The carbonate reservoir of the Yijianfang Formation - the 2nd Member of the Yingshan Formation in the Ordovician System of the Fuman Oilfield is a typical fault-controlled fractured-vuggy carbonate reservoir. For reservoir engineers, evaluating the dynamic reserves of single wells or connected units in this reservoir is a challenging task; improper evaluation will lead to large errors and even result in mistakes in development decisions. Based on the reservoir characteristics and flow characteristics of the Fuman Oilfield, this study established two well test analysis methods, namely the wellbore storage coefficient analysis method and the pressure drawdown well test analysis method. The basic principles and application conditions of each calculation method were elaborated respectively, and verification was conducted using field data. The calculation results show that the dynamic reserve calculation results obtained by the well test methods are consistent with those of the RTA (Rate Transient Analysis) method, which provides a reliable basis for formulating development technical policies of this type of reservoir and implementing enhanced oil recovery measures in the middle and later stages of reservoir development.

The carbonate reservoirs in the Ordovician Yijianfang Formation-Yingshan Formation of the Fuman Oilfield are typical fault-controlled fractured-cavity carbonate reservoirs. The well test analysis of single wells or interconnected units is challenging with three major difficulties: (1) The regimes of log–log curves are highly diverse, making well test model description difficult; (2) It is hard to determine the reservoir engineering parameters such as net thickness and porosity; (3) It is difficult to quantitatively determine the reservoir parameters such as permeability and cave volume. Based on well test data of more than 200 well times in the Fuman Oilfield, and by combining short-term well test data with long-term production history, this study classifies the reservoirs into four major categories (cave models, fracture models, pseudo-homogeneous models, and composite model) 1and sixteen subcategories, elucidates the characteristics of well test curves for each model, achieves the quantitative interpretation of wellbore storage factor and formation flow capacity, as well as qualitative description of reservoir dynamic characteristics in the Fuman Oilfield. It is important to note that the information obtained from the well test interpretation could be qualitative as well as quantitative. The well test interpretation results indicate that the wellbore storage factor and formation flow capacity are closely related to water injection effects; the cavity models have the highest wellbore storage factor and the best oil displacement effect by water injection; the composite model has the lowest wellbore storage factor and the poorest oil displacement effect by water injection. Based on the wellbore storage factor, water injection wells can be quickly optimized and the effects of water injection can be evaluated. The proposed method for well test analysis can provide reliable technical support for developing technical policies for such reservoirs and for enhancing oil recovery in the middle and later stages.

Because the binomial regression reserve evaluation method for geopressured gas reservoirs is only dependent on pressure and production data, which is simple and practical, it is widely used for reserve evaluation in the middle and late stages of development of such gas reservoirs. However, if the application conditions are not met, it can result in large errors which may affect development decisions. Currently, there is a lack of systematic definition on the applicable conditions of binomial regression method. This paper starts with the basic principle of binomial regression method, and proves that the method requires certain applicable conditions through field examples. Based on the material balance equation, the similarities and differences between the binomial and the limit form type curve are compared, and the binomial applicable range is given, and the workflow of binomial regression method is established. The results show that the error from binomial approximation method depends on the parameters representing the product of compressibility coefficient and reserves λD. The larger the λD, the higher the error. When λD = 0.43, the error of binomial approximation method is 10

Abstract A deep-water offshore oil field belongs to a carbonate reservoir with a depth of over 2000 meters, and is developed using large well spacing water gas alternating (WAG) flooding. Compared with onshore oilfields, single well investment in deepwater oilfields is high, and in order to achieve the goal of high production with thin wells, the requirements for well location deployment are higher. At the same time, the presence of heterogeneity in carbonate reservoirs further increases the difficulty of well layout. Therefore, optimizing the well location for the development of water gas alternative flooding in deep water carbonate reservoirs to achieve optimal cumulative production and economic benefits is a challenge. Optimization of well locations based on numerical simulation usually requires engineers to spend a lot of time and energy. With the rapid development of artificial intelligence (AI) technology, using machine learning algorithms to optimize well locations may be a fast and reliable solution. The research started with data processing. Firstly, data related to well location optimization parameters are collected and pre-processed, such as data filling and data normalization. Pearson algorithm is used to judge the importance of feature parameters according to correlation, and finally the interference between features is reduced by dimensionality reduction algorithm. After data processing, a reservoir agent model is established based on XGBoost (eXtreme Gradient Boosting), the Sparrow Search Algorithm (SSA) is used to optimize the hyperparameters of the model, and SSA-XGBoost is used to optimize the well location of deepwater carbonate reservoirs in multiple rounds. The results clearly show that AI is a powerful tool for optimizing well placement in deepwater carbonate reservoirs. SSA-XGBoost model scored 0.99 in the training set decision coefficient, 0.96 in the test set decision coefficient, and 0.83 in the verification set decision coefficient, which has higher prediction accuracy compared with other machine learning algorithms. This study provides a technical method for the location optimization of WAG flooding Wells in deep water carbonate reservoirs

Abstract Water gas alternate flooding is a successful oil recovery method applied in mining fields. Compared with conventional water gas alternate flooding in onshore oilfields, the use of water gas alternate flooding in deepwater oilfields has certain peculiarities. Due to limited gas export in deep-water oil fields, in order to improve oil recovery and meet environmental requirements, it is necessary to inject produced gas back into the ground, using a water gas alternating drive method based on the circulation of produced gas. However, there is little research on the optimization of injection and production parameters for water and gas alternate flooding in deepwater oil fields. This article conducts long core displacement experiments based on the geological characteristics and fluid properties of the studied deepwater oil fields, and compares the effects of three displacement methods: water injection, continuous gas drive, and water gas alternate drive. Based on the results of long core experiments and PVT fitting, a mechanism model for the development of water gas alternating mixed phase flooding at the field scale was established. The optimization of injection and production parameters, such as water injection timing, pressure maintenance level, water gas ratio, injection production ratio, and water gas alternation cycle, was carried out through numerical simulation in deepwater oil fields. The results of this study can provide a reference basis for optimizing injection and production parameters for the development of water and gas alternation in deepwater oil fields.

The interval from the Ordovician Yijianfang Formation to the 2nd member of Yingshan Formation in Fuman Oilfield is a typical fault-controlled carbonate fractured-vuggy reservoir. Its dynamic reserves estimation is a challenge for reservoir engineer. An improper estimation may result in large error and even mistakes in development decision-making. Based on the reservoir and flow characteristics as well as the challenges such as limited static pressure data, undefined development laws and difficult parameter determination in Fuman Oilfield, this paper proposes two methods, i.e. well test analysis and flowing material balance, to estimate the dynamic reserves. The basic principles and application conditions of the two methods are introduced, and verified with examples. The calculation results indicate that the dynamic and static reserves are basically consistent, providing a basis for the formulation of reservoir development strategies.

In order to overcome the defects that the analysis of multi-well typical curves of shale gas reservoirs is rarely applied to engineering,this study proposes a robust production data analysis method based on deconvolution,which is used for multi-well inter-well interference research.In this study,a multi-well conceptual trilinear seepage model for multi-stage fractured horizontal wells was established,and its Laplace solutions under two different outer boundary conditions were obtained.Then,an improved pressure deconvolution algorithm was used to normalize the scattered production data.Furthermore,the typical curve fitting was carried out using the production data and the seepage model solution.Finally,some reservoir parameters and fracturing parameters were interpreted,and the intensity of inter-well interference was compared.The effectiveness of the method was verified by analyzing the production dynamic data of six shale gas wells in Duvernay area.The results showed that the fitting effect of typical curves was greatly improved due to the mutual restriction between deconvolution calculation parameter debugging and seepage model parameter debugging.Besides,by using the morphological characteristics of the log-log typical curves and the time corresponding to the intersection point of the log-log typical curves of two models under different outer boundary conditions,the strength of the interference be-tween wells on the same well platform was well judged.This work can provide a reference for the optimization of well spacing and hydraulic fracturing measures for shale gas wells.

Estimating the original gas in place (OGIP) of high-pressure, ultra-high pressure, and fractured stress-sensitive gas reservoirs has always been challenging. This chapter focuses on 22 different methods for OGIP calculation based on the material balance equation combined with gas field examples, which generally fall into five categories, namely, classical slope two-segment analysis method, linear regression analysis method, nonlinear regression analysis method, type curve matching, and trial-and-error analysis method. In addition, the process and recommendations for OGIP estimation of high-pressure gas reservoirs are introduced.

The cretaceous gas reservoir in Kelasu Gas Field of the Tarim Basin is a rare ultra-deep and ultra-high pressure fractured tight sandstone gas reservoir where multi-scale discrete fractures of matrix, fracture and fault are developed, so its development cannot be conducted just based on static and dynamic reservoir description. In order to solve this problem, this paper establishes a numerical well test model of vertical wells based on matrix, fractures and faults (large fractures and small faults) by combining the random generation of natural fracture networks with the unstructured discrete fracture modeling method to break through the traditional continuous medium well test model. In addition, the model is solved by using the finite element method with mixed element, and the typical well test type curves under different random fracture networks are obtained. And the following research results are obtained. First, based on the observed data, the fracture network distribution modes of fractured tight sandstone gas reservoirs are classified into three categories. The influence of random generation of fracture networks on typical well test type curves is discussed. The results of discrete fracture well test model are compared with those of the traditional continuous medium well test model, and the applicable conditions of the traditional continuous medium well test model is determined. Second, there are great differences between the results of discrete fracture model and those of dual porosity medium model. 1 The dual porosity medium model is a special case of the discrete fracture model, in which the fractures are evenly distributed within infinitely small spacing. Third, the characteristics of well test type curves under three fracture network distribution modes are discussed. The well test type curves that cannot be interpreted by the conventional dual/triple porosity continuous medium model are successfully interpreted by using the established well test interpretation model of random discrete fracture. The curve matching effect is ideal and the interpreted parameters are reasonable. In conclusion, the new model and the new method reveal the development mechanism of step-by-step production and coordinated gas supply between media of different scales, explain the development characteristics of large inter-well productivity difference and abnormal rapid inter-well pressure response, and provide a reference for the development of similar gas reservoirs.

In order to improve the shale oil production rate and save fracturing costs, based on dynamic production data, a production-oriented optimization method for fracture spacing of multi-stage fractured horizontal wells is proposed in this study. First, M. Brown et al.'s trilinear seepage flow models and their pressure and flow rate solutions are applied. Second, deconvolution theory is introduced to normalize the production data. The data of variable pressure and variable flow rate are, respectively, transformed into the pressure data under unit flow rate and the flow rate data under unit production pressure drop; and the influence of data error is eliminated. Two kinds of typical curve of the normalized data are analyzed using the pressure and flow rate solutions of M. Brown et al.'s models. The two fitting methods constrain each other. Thus, reservoir and fracture parameters are interpretated. A practical model has been established to more accurately describe the seepage flow behavior in shale oil reservoirs. Third, using Duhamel's principle and the rate solution, the daily and cumulative production rate under any variable production pressure can be obtained. The productivity can be more accurately predicted. Finally, the analysis method is applied to analyze the actual dynamic production data. The fracture spacing of a shale oil producing well in an actual block is optimized from the aspects of production life, cumulative production, economic benefits and other influencing factors, and some significant conclusions are obtained. The research results show that with the goal of maximum cumulative production, the optimal fracture spacing is 5.5 m for 5 years and 11.4 m for 10 years. All in all, the fracture spacing optimization and design theory of multi-stage fractured horizontal wells is enriched.

Due to the randomness of fracture development in fractured reservoirs, natural fractures are highly discrete and irregular, and the existing continuous media seepage model cannot accurately describe the seepage law and reservoir dynamic characteristics. Therefore, based on the random generation of natural fracture network and unstructured discrete fracture modeling method, a stochastic discrete fracture unsteady seepage model of vertical wells in fractured gas reservoirs was established. The mixed element finite element method was used to solve the model, and the well test log-log type curves under different random fracture networks were obtained. The results of discrete fracture model and traditional continuum model are compared and analyzed, and the applicable conditions of traditional continuum model are clarified. The influence of random generation of fracture networks on well test curve is discussed, which provides theoretical guidance for well test interpretation using random generation of fracture networks. The results show that when the fracture networks are evenly distributed and the fracture spacing is very small, the results of the double porosity medium model are basically consistent with those of the discrete fracture model. The well test log-log type curves randomly generated by fracture networks are different, but the morphological characteristics are consistent. By analyzing the well test data of tight sandstone gas wells in Kelasu gas field of Tarim Basin, it is proved that the new model is reliable and practical. Through the model, the fracture network distribution parameters and conductivity similar to the actual reservoir can be obtained.

Multi-stage fractured horizontal wells are extensively used in unconventional reservoir; hence, optimizing the spacing between these hydraulic fractures is essential. Fracture spacing is an important factor that influences the production efficiency and costs. In this study, maximum fracture spacing in low-permeability liquid reservoirs is studied by building an integrated flow model incorporating key petrophysical characteristics. First, a kinematic equation for non-Darcy seepage flow is constructed using the fractal theory to consider the non-homogeneous characteristics of the stimulated rock volume area (StRV) and its stress sensitivity. Then, the kinematic equation is used to build an integrated mathematical model of one-dimensional steady-state flow within the StRV to analytically determine the pressure distribution in StRV. The resultant pressure distribution is utilized to propose an optimal value for the maximum fracture spacing. Finally, the effects of fractal index, initial matrix permeability, depletion, and stress sensitivity coefficient on the limit disturbed distance and pressure distribution are studied. This study not only enriches the fundamental theory of nonlinear seepage flow mechanics but also provides some technical guidance for choosing appropriate fracture spacing in horizontal wells.

The high-pressure physical properties of natural gas and formation water are essential parameters in calculating reserves using the material balance equation. This chapter discusses the physical properties of natural gas and formation water, commonly used empirical relations, and the conditions for their applications.

There are abundant marine carbonate rock resources in China, which are dominated by fractured-vuggy carbonate oil and gas reservoirs accounting for over two thirds of proved reserves. The fractured-vuggy carbonate condensate gas reservoir in the Tarim Basin is at a burial depth of 4500–7000 m with the characteristics of extremely strong reservoir heterogeneity, complicated and diverse reservoir seepage media, complex fluid properties and quite difficult static characterization, which brings many challenges to reserve evaluation, development plan design and performance analysis. In order to improve the recovery factor of this type of oil and gas reservoir, this paper takes the dynamic characterization to supplement the static characterization and combines each other to improve the accuracy. In addition, based on many years' of dynamic and static research and development practice, the key enhanced gas recovery (EGR) technologies for fractured-vuggy carbonate condensate gas reservoirs are innovatively developed, such as the high-accuracy dynamic characterization technology with dynamic and static iteration for fractured-vuggy body in the strongly attenuated area of desert by taking seismic inversion information as the basis and 3D numerical well test as the core, the multi-target 3D development technology in one well to improve reserve production of fractured-vuggy condensate gas reservoirs, and the gas-lift depressurization EGR technology for fractured-vuggy condensate gas reservoirs. In conclusion, this technological system better solves the key difficulties in the fine characterization of fractured-vuggy body, reserve production improvement and abandonment pressure reduction of well. What's more, it realizes the fine reservoir characterization of fractured zones and feather-shaped fractured zones and the accurate prediction of key development indexes, and increases the deployment success rate of effective wells and efficient wells by 26% compared with that in the initial stage of large-scale productivity construction. To sum up, these technologies provide powerful technical support and reference experience for the scientific and efficient development of fractured-vuggy carbonate condensate gas reservoirs.

In the exploitation process of unconventional tight oil reservoirs in modern times, the involved heterogeneous composite reservoirs are common; in such reservoirs, different rock compartments indicate different permeability properties. In ultra-low-permeability compartments, non-Darcy flow with a threshold pressure gradient (TPG) happens, but in relatively high-permeability compartments, Darcy flow happens. The existence of TPG introduces a nonlinear motion boundary problem, which makes a composite reservoir model coupling both Darcy flow and non-Darcy flow much more challenging. Here, a new model of one-dimensional flow in a heterogeneous composite reservoir with TPG is presented in consideration of a boundary motion process. Relying on a previous exact analytic solution for such a motion boundary problem in a homogeneous reservoir, semi-analytic solutions for the heterogeneous composite reservoir model are obtained by adopting the Laplace transformation method and mathematical arguments. Significantly, applications of Duhamel's principle in compartments with Darcy flow serve as a key procedure to analytically solve the model. And their semi-analytic versions are also validated. Finally, by relying on these solutions, the necessity of incorporating the motion boundary process is demonstrated in the mathematical modeling, and the deviation degree of the transient pressure type curves is also analyzed when the boundary motion process is neglected.

Non-Darcy flow with a threshold in fractal porous media has been widely used in the development of unconventional petroleum resources such as heavy oil and tight oil. Mathematical modeling of such challenging “threshold flow” problems with strong nonlinearity has great significance in improving petroleum science and technology. Based on a fractal theory, a new non-Darcy kinematic equation with a fractal threshold pressure gradient (TPG) is mathematically deduced in order to describe the non-Darcy flow of a non-Newtonian Bingham fluid with a threshold in fractal porous media. Then mathematical modeling of planar radial non-Darcy flow in a fractal heavy oil reservoir is performed as a nonlinear moving boundary problem. In addition, a steady analytical solution method and a transient numerical solution method are developed. The analytical solution of an ordinary differential equation system for a simple steady model is derived directly, and the transient numerical solution of a partial differential equation system for an unsteady flow model is obtained based on the finite element method with good convergence. These two model solutions are validated by cross-comparisons. It is found from the calculation results that for the steady state, the extremely disturbed moving boundary and its corresponding pressure distribution are affected only by a TPG, production pressure, and a transport exponent; by contrast, for the unsteady state, the moving boundary and its corresponding pressure distribution are affected by many more factors including the fractal dimension. Furthermore, neglect of the fractal TPG and the induced moving boundary can lead to high overestimation of well productivity.

The Keshen gas field in the Kuqa Depression, the Tarim Basin, China, contains multiple ultra-deep fractured tight sandstone gas reservoirs with edge/bottom water, which are remarkably complex in geologic structure, with fracture systems at different scales. There is still a lack of a method for effectively describing the flow behaviors of such reservoirs. In this paper, the fracture system was characterized by classes using the actual static and dynamic data of the gas reservoirs, and the mathematical models of gas (single-phase) and gas-water two-phase flows in “pore–fracture–fault” multi-porosity discrete systems. A fracture network system was generated randomly by the Monte-Carlo method and then discretized by unstructured grid. The flow models were solved by the hybrid-unit finite element method. Taking Keshen-2/8 reservoirs as examples, four types of dynamic formation modes were built up. Performances of reservoir of the same category were systematically analyzed, which revealed the coupling of gas supply and water invasion mechanisms in different fracture systems. The gas single-phase flow was found with the characteristic of “fault–fracture gas produced successively and matric-fracture system coupling overlaid”, while the gas-water two-phase flow showed the characteristic of “rapid water dash in fault, drained successive in fractures and matric block divided separately”. This study reveals the development features of this unique reservoir effectively, and designs development strategies of full life cycle water control for enhancing the gas recovery. It can be expected that the recovery factor of newly commissioning reservoirs would be increased by more than 10% as compared with the Keshen-2 gas reservoir. These findings will play an important role in guiding high and stable production of Keshen gas field development in the long term.

Ultra-deep major gas fields are typically characterized by high and ultra-high pressure, tight matrix and developed fractures, so the reserve estimation is of higher uncertainty. In order to accurately estimate the reserves of this type of gas reservoir, this paper analyzed the correlation between the effective rock compressibility and the cumulative effective rock compressibility based on the material balance equation of high and ultra-high pressure gas reservoirs, and accordingly selected the material balance based analysis method suitable for the reserves estimation of high and ultra-high pressure gas reservoirs. Then, the starting calculation conditions of reserve estimation were determined using the non-linear regression method. In addition, a semi-logarithmic type curve matching method was established for the cases where the starting conditions could not be met. Finally, this method was applied to calculate the reserves of three ultra-high pressure gas fields (reservoirs) to verify its reliability. And the following research results were obtained. First, the cumulative effective compressibility of gas reservoir in the material balance equation of high and ultra-high pressure gas reservoir is a key parameter influencing its reserves, and it is the function of original formation pressure and current average formation pressure, but its numerical value can be hardly obtained by core experiments. Second, it is recommended to adopt the nonlinear regression method without compressibility to estimate the reserves of high and ultra-high pressure gas reservoirs. Third, the calculation starting point of reserves by the nonlinear regression method (the starting point of dimensionless apparent formation pressure-cumulative gas production curve deviating from the straight line relationship) cannot be theoretically calculated. The calculation starting point for different dimensionless linear coefficients (ωD) obtained from the statistical results by the graphic method corresponds to the dimensionless apparent pressure depletion degree of 0.06–0.38, and that obtained based on the data statistics of the example gas reservoir falls within this interval. Fourth, when the starting conditions are not satisfied, the semi-logarithmic type curve matching method can be used for reserve estimation. The ratio of the reserves to the apparent geological reserves G/Gapp is a function of ωD.The higher the ωD, the lower the G/Gapp. Fifth, for the high and ultra-high pressure gas reservoirs in the production test stage, the test production time shall be extended as long as possible to improve the reliability of reserve estimation. And for those in the middle and late stages of development, it is necessary to prepare the comprehensive treatment measures on the basis of reserves so as to improve the development effects of gas reservoirs continuously.

There is high uncertainty in reserve estimation during the early development of deep ultrahigh pressure gas reservoirs, largely because it remains challenging in accurately determining the formation compressibility. To overcome this, starting from the definition of compressibility, a novel gas production of cumulative unit pressure drop analysis method was established, of which the effectiveness was proven by applications in calculating the reserves of three gas reservoirs. It has been found that, in the limiting case, i.e., when the formation pressure dropped to the normal atmospheric pressure, the dimensionless gas production of the cumulative unit pressure drop was the reciprocal of the initial formation pressure. Besides, the relationship curve of the dimensionless gas production of the cumulative unit pressure drop and pressure drop was a straight line in the medium term, extending the straight line and intersecting the vertical line passing through the original formation pressure point, and the reserves can be determined according to the intersection point and the initial formation pressure. However, due to the influence of natural gas properties, the value needs further correction, and the correction coefficient depends on the pseudocritical temperature of natural gas. Specifically, when the pseudocritical temperature is given, the correction coefficient would be close to the minimum value of the natural gas deviation factor. When the pseudocritical temperature is more than 1.9 and less than 3.0, the minimum deviation factor would be between 0.90 and 1.0, and the higher the pseudocritical temperature, the closer the ratio is to 1.0.