The multiple multi-stage fractured horizontal wells (MFHWs) interference has been identified in tight gas reservoirs, but current method and model cannot achieve quantitative inter-well interference evaluation of non-uniform fractured region. Therefore, MFHWs mathematical model is established with consideration of multiple sub-region permeability difference. Coupling method of boundary element and source function is employed to solved the mathematical model. Inter-well interference factor is defined and used to evaluate inter-well interference degree. Total interference factor minimum value is used to determine the optimal rate ratio. The result shows that larger production time and well distance leads to small inter-well interference factor, but they have no influence optimal rate ratio. The optimal rate ratio will increase with the increasing of number of adjacent well fractures. If permeability of center region is larger than that of other region, inter-well interference factor and total interference factor will decrease and optimal rate ratio will increase. The model and method can evaluate inter-well interference degree and optimal rate ratio quantitatively, which provides guidance for horizontal well fracturing and parameter optimization design.

Tight gas reservoirs show complex gas-water distribution and clear nonlinear seepage. Small well spacing development of the tight gas leads to significant inter-well interference. To conduct quantitative evaluation of inter-well interference, a gas-water seepage mathematical model considering Pre-Darcy flow and matrix-fractures coupling is established and coupling mathematical model is solved by the finite volume method, finite difference method and analytical EDFM (AEDFM). Transmissibility corrections of matrix-matrix, matrix-fracture system of the Pre-Darcy flow are improved based on the MRST framework. Inter-well interference factor is presented to evaluate the degree of inter-well interference quantitatively, the model is verified by the gas reservoirs commercial simulating software. Result shows that the interference factor of adjacent wells constant pressure production is greater than that during constant rate of adjacent wells. Increasing the production of adjacent wells, well spacing et al. will lead to an larger inter-well interference factors. The existence of natural fractures leads to earlier occurrence time of inter-well interference and interference degree. The inherent properties (such as water saturation and nonlinear coefficient) of tight gas reservoirs have no significant impact on inter-well interference factor. The research results can provide theoretical guidance for quantitative evaluation of inter-well interference.

The seepage mechanism of shale gas and the main controlling factors of production remain unclear because of the multiscale flow occurred in the fractured shale gas reservoirs. Therefore, the distribution characteristics of gas and water in different scale spaces are firstly clarified, and then a mathematical model considering the fluid-solid coupling for shale gas is established based on the features of gas-water two-phase distribution and elastic-plastic change of porous media in the shale reservoirs. The multi-physics field coupling mathematical model is solved by using the finite element method, and its reliability is verified by using actual shale gas well data from the Sichuan Basin. The results indicate that the estimated ultimate recovery (EUR) of shale gas wells is positively correlated with the adsorption and the hydraulic fracture conductivity, and negatively correlated with the primary water saturation and the stress sensitivity of hydraulic fracture. The grey correlation degree method indicates that the main controlling factors affecting the EUR of gas wells are the related fracturing parameters, followed by geological parameters such as matrix adsorption. Considering the influence of the effective stress on the stress sensitivity effect, it successfully demonstrates that the controlled pressure-drop production is superior to the aggressive pressure production. Compared with aggressive pressure production, controlled pressure-drop production appears a production reversal phenomenon where the initial productivity is low but the later productivity is high. This is because appropriate controlled pressure-drop production can reduce the adverse effects of stress sensitivity and is beneficial for the long-term production of gas wells.

The heterogeneous simulation zones will be caused by large-scale horizontal wells volume fracturing. The multiple multi-stage fractured horizontal wells interference has been observed in shale gas reservoirs. The adjacent well production and injection have obvious influence on test well wellbore pressure. The aim of this work is to establish a semi-analytical mathematical model of multiple multi-stage fractured horizontal wells interference with non-uniform simulated reservoir volume. The mathematical model is solved by coupling reservoirs and fracture and sub-zone interface model. This model solution is in agreement with numerical solution, and the calculation efficiency is higher than numerical solution. The result shows that adjacent well production leads to upturned pressure derivative curves and adjacent well injection leads to concave pressure derivative curves. Other vital parameters (such as fracture location, sub-region permeability, and width) have obvious influence on wellbore pressure and derivative curves. This can provide guides for fracturing optimization and optimal carbon dioxide injection rate.

Reservoir permeability and stress heterogeneous distribution lead to different hydraulic fracture lengths and angles. Gas reservoirs' heterogeneous characteristics lead that well is not the center of the circle high-permeability regions after large-scale fracturing. Traditional pressure transient model cannot be used in this case. When a horizontal well length is relatively small, radial composite model can be used to simulate wellbore pressure. Therefore, the aim of this paper is to present a semi-analytical mathematical model of the off-center fractured horizontal well with a circle high-permeability region. The coupling approach of hydraulic fracture and matrix model is employed to solve mathematical model. The wellbore pressure transient solution can be obtained by the Laplace transform, Gauss elimination and the Stehfest numerical inversion. The results show that the wellbore pressure response curve of this model includes eleven flow regimes. When the well is not the center of the reservoir, an obvious derivative curve "upwards" will emerge after the inner radial flow regime, which is different from the previous fractured horizontal well model. Hydraulic fracture properties and geometries distribution have obvious influence on derivative curves characteristic of the early regime. Off-center distance and reservoir properties have distinct influences on derivative curves characteristic of the middle regime. This semi-analytical mathematical model can provide a guide on high-permeability region depiction, hydraulic fracture, and reservoir parameter inversion.

Complex fracture network will be formed by horizontal wells large-scale volume fracturing. Local Simulated Reservoirs Volume (LSRV) region will form since uneven permeability distribution, which make parameter inversion and production prediction become difficult. The aim of this paper is to establish a semi-analytical model of fractured horizontal well with induced fractures in rectangular closed gas reservoirs under variable production style. Heterogeneous rectangular reservoir and fracture mathematical model are established and solved by the Laplace transform respectively. An innovative coupling solution method of reservoirs and fracture model is presented to obtain the wellbore pressure. Combining with the material balance equation of gas reservoirs and wellbore pressure solution of this model, production forecast model of constant rate changing constant wellbore pressure is established and calculation method is shown. Accuracy of this model and calculation method is validated by commercial numerical software. The influence of some important parameters on rate and pressure curves are analyzed in detail, mainly including initial rate, reservoirs parameters and fracture parameters.

Fe2O3/Fe3O4 composite films were successfully prepared on the surface of X80 steel through hydrothermal synthesis and annealing treatments. Subsequently, the oxidised films were modified using surfactants such as decanoic acid (DA), decyl silane triol (DS) and perfluorodecyl silane triol (FDS), resulting in the creation of three distinct films exhibiting superhydrophobic properties. The effects of the hydrophilic and hydrophobic groups of surfactants on the superhydrophobic films of X80 steel were analysed using electrochemical methods, surface analysis techniques and theoretical calculations. The results showed that all three superhydrophobic films exhibited excellent corrosion resistance, with the order being DA > FDS > DS after 72 h of immersion in acidic conditions (pH = 6, 60 °C). Theoretical calculations showed that the adsorption performance of carboxyl groups was superior to that of silyl alcohol bonds, whereas fluorination of hydrophobic groups helped to enhance the adsorption capacity of hydrophilic groups. This not only reveals the key role of surfactants in the preparation of superhydrophobic membranes but also provides a theoretical basis for the preparation of superhydrophobic membranes on carbon steel surfaces.

Blasingame production decline is an effective method to obtain permeability and single-well controlled reserves. The accurate Blasingame production decline curve needs an accurate wellbore pressure approximate solution of the real-time domain. Therefore, the aim of this study is to present a simple and accurate wellbore pressure approximate solution and Blasingame production decline curves calculation method of a multi-stage fractured horizontal well (MFHW) with complex fractures. A semi-analytical model of MFHWs in circle-closed reservoirs is presented. The wellbore pressure and dimensionless pseudo-steady productivity index JDpss (1/bDpss) are verified with a numerical solution. The comparison result reaches a good match. Wellbore pressure and Blasingame production decline curves are used to analyze parameter sensitivity. Results show that when the crossflow from matrix to natural fracture appears after the pseudo-state flow regime, the value of the inter-porosity coefficient has an obvious influence on the pressure approximate solution of the pseudo-steady flow regime in naturally fractured gas reservoirs. The effects of relevant parameters on wellbore pressure and the Blasingame decline curve are also analyzed. The method of pseudo-steady productivity index JDpss can applied to all well and reservoir models.

Horizontal well volume fracturing plays an important role on enhancing gas recovery. Microseismic map indicates that the secondary fracture has been observed obviously and irregular stimulated reservoir volume (SRV) region created. In order to simulate pressure response of this phenomenon, the aim of this paper presented the semi-analytical model of multi-stage fractured horizontal well with secondary fracture and SRV region. Composite model is used to describe irregular SRV, and high-precision boundary element method and coupling method are employed to solve the semi-analytical mathematical model. Compared with conventional fractured horizontal well model, pressure transient behavior of multi-stage fractured horizontal well with secondary fracture and irregular SRV region has unique flow regime. The supply regime from secondary fracture to hydraulic fracture, second bilinear flow regime. Pressure derivative curve shows obvious ‘dip’ for supply regime from secondary fracture to hydraulic fracture, and 1/2 slope line for second bilinear flow regime reflecting formation gas flow towards hydraulic fractures and secondary fractures. Fracture parameter (such as conductivity, length and number) have an obvious influence on pressure transient curve of early and middle flow regime, and they can cover up some flow regime of early flow regime. SRV parameter and shape have an obvious influence on pressure transient curve of late and middle flow regime, and they can cover up some flow regime of late and middle flow regime. Model verification indicates that semi-analytical solving method combining with high-precision boundary element method can enhance calculation accuracy of early flow regime.

Well test model identification is a challenging task due to the numerous types of well test interpretation models and the non-uniqueness of pressure responses generated by different reservoir models. An automated framework is crucial to aid in the identification of well test interpretation models. Since the identification of well test interpretation relies primarily on the various flow regimes appeared on different diagnostic plots. A novel approach is proposed for the well test model identification from the pressure transient test data using the syntactic pattern recognition in this study. In this study, the identification process of well test interpretation model is divided into six steps: preprocessing, feature primitive extraction, curve shape tracking, flow regime division, model preliminary inference, and model final validation incorporating TDS technology. The automatic identification framework developed with this method has been able to identify a variety of complex well test interpretation models correctly, and the non-uniqueness of model results can be well resolved by syntactic pattern recognition combined with TDS technology. In general, the findings of this study can help for better understanding of the process by which well test expert completes the task of model identification.

Tight gas reservoirs considering gas-water two phase is common and show obvious permeability stress sensitivity and non-Darcy seepage characteristic. However, conventional analytical and semi-analytical solving method cannot simulate wellbore pressure response of tight gas reservoirs considering gas-water two phase. Numerical model can overcome the disadvantage of analytical and semi-analytical method and achieve wellbore pressure response simulation of fractured well with complex fracture. Therefore, a gas-water two phase mathematical model of the fractured well is established and solved by embedded discrete-fracture method (EDFM) and finite volume method. Transmissibility corrections is improved on the basis of the framework of Matlab Reservoir Simulation Toolbox (MRST). Result shows that the seven flow regimes can be found according to the pressure drop derivative curves characteristic. When permeability stress sensitivity and non-Darcy is considered, pressure and derivative curve of middle-late stage shows obvious ‘upwarp’ and non-Darcy make reservoirs pressure uneven distribution. Induced fractures parameters have obvious influence on pressure and derivative curves during early and middle flow regime. In addition, fracture intersection and neighbor well production style has obvious influence on pressure curve.

In order to simulate accurately wellbore pressure transient performance of multi-stage fractured horizontal well（MFHW） with the complex fracture network and heterogeneous in tight oil reservoirs, an unsteady seepage mathematical model of the MFHW with induced fractures in rectangular heterogeneous reservoir is established. The wellbore pressure solution is obtained by coupling the fracture model, the reservoir model and heterogeneous reservoir interface model. The wellbore pressure accuracy of the two heterogeneous reservoir models is verified by numerical solutions, boundary element method and previous model. By flow stages analysis and parameters sensitivity analysis, the following results can be obtained. Compared with the wellbore pressure derivative curve of the MFHW in homogeneous reservoir, the unique flow stages of this model in the ideal case include: the complex linear flow stage, the "supply" stage from induced fractures to fractured fractures, the linear flow stage and the pseudo boundary control flow stage. The increase of induced fracture number extends the duration of the complex linear flow stage and reduces the fluid seepage resistance. Therefore, the pressure curve of the early stage is lower. If the conductivity of induced fracture and fractured fracture is constant, the greater the conductivity is, the longer the duration of the bilinear flow regime is. When all fractured fractures are different region, the two end low permeability region along the wellbore weakens the "supply" stage. Therefore, the lower the permeability along the wellbore is, the higher the pressure curve at the early stage is.When all fractured fractures are in same area, the permeability change only affects the pressure curve shape after the radial flow stage. The lower the permeability of the outer area is, the higher the pressure curve after the early radial flow stage is. The practicability and accuracy of the model and method are demonstrated by the field example.

Vertical hydraulic fracturing is widely used to develop low- permeability gas reservoirs. Uneven distribution of formation permeability and stress leads to multiple- wing hydraulic fractures with different lengths, which results in the wellbore not being the center of the circular stimulated reservoir volume (SRV) region. Therefore, to simulate the wellbore pressure of this phenomenon, a semianalytical model of the off- center multiwing fractured well in radial composite gas reservoirs is presented and the corresponding solution method is shown. The model is verified with the numerical solution, and eight flow regimes can be distinguished under the ideal case, which includes bilinear flow, fracture interference, linear flow, radial flow of inner region, transition flow of inner region, and radial flow of inner region. Compared with the previous model in which the well is at the center of radial composite gas reservoirs, in this paper we present an obvious "step" after the inner region radial flow regime, which is related to the off- center distance and radius of the inner region. In addition, the effects of some important parameters (such as off- center distance, permeability mobility, inner region radius, and fracture distribution) on typical curves are discussed. Finally, field well testing data are used to verify the accuracy of the model.

Since there are several hydraulic fractures around a wellbore after a large -scale hydraulic fracturing and the well is not in the center of the reservoir, no corresponding semianalytical model for wellbore pressure analysis has been proposed. To bridge this gap, this paper aims to present a semianalytical model of the off-center multiwing fractured well. With consideration of permeability stress sensitivi-ty, the reservoir model and hydraulic fracture model are established, respectively. The coupling approach of the reservoir model and hydraulic fracture model is used to obtain the wellbore pressure solution. Meanwhile, the off-center multiwing fractured well is veri-fied with a numerical solution. The seven flow regimes can be distinguished according to the characteristics of the pressure derivative curve. Furthermore, the effect of different fracture distributions on wellbore pressure and the derivative curve is discussed and analyzed. Assuming that the fracture wing number is equal to the average length of all fracture wings, the wellbore pressure is lowest before the radial flow regime when the fracture wing has a uniform distribution around the angle and all fracture wings are equal in length. Besides, the influence of other important parameters (fracture wing number, off-center distance, etc.) is discussed. According to the analysis, we conclude that fracture wing number has a significant influence on the pressure and derivative curves before the radial flow regime. The off-center distance has no influence on the pressure and derivative curve before the radial flow regime, but it has an obvious influence on arc boundary reaction time. Finally, the advantages of the semianalytical solution are fast calculation speed and high calculation accuracy (especially in the early flow regime).

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.

Due to the anisotropy influence of reservoir permeability, fractures extend along different directions and circle stimulated reservoir volume is formed. In this research, a semi-analytical mathematical model of off-center multi-fractured horizontal well in circle bi-zonal gas reservoir is established and solved by Laplace transform, pressure drop superposition and coupling method. Wellbore pressure response curve is plotted and eleven flow regimes is discussed. When well is not the reservoirs center, an obvious upwards will appear after inner radial flow regime. It is showed by sensitivity analysis that different fracture distribution has obvious influence on radial flow regime of region 1. Compared increasing of fracture length, increasing of fracture number with short fracture length has obvious advantages. pressure curve of fractures staggered distribution is lower than that of fractures equal length distribution. This semi-analytical mathematical model can provide guide on pressure transient analysis controlled by an off-center fractured horizontal well in gas reservoir.

In order to accurately and intuitively characterize the distribution of water and water invasion channel in complex edge water reservoir, a water invasion unit numerical simulation model (WINS) that can simulate complex edge water invasion dynamics is established, based on well geological data and production data. The model discretizes the edge water into water unit connected to the production well unit, and discretizes the locations with clear geological understanding into dense unit. The more dense units, the more accurate the water invasion dynamics. Based on the water unit, production well unit, dense unit, the material balance method is used to calculate the pressure of each unit, the water flooding front propulsion equation is used to calculate the saturation and water cut of each unit, and the genetic algorithm is combined to modify characteristic parameters of the water unit and the water invasion channel, fit automatically production data, realize the re-identification of water distribution and water invasion channel. Different edge water and high-permeability bands are constructed through numerical simulator, and the simulated production results are substituted into the model to automatically fit. The results show that the edge water distribution and water invasion dominant channel inversely performed by WINS are consistent with the results constructed by the numerical simulator. Compared with the process of constructing edge water at the reservoir by Eclipse numerical simulator, WINS saves the tedious steps of building a model, and its calculation efficiency is higher. Not only that, WINS can intelligently and automatically fit parameters, reducing errors caused by human interference.

致密油气、页岩油气等非常规油气资源由于其储层渗透率低,在开采过程中往往采用水平井多级压裂技术来提高单井产量,实现经济开采.基于渗流力学,建立了考虑应力敏感、变裂缝导流能力的裂缝性油气藏多段压裂水平井试井数学模型,通过Laplace和Fourier变换等方法求得模型在Laplace空间下的无因次井底压力解;用Stehfest数值反演计算了实空间无因次井底压力.研究表明,当所有无因次裂缝导流能力之和不变时,如果井筒两端裂缝导流能力高于中部裂缝导流能力,早期阶段生产压差小,压力曲线低;当无因次裂缝导流能力沿裂缝方向减小时,无因次裂缝导流能力变化梯度越大,生产压差越大,早期阶段无因次压力曲线越高;应力敏感系数越大,无因次压力及压力导数曲线上翘幅度越大;裂缝储容比越小,窜流段压力导数曲线"凹子"越深;窜流系数越大,窜流发生越早.

With the output of formation fluids, pore pressure in the rock reduced and formation stress increased. Moreover, it can cause great changes of physical properties in the water-drive gas reservoir, such as sharp stress-sensitive effects around the wellbore area etc. In view of the threshold pressure and stress sensitivity’ influences on the transient pressure response in the bottom hole, a water-gas numerical welltest model has been established and solved. The corresponding plots have been drawn and the relative factors have been analyzed. The results proved that influences of stress-sensitive and threshold pressure should not be ignored, and the new model can interpret well test data more correctly than conventional methods.

The inclined well is used widely to enhance the single well production of the triple-porosity carbonate gas reservoir. This work presents an analytical solution of the inclined well in triple-porosity carbonate gas reservoir by Laplace transform and pressure drop superposition. According to well deviation well deviation pseudoskin factor of inclined well and the structure of approximations solution for the vertical well during pseudo-steady flow regime, approximations solution of the inclined well during pseudo-steady flow regime is obtained and Blasingame production decline model of inclined well is constructed. Calculation method of production prediction is presented by combining with material balance equation of the closed gas reservoir. The method was verified by comparing with numerical model. According to characteristic of dimensionless pseudo-pressure and production decline integration derivative curves, the seven obvious flow regime can be distinguished and every flowing regime is analyzed. With the increasing of perforated degree and inclination degree, Blasingame production decline curves become larger before pseudo-steady flow regime and constant-rate production time become longer. The larger interporosity flow coefficient and storativity ratio of vug system and naturally fracture system lead to earlier ‘concave’ starting-time and more shallow ‘concave’ of Blasingame production decline integral derivative curve separately. The larger interporosity flow coefficient and storativity ratio of vug system and naturally fracture system can also lead to longer constant-rate production time. The larger of initial rate and constant wellbore pressure is, the longer duration of constant-rate production is. A field example is presented to demonstrate the application of the proposed model and method.