Wellbore Storage Research Articles

New Analytical Solutions for Constant Rate Pumping in Two‐Zone Double‐Porosity Confined Aquifer: A New Source Term Reflecting Effects of Well Skin and Wellbore Storage

AbstractThis study develops two new analytical models for constant rate pumping at a partially penetrating well in a double‐porosity confined aquifer, considering skin and formation zones. One model, referred to as the two‐zone model, incorporates a flow equation to depict the flow in the skin around the well. The other model, named the source‐term model, introduces a novel source term at the outer rim of the skin to reflect the effects of both the skin and wellbore storage. The analytical solutions for both models are derived by the Laplace transform and finite Fourier cosine transform. Additionally, a finite element solution for the source‐term model is presented. Results suggest the source‐term model is suitable to most wells when the width of the skin is less than 1 m and the radius of influence exceeds the outer rim of the skin. Temporal drawdown distribution for a negative skin exhibits a triple‐humped shape with two flat stages, while that for a positive skin shows monotonous increase. The source‐term model enables orthogonal 5 × 5 nodes for finite element approximation to discretize a well and its adjacent skin. The finite element solution aligns with early drawdown data measured at an observation well under the effects observed in two field constant rate pumping tests. In conclusion, this study introduces a novel approach to modeling two‐zone flow, which may find practical utility in field applications.

Multiphase flow analysis of complex wellbore–fracture–cave connections in condensate gas reservoirs

The significant heterogeneity of fracture-caved gas reservoirs and the phase transition behavior with pressure depletion pose great challenges for flow behavior analysis and property estimation. Therefore, the objective of this paper is to develop robust and novel pressure transient analysis models for condensate-gas flow under pressure depletion in fracture-caved gas reservoirs. To characterize the complex connections between wellbore, fracture region, and caves, four conceptual models of wellbore–fracture–cave distributions are determined. The fracture region is considered as a dynamic three-zone (dry gas zone, condensate-gas two-phase zone, and transition zone) to characterize the phase transition during pressure depletion, while a variable storage concept is introduced to describe the phase transition in the wellbore and caves. The results indicate that six typical flow stages can be observed from the type curves: constant wellbore storage flow, variable wellbore storage flow, fracture linear flow (FLS), constant cave storage flow, variable cave storage flow, and transition flow. Moreover, the phase transition behavior in the fracture region is reflected in the changes of one-half slope straight lines during the FLS period, while the phase transition behavior in the wellbore and caves is reflected in the pressure derivative curve as a positive upward bending of the straight line with unit slope at later stage. The property estimation in the fracture-caved gas reservoirs (i.e., length and permeability of the fracture region, the storage coefficient of wellbore and cave) by matching with the actual pressure monitoring data provides a better understanding of the geological evidence.

Evaluation of near wellbore damaged conditions with an injection - falloff tests during transient flow regime in clastic hydrocarbon reservoir

Low or near zero daily oil production from a well below its potential is undesirable and should be addressed. This problem is caused by permeability reduction or impairments in the vicinity of a wellbore and could be due to one or combinations of the following factors; mud filtrate invasion, fines redeposition due to production, microbial growth, fracturing fluid, and enhanced chemical processes. The extent of this problem has to be quantitatively evaluated, using a skin factor, before an appropriate solution can be developed. A set of secondary data was simulated with a commercial software package, for a reservoir undergoing transient flow condition acting infinitely. A water injection well, fully perforated, is placed at the centre of an infinite-acting reservoir, for constant water injection. The wellbore radius of 0.5 ft fully penetrated the entire length of 190 ft, and injected water at 250 bbls per day, with water viscosities of 0.8 cP to 1.2 cP, continuously for 4 days. Water injection pressure stabilized at 1300 psi. Analysis of both injectivity and falloff were performed with an initial assumption of zero wellbore storage effects to evaluate formation permeability and skin factor, S. The result showed that skin factor increases with decreasing water viscosities. At water viscosity of 0.8 cP to 1.2 cP, a constant value of skin factor was obtained. An S value of +0.09 indicated that the near wellbore environment is slightly damaged. Therefore, it requires light acidization.

Pressure Transient and Production Analysis of Fractured Vertical Wells in Tight Sand Gas Reservoirs Considering Threshold Pressure Gradient, Phase-Change Phenomenon, and Stress Sensitivity

The productivity and pressure response of the tight sand gas wells are influenced by multiple flow mechanisms, such as threshold pressure gradient, phase-change phenomena, and stress sensitivity. Understanding the sensitivity of these factors is crucial for the effective development of tight sand gas reservoirs. This study aims to clarify the sensitivity of various factors affecting the productivity and pressure response of tight sand gas wells. Based on the percolation theory of tight sand gas reservoirs, we considered stress sensitivity, threshold pressure gradient, and phase-change phenomena to derive an unsteady mathematical model of a fractured well with an infinite boundary, and a point source solution was obtained. The proposed model was solved using series function properties, variable substitution, perturbation technique, Poisson superposition formula, Laplace transform, and numerical inversion. The influence of several important parameters on pressure response and productivity is discussed in detail. The results show that the threshold pressure gradient, stress sensitivity, and skin factor significantly impact gas well production and pressure response, while the wellbore storage effect and phase-change effect primarily affect the initial production and pressure response, having little effect on the cumulative gas production. The proposed model can estimate the influence of the threshold pressure gradient and stress sensitivity on productivity and pressure, providing a guide for the development of technical measures for fractured wells in tight sand gas reservoirs.

Applications of Asymptotic Solutions of the Diffusivity Equation to Infinite Acting Pressure Transient Analysis

Summary Understanding how pressure propagates in a reservoir is fundamental to the interpretation of pressure and rate transient measurements at a well. Unconventional reservoirs provide unique technical challenges as the simple geometries and flow regimes [wellbore storage (WBS) and radial, linear, spherical, and boundary-dominated flow] applied in well test analysis are now replaced by nonideal flow patterns due to complex multistage fracture completions, nonplanar fractures, and the interaction of flow with the reservoir heterogeneity. In this paper, we introduce an asymptotic solution technique for the diffusivity equation applied to pressure transient analysis (PTA), in which the 3D depletion geometry is mapped to an equivalent 1D streamtube. This allows the potentially complex pressure depletion geometry within the reservoir to be treated as the primary unknown in an interpretation, compared with the usual method of interpretation in which the depletion geometry is assumed and parameters of the formation and well are the unknown properties. The construction is based upon the solution to the Eikonal equation, derived from the diffusivity equation in heterogeneous reservoirs. We develop a Green’s function that provides analytic solutions to the pressure transient equations for which the geometry of the flow pattern is abstracted from the transient solution. The analytic formulation provides an explicit solution for many well test pressure transient characteristics such as the well test semi-log pressure derivative (WTD), the depth of investigation (DOI), and the stabilized zone (SZ) (or dynamic drainage area), with new definitions for the limit of detectability (LOD), the transient drainage volume, and the pseudosteady-state (PSS) limit. Generalizations of the Green’s function approach to bounded reservoirs are possible (Wang et al. 2017) but are beyond the scope of the current study. We validate our approach against well-known PTA solutions solved using the Laplace transform, including pressure transients with WBS and skin. Our study concludes with a discussion of applications to unconventional reservoir performance analysis for which reference solutions do not otherwise exist.

How borehole wall elasticity affects wellbore storage capacity in periodic hydraulic tests

Characterizing fluid transport and pore pressure diffusion is key for monitoring and understanding many natural (e.g., seismically active zones and volcanic systems) and engineered environments (e.g., enhanced geothermal reservoirs and CO2 underground storage). Borehole hydraulic testing allows for inferring relevant properties of the probed subsurface volume, such as, for example, its transmissivity and diffusivity, assessing the governing flow regime as well as detecting the presence of hydraulic boundaries. Periodic hydraulic tests (PHT) achieve these objectives using an oscillatory fluid injection procedure while measuring the fluid pressure response in monitoring boreholes. The relevant information on the pressure diffusion process occurring in a probed formation is retrieved from the phase shifts and amplitude ratios between the flow rate and the interval pressure. In general, the interpretation of PHT data relies on the assumption that the pressure diffusion process is largely unaffected by the deformation of the probed rock volume. To assess this assumption, we present a conceptual PHT model based on the theory of poroelasticity to investigate the role played by hydromechanical coupling (HMC) effects during PHT and to assess whether and to what extent additional mechanical information can be extracted from these tests. These effects include the influence of the borehole wall deformation on the wellbore storage coefficient Sw, which quantifies the difference between the injected flow rates and those actually entering the porous formation. We show that, in homogeneous formations, the commonly taken approach based on the uncoupled diffusion solution for radial flow reproduces the results of our HMC model. However, neglecting the deformation effect of the borehole wall on the storage capacity of the system during injection can lead to underestimations of both transmissivity and diffusivity, particularly at shorter oscillation periods. We present analytical expressions for the borehole wall deformation contribution to Sw, which depends on the shear modulus and does not change with the oscillatory period. We show that it is possible to obtain the effective Sw along with the transmissivity and diffusivity using observations at various oscillatory periods. In the presence of hydraulic boundaries, such as no-flow or constant-pressure boundaries, at a given distance from the injection borehole, Sw becomes period-dependent, introducing apparent variations in the inferred shear modulus of the formation if the associated HMC effects are not accounted for. Our results thus highlight the importance of accounting for HMC effects in PHT data interpretation, not only to reliably and accurately characterize and monitor hydraulic properties but also to fully exploit the potential of PHT to provide additional information on the mechanical behavior of the probed rock volume.

A three-dimensional numerical well-test model for pressure transient analysis in fractured horizontal wells with secondary fractures

During oil and gas reservoir development, multi-stage horizontal wells (MFHWs) and hydraulic fracturing techniques can effectively increase estimated ultimate recovery. However, there still lacks an understanding of the three-dimensional (3D) pressure transient behaviors of multi-stage fractured horizontal wells with secondary fractures. To narrow this gap, a three-dimensional numerical well-test model based on a discrete fracture model and unstructured tetrahedral grids is developed to study the pressure transient behaviors of MFHWs with secondary fractures. The pressure transient solutions of MFHWs with secondary fractures have been demonstrated by model verifications. The results show that the proposed model can accurately capture the complex transient flow around fractures, including early radial flow that is not easily captured by two-dimensional numerical well test models. The proposed model classifies the flow regimes of a MFHW as: wellbore storage and skin effects, early radial flow, bilinear flow, linear flow, elliptical flow, pseudo radial flow, and pseudo-boundary dominated flow. It is found that the fracture geometry has a relatively large effect on the shape of the pressure derivative curve in this work. The hydraulic fracture half-length has the greatest impact on the pressure transient behaviors of the MFHW, followed by fracture height and secondary fracture half-length, as found in this study. Additionally, fracture parameters are evaluated, and actual well testing data are interpreted, taking into account the fracture height. This work is meaningful to understand the three-dimensional pressure transient behaviors of MFHWs with secondary fractures.

A dual-reciprocity boundary element method based transient seepage model with nonlinear distributed point source dual-porosity gas reservoir

As a result of advancements in gas reservoir development technologies and a deeper understanding of seepage theory, numerous nonlinear seepage problems have emerged. Consequently, conventional analytical solution models are no longer applicable. Moreover, existing semi-analytical and numerical solution models suffer from issues like high computational complexity and limited flexibility, significantly constraining their practical utility. For this purpose, a gas reservoir transient seepage model is established based on the dual-reciprocity boundary element method (DRBEM). This model couples the wellbore storage coefficients with skin factor and introduces a novel dual-porosity transient interporosity seepage algorithm, enabling the resolution of transient seepage problems in dual-porosity gas reservoirs with nonlinear point source distributions. Additionally, it investigates the dynamic behavior of bottomhole pressure during the early production stage of gas wells, while capturing the dynamic pressure distribution within the seepage field. This approach offers the advantages of semi-analyticity, meshless, and eliminates the need for Laplace transforms, resulting in a significant reduction in computational complexity. Ultimately, the application of our model to well-pattern production with the production system transition issues, in conjunction with the log-log type curves of bottomhole pressure, and the dynamics of gas reservoir pressure, enables the analysis of interference characteristics between injection-production wells. This showcases the practical advantages of the model's application. The findings of this study provide valuable assistance for modeling and solving transient seepage problems in dual-porosity oil and gas reservoirs production. The application of DRBEM in unsteady-state diffusion, heat conduction, stress fields, and other potential field problems is relevant for reference.

Analysis of Field Data Using Microsoft Excel and MATLAB Software to Evaluate Reservoir and Well Damage

Reservoir formation damage is a drop in a well's productivity caused by a decrease in reservoir rock permeability. To tackle this issue and maximize well production, obtained pressure build-up time data at a steady production rate from a vertical producing oil WELL 20A, was analysed to establish the wellbore and reservoir characteristics. A numerical well test simulator (Matlab) is used to simulate damage in the area close to the wellbore, a Microsoft Excel sheet and an analytical approach to calculate the impact of wellbore and reservoir factors such as skin, wellbore storage, and average reservoir permeability. In order to determine whether the numerical well test simulator was successful at performing pressure transient analysis on observed data, the findings from the analytical solutions using Microsoft Excel Sheet and numerical well test simulator Matlab were compared. Comparable outcomes for the permeability and skin values were obtained from the build-up test data analysis generated; hence, the negative skin values for wells 20A acquired after the analysis suggest that the formation is not damaged. This indicate that well 20A is not a candidate for workover operations.

A novel four phase slug single-well push–pull test with regional flux: forward modeling and parameter estimation

The single-well push–pull (SWPP) test has been widely used for several applications, including determination of transport parameters such as regional groundwater flux velocity, effective porosity and dispersivity. A complete SWPP test usually includes four phases of injection, chase, rest, and extraction, while previous models mostly ignore the chase phase for the sake of simplification. Actually, the chase phase is important to minimize the impact of well skins and wellbore storage on the shape of the breakthrough curves (BTCs), thus is necessary and should be included in the model. To this end, two simplified methods are proposed in this study based on two different time tp and ta during a four-phase SWPP test to estimate the parameters related to transport, where tp and ta correspond to the time of the peak concentration during the injection phase and the time when the center of tracer mass returns to the wellbore during the extraction phase, respectively. Specifically, the tp method can be used to estimate the regional groundwater flow velocity and dispersivity (transverse and longitudinal), while the ta method is used to estimate the regional groundwater flow velocity and the effective porosity. Finite-element numerical modeling of the SWPP test based on the coupling of two-dimensional transient groundwater flow and solute transport is employed to test the applicability of the proposed methods. Results indicate that both the tp and ta methods proposed in this study perform satisfactorily in estimation of regional groundwater flow velocity, effective porosity and dispersivity, and these two methods require fewer observations than traditional curve fitting methods and do not require any optimization algorithms. We have also compared the proposed two methods with several previous methods, and conclude that these two new methods generally perform better than those of previous studies in terms of parameter estimation reliability.

Multiphysics Modeling Investigation of Wellbore Storage Effect and Non‐Darcy Flow

AbstractThis study presents a comprehensive investigation of wellbore storage effects and non‐Darcy flow in pumping well systems using a multiphysics numerical model. The model incorporates the Reynolds‐averaged Navier‐Stokes equations coupled with a moving free surface to simulate the flow field and drawdown in the wellbore. Hydraulic behavior of the system, including well and aquifer drawdown, pumped water ratio, aquifer flow nonlinearity, and wellbore flow field, is analyzed and compared with simplified 1‐D models. This study highlights the presence of a vortex in the wellbore flow field induced by large Reynolds number and the uneven stress distribution at the screen. This vortex influences the wellbore drawdown and introduces 2‐D flow in the surrounding aquifer, which further contributes to the longer travel paths for groundwater particles and increased hydraulic pressure consumption. The results show that non‐Darcy flow, coupled with wellbore storage effects, leads to higher drawdown in the pumping well compared to Darcy flow cases. The aquifer drawdown exhibits a similar temporal pattern but with decreasing deviation at larger distances due to the cone of depression. The pumped water ratio indicates the challenge of supplying outflow at the intake from aquifer storage, with nonlinear flow resulting in a smaller ratio compared to linear cases. A nonlinearity ratio is defined to illustrate the expansion of nonlinear flow regions over time, their convergence to a predictable quasi‐steady‐state shape, which is influenced by the Forchheimer parameter, and the gradual transition to Darcy flow away from the wellbore.

Well-Testing Model for Dual-Porosity Reservoir considering Stress-Sensitivity and Elastic Outer Boundary Condition

Stress sensitivity and the elastic outer boundary (EOB) condition have a great effect on the analysis of the characteristics of the fluid flow in a reservoir. When researchers analyzed the characteristics of the fluid flow, they have considered the stress sensitivity and the EOB condition separately but have not considered them simultaneously. Therefore, errors are inevitable during the analysis of well testing. The main object of this work is to present a well-testing model for stress-sensitivity dual-porosity reservoir (DPR) with EOB to improve the accuracy of the analysis of well-testing data. To this end, in this paper, we established a well-testing model for the DPR, considering the stress sensitivity and the EOB simultaneously, and presented its semianalytical solution. On the basis of the consideration of the EOB condition and stress sensitivity of permeability (SSP), a seepage model for the DPR with the EOB is built using the continuity equation, motion equation, state equation, and interporosity flow equation between matrix and fracture, which considers the stress sensitivity, wellbore storage, and skin. To solve this model, a nonlinear partial differential equation is changed into a linear form of a partial differential equation by introducing an effective well radius and applying Pedrosa’s transformation and perturbation transformation. Applying the Laplace transformation, an analytical solution in the Laplace space is obtained, and curves of pressure and pressure derivative (PPD) are drawn by numerically inverting them. The model is verified by comparing it with the EOB without consideration of SSP and using case data. The sensitivity of parameters on the curves of PPD is analyzed. This work may be significant for evaluating more accurately the parameters of wells and reservoirs using well testing.

Effect of leakage on confined non-darcian aquifer considering storage in semipervious layers

A set of analytical solutions have been presented for non-Darcian flow to a well in a leaky confined aquifer system considering leakage from the storage of semipervious layers/adjacent aquifer lying above and below the main aquifer. Flow in the main aquifer has been assumed to be non-Darcian and horizontal, whereas flow in the semipervious layers is assumed to be Darcian and vertical. The Izbash equation has been employed to describe the non-Darcian flow. Six general cases have been considered with/without wellbore storage and different adjacent aquifer conditions. Analytical solutions under unsteady and steady-state conditions have been obtained in the Laplace domain. Talbot method has been utilized for numerical inversion Laplace domain solution to the actual solution domain. The obtained analytical solutions clearly quantifies the effect of storage.

Develop an empirical flow rate correlation to model wellbore storage phenomenon for wells produced at a constant wellhead pressure

Well-test operation with a constant flow rate for long-time production is not typical in practice. Therefore, reservoirs frequently produce fluids with constant pressure at the wellhead, into a constant pressure separator or pipeline. During the production under this condition, the pressure drop at the wellbore varies as a function of the rate because of changes in the friction flow; therefore, the wellbore formation pressure is not constant. As a consequence, the wellbore storage effect emerges and should be incorporated in the modeling of fluid flow under production at a constant wellhead pressure. All available methods considering the wellbore storage effect can merely be applied for production under the constant rate condition. Moreover, well-test modeling under these circumstances needs a specific function for production rate, which made this type of well-testing less common. Even though there are exact solutions for production under the constant wellbore pressure in the Laplace domain, their inverse transform is quite complex and cannot be applied for modeling the wellbore storage effect. In this study, a new function is introduced as an approximate solution of the diffusivity equation, for a well that produces at a constant wellbore pressure, using multiple steps of the optimization process. Consequently, an efficient correlation is developed for flow rate about or concerning this condition. Next, the effect of the wellbore storage at constant pressure well-test operation was enumerated for the first time, which was commonly neglected in previous studies. This endeavor concentrated on modeling the two types of well-test operation, producing at constant wellhead pressure and, pressure build-up following the production at a constant wellhead pressure (constant pressure Build-up test). The results were also verified with numerical simulation as well as field data further confirming the excellent accuracy of developed solutions.

Models and Interpretation Methods for Single-Hole Flowmeter Experiments

Subsurface and groundwater flow characterization is of great importance for various environmental applications, such as the dispersion of contaminants and their remediation. For single-hole flowmeter measurements, key characteristics, such as wellbore storage, skin factor heterogeneities, and variable pumping and aquifer flow rates, have a strong impact on the system characterization, whereas they are not fully considered in existing models and interpretation methods. In this study, we develop a new semi-analytical solution that considers all these characteristics in a physics-based consistent manner. We also present two new interpretation methods, the Double Flowmeter Test with Transient Flow rate (DFTTF) and the Transient Flow rate Flowmeter Test (TFFT), for interpreting data collected during single and multiple pumping tests, respectively. These solution and methods are used as follows. (i) The impact of wellbore storage, transient pumping rate, and property heterogeneities on the interpretation of data collected during single pumping tests are studied over 49 two-aquifer cases. (ii) The effect of the skin factor heterogeneity on transmissivity and storativity estimates, as well as the variability range of the (non-unique) corresponding solutions, are analyzed for the interpretation of multiple-pumping experiments. The results presented in this work show the importance of the various properties and processes that are considered, and the need for the new models and methods that are provided.

Pressure-Transient Behavior of Vertical Wells Considering Dynamic Water Hammer and Dynamic Induced Fracture: Theory and Case Studies.

Water injection can result in the creation of induced fracture by connecting natural fractures. The induced fracture penetrates the entire reservoir, leading to the interconnection of injection and production wells and ultimately resulting in water breakthrough and the abandonment of production wells. During well work, the induced fracture exhibits dynamic behavior characterized by extension and closure, known as the dynamic-induced fracture phenomena. During the shut-in process, fracture closure phenomena are often accompanied by water hammer phenomena, which can be detected bottom hole pressure data. However, numerical simulation methods are difficult to describe their dynamic processes. Therefore, we urgently need a mathematical model to fill this gap. In this work, we developed a waterflooding-induced dynamic fracture (WIDF) model. Dynamic water hammer phenomena, multi-dynamic closure phenomena, and fracture storage phenomena are introduced into the WIDF model to describe the induced fracture dynamic behavior. Field cases demonstrate that the WIDF model can improve the accuracy of interpreted parameters and correct incorrect model selection. Green function and Newman product method are used to characterize single-phase water flows within tight reservoirs. Then, the induced fracture is discrete into N segments through the boundary element method. Discrete-induced fractures are divided into n parts. Based on the induced fracture bending property, conductivity variation is independent in each part. The feature line method is used to solve the pressure response of the dynamic water hammer. The Duhamel principle is applied to couple the storage effects and reservoir pressure response. The Laplace transform method transforms the model into Laplace space so that it can be solved easily, and the Stehfest numerical inversion method transforms the model into real space to obtain the final solution. Our results show that the dynamic water hammer flow (DWH) regime with an oscillation curve and the multi-dynamic closure flow (MDCF) regime with peaks exist on the type curve. Resistance coefficient (f) and inertia coefficient (I) control the DWH regime. Fracture storage coefficient (Cf), dynamic fracture closure rates (Delpatm), and induced fracture closure half-lengths (xdfm) control the MDCF regime. It is worth noting that the peak position can be adjusted by the Delpatm and xdfm parameters, achieving a more accurate match to the field cases. The Cf is identified, which corrected for the amplified wellbore storage coefficient. Obtained permeability is also in a reasonable range of permeability for tight reservoirs. In summary, a series of mathematical methods are used to develop and solve an injection well model to identify the dynamic behavior of the induced fracture. Numerical simulation methods are used to verify the accuracy of the WIDF model. Two field cases from X Oilfield demonstrate the practicability of the WIDF model. Dynamic identification of the induced fracture would help engineers develop appropriate injection schemes to prevent water breakthroughs.

Study on seepage model of Multiple Horizontal wells with complex fracture networks in tight Reservoir Based on boundary element method

Horizontal well and volume fracturing technology are the key technologies to develop unconventional reservoirs. Tight reservoir is belonging to multi-scale seepage mediaafter fracturing, and theflow of fluid in it is extremely complicated. In this paper, based on the boundary element method (BEM), the seepage model of horizontal wells with complex fracture networks in irregular boundary reservoir is established for the first time. The model takes into account the influence of irregular reservoir boundary, dual media, complex fracture network and interference of multiple wells on horizontal well seepage. Using this model, the sensitivity analysis of wellbore storage coefficient, skin factor, fracture permeability and interporosity transfer coefficient is carried out. The model expands the application scope of BEM in the field of seepage simulation of unconventional oil and gas reservoirs and provides theoretical guidance for the development of tight oil reservoirs.

Transient Pressure Behavior of Finite-Conductivity Fractures in Horizontal Wells Considering Interference of Water-Injection Wells

Fractured horizontal wells and water-flooding development are effective means to stabilize oil production in low-permeability reservoirs; however, transient pressure behavior analysis based on a single-well testing model ignores the interference effect caused by water-injection wells. With advancements in horizontal drilling technology, multiple-fracture horizontal wells are widely used in tight reservoirs, and researchers have concluded that pressure drops in hydraulic fractures cannot be ignored. In this paper, we present a well testing model that considers the effects of finite-conductivity fractures and the interference of water-injection wells. The analytical solutions were derived based on the source function and superposition principle, and the characteristics of the transient pressure behavior at the bottom hole are analyzed and discussed. The typical pressure curve of our model showed that seven flow regimes exist: wellbore storage stage, transitional flow, first linear flow, fracture interference flow, second linear flow, pseudoradial flow, and interference flow. Furthermore, the results of the sensitivity analysis indicated that the flow regimes are greatly affected by the properties of the fractures and water-injection wells. The length of the fracture mainly affects the transitional flow, first linear flow, fracture interference flow, and second linear flow regimes, whereas the number of fractures predominantly affects the first two stages. The fracture spacing has a significant effect on the fracture interference flow and second linear flow regimes, and the water-injection rate mainly affects the interference flow regime. The well spacing determines when the interference effect occurs. These findings will support more accurate modeling of well production performance considering the impact of water-injection wells.

Capillary Impact on Tidal Response of Groundwater in Unconfined Aquifers With Finite Thickness, Anisotropy and Wellbore Storage—An Analytical Model

AbstractThis study develops a novel, two‐dimensional analytical model to study capillary effects on Earth tidal responses of groundwater in unconfined aquifers. It differs from the previous model by accounting for effects of finite aquifer thickness, anisotropy and wellbore storage. We test the present model against the previous model and numerical simulations and apply it to the field data. Several significant results are obtained: (a) At high conductivity ( m/s), the effect of capillary zones dominates tidal responses of groundwater and causes higher amplitude ratio and smaller phase shift compared with that predicted by the unconfined aquifer model without a capillary zone. At low conductivity ( m/s), the effect of capillary zones on the tidal responses diminishes. (b) The impact of the finite thickness on the tidal response is regulated by the anisotropy. If the anisotropic ratio is small (), the impact of thickness may be negligible; at high anisotropic ratio (), however, the amplitude ratio decreases and the phase shift increases, and the response differs substantially from that of the previous model, which is caused by a change in the flow pattern. (c) Wellbore storage have significant impacts on the tidal response at low conductivity ( 10−5 m/s) but negligible impact at higher conductivity. (d) The present model marginally improved the fit by the half‐space model to the field data from a well in SW China, showing that the remaining misfit to the field data by models with capillarity cannot be due to finite aquifer thickness, anisotropy, or wellbore storage.

Role of gas multiple transport mechanisms and fracture network heterogeneity on the performance of hydraulic fractured multiwell-pad in unconventional reservoirs

The hydraulic fractured multiwell-pad (HFMP) is gradually adopted as an efficient way to enhance shale gas recovery in shale reservoirs. Microseismic evidence supports that the fracture network heterogeneity can be expected in the overlap region initiated by multi-well fracturing. However, most modeling studies have focused on a single well, neglecting the enhanced stimulated reservoir volume (ESRV) between adjacent wells and the associated well interference. In this research, a novel semi-analytical solution for a shale gas reservoir model coupling fracture network heterogeneity and gas multiple transport mechanisms is derived. The proposed model can capture the gas desorption, diffusion, and viscous flow in matrix and gas viscous flow in fracture system as well as the properties of ESRV and SRV. The bottom-hole pressure (BHP) and production rate dynamics illustrate that the HFMP in a shale reservoir with ESRV and SRV apparently differs from the common single well model in the shale reservoir with homogeneous fracture network. Eight flow regimes can be recognized during shale gas development: wellbore storage flow, short-term transition flow, the first linear flow perpendicular to hydraulic fractures (HFs), the first radial flow around HFs, the second linear flow beyond the tip of HFs, the second radial flow in SRV region, transition flow, and the third radial flow regimes in USRV. Sensitive analyses demonstrate that ESRV permeability, well spacing, SRV size and permeability, and production rate difference between adjacent wells all exhibit significant effects on BHP and production rate performances. The findings obtained in this research shed light on the proper consideration of fracture network heterogeneity and gas viscous flow in shale matrix for reservoir evaluation and development.