Fractured Vertical Wells Research Articles

A Method for Evaluating Coalbed Methane Reservoir Productivity Considering Drilling Fluid Damage

In the process of coalbed methane development, drilling fluid and fracturing fluid cannot achieve absolute compatibility with formation. The incompatibility between the working fluid and reservoir will lead to the intrusion of working fluid into the reservoir and cause reservoir pollution. This is a very common phenomenon. There is a large amount of pulverized coal in the coal seam, and the intrusion of working liquid will be combined with the pulverized coal to form cement to block the seepage space in the reservoir. Since pressure relief and fracturing fluid backflow will be performed at the first time after fracturing, the intrusion range of the working fluid is small, generally reaching 10 m to 50 m. Compared with a conventional gas reservoir or shale gas reservoir, the working fluid loss during CBM development will seriously affect the subsequent production project and even make the gas well lose production capacity. On the other hand, in order to avoid this phenomenon, measures such as acidification or volumetric fracturing are sometimes used to improve the seepage environment near the well and near the fracture. The purpose of this study is to quantitatively evaluate the impacts of working fluid filtration and reservoir reconstruction on production. In this study, a single well productivity evaluation model and sensitivity analysis method considering drilling fluid filtration loss, fracturing fluid filtration loss, reservoir reconstruction and other processes is proposed. The formation mechanism of fluid loss during drilling and fracturing is described, and the productivity evaluation model considering fluid loss is combined with the Langmuir isothermal adsorption equation, steady-state diffusion law, Darcy’s seepage law and Duhamel convolution formation. Combined with the distribution of actual gas reservoir flow characteristics, the sensitivity of single well productivity to gas reservoir porosity, gas reservoir permeability, coal seam adsorption coefficient, working fluid filtration loss and reservoir reconstruction measures are analyzed. Through the analysis and fitting of the actual production data on site, the relationship curve can better fit the field production data, and the evaluation results are in line with the drilling and fracturing conditions at that time and the subsequent production conditions, with small errors. The obtained method is suitable for predicting the productivity of fractured vertical wells in different working conditions and provides a basis for the development and productivity prediction of CBM reservoirs in China and in international cooperation.

Optimization of tight gas reservoir fracturing parameters via gradient boosting regression modeling

In China, the exploitation of most unconventional oil and gas reservoirs is dependent on hydraulic fracturing, which is a key method employed when developing tight gas formations. Numerous scholars and field engineers, both domestically and internationally, have conducted extensive numerical simulations and physical experiments to study crack propagation and predict post-fracturing productivity in hydraulic fracturing. Although some progress has been reported in this regard, it is difficult to accurately predict the well productivity using mechanistic models owing to the vertical multilayered development of tight gas reservoirs. In this study, vertical fractured wells in a block of Sulige gas field were examined. The block relied on hydraulic fracturing to produce tight gases. However, as development progressed, the available reservoir environment deteriorated, large differences emerged between wells after fracturing, and the fracturing results did not meet the expectations. In this study, geological, construction, and generation data for this block that had been collected since 2007 were analyzed. After applying multiple machine-learning methods to filter outliers and fill in missing values, k-means clustering, classification enhancement, extreme gradient enhancement, and LightGBM algorithms were used to establish a regression model. The analysis results revealed that the regression accuracy of the cluster test set was as high as 70% and that the LightGBM model had the best regression effect among the 227 stripper wells in the block. After optimizing the fracturing construction parameters (fracturing fluid volume, proppant volume, liquid-nitrogen volume, and pumping rate), the average fracturing fluid and liquid-nitrogen volumes per well decreased, whereas the unit reservoir proppant and liquid-nitrogen volumes increased. The results also revealed that 182 wells showed an improved initial production capacity during fracturing. The average gas production index per meter increased by 22.04%. This approach enabled rapid and efficient production forecasting and construction optimization. Moreover, this represents a novel fracture design method that is applicable to onsite engineers in tight gas production fields in the Ordos region.

An Analytical Method for Determining the Bottom‐Hole Pressure of Vertical Well With Multiple Fractures

Hydraulic fracturing has been a common treatment to enhance well productivity, especially in tight oil and gas reservoirs. Studying the pressure response characteristics of fractured reservoir has been a hot topic due to the significant contribution of fractures to conductivity enhancement. Because of the difficulty in describing the flow problems in vertical fractured well and the lack of related literatures, a novel method to determine the bottom‐hole pressure of a vertical well with multiple fractures based on Newman product method is proposed in this paper. First, the physical model and corresponding mathematical model are established. Then, the solution of bottom‐hole pressure can be obtained through Laplace transformation. Sequentially, the validations of computational method and computational codes contain are presented. From the view of curve fitting and interpretation results, the calculations in this paper are in good agreement with the previous numerical results and our computation method is reliable. Next, a group of typical curves are generated to analyze the flow regimes. And a series of curves are generated to demonstrate effects of key parameters on curve shape. The results indicate that increasing the fracture wings, fracture intersection angle, and fracture length uniformity can enhance the well productivity. Lastly, a case study is exhibited to show the application of the proposed method.

Seepage Model and Pressure Response Characteristics of Non-Orthogonal Multi-Fracture Vertical Wells with Superimposed Sand Body in Tight Gas Reservoirs

Faced with difficulties stemming from the complex interactions between tight gas sand bodies and fractures, when describing and identifying reservoirs, a composite reservoir model was established. By setting the supply boundary to characterize the superposition characteristics of sand bodies, a mathematical model of unstable seepage in fractured vertical wells in tight sandstone gas reservoirs was developed, considering factors such as stress sensitivity, fracture density and fracture symmetry. The seepage law and pressure response characteristics of gas wells in tight sandstone discontinuous reservoirs with stress sensitivity, semi-permeable supply boundary and complex fracture topology were determined, and the reliability of the model was verified. The research results more accurately display the pressure characteristic of a vertical well in the superimposed sand body with complex fractures and provide a more comprehensive model for tight gas production dynamic analysis and well test data analysis, which can more accurately guide the dynamic inversion of reservoir and fracture parameters.

Fast Assisted History Matching of Fractured Vertical Well in Coalbed Methane Reservoirs Using the Bayesian Adaptive Direct Searching Algorithm

The proper understanding of reservoir properties is an important step prior to forecasting fluid productions and deploying development strategies of a coalbed methane (CBM) reservoir. The assisted history matching (AHM) technique is a powerful technique that can derive reservoir properties based on production data, which however is usually rather time-consuming because hundreds or even thousands of numerical simulation runs are required before reasonable results can be obtained. This paper proposed the use of a newly developed algorithm, namely the Bayesian adaptive direct searching (BADS) algorithm, for assisting history matching of fractured vertical CBM wells to derive reservoir property values. The proposed method was applied on representative fractured vertical wells in the low-permeable CBM reservoirs in the Qinshui Basin, China. Results showed that the proposed method is capable of deriving reasonable estimates of key reservoir properties within a number of 50 numerical simulation runs, which is far more efficient than existing methods. The superiority of the BADS algorithm in terms of matching accuracy and robustness was highlighted by comparing with two commonly used algorithms, namely particle swarm optimization (PSO) and CMA-ES. The proposed method is a perspective in laboring manual efforts and accelerating the matching process while ensuring reasonable interpretation results.

Predicting methane emissions and developing reduction strategies for a Central Appalachian Basin, USA, longwall mine through analysis and modeling of geology and degasification system performance

Coal mine methane is a safety concern in active mines due to explosion risk and an environmental concern due to the greenhouse gas (GHG) properties of methane emissions to the atmosphere. Depending on the mine design and operation, structural and stratigraphic characteristics of the geology, and the properties of coal beds affected by mining, a significant amount of methane can be released during coal extraction. These emissions may be low and uniform, but they also can be high and abrupt, if not captured by using pre- and post-mining methods of degasification or not controlled by ventilation during mining. Therefore, emissions should be monitored and predicted accurately for underground safety and GHG reduction. Ventilation and degasification systems should be designed accordingly by taking into account the mine geological properties and the degasification system's performance.This paper presents a comprehensive study to predict emissions and proposes alternatives to reduce emissions in a longwall mine extracting metallurgical coal from the Pocahontas No. 3 coal bed in Virginia (Central Appalachian Basin), USA. The work focused on mining activity in four adjacent panels through analysis and modeling of geology and evaluation of the performance of the methane control system. Results showed that the mine geology contained a significant amount of gas within and around the panel areas, which was controlled by utilizing different degasification methods besides ventilation during mining. The study showed that after pre-mining degasification using fractured vertical wells and in-seam horizontal wells, each panel potentially contained ∼19 MMscf and ∼ 2 MMscf of gas remaining to be handled by the gob gas ventholes (GGVs) and the ventilation, respectively, per acre of mining. It was shown that extending the pre-mining degasification duration of vertical wells by as much as 4 years or drilling more horizontal wells with closer spacing could significantly reduce ventilation and gob emissions during the mining of coal.

Data-Driven Inversion-Free Workflow of Well Performance Forecast Under Uncertainty for Fractured Shale Gas Reservoirs

Abstract Well performance prediction and uncertainty quantification of fractured shale reservoir are crucial aspects of efficient development and economic management of unconventional oil and gas resources. The uncertainty related to the characterization of fracture topology is highly difficult to be quantified by the conventional model-based history matching procedure in practical applications. Data-space inversion (DSI) is a recently developed inversion-free and rapid forecast approach that directly samples the posterior distribution of quantities of interest using only prior model simulation results and historical data. This paper presents some comparative studies between a recent DSI implementation based on iterative ensemble smoother (DSI-IES), model-based history matching, and conventional decline curve analysis (DCA) for shale gas rate forecast. The DSI-IES method treats the shale gas production rate as target variables, which are directly predicted via conditioning to historical data. Dimensionality reduction is also used to regularize the time-series production data by low-order representation. This approach is tested on two examples with increasing complexity, e.g., a fractured vertical well and a multistage fractured horizontal well in the actual fractured Barnett shale reservoir. The results indicate that compared with the traditional history matching and DCA methods, the DSI-IES obtains high robustness with a high computational efficiency. The application of data-space inversion-free method can effectively tap the potential value directly from historical data, which provides theoretical guidance and technical support for rapid decision-making and risk assessment.

A Semianalytical Mathematical Model and Seepage Characteristics of Off‐Center Fractured Vertical Wells with Multiwing Asymmetrical Fractures

The complexity of formation conditions leads to multiwing asymmetric fractures after large‐scale fracturing. According to a well pattern model and reservoir characteristics, a testing well is away from the center of the reservoir, and the existing well‐test mathematical model cannot meet the field data analysis demand. Therefore, the mathematical model for the fractured wells with multiwing asymmetrical fractures is established. The model solution of the Laplace domain is obtained by the Laplace transform, nonuniform fracture discretization, and pressure drop superposition principle. The model is compared with the numerical model in this paper, and the result shows that the presented semianalytical model and the calculation method are correct. The eight main flow stages are divided according to pressure derivative characteristics and the seepage process of off‐center fractured vertical wells with multiwing asymmetrical fractures. The larger off‐center distance will lead to higher pressures and derivative curves. Larger fracture asymmetry factors are higher pressures and derivative curves during bilinear and linear flow regimes. The field data show that the model is applicable and that the model can give the guidance of fractured well formation evaluation.

A HYBRID NUMERICAL/ANALYTICAL MODEL OF TRANSIENT SEEPAGE FOR VERTICAL FRACTURED WELL IN TIGHT GAS RESERVOIR BY USE OF FRACTAL THEORY AND CONFORMAL MAPPING METHOD

Insufficient consideration of the complex morphology of hydraulic fractures (HF) and heterogeneous physical properties of fractured reservoirs in seepage models can result in unreliable well testing analyses. The fractal porosity and permeability (FPP) model provides an effective method for characterizing reservoir heterogeneity in the near-wellbore zone. However, its application to scenarios involving irregularly-shaped hydraulic fracture networks and multiple fracture clusters is challenging due to the lack of spatial symmetry. To address this issue, this paper proposes a combined approach of FPP and conformal mapping (FPP-CM) to transform the region of fractured formation into the exterior of the unit disk domain using numerical conformal mapping. The transient seepage flow model of the vertical fracture well (VFW) is then established by coupling it with the FPP model. The typical curve of pressure transient behavior with the division of flow stages was plotted, and the model verification and sensitivity analysis of parameters were conducted. The results indicate that the fractal dimension primarily affects the formation linear flow stage and its subsequent flow stages; with a decrease in fractal dimension resulting in an increase in the position of the typical curve. For VFW with multiple HF wings, a decrease in the included angle of fracture wings causes an increase in the heterogeneity distribution of microfracture physical properties, resulting in an increase in the position of the pseudo-pressure derivative curve during the late flow stage.

Analysis of the transient pressure of fractured wells coupling with irregular flow fracture: Semi-analytical model and case study

A strange phenomenon happens all the time that the obtained permeability by the conventional finite-conductivity model (FC) is much larger than the actual value in tight reservoir. The conventional pressure-transient analysis models of vertical-fractured wells regard fracture as a regularly non-uniform flow rate. However, due to fracture bending, irregular proppant filling, proppant crushing, and inadequate fracturing fluid backflowing, the fracture may show an irregular flow rate in different fracture segments. An additional horizontal line or concave curve appears on the pressure derivative curve by considering the irregular flow rate in the fracture. In the past, the concave curve would be regarded as an error from field data, and the horizontal line on the pressure derivative curve would be regarded as the quasi-radial flow regime. If the horizontal line is recognized as the quasi-radial flow regime in tight reservoir, the interpreted permeability will be magnified many times. In this work, we proposed a multi-segment irregular non-uniform flow model with changing wellbore storage effect (MINFC) to characterize the pressure response of irregular fractures better, making the pressure response in the fracture more realistic. The MINFC model can correct the magnified permeability and diagnose the partial closure fracture location, length, and flow rate. Green function and Newman product method are applied to obtain the bottom-hole pressure behavior. The results demonstrate that the pressure derivative curve is not a line with a slope of 0.5 in the irregular fracture flow regime but a horizontal or concave curve. Sensitivity analysis demonstrates that the location and length of the irregular proppant filling will affect the duration of the horizontal line. In conclusion, the reservoir permeability and fracture half-length obtained by the MINFC model are closer to the actual value. The locations of irregular proppant filling and low flow rete are quantified so that researchers can take steps to improve fracture performance. Finally, the comparison between the MINFC model and the finite-conductivity model verifies the MINFC model's accuracy. The MINFC model matches field data to verify its practicability.

Pressure transient analysis for multi-wing fractured vertical well in coalbed methane reservoir based on fractal geometry and fractional calculus

In this paper, a semi-analytical mathematical model of pressure transient analysis (PTA) for multi-wing fractured vertical well (MWFV) in coalbed methane (CBM) reservoir is proposed, which considers the complexity of porous media by fractal geometry, the anomalous diffusion based on fractional calculus and the stress sensitivity represented by the exponential expression. Then through line source theory, dimensionless transformation, Pedrosa transformation, and other methods, the solution of the bottom hole pressure is obtained. At last, the PTA curve is presented by the Stehfest inversion method, and seven flowing regimes are identified. It can be observed that after introducing fractal geometry and fractional calculus, the PTA curve is quite different from the traditional curve in the slope of the derivative curve. The influences of related parameters are discussed, including mass fractal dimension, anomalous diffusion coefficient, number of hydraulic fractures, fracture angle, and stress sensitivity factor. Relevant results can provide better guidance to understand the CBM production performance in MWFV.

A Semi-Analytical Mathematical Model for Off-Center Fractured Vertical Wells With Asymmetrical Fractures in Columnar Coalbed Methane

Coalbed methane (CBM) is one of the important unconventional oil and gas resources. Since the permeability of the CBM reservoir is very low, CBM is usually developed by hydraulic fracturing technology to enhance gas productivity. In fact, most of the wells are not at the center of the columnar CBM reservoirs, which leads to different wellbore pressure responses. It is meaningful to analyze the wellbore pressure response of the off-center fractured vertical wells with asymmetrical fracture. The adsorption-desorption, fracture asymmetry are considered and a semi-analytical mathematical model is established. The pressure wellbore solution of the Laplace domain can be obtained by Laplace transformation, model coupling, and Gauss elimination. Then, the Stehfest numerical inversion is employed to obtain the pressure solution and rate distribution in the real-time domain. This semi-analytical solution is verified; the results show that the wellbore pressure includes six flow regimes, which include bilinear flow, linear flow, elliptic flow, radial flow, arc boundary reflection, and boundary dominated flow regime. The influence of fracture angle, dimensionless conductivity, and off-center distance on wellbore pressure and rate distribution are discussed in detail.

An Effective Numerical Simulation Method for Steam Injection Assisted In Situ Recovery of Oil Shale

This paper presents an effective numerical simulation method for production prediction of in situ recovery of oil shale reservoirs with steam injection. In this method, finite volume-based discretization schemes of heat and mass transfer equations of the thermal compositional model are derived and used. The embedded discrete fracture model is used to accurately handle the fractured vertical well. A smooth non-linear solver is proposed to solve the global equations, then cell pressure, temperature, saturation, component mole fractions, and well production rates can be obtained. Compared with the existing commercial software, this new method can have a smoother non-linear solution and handle the complex fracture geometry theoretically. A numerical example is used to test this presented method and can realize accurate calculation results compared with CMG. Another numerical case with a hydraulic fracture and an open thermal boundary condition is implemented to validate the presented method and can effectively handle the actual situation of steam injection-assisted in situ recovery of oil shale, which was difficult to handle using previous methods.

Production decline analysis for a fractured vertical well with reorientated fractures in an anisotropic formation with an arbitrary shape using the boundary element method

In this work, theoretical models have been formulated, validated, and applied to evaluate the production decline performance of a fractured vertical well with reorientated fractures in an anisotropic formation with an arbitrary shape by using the boundary element method. More specifically, the coordinate transformation method was applied to convert the anisotropic system to an equivalent isotropic system, while a coupled matrix-fracture flow model is proposed in the Laplace domain. Then, the boundary element method is applied to solve the fluid flow problem in the matrix, while the Laplace-transform finite difference method is used to numerically obtain the pressure solutions for each fracture segment. Furthermore, the effect of orientated fractures can be examined by generating the Agarwal-Gardner type decline curves, during which two flow regimes including transient flow regime and boundary dominant flow regime can be found. The orientated fractures only affect the transient flow regimes and the boundary dominant flow can be affected by the area and shape of the reservoir. The fracture conductivity is found to be the most important parameter dominating the early production rate. The larger the anisotropic factor, the larger production rate during the early times. Also, the primary fracture angle is more sensitive than the orientated fracture angle. Subsequently, this newly proposed method has been validated and then extended to a field application, demonstrating that the production decline curves for a fractured well with reorientated fractures can be analyzed in a reasonable and accurate manner.

Semi-analytical modeling of rate transient for a multi-wing fractured vertical well with partially propped fractures considering different stress-sensitive systems

Multi-fracture wings can be generated around vertical well after hydraulic fracturing, and damage usually occurs in far from wellbore fracture due to poor proppant transport. The existing rate transient models ignore the different stress-sensitive behaviors in propped and un-propped fractures. For tight reservoir characterization and production prediction, in this paper, a semi-analytical Blasingame decline analysis model of a multi-wing fractured vertical well (MFVW) is formulated with partially propped fractures under different stress-sensitive effects. Compared to propped section, lower initial conductivity and larger stress sensitivity are considered in un-propped section. Employing Laplace transformation, numerical inversion, node analysis, and an iteration method, the production rate is obtained and then verified. Afterward systematic sensitivity analyses are carried out. The influences of parameters such as un-propped section length and different stress-sensitive behavior on production rate are studied in detail. A big difference is observed between type curves of the uniform and non-uniform stress-sensitive models. The properties of propped fracture section mainly put an impact on the early time production rate. The stress-sensitive un-propped fracture section makes production rate reduction at the middle time, and such an influence is enhanced with a longer un-propped section. Sharper decline rate and smaller minimum conductivity both would enhance the production reduction caused by stress-sensitivity. For the first time, the flow flux and pressure along the partially propped fracture of MFVW are analyzed. It has been found that the max flux rate would not appear in the first near wellbore segment with smaller θ in MWFV. And flow flux in un-propped section is lower by order of magnitude than that of the propped section at early time, the majority of the total production at early time is contributed by the near wellbore propped fracture section. The model can help for better understand of the flow mechanism and achieve more realistically fracture flow simulation. It has practical significance for better development of tight resources.

A novel semi-analytical model for oil-water two-phase flow of a fractured vertical well in triple media carbonate reservoir

A novel semi-analytical model for oil-water two-phase flow of a fractured vertical well in triple media carbonate reservoir

Experimental research on inter-fracture asynchronous injection-production cycle for a horizontal well in a tight oil reservoir

One of the existing tight oil reservoir development methods is development after hydraulic fracturing of horizontal wells. This type of development method severely limits the recovery rate of tight oil reservoirs. The other conventional enhanced oil recovery methods are not suitable for tight oil reservoirs. The water injection performance of fractured vertical wells is poor, and water breakthrough easily occurs during water injection in horizontal wells. In order to improve the recovery factor of tight oil reservoirs and to achieve sustainable development of tight oil reservoirs, finding a suitable method of enhancing the recovery factor of tight oil reservoirs is the top priority. Based on the concept of periodic asynchronous water flooding to supplement energy between horizontal fractures, in this paper, an effective method of improving the recovery rate of tight oil reservoirs is discussed. Physical simulation experiments were designed to improve the recovery efficiency of horizontal wells with an inter-fracture asynchronous injection-production cycle (IFAIPC). The feasibility of the method was verified. Two different sets of experiments were designed: 1) the experiment that simulates a homogeneous reservoir with a section with two fractures (M1), and 2) an experiment that simulates a heterogeneous reservoir with three sections of four fractures (M2) and the fourth section with five fractures (M3). The results show that during the IFAIPC process, the permeability of the rock sample tends to decrease gradually. In particular, in the first five cycles, the permeability decreases significantly. Water injection becomes difficult as the permeability decreases, and there is a feasible critical value for water injection. In homogeneous reservoirs, water breakthrough is slow. The degree of recovery and the ultimate recovery rate before water breakthrough are high. The use of IFAIPC in heterogeneous reservoirs can effectively increase the swept volume and delay the rise of water saturation. The IFAIPC method can effectively improve the recovery of tight oil reservoirs by more than 10% in the first five injection-production cycles. The experiments confirm the feasibility and effectiveness of using the IFAIPC method in tight oil reservoirs.

Semianalytical model of complex fracture growth in vertical wells based on boundary element theory

The recent developments in low-permeability oil and gas reservoir mining technology have led to the application of various forms of well fracturing models to determine the physical formation parameters and flow laws in porous media. However, most related studies have been aimed at conducting a pressure transient analysis after the formation of fractures, ignoring the pressure change characteristics during fracture formation. In this study, a fracture growth model based on vertical fractured wells was established and solved using the source function theory and boundary element method. The rationality of the model calculation method was verified by the superposition principle. The pressure change laws before and after fracture growth were analyzed, and the model was subjected to hydraulic fracturing experiments. The results showed that with the increase in the local pressure at the bottom of the well, main fractures, branch fractures, and microfractures were generated in three stages. When the fracture was formed, the pressure and pressure derivative curves fluctuated but gradually returned to a stable state under the fracture shape with the extension of the flow time. Moreover, from the main fracture to the microfracture stage, the pressure recovery time period was gradually shortened. The fitting results of the analysis model and fracturing experiment were found to be accurate, providing a theoretical support for analyzing the transient pressure changes during the formation of complex fractures. The different curve characteristics also provide a new reference basis for evaluating the fracture propagation behavior and predicting the fracture conductivity.

Production forecast of fractured vertical wells in coalbed methane reservoirs: coupling dynamic drainage area

Production forecast of fractured vertical wells in coalbed methane reservoirs: coupling dynamic drainage area

Semi-analytical modeling for multi-wing fractured vertical wells in a bilaterally heterogeneous gas reservoir

Many prolific hydrocarbon reservoirs show the lateral heterogeneity of rock properties, where the formation is composed of several regions with different rock properties separated by linear interfaces. Although there have been many studies on laterally heterogeneous reservoirs by linear composite models, most of them focus on vertical well without hydraulic fracturing. The modeling for fractured vertical wells in laterally heterogeneous reservoirs remains limited. The goal of this study is to develop a semi-analytical three-region linear composite model for multi-wing fractured vertical (MWFV) wells in a bilaterally heterogeneous gas reservoir. This model can take into account the common situation in practice, where the heterogeneity occurs on both sides of the reservoir region with the MWFV well. Based on the point-source function method, a semi-analytical modeling for an MWFV well in a bilaterally heterogeneous gas reservoir is developed by using pressure drop superposition, fracture wing discretization, and Stehfest algorithm. Compared with the simplified semi-analytical and numerical models, the correctness of the present model is verified. Log-log type curves for MWFV wells in a bilaterally heterogeneous gas reservoir are drawn. The flow regimes of the MWFV well in a bilaterally heterogeneous gas reservoir are identified. The influences of some well and reservoir parameters on the pressure response and rate decline of MWFV wells are investigated thoroughly. It is found that the pressure response and rate decline of MWFV wells are significantly affected by the well location, fracture wing properties, and reservoir heterogeneity.