Model For Pressure Transient Analysis Research Articles

Application of pressure small signals extraction and amplification technology in abandoned well pattern for geothermal energy extraction and H2 storage: Numerical modeling and economic analysis

Using abandoned reservoirs for geothermal energy development and H2 storage is economical. The impact of complex fractures from long-term oil and gas extraction on geothermal energy and H2 storage is not yet clearly understood. Here, a pressure small signals extraction and amplification (PSEA) technology is developed to improve reservoir monitoring accuracy. This technology is capable of coupling many pressure transient analysis models to invert parameters for multiple scenarios. This work establishes numerical models to simulate the effects of geothermal energy extraction and H2 storage over 5000 days. Results show that this technology improves the accuracy of inverted parameters by 4–14 times. This technology adjusts the production temperature differences in a single injection-production system from 1.4K to 6.5K and the net heat power from 0.25 MW to 1.1 MW, and it can also identify an early low-rate H2 storage phase. The Non-Sorting Genetic Algorithm II calculates that the PSEA technology brings economic benefits of $704,000 and $352,000 for geothermal energy extraction and H2 storage in a single injection-production system. In conclusion, the developed monitoring technology and models improve accuracy in assessing geothermal energy development and H2 storage, preventing failures in residential heating or H2 storage projects.

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.

A new analytically modified embedded discrete fracture model for pressure transient analysis in fluid flow

In the past few decades, multi-stage hydraulic fracturing has emerged as a crucial technology for the commercial development of unconventional oil and gas (UOG) resources. It is crucial to accurately and efficiently characterize transient fluid flow near fractures, which is a critical concern for many researchers. Discrete fracture models (DFMs) are primarily used to analyze the pressure transient behaviors of fluid flow in naturally fractured porous media. DFMs can accurately capture transient fluid flow near fractures, but they require a substantial number of grids to ensure computational accuracy, leading to higher computational costs. On the other hand, standard embedded discrete fracture models (EDFMs) based on pseudo-steady-state assumptions are computationally efficient, but they struggle to model the early transient fluid flow near fractures accurately. To address this limitation, we propose a new analytically modified EDFM (AEDFM) with structured Cartesian grids for analyzing the pressure transient behaviors of fluid flow in naturally fractured porous media.The transmissibility between the matrix and fractures is adjusted by multiplying it with a transient factor. In addition, we have validated the accuracy and efficiency of our proposed model through comparisons with results from analytical models and a standard well-testing software package. The results demonstrate the significance of our proposed model in accurately capturing transient fluid flow around fractures and reducing computational costs. In this work, we analyze the pressure transient behaviors of fluid flow using various parameter values and further evaluate the significance of the proposed modifications. The results indicate that AEDFM can effectively match the early nonlinear pressure drop near fractures compared to the standard EDFM. This work presents a powerful tool for the fast and accurate analysis of pressure transient behaviors of fluid flow in naturally fractured porous media.

A novel pressure transient analysis model for fracturing wells in fracture–cavity carbonate reservoirs

Large-scale karst caves are the principal storage spaces for hydrocarbon resources in fracture–cavity carbonate reservoirs. Drilling directly into these caves is considered the ideal mode of development, but many wells do not effectively penetrate karst caves. Therefore, acid fracturing is employed to generate artificial fractures that can connect with these caves. However, there are no appropriate well test methods for fracturing wells in fracture–cavity reservoirs. This study establishes a novel pressure transient analysis model for such wells. A new mathematical model is proposed that couples linear flow in acid fracturing cracks with radial flow in the oil drainage area. The Laplace transform and Stehfest numerical inversion provided analytical solutions for the bottomhole pressure. Typical log–log well testing curves were plotted to analyze oil flow, which occurs in ten stages. During the flow stage in fracturing cracks, the pressure and pressure derivative curves are parallel lines with a slope of 0.5. In the stage of karst cave storage, the pressure derivative curve is a straight line with a slope of 1. A comparison with previous models confirmed the validity of the proposed model. The influence of key parameters on the behavior of typical curves is analyzed. A field case study of the proposed model was carried out. Parameters related to fracturing cracks and karst caves, such as the crack length and cave radius, were successfully estimated. The proposed model has great potential for determining formation parameters of fracture–cavity reservoirs.

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 three-dimensional numerical pressure transient analysis model for fractured horizontal wells in shale gas reservoirs

Shale gas development has greatly contributed to the world's energy supply. Pressure transient analysis (PTA) has extremely helped the development of shale gas. In this paper, a three-dimensional numerical model for transient pressure analysis of multi-stage fractured horizontal wells (MFHWs) in shale gas reservoirs was proposed, which was based on the embedded discrete fracture model (EDFM). The adsorption effect of shale gas, stress sensitivity of shale reservoir, and high-velocity non-Darcy flow in fractures were considered in this model, and the model was solved by Matlab Reservoir Simulation Tool (MRST). The discrete process of governing equations is described in detail, the typical MFHW pressure transient response curve of a shale gas reservoir was obtained, different flow regimes were divided, and three-dimensional pressure distribution profile of different flow stages were drawn to clearly understand the flow states of shale gas in the reservoir. The effects of different flow mechanisms and fracture properties on the log–log curves of the MFHW pressure transient response were analyzed in detail. The numerical PTA model proposed in this paper not only considers a variety of complex flow mechanisms of shale gas, but also accurately describes the characteristics of complex fracture network of shale reservoirs in three-dimensional conditions through EDFM. In addition, the problems of the incomplete description of shale gas flow stages by conventional analytical methods and semi-analytical methods were avoided through the numerical solution. The pressure response behavior of fluid in shale gas reservoir can be better explained by using this model, which helps to reduce the uncertainty of shale reservoir development.

Pressure Transient Analysis for a Well Drilling into a Large-Size Cave in Fracture-Caved Carbonate Gas Reservoirs

This paper studies the influence of large-size cave on pressure transient characteristics in fracture-caved carbonate gas reservoirs (FCCGR). With the rapid increase of energy demand, the exploration and development of unconventional oil and gas becomes more and more important. In recent years, many FCCGR have been discovered in western China and contribute significantly to Chinese gas reserves. However, with the presence of large-size cave, FCCGR have complex pore structures and strong heterogeneity. Traditional pressure transient analysis models cannot describe the gas flow accurately. This paper develops a novel pressure transient analysis model for FCCGR by coupling the fluctuating pressure and minor energy loss. Based on the solutions, the typical curves are plotted to analyze the pressure transient characteristics. It is found that the flow process can be subdivided into six stages, including the following: (I) wellbore storage, (II) first transition stage, (III) cave storage, (IV) second transition stage, (V) interporosity flow, and (VI) radial flow. The findings indicate that a concave is added, and the wellbore storage occurs earlier due to the existence of cave. Then, the influences of key parameters are studied. The pressure propagation coefficient and cave volume factor influence the stages I, II, III, and IV. When pressure propagation coefficient increases, the wellbore storage becomes larger and cave storage becomes smaller. The first concave moves to upper right. When cave volume factor increases, the wellbore storage occurs earlier and the curves move left in stage I. Interporosity flow factor and storage ratio influence the location and depth of the second concave. Finally, a field gas well is interpreted by using the proposed model, which verifies the reliability and correctness of the model. The findings of this study can help to better understand the influence of large-size cave on pressure transient characteristics. In addition, it can help engineers invert the cave volume, which is of great significance for the development in FCCGR.

A semi-analytical water content model for pressure transient analysis of fractured horizontal well with complex fracture networks

A semi-analytical water content model for pressure transient analysis of fractured horizontal well with complex fracture networks

A high-resolution numerical well-test model for pressure transient analysis of multistage fractured horizontal wells in naturally fractured reservoirs

In this study, a high-resolution numerical well-test model based on hybrid discrete fracture methods for pressure transient analysis of multistage fractured horizontal wells in naturally fractured reservoirs is proposed. Given the complexity of gridding for a numerical transient model, a new type of hybrid grid system honoring complex geometries of high-velocity transient flow near wellbore and hydraulic fractures is developed. Meanwhile, the methods of identifying fracture intersections in 3D unstructured space, transmissibility corrections and stochastic fracture network generation algorithm are proposed to greatly improve the accuracy and efficiency of capturing the pressure transients in complex fracture networks. After comparison with the well-test software KAPPA, it shows that the model can not only accurately reproduce the complex 3D convergence of flow regimes but also has a much better computational performance. Then, the type curves of a multistage fractured horizontal well with complex fracture networks and the sensitivity analysis of nonuniform properties of fracture networks are developed and analyzed in detail. The results show that the early-time horizontal radial flow and dip are positively related to the properties of natural fractures, and the fluid contribution and pressure distribution mainly depend on fracture connectivity rather than fracture number. The orthogonal fracture connections can result in stronger fluid supply and less fracture interference. Besides, the fracture linear flow and first/second bilinear flow are mainly affected by hydraulic and natural fractures, respectively. Finally, it proves that the proposed model can be much more efficient than KAPPA in history match for well-test data by an actual fractured field case.

Evaluation of fracture closure and its contribution to total production for a well with non-planar asymmetrical vertical fracture based on bottom-hole pressure

Hydraulic-fracturing is an important well-stimulation technique, the fracture closure is inevitable during production. The existing pressure transient analysis models either ignore the length of fracture-closure segment that causes the explained fracture half-length to be smaller, or only use the fracture conductivity to evaluate fracture closure. To fully evaluate fracture closure and provide a reference for oilfield engineers determining whether need measures to improve the well performance, meanwhile considering the non-planar asymmetrical fracture is common met in low-permeability reservoirs, this paper proposes to use two parameters (flowrate proportion and conductivity of fracture-closure segment) to comprehensively evaluate fracture closure, and hence develops double-segment non-planar asymmetrical fracture model (DPAFM). Planar asymmetrical fracture model is simplified case of proposed model. The semi-analytical solution is obtained by using finite difference method (FDM) and Gonzalez-Chavez and Cinco-Ley (2006) model is used to verify the solution. The results of this work show that (a) The example of actual well simulation proves the model is more suitable for the actual field data, and the model established is better matched than the saphir software; (b) The proposed model can obtain production proportion and conductivity of fracture-closure segment to comprehensively evaluate fracture closure; (c) There are four typical flow regimes for the DPAFM, including bilinear flow, interference linear flow, formation linear flow, pseudo-radial flow. The interference linear flow regime with ‘V-shape’ characteristic is unique; (d) Conventional explanation thinks the ‘V-shape’ characteristic represents the secondary fracture developed (e.g., OFFN, TLFN and MOFN). However, this paper gives another possibility that the ‘V-shape’ reflects fracture closure. The findings of this study can help for better understanding of illustrating the practicability of proposed methodology in evaluating the fracture closure and reservoir parameters. This research provides guidance for technicians to formulate the next step to increase production plan and helps the oilfield engineers determine whether take measures to improve the well performance. • We present a double-segment non-planar asymmetrical fracture model (DPAFM) considering the effect of conditions inside fracture. • We provide an additional explanation about ‘V-shape’ characteristic on the pressure derivative curve besides the complex fracture geometries. • The field cases illustrate the practicability of proposed methodology in evaluating the reservoir parameters, fracture closure, fracture segment flow rate and fracture propagation.

A Discrete Model for Pressure Transient Analysis in Discretely Fractured Reservoirs

Summary Natural fractures are of great significance to the management of petroleum resources, groundwater, and carbon sequestration. Given that many naturally fractured reservoirs have poorly connected fractures, the traditional dual-porosity model like Warren and Root’s model is not reasonable for pressure transient analysis in these reservoirs. Therefore, the objective of this study is to develop a new discrete model (DM) in discretely fractured reservoirs based on a semianalytical approach. The DM comprises three domains: wellbore-connecting (WC) fractures and/or wellbore-isolating (WI) fractures, and matrix. The DM is verified by case studies with numerical simulators for four kinds of discretely fractured reservoirs with (1) WC fracture networks, (2) WI fracture networks, (3) WC and WI fractures, and (4) WI fractures. Results indicate that the pressure transient behaviors in discretely fractured reservoirs can be classified into three types: WC fracture networks, WC and WI fractures, and WI fracture (networks). The special flow regimes of WC fracture networks are fluid supply and pseudoboundary dominated flow. For WC and WI fractures, the special flow regimes are bilinear flow, linear flow, and isolated fracture effect. The early pseudoradial flow and isolated fracture effect (“V-shaped” or “dip”) are the special flow regimes of WI fracture (networks), and they are similar to traditional dual-porosity models like the Warren and Root model. However, the source of “V-shaped” in DM is quite different from that in the Warren and Root model. This paper gives a new insight into the well testing in discretely fractured reservoirs.

Pressure transient behavior and flow regimes characteristics of vertical commingled well with vertical combined boundary: A field case in XC gas field of northwest Sichuan Basin, China

The multilayered deposition is the main feature of the XC gas reservoir in the northwestern Sichuan Basin. The boundaries among layers of the XC gas reservoir is different. In this paper, we propose an extended pressure transient analysis model for vertical commingle well, considering different boundary radii and boundary types, to capture the Vertical Combined Boundary (VCB) effect on the pressure transient behavior and flow regime characteristics.The analytical solution is yielded by the Laplace transform, Bessel functions, Duhamel's superposition principle, and Stehfest inversion algorithm, and new flow regimes under different boundary combinations are identified by the pressure derivative curve. Taking the dual-layer VCB model as a type example, nine combinations of boundaries are analyzed. Compared with the current vertical commingled well model with the same boundary radii or single boundary types, this model has novel flow regimes controlled by the VCB.The research results indicate that the pressure derivative type curve during the novel flow regimes stage can diagnosis the VCB type. On the one hand, there are quantitative linear relationships between the pressure derivative feature value and interlayer heterogeneity of the VCB model with the same boundary radii. These linear relationships provide a new perspective to quickly capture interlay heterogeneity through the of the pressure derivative feature value. One the other hand, the pressure behavior and flow regimes of the VCB model with different boundary radii obey the successive superposition rule. This rule provides a method to recognize the VCB type with different boundary radii based on that of the VCB with the same boundary radii.Finally, a field case from the northwestern Sichuan Basin gas reservoir is discussed in detail to exhibit the workflow of our model application and validate the capability of our model.

A Discrete fracture–matrix model for pressure transient analysis in multistage fractured horizontal wells with discretely distributed natural fractures

Analysis of transient pressure test has become a reliable and powerful tool for petroleum engineers to study the impacts of complex fracture networks on multistage fractured horizontal wells (MFHWs) in unconventional reservoirs. Although lots of models have been established in the past decades, such as well-known dual-porosity model (DPM), dual-permeability model (DKM) and stripe fracture model (SFM), they have been proven unsuitable for modeling discretely distributed natural fractures (NFs).In this study, to overcome the disadvantages of existing models, a Discrete fracture–matrix method based on numerical well testing model (DFM-WTM) is proposed to study the pressure transient responses of MFHW with discretely distributed NFs. In DFM-WTM, local grid refinement method, well model and transmissibility corrections, natural fracture generation and time-step size are improved based on the framework of Matlab Reservoir Simulation Toolbox (MRST) (Lie, 2019), ensuring that pressure transient responses of MFHW with complex fracture networks can be obtained accurately and efficiently. Then, sensitivity analysis is conducted to study the impacts of different fracture properties. Finally, a case study is performed to further demonstrate the reliability and practicality of DFM-WTM.The results show that MFHW with discretely distributed NFs can be divided into 8 flow regimes, including (1) wellbore storage and skin effect, (2) fracture linear flow, (3) bilinear flow, (4) NF–HF fluid supply, (5) second bilinear flow, (6) formation linear flow, (7) pseudo boundary flow and (8) pseudo radial flow. Besides, a “dip” is found in the pressure derivative curve which is caused by the NF–HF fluid supply. Through the sensitivity analysis, it is found that this “dip” is an important signal to identify the impacts of NFs. It can also help us fathom the properties of HFs and NFs because this “dip” can be mainly affected by the number and conductivity of both HFs and NFs.

Pressure Transient Analysis for a Horizontal Well in Heterogeneous Carbonate Reservoirs Using a Linear Composite Model

Carbonate reservoirs usually have strong anisotropy. Oil and gas recovery from fractured reservoirs is highly challenging due to complicated mechanisms involved in production from these reservoirs. A horizontal well completed in these reservoirs may extend through multiple zones, including homogeneous, dual-porosity, and triple-porosity formations. Traditional well test models assume that the entire length of a horizontal or multilateral well remains in the same formation with uniform properties. A well test model for pressure transient analysis of horizontal wells extending through a carbonate reservoir consisting of natural fractures, rock matrix, and vugs with different properties is presented in this study. The focus of this study is on dual-porosity (fracture-matrix) and triple-porosity (fracture-matrix-vug) reservoirs, considering the pseudosteady interporosity flows from rock matrix and vugs into fractures. A multizone triple-porosity model was established and solved by using the point source function, Green’s function, and coupling of multiple reservoir sections. The corresponding type curves were developed, and sensitivity analysis was carried out. The type curves of flow stage division reveal that a horizontal well traversing a three-section reservoir including homogeneous, dual-porosity (fracture-matrix)/triple-porosity (fracture-vug-matrix), and homogeneous sections identifies the stages of pseudosteady interporosity flow from matrix and vug into fracture, fracture pseudoradial flow, system linear flow, system pseudoradial flow, and pseudosteady flow occur in sequence. The greater the difference of permeability between the dual-porosity/triple-porosity section and the two homogeneous sections, the more obvious the interporosity flow on the pressure derivative curve. This approach satisfies the need for pressure transient analysis for a horizontal well that traverses two or more regions with distinct properties in heterogeneous carbonate reservoirs.

A semi-analytical model for pressure transient analysis of hydraulic reorientation fracture in an anisotropic reservoir

Fracture reorientation can be used to increase well production in an anisotropic reservoir. The principal focus of this work is on the transient pressure analysis for a hydraulic reorientation fracture in a rectangular anisotropic reservoir. By employing the nodal analysis technique, a set of diffusivity equations are developed to describe the flow in a hydraulic reorientation fracture. Then, a semi-analytical solution is obtained by coupling the point source solution and the discrete fracture solution. The validation of this work is demonstrated by comparing the previous study and the numerical simulation for a reorientation fracture. Five typical flow regimes can be observed on this model's transient response. Flux along the reorientation fracture is also generated to analyze the flux distribution at different time. Furthermore, type curves are obtained to investigate the effect of the key parameters on the transient flow behavior, including principal fracture angle, reoriented fracture angle, permeability anisotropy, fracture conductivity and fracture length ratio. For a rectangular anisotropic reservoir, the influence of principal fracture angle, permeability anisotropy and fracture conductivity on the type curves is concentrated in the early-time and middle-time periods, and reoriented fracture angle and fracture length ratio mainly affect the formation linear flow regime.

A Two-Phase Flow Model for Pressure Transient Analysis of Water Injection Well considering Water Imbibition in Natural Fractured Reservoirs

The pressure injection falloff test for water injection well has the advantages of briefness and convenience, with no effect on the oil production. It has been widely used in the oil field. Tremendous attention has been focused on oil-water two-phase flow model based on the Perrine-Martin theory. However, the saturation gradient is not considered in the Perrine-Martin method, which may result in errors in computation. Moreover, water imbibition is important for water flooding in natural fractured reservoirs, while the pressure transient analysis model has rarely considered water imbibition. In this paper, we proposed a semianalytical oil-water two-phase flow imbibition model for pressure transient analysis of a water injection well in natural fractured reservoirs. The parameters in this model, including total compressibility coefficient, interporosity flow coefficient, and total mobility, change with water saturation. The model was solved by Laplace transform finite-difference (LTFD) method coupled with the quasi-stationary method. Based on the solution, the model was verified by the analytical method and a field water injection test. The features of typical curves and the influences of the parameters on the typical curves were analyzed. Results show that the shape of pressure curves for single phase flow resembles two-phase flow, but the position of the two-phase flow curves is on the upper right of the single phase flow curves. The skin factor and wellbore storage coefficient mainly influence the peak value of the pressure derivatives and the straight line of the early period. The shape factor has a major effect on the position of the “dip” of pressure derivatives. The imbibition rate coefficient mainly influences the whole system radial flow period of the curves. This work provides valuable information in the design and evaluation of stimulation treatments in natural fractured reservoirs.

A Mathematical Pressure Transient Analysis Model for Multiple Fractured Horizontal Wells in Shale Gas Reservoirs

Multistage fractured horizontal wells (MFHWs) have become the main technology for shale gas exploration. However, the existing models have neglected the percolation mechanism in nanopores of organic matter and failed to consider the differences among the reservoir properties in different areas. On that account, in this study, a modified apparent permeability model was proposed describing gas flow in shale gas reservoirs by integrating bulk gas flow in nanopores and gas desorption from nanopores. The apparent permeability was introduced into the macroseepage model to establish a dynamic pressure analysis model for MFHWs dual-porosity formations. The Laplace transformation and the regular perturbation method were used to obtain an analytical solution. The influences of fracture half-length, fracture permeability, Langmuir volume, matrix radius, matrix permeability, and induced fracture permeability on pressure and production were discussed. Results show that fracture half-length, fracture permeability, and induced fracture permeability exert a significant influence on production. A larger Langmuir volume results in a smaller pressure and pressure derivative. An increase in matrix permeability increases the production rate. Besides, this model fits the actual field data relatively well. It has a reliable theoretical foundation and can preferably describe the dynamic changes of pressure in the exploration process.

A Finite-Conductivity Horizontal-Well Model for Pressure-Transient Analysis in Multiple-Fractured Horizontal Wells

Summary In this paper, we propose a new model for pressure-transient analysis in multiple-fractured horizontal wells (MFHWs) with consideration of pressure drop along the wellbore. To make the physical model better understood, the whole formation is divided into three parts: (1) reservoir, (2) fracture, and (3) wellbore. With incorporating frictional and acceleration pressure drops, a mathematical model with a finite-conductivity horizontal well (FCHW) is developed. Newton-Raphson iterations are used to solve the mathematical model and obtain the transient-pressure solutions of the MFHW. Model verification is performed by comparing with the solutions from a numerical software. On the basis of the field cases from the Ordos Basin, performance prediction, sensitivity analysis, type-curve matching, and evaluations of uncertainty parameters are conducted. Results show that the contribution of wellbore hydraulics to the total pressure drop increases first and then decreases after reaching the peak value. Ignoring wellbore hydraulics would cause erroneous results during the well-performance forecast. In addition, the dimensionless wellbore pressure of the MFHW increases with an increase in Reynolds number (Re); it decreases as the reservoir/wellbore constant (ChD) increases. Furthermore, the impact of pressure drop on the pressure performance of the MFHW becomes more serious with the increasing Re or the decreasing ChD.

A new semi-analytical model for simulating the effectively stimulated volume of fractured wells in tight reservoirs

The interaction of hydraulic fractures and natural fractures results in a complex fracture network system around a producing well, which is the primary contributing region for production in unconventional reservoirs. Currently, most models for simulating fluid flow in formations penetrated by fractured wells are based on the assumption of a homogeneous dual–porosity medium.In this paper, a new semi-analytical model is presented for vertically fractured wells with stimulated reservoir volumes (SRV). Specifically, we employ fractal porosity and permeability to describe the heterogeneous distribution of porous media in a SRV. An approach is given for estimating the size and equivalent permeability of the fractal SRV for vertically fractured wells in tight reservoirs. The line source function, Laplace transformation, integral of the modified Bessel function and Stehfest numerical inversion algorithms are used to solve the composite model. Based on the Duhamel principle, the dimensionless pressure responses of tight oil and gas wells in the Laplace domain and time domain are obtained. Flow regime diagnostics of vertically fractured wells in tight reservoirs are characterized. Sensitivity analysis, including the effects of SRV parameters and fractal parameters on pressure responses and linear flow, are performed. The results show that seven primary regimes can be divided into pressure response curves. The size and equivalent permeability of the fractal SRV can be calculated by the dimensionless pressure derivative curves. In a complex fractal reservoir, the larger the connectivity index is and the smaller the fractal dimension is, the more significant the heterogeneity of the fractal SRV is and the larger the slopes of linear flow are, which leads to a smaller equivalent permeability of the fractal SRV radius. The presented model and the results in this paper can enrich the pressure transient analysis models for vertically fractured wells in unconventional reservoirs.

Unified fluid flow model for pressure transient analysis in naturally fractured media

Naturally fractured reservoirs present special challenges for flow modeling with regards to their internal geometrical structure. The shape and distribution of matrix porous blocks and the geometry of fractures play key roles in the formulation of transient interporosity flow models. Although these models have been formulated for several typical geometries of the fracture networks, they appeared to be very dissimilar for different shapes of matrix blocks, and their analysis presents many technical challenges. The aim of this paper is to derive and analyze a unified approach to transient interporosity flow models for slightly compressible fluids that can be used for any matrix geometry and fracture network. A unified fractional differential transient interporosity flow model is derived using asymptotic analysis for singularly perturbed problems with small parameters arising from the assumption of a much smaller permeability of the matrix blocks compared to that of the fractures. This methodology allowed us to unify existing transient interporosity flow models formulated for different shapes of matrix blocks including bounded matrix blocks, unbounded matrix cylinders with any orthogonal crossection, and matrix slabs. The model is formulated using a fractional order diffusion equation for fluid pressure that involves Caputo derivative of order 1/2 with respect to time. Analysis of the unified fractional derivative model revealed that the surface area-to-volume ratio is the key parameter in the description of the flow through naturally fractured media. Expressions of this parameter are presented for matrix blocks of the same geometrical shape as well as combinations of different shapes with constant and random sizes. Numerical comparisons between the predictions of the unified model and those obtained from existing transient interporosity ones for matrix blocks in the form of slabs, spheres and cylinders are presented for linear, radial and spherical flow types for both fixed boundary pressure and rate.