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.

Well-test interpretation is an important means to obtain reservoir parameters. However, the traditional well test interpretation method of fractured horizontal wells is limited due to the computational efficiency of the well test model. This paper proposes an automatic interpretation method for well-test curves based on neural networks. Considering the basic parameters of the reservoir, the dimensional pressure, pressure derivative, and time data are used as samples to train the network. The well test data are processed and input into the trained optimal network to automatically identify well test parameters such as reservoir permeability. Mini-batch gradient descent with a batch size of 32 was used to train the network. The results showed that the network training achieved a lower loss function value and the best performance. Adaptive learning rate decay and increased samples were adopted to improve the parameter inversion accuracy. In addition, the two-dimensional convolutional neural network was compared with the fully connected neural network. We validate the results that the two-dimensional convolutional neural network had better parameter inversion accuracy and noise resistance than the fully connected neural network. Finally, two cases were used to further verify the parameter inversion 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).

近期,国家规划在四川盆地建设天然气千亿立方米产能基地.为了推动和保障该产能基地的顺利建设,在回顾四川盆地天然气开发历程的基础上,提炼了各发展阶段的特点,论述了天然气开发领域基础理论和关键技术进展,展望了天然气开发关键技术发展方向.研究结果表明:①四川盆地现代天然气工业经历了探索起步期、储产缓增期、快速增长期、多源全兴期四个阶段;②钻井、储层改造技术主要体现在深井超深井钻井、水平井分段多簇密切割压裂和碳酸盐岩体积酸压,气藏工程主要体现在碳酸盐岩渗流模型表征、复杂气藏流体相态分析、压裂—生产一体化数值模拟、复杂气藏气井试井方面,排水采气技术主要体现在井筒积液规律诊断和组合式排采工艺,高含硫气藏安全生产在深井超深井安全高效建井和井下、地面设施腐蚀控制技术等方面取得长足进步;③未来发展主要面向碳酸盐岩气、致密砂岩气、页岩气和煤层气,深化复杂多重介质传质理论研究,着力提升钻完井、储层改造、排水采气等关键技术的信息化、智能化水平.结论认为,梳理的关键技术和发展方向将加快四川盆地天然气工业发展,促进该盆地尽快建成千亿立方米天然气生产基地.

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.

Normalized Pressure Integral（NPI） Production Analysis is a kind of modern production decline analysis method which defines new parameters by integral. It can not only reflect the pseudo-steady state flow stage influenced by outer boundary, but also can reflect the unsteady state flow stage. In order to study the NPI production decline analysis method of carbonate reservoir, we established triporate-uniphase parallel inter-porosity flow model. In this model, fracture is the main flow channel and inter-porosity flow happens from cave to fracture and matrix to fracture. The bottom hole pseudopressure solution with considering the effect of skin factor of this model was obtained by Laplace transform and Duhamel principle. The NPI method curves were plotted by using normalized pressure integral method and Stehfest numerical inversion. And the curves can reflect the production performance of this model accurately. The storage ratio, inter-porosity flow coefficient, and dimensionless outer boundary radius were chosen to be sensibility parameter for sensibility analysis. The result shows that the storage ratio mainly influences the depth of depression on derivative curve and the inter-porosity flow coefficient mainly influences the time when inter-porosity flow stages happen. The skin factor just influences the dimensionless pseudopressure and dimensionless pseudopressure integral curves, while the dimensionless outer boundary radius will also influence the unsteady state flow stage of derivative of dimensionless pseudopressure integral curve.

规整化压力积分(NPI)产量递减分析方法是一种使用积分定义新参数的现代产量递减分析方法,它不仅可以反映出受边界影响的拟稳定流动阶段特征,还可以反映出早期不稳定流动阶段特征.为了研究碳酸盐岩储层NPI产量递减分析方法,建立三孔单渗并行窜流模型,其中裂缝为主要渗流通道,溶洞与基质流体分别向裂缝窜流,通过拉普拉斯变换和杜哈美原理求得了考虑表皮效应影响下的井底无因次拟压力解;再通过压力积分方法和Stehfest数值反演方法,绘制的NPI产量递减分析方法复合曲线反映出了三孔单渗并行窜流碳酸盐岩储层的生产特征;讨论了弹性储容比、窜流系数和供给半径对NPI方法复合曲线的影响.研究表明:弹性储容比主要影响导数曲线下凹段的深浅,窜流系数主要影响导数曲线下凹段出现的早晚,供给半径主要影响曲线的早中期不稳定流动阶段特征.

寻求一种实用、有效的油气藏形状位置因子(以下简称形状因子)计算方法,对于准确获取复杂结构井拟稳态流动阶段井底压力渐近解及产能指数具有重要的意义.为此,针对不同形状封闭边界油气藏中的直井,根据试井分析曲线——压力及压力导数曲线之间的关系,重新计算形状因子,并且与Dietz形状因子进行对比;在此基础上,推导出复杂结构井拟稳态流动阶段井底压力渐近解并进行验证,进而绘制了 Blasingame递减曲线典型图版.研究结果表明:①通过计算不同形状封闭边界直井拟稳态流动阶段无因次井底压力及压力导数,求得两者的差值,则可以反求形状因子,并且采用该方法计算的形状因子与Dietz形状因子结果非常接近,验证了该方法的准确性;②通过求取复杂结构井拟稳态流动阶段无因次井底压力及压力导数之差,可以求得复杂结构井拟稳态流动阶段井底压力渐近解系数(bDpss),进而可以获得任意复杂结构井拟稳态流动阶段井底压力渐近解;③基于新方法计算的大斜度井拟表皮因子与Ozkan等的计算结果相对误差在1％以内,验证了新方法的准确性;④对于矩形封闭边界油气藏中的常规直井,拟稳态流动阶段Blasingame递减曲线的无因次产量曲线斜率为-1,并且长宽比越大,晚期线性流特征越明显;⑤对于矩形封闭边界油气藏中压裂直井,在外边界长度一定的情况下,若长宽比越大,单井控制面积则越小,bDpss越大,晚期线性流特征越明显,Blasingame递减曲线在非稳态流动阶段所处的位置越高,而在单井控制面积相同的情况下,若无因次裂缝导流能力越大,bDpss则越小,Blasingame递减曲线在非稳态流动阶段所处的位置越高.结论认为,采用该新方法可以快速、准确地获取任意复杂结构井拟稳态流动阶段井底压力渐近解,为复杂结构井Blasingame递减曲线典型图版的绘制提供了便捷有效的方法.

Large-scale vertical well fracturing leads to formation of multi-wing fractures, which can effectively reduce fluid seepage resistance and increase single well production. As one of the post-fracture evaluation methods, pressure transient analysis is used widely in oil/gas field evaluation by engineers. It is of great significance for petroleum engineers to choose the correct and appropriate well test model for the accurate evaluation of formation parameters. Since oil/gas outer boundary is often rectangle or arbitrarily shape, a semi-analytical model of multiwing fractured well (MWFW) with arbitrarily shaped outer boundary gas reservoirs is presented. The reservoirs and hydraulic fracture mathematical models are established and solved. Coupling reservoirs and hydraulic fracture solution, and then discreting hydraulic fracture and outer boundary. The wellbore pressure solution with arbitrarily shaped outer boundary is obtained by pressure drop superposition, boundary element method (BEM) and Stehfest numerical inversion method. The bi-wing symmetrical hydraulic fracture and MWFW with finite conductivity are verified respectively by using numerical solution and comparison results reaches a good match, which certifies the correctness of the model and solving method. Typical curves of wellbore pressure and rate decline are discussed and influence of conductivity, hydraulic fracture number and hydraulic fracture distribution style et al. on wellbore pressure and rate decline is analyzes by combining with rate distribution of different time and segment. Influence of other parameters (Storativity ratio, interporosity coefficient and boundary shape size) on wellbore pressure and rate decline is also discussed in the end of paper.

Vertical wells large scale fracturing and stimulated reservoir volume (SRV) treatments is an important method to enhance productivity of shale gas wells. Since the existence of micro-fractures in shale reservoirs, micro-fractures are opened and connect with hydraulic fracture after vertical wells large scale fracturing. Of course, some microfractures do not connect with hydraulic fracture, which leads that average permeability around wellbore is higher than reservoirs permeability. A radial composite model is used to describe the physical phenomenon with SRV region. Therefore, a semi-analytical model of hydraulic fractured well with induced fractures in composite shale gas reservoirs is established and solved by the Laplace transform, pressure drop superposition, vertex rate balance. Wellbore pressure solution of real domain is obtained by the Stehfest numerical inversion. The simplified model is verified by numerical solution and comparison result gets a good match. According to the difference between pressure and pressure derivative curve, wellbore pressure approximate solution of this model during pseudo-steady flowing regime is obtained. According to the wellbore pressure derivative curve and Blasingame production decline integral derivative curve, the seven flow regimes can be distinguished and curve characteristic of every flow regime is analyzed. The influence of hydraulic fracture conductivity, induced fracture number, Langmuir volume, SRV region radius, permeability ration et al. on wellbore pressure response, Blasingame production decline curve is discussed in detail. This work provides a method to calculate single well controlled reserves with short production time by pressure transient and Blasingame production decline analysis for hydraulic fractured wells with induced fracture.

Generally, the horizontal well multi-stage fracturing technology is widely used to enhance single well production of tight or ultra-low permeability gas reservoirs. The deformation of the rock pore structure makes the permeability of the reservoir impossible to be a constant. The pressure transient analysis mathematical model of the multi-stage fractured horizontal wells (MFHWs) with consideration of stress sensitivity, varying conductivity and dual-porosity dual-permeability (DPDP) is established. Laplace transformation, pressure drop superposition and Gaussian elimination are utilized to obtain the wellbore pressure solution of MFHWs. Comparison result reaches a good agreement by model validation. On the basis of pseudo-pressure derivative curve characteristics, eight flow regimes can be diagnosed, namely, well storage, skin affection, bi-linear flow, early linear flow, early radial flow, middle linear flow, inter-porosity flow and later radial flow regime. The influences of some vital parameters on pseudo-pressure and its derivative curve is discussed in detail. The proposed model can help engineers understand the pressure dynamic characteristic of the MFHWs with stress sensitivity, varying conductivity and DPDP performance.

致密油藏由于渗透率低,表现出很强的非线性渗流特征,因此多采用水平井多级压裂技术提高单井产量.基于此,考虑了应力敏感和启动压力梯度的影响,根据物理模型建立裂缝性致密油藏多级压裂水平井试井模型,通过Laplace变换和有限余弦Fourier变换对数学模型进行求解,离散压裂裂缝并结合压降叠加原理,求得有限导流多级压裂水平井井底压力解.将文中的简化模型解与Saphir模型数值解进行对比,验证了简化模型的准确性;根据压力导数曲线特征,将裂缝性致密油藏多级压裂水平井井底压力响应特征曲线分为9个流动阶段,并分析了每个阶段渗流特征及各参数(裂缝分布、窜流系数等)对曲线的影响.该模型可以为裂缝性致密油藏多级压裂水平井试井资料解释和压裂方案设计提供理论依据.

With the development of hydraulic fracturing technology of horizontal well, most unconventional gas reservoirs are developed by horizontal well multi-stage fracturing technology to improve gas well production. In this paper, we present a semi-analytical model of multi-stage fractured horizontal well (MFHWs) with consideration of adsorbed gas desorption and the irregular hydraulic fractures distribution in shale gas with the stimulated reservoir volume (SRV). On the bases of the point source function, Langmuir isotherm adsorption and Fick's law, wellbore pseudo-pressure solution of finite-conductivity MFHWs model is obtained by employing Laplace transform, finite cosine Fourier transform. and the discrete fracture approach in shale gas. The pressure transient responses log-log curves of MFHWs are drawn by Gauss elimination method and Stehfest numerical algorithm. In the light of the characteristics of the pressure derivative curve, the characteristics of each flow stage are identified and analyzed in detail. With the comparison of the commercial well test software numerical solution and the previous literature, the comparison results reach a good agreement under condition of same parameter. The effects of vital parameters, such as hydraulic fractures number and size of the SRV region, hydraulic fractures distribution styles and crossflow coefficient, on pressure transient curve are analyzed in detail. The presented model in this paper not only provides some insights for pressure dynamic analysis of shale gas reservoir development, but can help to engineers understand the pressure dynamics in shale gas reservoirs with SRV and irregular fracture distribution.

It is commonly believed that matrix and natural fractures randomly distribute in carbonate gas reservoirs. In order to increase the effective connected area to the storage space as much as possible, highly deviated wells are widely used for development. Although there have been some studies on the composite model for highly deviated wells, they have not considered the effects of stress sensitivity and threshold pressure gradient in a dual-porosity gas reservoir. In this paper, a semi-analytical composite model for low permeability carbonate gas reservoir was established to study the effect of non-Darcy flow. By employing source function, Fourier transform and the perturbation method, the pressure performance and typical well test curves were obtained. Eight flow regimes were identified, and their characteristics were discussed. As a result, it can be concluded that the effects of stress sensitivity and threshold pressure gradient would make pseudo-pressure and derivative curves rise, which is the characteristic of non-Darcy flow to determine whether there is stress sensitivity or threshold pressure gradient.

Selectively completed horizontal wells (SCHWs) can significantly reduce cost of completing wells and delay water breakthrough and prevent wellbore collapse in weak formations. Thus, SCHWs have been widely used in petroleum development industry. SCHWs can shorten the effective length of horizontal wells and thus have a vital effect on production. It is significant for SCHWs to study their rate decline and flux distribution in naturally fractured reservoirs. In this paper, by employing motion equation, state equation, and mass conservation equation, three-dimension seepage differential equation is established and corresponding analytical solution is obtained by Laplace transform and finite cosine Fourier transform. According to the relationship of constant production and wellbore pressure in Laplace domain, dimensionless rate solution is gotten under constant wellbore pressure in Laplace domain. Dimensionless pressure and pressure derivate curves and rate decline curves are drawn in log-log plot and seven flow regimes are identified by Stehfest numerical inversion. We compared the simplified results of this paper with the results calculated by Saphir for horizontal wells in naturally fractured reservoirs. The results showed excellent agreement. Some parameters, such as outer boundary radius, storativity ratio, cross-flow coefficient, number and length of open segments, can obviously affect the rate integral and rate integral derivative log-log curves of the SCHWs. The proposed model in this paper can help better understand the flow regime characteristics of the SCHWs and provide more accurate rate decline analysis of the SCHWs data to evaluate formation.

Multi-wing and asymmetrical hydraulic fractures around wellbore are usually observed in hydraulic fracturing and refracturing treatments. Therefore, it is significant for us to study pressure transient analysis. In this paper, by employing Laplace transform and finite cosine Fourier transform, a new semi-analytical model was deviated and solved under condition of constant rate for multi-wing fractured wells (MWFWs) of finite conductivity in hydrocarbon reservoirs with dual-permeability behavior in Laplace domain. Stehfest inversion algorithm can be adopted to obtain wellbore pressure of MWFWs in real domain. The solution of the simplified model in this paper was validated with dual porosity dual-permeability and asymmetrical hydraulic fracture, and results reach a good agreement. Type curve, according to pressure derivative characteristic, can be divided into six regimes (bilinear flow, linear flow, radial flow of natural fractures, cross flow and radial flow of system). The influence of some vital parameters (dimensionless conductivity, storage coefficient, crossflow coefficient, permeability ratio et al.) on dimensionless pressure and its derivative curves were analyzed in details. The presented model can be used to understand pressure transient characteristic of MWFWs in hydrocarbon reservoirs with dual-permeability behavior.

为了分析聚合物驱油藏压力动态特征,根据聚合物驱油过程,建立牛顿-非牛顿双区复合直井压裂井试井解释数学模型.基于点源函数基本理论,利用Laplace积分变换和有限余弦傅立叶变换求得无限导流压裂井拉氏空间解析解,结合裂缝导流能力函数求得牛顿-非牛顿双区复合油藏有限导流垂直裂缝井试井解释数学模型的解析解,通过Stehfest数值反演计算并绘制典型无因次井底压力、压力导数特征曲线.研究表明,幂律指数对井底压力变化具有一定的影响,幂律指数小,非牛顿区压力、压力导数曲线上翘越明显,且呈斜率为(1-m)/(3-m)的直线;导流能力越大,双线性流阶段特征越不明显;牛顿-非牛顿区流度比越大、牛顿区半径越小,非牛顿区压力和压力导数曲线位置越高.该模型对聚合物驱试井资料解释和聚驱效果评价具有重要作用.

压裂改造是提高油田产量、改善井筒附近储层物性的重要方法,但在实际多段压裂体积改造过程中,由于地层条件复杂,导致井筒附近形成了复杂的缝网体积,因此,加强对水平井体积压裂改造试井模型的研究十分必要.基于体积压裂水平井复杂裂缝分布的渗流特征,建立径向复合多段压裂水平井试井解释数学模型,耦合储层与裂缝模型解求得Laplace空间井底压力半解析解,应用Duhamel原理得到考虑井储和表皮影响的Laplace空间井底压力解,利用Stehfest数值反演求得实空间井底压力,并绘制实空间压力动态特征曲线.根据压力导数曲线特征划分流动阶段,通过模型验证证明了该方法的正确性,进而分析了裂缝不对称、裂缝夹角、裂缝分布方式、内区半径和流度比对特征曲线的影响.结果表明,裂缝不对称交错分布有助于增大裂缝控制面积,从而减少流体流入井筒的压力消耗,早期阶段对应的压力曲线也越低;内区半径越大,压裂改造效果越明显,对应压力曲线越靠下.该模型可为多段压裂水平井所形成的复杂裂缝试井资料解释和压裂方案设计提供理论依据.

Here, the adsorption and diffusion of CH4 and the intruding gases in coal were systematically simulated via Monte Carlo. The adsorption selectivity of carbon dioxide over methane (SCO2/CH4, >1) decreases significantly at P < 6 MPa and is kept stable when P > 6 MPa. However, S-N2/(CH4) (<1) monotonously increases with the increasing pressure, temperature, and bulk mole fraction (BMF) of N-2. Both the cross exchange (D-i,D-j) and diagonal diffusion (D-i,D-i) coefficients in the nCO(2) + mCH(4) and nN(2) + mCH(4) systems gradually increase with the increasing temperature. D-i,D-j is far higher than D-i,D-i for these two systems, indicating the weaker coupling strength of gas-gas interactions than the gas-coal interactions. D-11(1) (or D-11(2)) increases while D-22(1) (or D-22(2)) decreases with the increase of CO2 (or N-2) BMF. The swelling ratios of nCO(2) + mCH(4) and nN(2) + mCH(4) increase slightly at temperatures lower than 338 K and significantly at temperatures higher than 338 K, and both of them are positively related to BMFs of CO2 and CH4, respectively. Both S-CO2(/CH4)d and S-N2(/CH4)d increase with the increasing BMF of carbon dioxide and methane, respectively, indicating that the replacement effects of CO2 and N-2 engineering are weightily related to the mole fractions of the invading gases. S-CO2(/CH4)d first increases (<= 398 K) and then decreases (398 < T < 438 K). Concerning the geological conditions, the optimization injection depths were 800-1100 m (7.94-10.88 MPa) and 600-900 m (5.98-8.92 MPa) for carbon dioxide and nitrogen, respectively.

The use of multiple hydraulically fractured horizontal wells has been proven to be an efficient and effective way to enable shale gas production. Meanwhile, analytical models represent a rapid evaluation method that has been developed to investigate the pressure-transient behaviors in shale gas reservoirs. Furthermore, fractal-anomalous diffusion, which describes a sub-diffusion process by a non-linear relationship with time and cannot be represented by Darcy’s law, has been noticed in heterogeneous porous media. In order to describe the pressure-transient behaviors in shale gas reservoirs more accurately, an improved analytical model based on the fractal-anomalous diffusion is established. Various diffusions in the shale matrix, pressure-dependent permeability, fractal geometry features, and anomalous diffusion in the stimulated reservoir volume region are considered. Type curves of pressure and pressure derivatives are plotted, and the effects of anomalous diffusion and mass fractal dimension are investigated in a sensitivity analysis. The impact of anomalous diffusion is recognized as two opposite aspects in the early linear flow regime and after that period, when it changes from 1 to 0.75. The smaller mass fractal dimension, which changes from 2 to 1.8, results in more pressure and a drop in the pressure derivative.