on lin-bose problem

This paper study generalized Serre problem proposed by Lin and Bose in multidimensional system theory context [Multidimens. Systems and Signal Process. 10 (1999) 379; Linear Algebra Appl. 338 (2001) 125]. This problem is stated as follows. Let F ∈ Al×m be a full row rank matrix, and d be the greatest common divisor of all the l × l minors of F. Assume that the reduced minors of F generate the unit ideal, where A = K[x 1,...,xn] is the polynomial ring in n variables x 1,...,xn over any coefficient field K. Then there exist matrices G ∈ Al×l and F1 ∈ A l×m such that F = GF1 with det G = d and F 1 is a ZLP matrix. We provide an elementary proof to this problem, and treat non-full rank case.

珠江口盆地流花11-1油田储层非均质性及流体分布规律研究

In order to discover the distribution law of the remaining oil, the paper focuses on the quantitative characterization of the reservoir heterogeneity and the distribution law of the fluid barrier and interbed, based on fine geological study of the reservoir in Liuhuall-1 oil field. The refined quantitative reservoir geological model has been established by means of the study of core analysis, logging evaluation on vertical well and parallel well, and seismic interpretation and prediction. Utilizing a comprehensive technology combining dynamic data with static data, the distribution characteristics, formation condition and controlling factors of remaining oil in Liuhuall-1 oil field have been illustrated. The study plays an important role in the enrichment regions of the remaining oil and gives scientific direction for the next development of the remaining oil. Several achievements have been obtained as follows: l.On the basis of the study of reservoir division and correlation,eight lithohorizons (layer A, B_1, B_2, B_3, C, D, E, and F) from the top to the bottom of the reservoir are discriminated. The reef facies is subdivided into reef-core facies, fore-reef facies and backreef facies. These three subfacies are further subdivided into five microfacies: coral algal limestone, coralgal micrite, coral algal clastic limestone, bioclastic limestone and foraminiferal limestone. In order to illustrate the distribution law of remaining oil in high watercut period, the stratigraphic structure model and sedimentary model are reconstructed. 2.1n order to research intra-layer, inter-layer and plane reservoir heterogeneity, a new method to characterize reservoir heterogeneity by using IRH (Index of Reservoir Heterogeneity) is introduced. The result indicates that reservoir heterogeneity is medium in layer B_1 and B_3, hard in layer A, B_2, C, E, poor in layer D. 3.Based on the study of the distribution law of fluid barrier and interbed, the effect of fluid battier and interbed on fluid seepage is revealed. Fluid barrier and interbed is abundant in layer A, which control the distribution of crude oil in reservoir. Fluid barrier and interbed is abundant relatively in layer B_2,C and E, which control the spill movement of the bottom water. Layer B_1, B_3 and D tend to be waterflooded due to fluid barrier and interbed is poor. 4.Based on the analysis of reservoir heterogeneity, fluid barrier and interbed and the distribution of bottom water, four contributing regions are discovered. The main lies on the north of well LH11-1A. Two minors lie on the east of well LH11-1-3 and between well LH11-1-3 and well LH11-1-5. The last one lies in layer E in which the interbed is discontinuous. 5.The parameters of reservoir and fluid are obtained recurring to core analysis, logging evaluation on vertical well and parallel well, and seismic interpretation and prediction. Theses parameters provide data for the quantitative characterization of the reservoir heterogeneity and the distribution law of the fluid barrier and interbed. 6.1n the paper, an integrated method about the distribution prediction of remaining oil is put forward on basis of refined reservoir geological model and reservoir numerical simulation. The precision in history match and prediction of remaining oil is improved greatly. The integrated study embodies latest trend in this research field. 7.It is shown that the enrichment of the remaining oil with high watercut in Liuhua 11-1 oil field is influenced by reservoir heterogeneity, fluid barrier and interbed, sealing property of fault, driving manner of bottom water and exploitation manner of parallel well. 8.Using microfacies, IRH, reservoir structure, effective thickness, physical property of reservoir, distribution of fluid barrier and interbed, the analysis of oil and water movement and production data, twelve new sidetracked holes are proposed and demonstrated. The result is favorable to instruct oil field development and have gotten a good effect.