Advanced Methods of Mathematical Modeling and Experimental Study in Oil and Gas Reservoirs

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The results of core displacement experiments show that increasing the water drive velocity when it is bigger than the limit value can effectively reduce the residual oil saturation and improve the oil displacement efficiency under the same PV. However, the existing commercial simulators (Eclipse, CMG et al.) cannot simulate the effect of water velocity on the relative permeability curve in the process of numerical simulation.

In this article, capillary number (Ca), defined as the dimensionless ratio of viscous force to capillary force, is used to characterize the relationship between water drive velocity and residual oil. Second, a new Boltzmann (BG) equation is proposed to match the nonlinear relationship between Ca and residual oil. The BG equation is a continuous function, which is very beneficial to the stability of numerical calculation. Finally, a new reservoir numerical simulator is established which captures the dynamic variation of residual oil saturation with water drive velocity in a water flooding reservoir based on the black oil model. The new simulator was verified by comparing it with the commercial reservoir simulator ECLIPSE and experimental data. The simulation results show that compared with the common model, the model considering the dynamic variation of residual oil saturation with water drive velocity reduced the residual oil saturation near the main flow line after enhanced injection rate. The oil phase flow capacity in the model is enhanced, the water cut is decreased, and the oil recovery rate is higher. The history matching of the S oilfield in Bohai Bay is achieved with the new simulator, and the history matching accuracy is obviously higher than that of Eclipse. The findings of this study can help with a better understanding of the distribution law and flow law of remaining oil in the high water cut stage of the reservoir and have good theory and application value for water flooding offshore oilfields.

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Original Research
05 January 2023

The physical property of Chang 6 reservoir in Yanchang oilfield is poor, and the heterogeneity is strong. Multistage fracturing of horizontal wells is easy to form only one large horizontal fracture, but it is difficult to control the fracture height and length. The new mining method of “bow horizontal well + multistage horizontal joint” can effectively increase the multistage horizontal joint’s spatial position, which improves the drainage area and stimulation efficiency of oil wells. Due to the reservoir’s low permeability and strong heterogeneity, the single well mode of “bow horizontal well + multistage horizontal fracture” cannot effectively produce Chang 6 reservoir. To improve the production degree of the g 6 reservoir, the fracture model is established using equivalent conductivity and the multigrid method. The pressure response functions of horizontal wells and volume fracturing horizontal wells are established by using the source function, and the relationship between reservoir permeability and starting pressure gradient in the block is calculated. On this basis, the reservoir productivity equation of the block is established, which provides a basis for optimizing the fracturing design parameters of horizontal wells. It is proposed that the flow unit should be considered in the design of fracturing parameters of horizontal fractures, the number of fractures should comprehensively consider whether the fractures can make each flow unit be used, and have large controlled reserves, and the scale of fracturing should comprehensively consider the output and cost. The fracture network model is established by using equivalent conductivity and multi-gridthod, and the volume fracturing design parameters of horizontal wells are optimized, considering the seepage characteristics of the flow unit. The fracturing design parameters of the horizontal section are further defined, which provides a theoretical basis for the efficient development of shallow tight reservoirs.

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Section of the Kelasu structural belt.
Original Research
10 August 2022

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.

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