacity and adsorption rate. The mathematical model developed in this study is of great importance in predicting CO2 transport behavior in radial miscible flooding.

This paper proposes a novel green element method (GEM) by mixing the idea of finite difference method (FDM). In the novel method, We come to the original formula when boundary integral equation is applied to an element, and use difference quotient of the central nodal value on two sides of the shared edge of adjoining elements to approximate the boundary integration ∫ΓG∇p · nds. This treatment is similar to FDM, and the integral operator relevant to element size controls the estimated error. The novel GEM makes the numerical solution correspond to the actual physical meaning, and the coefficient matrix of the global matrix is a banded sparse matrix with larger bandwidth than previous GEMs. Meanwhile, the instability of the original GEM is illuminated. We have proven it by theoretical error analysis and five numerical examples that, the accuracy of the novel GEM is three-order higher than the original GEM, and the novel GEM has a good convergence and stability, which is the property that the original GEM does not have. Indeed, the novel GEM proposed in this paper is essentially a new numerical method mixed with the idea of boundary element method (BEM), finite element method (FEM), and FDM. In contrast with BEM, FEM, FDM and previous GEM, the characteristics of our novel GEM include: (i) Compared with FEM and FDM, the novel GEM has the accuracy of BEM and can better accord with material balance. (ii) Compared with BEM, the novel GEM can solve nonlinear problems with heterogeneous media, which are hard to be handled by BEM. (iii) Compared with previous GEMs, the novel GEM has a three-order accuracy, and has a better convergence that the calculation error can be well controlled by the element size.

This paper presented a novel Green element method (GEM) based on two sets of nodes, one of which contains all vertices of the polygon representing the value of the pressure, called pressure nodes, the other contains all midpoints of the edges of the polygon representing the value of the normal flux, called flux nodes. The novel method considers both the pressure and the normal flux explicitly, and utilizes the physical fact that, the algebraic sum of normal fluxes at the flux nodes which are on the edge shared by adjacent elements is zero. Therefore, the normal flux term at each internal flux node can be offset in the final global equations, and the order of the global coefficient matrix is only the number of pressure nodes. Compared to previous GEMs, the novel method has actual second-order accuracy. Moreover, because we selected the flux node at the midpoints of edges, the novel method made the solution process more in accordance with physical meaning, and the numerical solution has a better continuity in the computational domain than previous GEMs. It is worth mentioning that, to the authors’ knowledge, this is the first time to utilize two sets of nodes when estimating the numerical solution to the problem described by only one differential equation. Therefore, the novel method may bring new ideas to other numerical methods, such as finite difference or finite element method, etc.

The large uncertainty in fracture characterization for shale gas reservoirs seriously affects the confidence in making forecasts, fracturing design, and taking recovery enhancement measures. It is of significance to make the most of multiple data in fracture characterization, including the measurements of hydraulic fracturing treatment, core, microseismic, production data, etc. Besides, handling the complex fracture networks (CFNs) explicitly is demanded in large-scale field case studies. This paper presents an efficient method to characterize the complex fracture networks (CFNs) and reduce the uncertainties by integrating stochastic CFNs modeling, reservoir simulation, and assisted history matching. In CFNs modeling, the geometry of CFNs is generated stochastically constrained by the measurements of hydraulic fracturing treatment, core, and microseismic data, and a stochastic parameterization model is used to generate an ensemble of initial realizations of the stress-dependent fracture conductivities. To efficiently simulate the discrete fractures in field cases, the edge-based Green Element Method (eGEM) is modified by applying a steady-state fundamental solution and the technique of local grid refinement (LGR). Assisted-history-matching based on EnKF is implemented to calibrate the CFNs models and further quantify the uncertainties. The proposed method is applied to a field case from a multi-fractured horizontal shale gas well. The results show that the computation of the modified eGEM is much cheaper than the original eGEM when the steady-state fundamental solution and the technique of LGR are applied. Besides, acceptable precision can be obtained with relative coarse grids, for example, 50 m primary grids and 25 m refined grids near the fractures can be used in the test case. These advantages make the modified eGEM quite efficient in assisted history matching of large-scale field applications. The history matching results and EUR distributions show that the uncertainties are significantly reduced after 5 steps assimilation, and good results can be obtained after 10 steps assimilation. The distribution ranges of the matrix permeability and porosity are significantly narrowed down after history matching, while the matrix compressibility is hard to be determined because the rock compressibility is so small comparing to gas compressibility that gas production is not sensitive to it. The results also show that only part of the fractures are well-propped because only the fractures in a certain range of the wellbore are with good properties, that is high initial fracture conductivities and low conductivity moduli.

The temperature of the fluids injected is usually cooler than the in-situ reservoir temperature in the fractured reservoir's development. It is essential to study thermal changes between matrix and fracture. This paper establishes a fully implicit solution model for the coupling of the oil-water two-phase temperature field and seepage field based on the embedded discrete fracture model (EDFM) method. We deduced the mass and heat transfer between the local matrix grid and the fracture grid by the boundary element method (BEM) instead of a simple linear hypothesis to improve the traditional EDFM method. The model can accurately calculate the seepage field and temperature field in the two-dimensional or three-dimensional problem. Compared with the analytical solution, the discrete fracture model (DFM) and the traditional EDFM method proved that the modified EDFM method could significantly improve the calculation accuracy(especially the temperature field). Furthermore, the modified EDFM method is applied to four examples: waterflooding, huff and puff development, heterogeneous and natural fractured reservoirs, and multilayer enhanced geothermal system (EGS), which verifies the applicability, robustness, and computational convenience, of the new method and illustrates the influence and necessity of considering the coupling effect of temperature field and seepage field on the development effect. It provides an efficient and accurate new method for the study of non-isothermal seepage in fractured reservoirs.

This paper provides a comprehensive model for the flow behavior of a two-zone system with discrete fracture network. The discrete fracture network within the inner zone is represented explicitly by fracture segments. The Laplace-transform finite-difference method is used to numerically model discrete fracture network flow, with sufficient flexibility to consider arbitrary fracture geometries and conductivity distributions. Boundary-element method and line-source functions in the Laplace domain are employed to derive a semi-analytical flow solution for the two-zone system. By imposing the continuity of flux and pressure on discrete fracture surfaces, the semi-analytical two-zone system flow model and the numerical fracture flow model are coupled dynamically. The main advantage of the approach occurring in the Laplace domain is that simulation can be done with nodes only for discrete fractures and elements for boundaries and at predetermined, discrete times. Thus, stability and convergence problems caused by time discretization are avoided and the burden of gridding and computation is decreased without loss of important fracture characteristics. The model is validated by comparison with the results from an analytical solution and a fully numerical solution. Flow regime analysis shows that a two-zone system with discrete fracture network may develop six flow regimes: fracture linear flow, bilinear flow, inner zone linear flow, inner zone pseudosteady-state flow, outer zone pseudoradial flow and outer zone boundary-dominated flow. Especially, local solutions for the inner-zone linear flow have the same form with that of a finite conductivity planar fracture and can be correlated with the total length of discrete fractures and an intercept term. In the inner zone pseudosteady-state flow period, the discrete fractures, along with the boundary of the inner zone, will act as virtual closed boundaries, due to the pressure interference caused by fracture network and the mobility contrast of the two zones. The dimensionless fracture conductivity of the fracture network determines the characteristics of the bilinear flow and the inner zone linear flow. The mobility ratio, M, and storability ratio, Fs, primarily influence the flow behavior of the middle to later time. For a larger M, the ending time of the inner zone pseudosteady-state flow will be advanced and the beginning time of the outer-zone pseudoradial flow will be delayed. And the larger M also results in increasing of the values of the transient responses in these two periods. Duration of the outer-zone pseudoradial flow becomes longer, as Fs increases; the development of the outer-zone boundary-dominated flow is therefore postponed. Finally, idealization of dual-porosity model for the two zones will introduce two dips on the pressure derivatives on the log/log plot. Depending on the interporosity flow parameter, the time of the two dips varies. However, the dips are not very appreciable for the transient dual-porosity model, when the permeability of matrix system or fracture density is relatively high.

Summary In a multiwell pad, the chance of interwell communication increases because of the creation of primary and secondary fractures during hydraulic-fracture stimulation. The flow behavior associated with communicating wells is significantly different from that of a single isolated well, because of interplay of flow caused by the interconnected fractures, complex connections, and multiple production conditions. The main purpose of this paper is to develop a rigorous and efficient flow model and quantify flow characteristics of multiple pad wells communicating through primary and secondary fractures. In the model, matrix and primary- and secondary-fracture flows are captured. Fractures are explicitly represented by discrete segments. The Laplace-transform finite-difference (LTFD) method is used to numerically model fracture flow, with sufficient flexibility to consider arbitrary fracture geometries and fracture-conductivity distributions. The analytical matrix-flow model, derived with the line-source function in the Laplace domain, is dynamically coupled with the fracture-flow model, by imposing the continuity of pressure and flux on the fracture surface. Thus, a hybrid model in the Laplace domain is constructed. The main advantage of the solution occurring in Laplace domain is that computations can be performed at predetermined, discrete times, and with grids only for fractures. Thus, stability and convergence problems caused by time discretization are avoided, and the burden of gridding and computation is decreased without loss of important fracture characteristics. The model is validated through comparison with a fully numerical simulator and a semi-analytical model. Detailed flow-regime analysis reveals that pressure interference caused by communication significantly alters the flow signature compared with single (isolated) wells. Before interference, the communicating wells behave as single isolated wells, and will exhibit a fracture linear-flow period and possibly even a matrix linear-flow period. After interference, the flow behavior of the system will vary largely with different production strategies. When the communicating wells all operate under the constant-rate condition, the transient responses of the wells will gradually merge to develop another matrix linear-flow period. If the wells are operated under the constant-bottomhole-pressure (BHP) conditions, the response deviation caused by interference will increase with production; therefore, one of the wells will undergo a rate loss. The results of a sensitivity analysis for a two-well system demonstrate that the time to well interference is primarily determined by secondary-fracture conductivity, number of connections, and communicating-well operating conditions. With larger contrasts in these properties, interference time is accelerated. However, for different production strategies, the effects on the flow behavior after interference are variable.

During the water driving process in reservoir which has complex fracture networks, water flows in the fractures and matrix blocks are surrounded by fractures, under this circumstance, spontaneous counter-current imbibition is the dominant mechanism for oil recovery. Therefore, modelling the counter-current behavior properly is such essential when evaluate the production performance of fractured reservoir that contains large amount of water. In this paper, the Radical Integral Boundary Element Method(RIBEM) is firstly introduced to simulate spontaneous counter-current imbibition process, this method successfully transforms the governing equation of counter-current imbibition into the complete boundary integral form and thus the boundary element method can be applied to calculate counter-current imbibition rate, the core advantage of this method is that RIBEM can achieve acceptable results without the need to divid the matrix block into many subgrids, which is convinient for application and reducing a lot computational burden. The validation of RIBEM is tested both on core and field scale, simulated results are in good agreement with corresponding experiment and fine grid simulation data.

As throat radius decrease to micro-nanoscale, seepage in unconventional reservoirs such as ultra-low permeability and tight reservoirs differs from conventional ones. Flow experiment in micropores is a promising approach to study characteristics of microflow. In this paper, a visual experimental device was established. Water flow through micropores with radius of 1.38–10.03 $$\upmu \hbox {m}$$ was investigated, under 0.033–16 MPa/m. The results showed that in microscale, water flow did not agree with Poiseuille equation. Flow rate was lower than theoretical value and showed nonlinear characteristics. In the near wall area, due to the attraction of solid wall, a stagnant fluid layer was formed. It occupied flow space and thus lowered flow rate. Its thickness declined with pressure gradient increasing, which led to nonlinear flow characteristics. When the pressure gradient was very high, the thickness stopped declining and kept constant. Afterward, the flow transited to linear. In pores with smaller radius, the steady stagnant layer was thinner, but took a larger proportion of the flow space. For tubes of $$r = 1.38, 4.81, 10.03\,\upmu \hbox {m}$$ , the thickness of steady stagnant layer was 0.11, 0.23, 0.27 $$\upmu \hbox {m}$$ , respectively.