Stable and efficient time integration of a dynamic pore network model for two-phase flow in porous media

We study three different time integration methods for a dynamic pore network model for immiscible two-phase flow in porous media. Considered are two explicit methods, the forward Euler and midpoint methods, and a new semi-implicit method developed herein. The explicit methods are known to suffer from numerical instabilities at low capillary numbers. A new time-step criterion is suggested in order to stabilize them. Numerical experiments, including a Haines jump case, are performed and these demonstrate that stabilization is achieved. Further, the results from the Haines jump case are consistent with experimental observations. A performance analysis reveals that the semi-implicit method is able to perform stable simulations with much less computational effort than the explicit methods at low capillary numbers. The relative benefit of using the semi-implicit method increases with decreasing capillary number $\mathrm{Ca}$, and at $\mathrm{Ca} \sim 10^{-8}$ the computational time needed is reduced by three orders of magnitude. This increased efficiency enables simulations in the low-capillary number regime that are unfeasible with explicit methods and the range of capillary numbers for which the pore network model is a tractable modeling alternative is thus greatly extended by the semi-implicit method.Comment: 33 pages, 12 figure

Red cell antibody screening in pregnancy: a preliminary insight?

Aloimunisasi sel darah merah ditakrifkan sebagai pembentukan antibodi di dalam respons kepada antigen asing sel merah melalui proses transfusi atau mengandung. Di kalangan wanita hamil yang tidak mempunyai sejarah transfusi darah, mereka boleh mengalami aloimunisasi pada kehamilan yang lalu atau semasa disebabkan oleh kehadiran antigen sel merah bapa yang diwarisi kepada janin. Kajian ini bertujuan untuk menentukan prevalens aloimunisasi sel darah merah di kalangan wanita hamil tanpa sejarah transfusi darah di PPUKM dan juga untuk mengaitkan kelazimannya dengan nombor kehamilan dan sejarah komplikasi obstetrik. Ini adalah satu kajian keratan rentas di mana 150 wanita hamil telah dipilih secara rawak di klinik antenatal PPUKM. Sepuluh ml darah periferal telah diperolehi selepas persetujuan diambil dari setiap pesakit. Ujian yang dijalankan ke atas sampel-sampel darah tersebut termasuk ujian jenis kumpulan darah ABO dan Rh D dan saringan antibodi dengan menggunakan teknik ujian antiglobulin tidak langsung. Sampel positif terus dikenalpasti untuk pengkhususan antibodi. Dalam kajian kami, majoriti (37.3%) daripada wanita adalah primigravida. Aloantibodi sel darah merah telah dikesan pada dua daripada 150 (1.3%) pesakit yang kemudiannya dikenalpasti sebagai anti-C dan anti-D. Namun tiada seorang pun daripada primigravida yang mengalami aloimunisasi. Seorang wanita dari gravida 2 (2.9%) dan gravida 3 (3.6%) didapati positif bagi aloimunisasi. Salah seorang daripada mereka juga mempunyai sejarah obstetrik buruk. Kajian ini menunjukkan bahawa kelaziman aloimunisasi sel darah merah di kalangan wanita hamil adalah rendah di pusat ini. Walau bagaimanapun, ujian saringan bagi aloantibodi sel darah merah perlu disediakan untuk mengurangkan komplikasi kepada janin atau ibu yang mungkin timbul akibat aloimunisasi sel darah merah

Small bowel perforation by a piece of china with a synchronous asymptomatic sigmoid carcinoma: A case report

A 75 year old gentleman who presented with an incarcerated paraumibilical hernia was found intraoperatively to have small bowel perforation due to a piece of china with a synchronous asymptomatic sigmoid carcinoma

Climate Dynamics: A Network-Based Approach for the Analysis of Global Precipitation

Precipitation is one of the most important meteorological variables for defining the climate dynamics, but the spatial patterns of precipitation have not been fully investigated yet. The complex network theory, which provides a robust tool to investigate the statistical interdependence of many interacting elements, is used here to analyze the spatial dynamics of annual precipitation over seventy years (1941-2010). The precipitation network is built associating a node to a geographical region, which has a temporal distribution of precipitation, and identifying possible links among nodes through the correlation function. The precipitation network reveals significant spatial variability with barely connected regions, as Eastern China and Japan, and highly connected regions, such as the African Sahel, Eastern Australia and, to a lesser extent, Northern Europe. Sahel and Eastern Australia are remarkably dry regions, where low amounts of rainfall are uniformly distributed on continental scales and small-scale extreme events are rare. As a consequence, the precipitation gradient is low, making these regions well connected on a large spatial scale. On the contrary, the Asiatic South-East is often reached by extreme events such as monsoons, tropical cyclones and heat waves, which can all contribute to reduce the correlation to the short-range scale only. Some patterns emerging between mid-latitude and tropical regions suggest a possible impact of the propagation of planetary waves on precipitation at a global scale. Other links can be qualitatively associated to the atmospheric and oceanic circulation. To analyze the sensitivity of the network to the physical closeness of the nodes, short-term connections are broken. The African Sahel, Eastern Australia and Northern Europe regions again appear as the supernodes of the network, confirming furthermore their long-range connection structure. Almost all North-American and Asian nodes vanish, revealing that extreme events can enhance high precipitation gradients, leading to a systematic absence of long-range patterns

Rheology of High-Capillary Number Two-Phase Flow in Porous Media

Flow of immiscible fluids in porous media at high capillary numbers may be characterized by an effective viscosity. We demonstrate that the effective viscosity is well-described by the Lichtenecker-Rother equation. Depending on the pore geometry, wettability, and viscosity of the fluids, the exponent α in this equation can have different values. We find α = 1 when fluids are well-mixed with small bubbles, α = 0.6 in two- and 0.5 in three-dimensional systems when there is less mixing with the appearance of big bubbles, and α = −0.5 when lubrication layers are formed along the pore walls. Our arguments are based on analytical and numerical methods