Prediction of vertical flows in large diameter pipes

There is an increasing interest in multiphase flows in large diameter vertical pipes (typically with diameters greater that 100 mm) in the context of hydrocarbon production systems. There are strong indications that flows in such pipes differ greatly from those in smaller diameter pipes on which most of the prediction methodologies are based. In small diameter pipes, an important mechanism for the bubble flow to slug flow transition is the formation of void waves. This research reveal this wave growth and also predict the breakdown points from bubble-to-slug flow transition using Biesheuvel and Gorissen (1990) approximate void wave model based on Harwell small tube bubble flow experiments. As the gas velocity is further increased, the slug flow itself breaks down into churn flow by a process of flooding in the Taylor bubbles. In large diameter pipes, it appears that conventional slug flow does not occur; this is probably due to the fact that there is a size limit on spherical cap bubbles. Thus, this study reviews most of literatures in terms of bubble coalescence and breakup kernels in order to evaluate dynamic bubble size changes by applying population balance model. Unfortunately, these kernels have their own problems to be solved. Therefore we establish a simplified two-group bubble interaction model by taking into account mechanisms of large bubble shearing-off breakup and small bubble coalescence in large bubble wakes, respectively, assuming small bubbles do not coalesce to each other. In large diameter pipes, the bubble/slug and slug/churn transitions appear to be by-passed in favour of a direct transition from bubble to churn flow with increasing gas mass flux. Note that the churn flow studied here is emphasized by a continuous path for the gas phase. This study also describes work aimed at developing a phenomenological understanding of the bubble/churn and churn/annular transition regions in large diameter pipes. Investigation of the liquid transport mechanisms has led to the definition of two new flow regime transition criteria, namely liquid upflow potential and minimum entrained fraction. To estimate the bubble-to-churn flow transition, the liquid upflow potential of a churn flow at the particular local set of gas and liquid flow rates is estimated by using axial view experiments and the existing adiabatic equilibrium data. In churn flow, liquid upflow is achieved by the net upward flow in the film (bearing in mind that both upflow and downflow are occurring in the film, though the net value must be positive) and by droplet transport in the gas core. Once the Kutateladse flooding is reached, suggested by Pushkina and Sorokin (1969), then it is postulated that the transition to churn flow occurs. As the gas velocity is further increased, the flow rate of entrained drops in the gas core decreases to a minimum and then rises again. This minimum is observed to occur at a dimensionless gas velocity approximately equal to one and this serves as a possible criterion for the churn-to-annular flow transition. As a framework for prediction, an existing one-dimensional steady state modelling code (GRAMP2) has been selected. This code takes account of regime changes and predicts void fraction and pressure gradient using phenomenological models. Work on connecting the void wave growth, bubble size evaluation and GRAMP2 code for large diameter pipes will be the main target for the nearly future. In the meantime, CFD simulation is also being undertaken using a finite volume method based the STARCD software in order to numerically predict the evaluations of dynamic bubble size and flow regime changes in large diameter pipes

Fast decoding of a d(min) = 6 RS code

A method for high speed decoding a d sub min = 6 Reed-Solomon (RS) code is presented. Properties of the two byte error correcting and three byte error detecting RS code are discussed. Decoding using a quadratic equation is shown. Theorems and concomitant proofs are included to substantiate this decoding method

On the undetected error probability of a concatenated coding scheme for error control

Consider a concatenated coding scheme for error control on a binary symmetric channel, called the inner channel. The bit error rate (BER) of the channel is correspondingly called the inner BER, and is denoted by Epsilon (sub i). Two linear block codes, C(sub f) and C(sub b), are used. The inner code C(sub f), called the frame code, is an (n,k) systematic binary block code with minimum distance, d(sub f). The frame code is designed to correct + or fewer errors and simultaneously detect gamma (gamma +) or fewer errors, where + + gamma + 1 = to or d(sub f). The outer code C(sub b) is either an (n(sub b), K(sub b)) binary block with a n(sub b) = mk, or an (n(sub b), k(Sub b) maximum distance separable (MDS) code with symbols from GF(q), where q = 2(b) and the code length n(sub b) satisfies n(sub)(b) = mk. The integerim is the number of frames. The outercode is designed for error detection only

An extended d(min) = 4 RS code

A minimum distance d sub m - 4 extended Reed - Solomon (RS) code over GF (2 to the b power) was constructed. This code is used to correct any single byte error and simultaneously detect any double byte error. Features of the code; including fast encoding and decoding, are presented

Error control for reliable digital data transmission and storage systems

A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. In LSI and VLSI technology, memories are often organized on a multiple bit (or byte) per chip basis. For example, some 256K-bit DRAM's are organized in 32Kx8 bit-bytes. Byte oriented codes such as Reed Solomon (RS) codes can provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. In this paper we present some special decoding techniques for extended single-and-double-error-correcting RS codes which are capable of high speed operation. These techniques are designed to find the error locations and the error values directly from the syndrome without having to use the iterative alorithm to find the error locator polynomial. Two codes are considered: (1) a d sub min = 4 single-byte-error-correcting (SBEC), double-byte-error-detecting (DBED) RS code; and (2) a d sub min = 6 double-byte-error-correcting (DBEC), triple-byte-error-detecting (TBED) RS code

Fast decoding techniques for extended single-and-double-error-correcting Reed Solomon codes

A problem in designing semiconductor memories is to provide some measure of error control without requiring excessive coding overhead or decoding time. For example, some 256K-bit dynamic random access memories are organized as 32K x 8 bit-bytes. Byte-oriented codes such as Reed Solomon (RS) codes provide efficient low overhead error control for such memories. However, the standard iterative algorithm for decoding RS codes is too slow for these applications. Some special high speed decoding techniques for extended single and double error correcting RS codes. These techniques are designed to find the error locations and the error values directly from the syndrome without having to form the error locator polynomial and solve for its roots

Using bootstrap to compare the validity of PRO measures in discriminating among CKD patients

BACKGROUND: Patient-reported outcome (PRO) research requires valid and sensitive measures. Relative Validity (RV) offers an objective way to compare the validity of different PRO measures in discriminating groups of patients or occasions. There is no significance test associated with RV. We applied bootstrap to estimate the confidence interval (CI) of RV to better interpret the differences in RV. METHODS: The CKD-specific legacy (KDQOL Burden, Symptom, and Effect), generic health scales (SF-12), and Kidney Disease Impact Scale (KDIS) were administrated to 453 CKD patients. ANOVA-based RV coefficients were computed to compare how well each scale discriminated between three clinically-defined severity groups (Dialysis \u3e Stage 3-5 \u3e Transplant). Bootstrap was used to construct CI to determine whether the differences in RV were significant in comparisons between each scale and the best legacy standard- KDQOL Burden. Factors of sample size, number of bootstrap replications, bootstrap method were varied to investigate their impacts. RESULTS: In comparison with KDQOL Burden (RV=1), using 95% CI, differences were non-significant for KDIS (RV=1.13), KDQOL Effect (RV=.99), SF-12 RP (RV=.77) and PF (RV=.70). SF-12 PCS (RV=.60) was at borderline. The other measures were significantly poorer in discriminating the patients. Sample size played a substantial role. 300 patients for 3 groups greatly reduced the standard errors compared to 100 patients. A larger sample size greatly increased the power of detecting the differences. The number of replications did not have consequential influence. The types of BCa and percentile intervals were preferred as all bootstrap distributions were skewed. The magnitude of chosen standard measure’s F-statistics appeared to have a noticeable impact on CI too. CONCLUSIONS: Bootstrapping appears to be valuable in comparing the validity of PRO measures from a statistical perspective. The significance test of RV was affected by the sample size, magnitude of RV, and F-statistic of standard measure

ZIP2DL: An Elastic-Plastic, Large-Rotation Finite-Element Stress Analysis and Crack-Growth Simulation Program

ZIP2DL is a two-dimensional, elastic-plastic finte element program for stress analysis and crack growth simulations, developed for the NASA Langley Research Center. It has many of the salient features of the ZIP2D program. For example, ZIP2DL contains five material models (linearly elastic, elastic-perfectly plastic, power-law hardening, linear hardening, and multi-linear hardening models), and it can simulate mixed-mode crack growth for prescribed crack growth paths under plane stress, plane strain and mixed state of stress conditions. Further, as an extension of ZIP2D, it also includes a number of new capabilities. The large-deformation kinematics in ZIP2DL will allow it to handle elastic problems with large strains and large rotations, and elastic-plastic problems with small strains and large rotations. Loading conditions in terms of surface traction, concentrated load, and nodal displacement can be applied with a default linear time dependence or they can be programmed according to a user-defined time dependence through a user subroutine. The restart capability of ZIP2DL will make it possible to stop the execution of the program at any time, analyze the results and/or modify execution options and resume and continue the execution of the program. This report includes three sectons: a theoretical manual section, a user manual section, and an example manual secton. In the theoretical secton, the mathematics behind the various aspects of the program are concisely outlined. In the user manual section, a line-by-line explanation of the input data is given. In the example manual secton, three types of examples are presented to demonstrate the accuracy and illustrate the use of this program