Summary: Accurate identification of the individual-layer parameters for vertically fractured wells in commingled reservoirs is essential for development plan design, reservoir numerical simulation, and stimulation measure selection. Different semi-analytical and numerical models are generally applied in multilayer transient testing (MLT) analysis to determine the properties of individual layer. However, these approaches require numerous computations and are complicated to program due to the fracture and reservoir discretization. This work thus presents the generalized analytical solutions of vertically fractured wells in infinite, closed, or constant-pressure commingled reservoirs with both computational and functional simplicity. The fully analytical solutions are derived based on the early-time approximate solutions of infinite-conductivity fracture and trilinear flow models, infinite-conductivity fracture solutions, pressure superposition principle, and Duhamel principle. A systematic verification by employing a standardized well testing software and trilinear flow model is conducted to ensure the general application accuracy of the presented solutions. The results show that the developed analytical solutions are valid when the dimensionless fracture conductivity is more than 2 (FcD > 2) with an average absolute percent deviation (AAD) of ~2% for pressure and that is ~4% for pressure derivative. The developed analytical solutions also exhibit improvements in early-time pressure and derivative calculation. Finally, a field case of a four-layer fractured well is interpreted by the developed solutions and well testing software to illustrate the feasibility. The interpretation results of two methods are nearly identical, with only a minor difference. The developed analytical solutions are computationally accurate while maintaining functional simplicity and can be considered as an alternative to the current semi-analytical and numerical approaches in MLT analysis.

Water huff and puff in horizontal wells in tight reservoirs has achieved good results in replenishing formation energy. However, after multiple rounds of treatment, a rapid decrease in formation pressure takes place making it difficult to maintain stable production. To improve the oil recovery rate of tight reservoirs, it is imminent to change the development mode. In this work, the stress distribution characteristics at fracture tips were analyzed based on Irwin theory and elastic theory. A model of propagation and closure length of fractures was established based on the propagation mechanism of water injection-induced natural fracture and the energy balance principle of fracture mechanics. Surfactant imbibition experiments were carried out according to the imbibition principle of surfactant system, and the propagation law of natural fractures was described with numerical simulation to analyze the seepage characteristics of dynamic fracture network. On the basis of the above works, alternating water huff and puff into segmented injection and production was proposed according to the distribution law of dynamic fracture network. The developing process of an actual well case by these two developing modes was simulated to predict 18 years of cumulative recovery, pressure distribution, and recovery rate. Results showed that when stress intensity factor exceeds the fracture toughness, the natural fractures will extend along their original directions and get connected, forming an irregular fracture network. The lengths of fractures after propagation and closure will not bring about water channeling for they are far shorter than well and interval spacing. Surfactant could diminish the resistance of boundary layer by reducing the wetting contact angle, ending up with an improvement in imbibition efficiency. Radial displacement and dynamic imbibition occur simultaneously in a dynamic fracture network during the early stage of water injection, while static imbibition mainly occurs during injection shutdown period and well soaking. According to comparison, the swept area of segmented injection and production was larger, ending up with a continuous increase of simulated recovery rate and cumulative recovery. The findings of this study show alternating water huff and puff after to segmented injection and production in fractured tight reservoir can allow full play of dynamic fracture network’s potential and achieve effective enhancement in oil recovery rate.

The newly discovered the fault-karst carbonate reservoirs in Tarim Basin are formed by large-scale tectonic fault activities and multiple-stage karstification. The ground outcrop, seismic reflection and well logging show that the large caves, vugs, tectonic fractures and matrix coexist in the reservoirs. The fractures interconnecting with caves in series to form vertical beads-on-string structure is the most common pattern. It is found that conventional models are difficult to match the recorded pressure data. To fill this gap, this work summarizes three kinds of patterns for this structure and presents three novel models to estimate formation properties. The physical models of multi-fracture-region multi-cave-region series connection are established by simplifying vertical beads-on-string structure. The corresponding mathematical models are developed, in which the flow in fracture regions obey Darcy's law, while the flow in cave regions obeys free flow. Importantly, the gravity is considered due to the flow along vertical direction. Then typical flow regimes are analyzed and sensitivity analysis is conducted. Our work shows that pressure-derivative curves show similar ‘concave’ characteristic for the cave storage regime and vug/matrix interporosity flow regime. The difference is that the pressure derivative for cave storage regime is unit slope, while this slope is not equal to unity for vug/matrix interporosity flow regime. Therefore, large cave and vug/matrix medium can be distinguished by slope of pressure derivative. More than that, the typical characteristic of vertical beads-on-string structure on type curve is that the cave storage regimes and linear flow regimes alternately appear. This characteristic helps the engineers identify vertical beads-on-string structure. A novel finding is that gravity effect could lead to unit-slope pressure and pressure derivative at late times, which is traditional recognized as the presence of a closed boundary when it may not be the case. Lastly, this methodology is applied to two cases from Shunbei Oilfield in which it is difficult to obtain good fitting quality and interpretation results using traditional methods. Besides conventional properties, the proposed methodology allows us to estimate other properties (e.g., cave height, cave radius), which are not readily obtained from conventional methods.