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Purpose: The application of compressed sensing (CS) technology in magnetic resonance imaging (MRI) is to accelerate the MRI scan speed by incoherent undersampling of k‐space data and nonlinear iterative reconstruction of MRI images. This paper generalizes the existing rosette trajectories to configure the sampling patterns for undersampled k‐space data acquisition in MRI scans. The arch and curvature characteristics of the generalized rosette trajectories are analyzed to explore their feasibility and advantages for CS reconstruction of MRI images. Methods: Two key properties crucial to the CS MRI application, the scan speed and sampling incoherence of the generalized rosette trajectories, are analyzed. The analysis on the scan speed of generalized rosette trajectories is based on the transversal time derived from the curvature of the trajectories, and the sampling incoherence is based on the evaluation of the point spread function for the measurement matrix. The results of analysis are supported by extensive simulations where the performances of rosette, spiral, and radial sampling patterns at different acceleration factors are compared. Results: It is shown that compared with spiral trajectories, the arch and curvature characteristics of the generalized rosette trajectories are more feasible to meet the physical requirements of undersampled k‐space data acquisition in terms of time shortness and scan area. It is further shown that the sampling pattern of the rosette trajectory has higher incoherence than that of the other trajectories and can thus achieve higher reconstruction performance. Reconstruction performances illustrate that the rosette trajectory can achieve about 10% higher peak signal‐to‐noise ratio than radial and spiral trajectories under the high acceleration factor R = 10. Conclusions: The generalized rosette trajectories can be a desirable candidate for CS reconstruction of MRI.

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Multistage hydraulic fracturing is used in horizontal wells to increase the production of tight oil. Fracturing fluids are used in hydraulic fracturing to ensure proppants are suspended, but fluid residuals can cause formation damage and reduce rock permeability; meanwhile, fracture conductivity can be further reduced due to the flowback of proppants during the early stage of production. In this study, steel plates and hydraulically fractured reservoir rocks are tested in a modified API cell to understand the impacts of flowback rate, fracturing fluid, and closure stress on proppant flowback and fracture conductivity. When the closure stress increased from 21 to 30 MPa, retained permeability decreased by slickwater from 35.71 to 29.84% in steel plates; during the flowback, more than 47% of proppants flowed back, and the fracture conductivity increased by 10 times under 21 MPa, which shows the limitation of the API method on the study of proppant flowback. When shale plates are used, the critical flow rate that prevents the proppant flowback was found to be 5.5 × 10 –4 –1.6 × 10 –3 m/s for the 30/50 mesh sands (around 55–340 m 3 /d for a typical horizontal well), and the retained permeability decreased from 23.33 to 22.86% due to an increase of closure stress from 21 to 30 MPa. Results of this study can guide the optimizing of the flowback scheme in the field that minimizes the proppant flowback in different fracturing fluids.