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Fracture-caved carbonate reservoirs (FCCRs) have been developed worldwide and contribute significantly to world's hydrocarbon reserves. Numerous models for FCCRs were proposed in the previous works. However, with more and more exploitations, some kinds of FCCRs are observed from the field geological information but not reported in the existing literature. In this paper, a novel model for FCCRs is proposed and its corresponding pressure transient analysis (PTA) and rate transient analysis (RTA) solutions are presented. This model has a wider applicability than the previous models proposed by our research team. First, the geological model is established based on the geological information. Sequentially, the simplified physical model and the mathematical model are developed. Through Laplace transformation, Duhamel's principle, and Stehfest numerical inversion, the solutions of dimensionless bottom-hole pressure and dimensionless flow rate integral are derived. Then, the RTA type curves of two-cave model are plotted to recognize the flow characteristics, which can be divided into five regimes comprehensively. In addition, two concaves are observed on the derivative curve. The RTA type curves of three-cave model are also presented. A comparison between the RTA type curves of two-cave model and three-cave model shows that when one more cave exists in the formation, one more concave will be added to the derivative curve. Furthermore, the differences between the proposed model and previous models are presented through comparing the PTA type curves. Next, the effects of key parameters on the RTA curve behavior of two-cave model are demonstrated. Results indicate that the RTA curves are controlled by the friction and fluctuation coefficients, mobility, storage ratio, region radius, and cave storage constant. The friction and fluctuation coefficients influence the depth of first concave, while the storage ratio, region radius, and cave storage constant dominate the middle flow period, and the mobility has an impact on the boundary dominated flow regime. Finally, the application of proposed model on a field well from Shunbei Oilfield, western China is presented to calibrate its accuracy and reliability. ∙ A novel model for fracture-caved carbonate reservoirs is established. ∙The rate transient characteristics of this model is conducted. ∙Sensitivity studies of some key parameters on the pressure response are conducted. ∙An application of proposed model on a field well is presented. [ABSTRACT FROM AUTHOR]

Shale gas reservoirs contribute significantly to hydrocarbon production because of their abundant reserves. Shale formation is characterized by low permeability and extremely low porosity. Horizontal well drilling and hydraulic fracturing treatments are typical methods for stimulating the shale gas reservoirs. The discrete fracture model has been widely used to describe flow problems in fractured media. Rock deformation is an important process that occurs simultaneously with the gas flow during the production period and cannot be neglected when modeling the gas flow in shale formations. The matrix permeability, matrix porosity, fracture permeability, and fracture aperture are all considered pressure-dependent parameters when accounting for rock deformation. Two inadequacies exist in previous studies on modeling shale gas flow in deformable rock. One is determining the values of pressure-dependent parameters using an explicit method, which means that the pressure-dependent parameters in the next time step are calculated according to the pore pressure of the last time step and remain constant in the iterative solving process of the next time step. During the production, the pore pressure always decreasing, which leads to compression in fractures and a reduction in the fracture permeability and aperture. The explicit method inevitably causes an overestimation of the reservoir productivity. Another inadequacy is neglecting the effect of the change in fracture geometry. In this paper, a fully implicit and fully coupled numerical scheme for discrete fracture modeling of shale gas flow in deformable rock is proposed to reduce the computational error. A comparison between the results of no rock deformation, an explicit method, and implicit method and a field example are presented to calibrate the accuracy of proposed scheme. Another comparison between the explicit and implicit methods shows that the implicit method can noticeably reduce the overestimation caused by the explicit method. The effects of the controlling parameters on the relative difference between the explicit and implicit methods are demonstrated. The results show that the initial permeability of the hydraulic fracture has negligible influence on the relative difference. The initial permeability and compression coefficient of the natural fracture are the main influencing parameters, the initial matrix permeability has a limited impact on the relative difference. The relative difference is caused by the comprehensive effect of k ij and (A / d) ij terms. • A fully implicit and fully coupled numerical scheme for DFM is proposed. • The numerical scheme is derived in detail. • The comparison between the explicit and implicit methods are presented. • Sensitivity study of key parameters on the relative difference are conducted. [ABSTRACT FROM AUTHOR]

The bead-on-a-string structure has been widely observed in many fractured vuggy carbonate reservoirs, especially in Shunbei oilfield, northwestern China. To date, there are still no appropriate well test methods for analyzing these reservoirs with the vertical bead-on-a-string structure. This paper proposes a new theoretical well test model, which considers the gravity effect and the natural fractures connecting the vuggs, to analyze this kind of reservoirs. First, we establish the mathematical model of fractured vuggy reservoirs with the vertical bead-on-a-string structure. With the different outer boundary conditions, Laplace transform and inversion are employed to solve the well test model. Then, the type curves for the well test model are plotted and discussed. It is found that the gravity effect can be equivalent to a type of constant pressure boundary condition. Take the three-region-two-cave as an example, type curves can be divided into nine distinct flow regimes, including wellbore storage, skin, linear flow I and II, transition flow I and II, vug storage I and II, and boundary flow. The transition flow and vug storage period are named as the vug storage effect. Subsequently, the effects of relevant parameters are studied. It is concluded that the depth of the drop during vug storage effect increases with increasing dimensionless vug storage constant C vD and dimensionless vug height z D 2 - z D 1 ; the greater dimensionless gravity effect coefficient G D leads to the smaller equivalent boundary distance of the constant pressure boundary condition; the smaller the mobility ratio M 12 , the earlier the appearance of the second linear flow regime; the larger the storage ratio ω 12 , the more distinct the vug storage effect. Finally, two field case studies are carried out by using the proposed method. The locations and volumes of the caves are estimated, which shows that the proposed theoretical well test model has a great potential of obtaining the formation and cave parameters accurately. However, there is not available data that enable an accurate description of the locations and volumes of the caves by now, the proposed model still needs further field verifications. • A new mathematical model of fractured vuggy carbonate reservoirs considering the gravity effect is established. • It is found that the gravity effect can be equivalent to a type of constant pressure boundary condition. • Two filed cases show the great potential of the proposed method to the fractured vuggy carbonate reservoirs. [ABSTRACT FROM AUTHOR]

Vugs usually exist dispersedly in the formation of fractured vuggy carbonate reservoirs. The vug volume is an important parameter, owing to its significant contribution to oil reserves. However, at present, no reliable method is available for estimating the vug volume. This paper presents an analytical multi-zonal composite reservoir well test model that can determine the vug volume. First, the mathematical model is established according to the simplified physical model, and the analytical solution to the mathematical model is derived using Laplace transform. Second, based on the analytical solution, the type curves of dimensionless wellbore pressure and derivative versus dimensionless time, are plotted through numerical inversion. We use the two-vug model as an example to recognize the flow characteristics, and observe that 10 distinct flow regimes exist with two concaves. Furthermore, by comparing the single-vug and multi-vug models, an interesting finding is that one more concave will be added into the derivative curve when one more vug is present in the formation. The vug volume can be obtained by means of the pressure transient analysis. Also, the characteristics of our model are further exhibited by comparing it with the dual porosity model and the conventional composite model. And, a comparison with the conventional composite model and a field case are conducted to verify the validity and reliability of the proposed model in this study. Finally, the effects of each parameter on the pressure and derivative responses are analyzed. The pressure behavior is influenced by the mobility ratio, storage ratio, vug storage constant, and region radius. The mobility and storage ratios mainly affect the vug storage regimes, while the vug storage constant has an important impact on the concave depth and location, and the radial flow regime is dominated by the region radius. • An novel analytical well test model for multi-vug fractured vuggy carbonate reservoirs is established. • The analytical solutions of the well pressure response are obtained. • The pressure response of a well in this reservoir is analyzed. • Sensitivity studies of some key parameters on the pressure response are conducted. [ABSTRACT FROM AUTHOR]

The binomial deliverability equation is one of the essential parameters that control the fluid production/injection rate from wells. The presence of caves and fractures introduces many difficulties related to the determination of the binomial deliverability equation of fractured caved carbonate reservoirs. In this work, a novel method for determining the binomial deliverability equation of fractured caved carbonate reservoirs is proposed for the first time. First, the detailed procedure of our method is illustrated. More specifically, the superposition principle is used to derive the expressions of (Δ p / Q). The pressure buildup data and type curve matching are employed to induce the dimensionless bottom-hole pressure solution. Sequentially, the binomial deliverability equation can be obtained through the least square method. Then, we employ our method to a simple case and compare the calculation results with the literature data to calibrate the accuracy of our method. Next, we present the applications of our method to two example wells from the Shunbei Oilfield, western China. The results show that our method is reliable. Moreover, the results also indicate that our method is more suitable for fractured caved carbonate reservoirs than the deliverability test. Meanwhile, through the calculations of massive field data and theoretical analysis, we conclude three constraints on the input parameters. They are as follows: (i) the flow rate of each production system must be incremental; (ii) the production time must satisfy t p 1 = t p 2 – t p 1 = t p 3 – t p 2 = t p 4 – t p 3 ; and (iii) the flow rate must satisfy Q 2 = 2 Q 1 , Q 3 = 3 Q 1 , Q 4 = 4 Q 1. Finally, we prove the necessity of these constraints. • A new method for determining the binomial deliverability equation of fractured caved carbonate reservoirs is proposed. • Applications of proposed method on two field wells are presented. • Three constraints on input parameters are concluded and their necessities are calibrated. [ABSTRACT FROM AUTHOR]