Gongchang Wang

Shack-Hartmann wavefront sensor plays a key role in adaptive optics (AO) systems, which detect the aberrant wavefront by an array of micro-lenslets across the aperture pupil. However, some sub-apertures would be a lack of light induced by the imperfectness of micro-lenslets or pupil shift away from the optical path. Thus, the wavefront detection would be under-sampled and the performance of wavefront reconstruction would be severely degraded. It is therefore important to evaluate the influence of under-sampling on the wavefront reconstruction. In this paper, an AO system was established by the OOMAO simulation platform. For dynamical turbulence aberrations or statistic defocus aberrations, three cases including a single sub-aperture, a row of sub-apertures, and a quadrant sub-apertures lack of light were simulated. Compared with the uncorrected aberrant wavefront, our results showed that the RMS of the residual wavefront for a typical atmospheric condition (Fried parameter (r0) ranges from 5 cm to 15 cm) can be reduced by a factor of 5~8, 4~6, and 2~3 with these three cases of under-sampling, respectively.

Considering the rheological properties of fluid, reservoir heterogeneity, and eccentricity factor, the productivity formula of horizontal well for the power-law fluid heavy oil reservoir is derived by transforming the three-dimensional seepage problem into a two-dimensional seepage problem. The heavy oil production calculated by this formula is in good agreement with the actual production in the offshore oil field. Then, the influencing factors of production are analyzed, and the results show that the power-law index has the greatest influence on production. When the power-law index is less than 0.8, the production increases slowly with the power-law index and when it is greater than 0.8, the production increases faster. The power-law index has a greater impact on production for higher production pressure differential and longer horizontal well. Anisotropy has significant influence on the production. When the value of K h /K v is less than 10, the production decreases rapidly with the K h /K v ; after the value of K h /K v is greater than 10, the production decreases slower. Eccentricity has trivial impact on the production.

Corrigendum: Research and Application of ColdProductivity Formula of HorizontalWell in the Power-Law Fluid Heavy OilReservoirName of all authors as they appear in the published original article (If correcting author names please put the correct spelling. If adding authors, please include additional authors.)Wang Gongchang , Liu Yingxian ， Liu ZongbinAffiliations of all authors as they appear in the published original version of the article (If correcting affiliations please put the correct version. If adding affiliations, please include additional affiliations).Tianjin Branch of CNOOC Ltd.，Tianjin, China.* Correspondence: mailto:wanggch12@cnooc.com.cnKeywords: heavy oil reservoir, power-law fluid, horizontal well, productivity, cold productionCorrigendum on: Gongchang W, Yingxian L and Zongbin L (2021) Research and Application of Cold Productivity Formula of Horizontal Well in the Power-Law Fluid Heavy Oil Reservoir.Front. Energy Res. 9:792427. doi: 10.3389/fenrg.2021.792427Incorrect AffiliationIn the published article, there was an error in affiliation **1**. Instead of “**CNOOC Tianjin Company, Tianjin, China**”, it should be “** Tianjin Branch of CNOOC Ltd.，Tianjin, China.**”. The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated.

Sodium beacon adaptive optics (AO) system has been proved to be a highly productive tool for improving the resolving power of large-aperture ground-based telescope imaging. The performance of the AO system is mainly limited by photon return of the sodium beacon, which is determined by the coupling efficiency that characterizes the interaction rate between sodium laser and sodium atoms. The interaction processing is strictly influenced by the collisions of sodium atoms with other molecules (N 2 , O 2 ). Most of the existing collision kernels are assumed as the “memoryless” hard collision, which is completely velocity reset in a Maxwellian distribution of the sodium atoms after scattering. To be more realistic, we adopt a more practical “memory” Cusp weak collision kernel, considering the velocity distribution of sodium atoms after collisions are correlated with the velocity before collision. By solving the Bloch equations, the processing for the interaction between sodium laser and sodium atom with Cusp kernel is established, and the coupling efficiency of sodium beacon with different collision kernel by analyzing the population is obtained. The researching results show that, for “memoryless” kernel, comparing to Cusp kernel with shaping parameter (s) of 100, the coupling efficiency is larger than 56% at best case; for sodium laser with 12% power detuned to D 2b line and at a power density ranges from 10 to 100 W/m 2 , the coupling efficiency of “memoryless” kernel is nearly the same as “memory” Cusp kernel with s of 10, 100 and 3 Cusp kernel.

The calibration accuracy of inertial measurement unit (IMU) is one of the important factors affecting the positioning accuracy of strapdown inertial navigation system (SINS). A 24-sequence calibration rotation scheme is proposed in this paper, which improves the observability and observability degree compared with the traditional 18-sequence scheme, and makes the calibration results more accurate. Simulation results show that the calibration results of 24-sequence scheme are closer to the actual value than those of 18-sequence scheme.