Casing Collapse Strength Analysis under Nonuniform Loading Using Experimental and Numerical Approach

Multistage fracturing is the main means of shale gas development, and casing deformation frequently occurs during fracturing of shale gas horizontal wells. Fracturing fluid entering the formation will change in situ stress nearby the wellbore. The changes of in situ stress are mainly reflected in the following two aspects: one is the increase of in situ stress and the other is the nonuniformity of in situ stress along the wellbore. And it is for this reason that the production casing is more likely to collapse under the nonuniform in situ stress load. According to the service conditions of production casing in shale gas reservoir, this paper studied the casing deformation and the collapsing strength subjected to the nonuniform loading by the experimental and numerical simulation method. The results show that under the condition of nonuniform loading, (1) the diameter variation rate of the casing reduces with the increase in the ratio of sample to tooling length. When the ratio is less than 3, the casing collapse strength will be significantly reduced. And when the ratio is greater than 6, the impact of sample length on casing collapse strength can be ignored. (2) The increase in the applied loading angle will decrease the diameter variation rate. When the loading angle increases from 0° to 90°, the critical load value increases from 1600 kN to 4000 kN. (3) The increase in load unevenness coefficient will rapidly decrease the casing collapse strength. When the load unevenness coefficient n is 0.8, the casing collapse strength reduces to 60%, and when the load unevenness coefficient n is 0, the casing collapse strength reduces to 28%. The findings of this study can help for better understanding of casing damage mechanism in volume fracturing of shale gas horizontal well and guide the selection of multistage fracturing casing type and fracturing interval design.

Estimating the Error of Calculating the Load Losses in 6—10 kV Distribution Electric Networks

The aim of the study is to estimate the level of load losses for actual (nonuniform) loading of transformer substations in comparison with the load loss level under the conditions of their being uniformly loaded for a typical 6 kV urban distribution electric network. The extent to which such networks are equipped with automated information and measurement systems for fiscal electricity metering is extremely poor. Therefore, not only the load curves of the 6--10/0.4 kV substation transformers, but also their load factors are unknown in the majority of cases. Under these conditions, in calculating the load losses in 6--10 kV distribution electric networks, it is assumed that all substation transformers are uniformly (equally) loaded. The load losses in these electrical networks are calculated with a certain error associated with the assumption according to which the substation transformers are supposed to be uniformly loaded. Under these conditions, estimation of this error becomes of issue. The article describes the modeling, calculation and analysis of technical losses of electricity under the conditions of nonuniformly loaded transformers of a typical urban distribution network consisting of four transformers and four cables interconnecting them. The modeling and calculation of power losses were carried out using the RAP-10-st computer program for several different groups of transformer loading factors. Within each group, different subgroups were produced by rearranging the group loading factors. Each subgroup modeled a nonuniform transformers loading mode in the studied network. For each of these modes, the power losses were calculated and studied with the use of the RAP-10-st computer program. A conclusion has been drawn from the obtained analysis results regarding the error in determining the load losses associated with the assumption about the uniform loading of the substation transformers in the network. The obtained results may prompt electric grid companies to increase the extent of fitting their networks with automated information and measurement systems for fiscal electricity metering to improve the accuracy of determining the load losses.

Modification of the edge crack torsion specimen for mode III delamination testing. Part II – experimental study

Experimental studies of carbon/epoxy edge crack torsion specimen have been conducted using a specially designed twist test fixture. Of particular concern was verification of the recommendations expressed in the analytical part of this study (Part 1), where it was suggested that overhang (sections of specimen laying outside of the loading and support pins) in the x- and y-directions should be minimized, and fracture testing at longer delamination lengths should be avoided. The experimental test results verified that the specimens with the smallest overhang produced the most consistent delamination toughness data, GIIIc. Specimens with large overhangs exhibited high apparent GIIIc values at long delamination lengths. This was most likely due to nonuniform loading and associated nonuniform delamination extension.