Numerical simulation on the multiple planar fracture propagation with perforation plugging in horizontal wells

Intra-stage multi-cluster temporary plugging and diverting fracturing(ITPF)is one of the fastest-growing techniques to obtain uniform reservoir stimulation in shale gas reservoirs.However,propagation geometries of multiple fractures during ITPF are not clear due that the existing numerical models cannot capture the effects of perforation plugging.In this paper,a new three-dimensional FEM based on CZM was developed to investigate multiple planar fracture propagation considering perforation plugging during ITPF.Meanwhile,the fluid pipe element and its subroutine were first developed to realize the flux partitioning before or after perforation plugging.The results showed that the perforation plugging changed the original distribution of the number of perforations in each fracture,thus changing the flux partitioning after perforation plugging,which could eliminate the effect of stress interference between multiple fractures and promote a uniform fluid distribution.The standard deviation of fluid distribution in the perforation plugging case was only 8.48%of that in the non-diversion case.Furthermore,critical plugging parameters have been investigated quantitatively.Specifically,injecting more diverters will create a higher fluid pressure rise in the wellbore,which will increase the risk of wellbore integrity.Comprehensively considering pressure rise and fluid distribution,the number of diverters should be 50%of the total number of perforations(N_(pt)),whose standard deviation of fluid distribution of multiple fractures was lower than those in the cases of injecting 10%N_(pt),30%N_(pt)and 70%N_(pt).The diverters should be injected at an appropriate timing,i.e.40%or 50%of the total fracturing time(tft),whose standard deviation of the fluid distribution was only about 20%of standard deviations in the cases of injecting at20%tftor 70%tft.A single injection with all diverters can maintain high bottom-hole pressure for a longer period and promote a more uniform fluid distribution.The standard deviation of the fluid distribution in the case of a single injection was 43.62%-55.41%of the other cases with multiple injection times.This study provides a meaningful perspective and some optimal plugging parameters on the field design during IPTF.

A theoretical model of rigid projectile perforation of concrete slabs using the energy method

Projectile perforation of concrete slabs will produce numerous concrete fragments on the rear face of the concrete slabs. These concrete fragments will cause serious secondary damage to the indoor personnel and equipment of protective structures.Accurately evaluating the damage area of concrete slabs is an important problem. Therefore, a theoretical model of a rigid projectile perforation of concrete slabs is constructed using the energy method in this paper. In this model, a new shear failure method is proposed to calculate the energy consumption of the shear formation by combining with the von-Mises failure criterion and failure strain. Based on the energy conservation and principle of minimum potential energy, explicit equations for the perforation performance are formulated. The theoretical predictions agree well with the experimental results. Furthermore,experiments on a high-speed projectile normal perforation of concrete are carried out to verify the accuracy of the corresponding theoretical prediction.

Evaluation of implanted perforated lacrimal punctal plugs using anterior segment optical coherence tomography

Purpose:Evaluation of the patency and position of perforated lacrimal punctal plugs implanted for treating punctal stenosis together with quantitative assessment of the precorneal tear film using anterior segment optical coherence tomography(AS-OCT).Methods:In a prospective study,the lower punctum of 54 eyes of 29 patients implanted with perforated punctal plugs were examined using AS-OCT during the early postoperative period.Preoperative tear meniscus height(TMH)and tear meniscus area(TMA)were evaluated.Postoperatively,the patency of the plug,its position,TMH and TMA were evaluated,and the results were correlated with postoperative epiphora.Munk scale was used for epiphora grading.Results:Using AS-OCT,48(88.9%)plugs were found in proper position while 6(11.1%)were rotated.The lumen of the plugs was completely patent in 47(87%)plugs,partially obstructed in 2(3.7%)plugs and completely occluded in 5(9.2%)plugs.There was a statistically significant postoperative decrease of TMH and TMA(P<0.001)and postoperative epiphora Munk score(P<0.001).Conclusion:AS-OCT is a valuable,reliable,and noninvasive investigative tool that can detect the proper positioning,patency,and contents of the implanted perforated lacrimal punctal plugs in addition to measurement of TMH and TMA.