Lakshmi Sutha Kumar

Truncated Gamma Drop Size Distribution Models for Rain Attenuation in Singapore

A model that is less sensitive to errors in the extreme small and large drop diameters, the gamma model with central moments (3, 4 and 6), is proposed to model the rain drop size distribution of Singapore. This is because, the rain rate estimated using measured drop size distribution shows that the contributions of lower drop diameters are small as compared to the central drop diameters. This is expected since the sensitivity of the Joss distrometer degrades for small drop diameters. The lower drop diameters are therefore removed from the drop size data and the gamma model is redesigned for its moments. The effects of the removal of a particular rain drop size diameter on the specific rain attenuation (in dB) and the slant-path rain attenuation calculations with forward scattering coefficients for vertical polarization are analyzed at Ku-band, Ka-band and Q-band frequencies. It is concluded that the sensitivity of the Joss distrometer although affects the rain rate estimation at low rain rates, does not affect the slant path rain attenuation on microwave links. Therefore, the small drop diameters can be ignored completely for slant path rain attenuation calculations in the tropical region of Singapore.

Two-Parameter Gamma Drop Size Distribution Models for Singapore

Gamma model is fitted using the second, fourth, and sixth moments to model the rain drop size distribution (DSD) of Singapore. As the Joss distrometer measures the number of rain drops between the drop diameters from 0.3 to 5 mm, the truncated moment fitting between these drop diameter ranges is also used for modeling the DSD. Gamma DSD requires three-parameter estimation:N0, the intercept parameter; μ, the shape parameter; and Λ, the slope parameter. The aim of this paper is to find a suitable fixed μ and derive an appropriate μ-Λ relation for the tropical region in order to form a two-parameter gamma model. To find an appropriate μ value, observed DSDs are fitted with different μ values to estimate the rain rates, which are assessed by rain rate observations of the distrometer. Shape-slope relationships are fitted for different categories according to the rain rate and the number of drops. The derived μ-Λ relationships for the Singapore region are compared to the published results from two other regions, and the analysis is presented. Two-parameter gamma models are compared by retrieving the rain rate using the polarimetric radar variables. The effect of truncation on rain rate retrieval is also studied, and the use of the μ-Λ relationship for rain retrieval is recommended for the tropical region. The μ-Λ relation using the truncated moment method for the rain category R ≥ 5 mm/hr and rain counts ≥ 1000 drops retrieves the rain rates well compared to other μ-Λ relations.

Comparison of S-Band Radar Attenuation Prediction With Beacon Measurements

A comparative analysis of the rain attenuation evaluated from beacon measurements and from a single polarization S-band Radar is performed. The beacon measurements are obtained for two slant satellite paths with different elevation angles in the Ku- and Ka-band. The single polarization S-band Radar reflectivity data is used to predict the attenuation along the satellite propagation paths. This is done by first converting the reflectivity into rain rate using the Z-R relations suitable for the tropical region and, afterwards, by evaluating the slant path attenuation through the integration of the specific rain attenuation derived from the point rainfall rate. An empirical calibration factor for the Radar reflectivity is provided. A comparison of the rain fade suffered from the two satellite paths is presented both on event basis and in terms of cumulative distribution functions. The empirical calibration factor and a single Z-R relation suitable for the tropical region are used for rain attenuation evaluation from single polarization Radar data.

Slant-path rain attenuation at different elevation angles for tropical region

Gamma model is used to model the drop size distribution of Singapore. Specific rain attenuation is calculated using forward scattering coefficients and using ITU-R P.838-3 recommendations for vertically polarized waves at 11 GHz, 20 GHz, 30 GHz and 38 GHz at different elevation angles. Slant path attenuation is calculated using the specific rain attenuation at different elevation angles using ITU-R P.618-9 recommendations for 11 GHz, 20 GHz, 30 GHz and 38 GHz. Both the specific rain attenuation and slant-path rain attenuation are calculated at the point rainfall rate, 120.30 mm/hr, of Singapore and at a lower rainfall rate 66.54 mm/hr. The trend of slant-path rain attenuation at different elevation angles for the four frequencies is analyzed.

Optimal Energy Transfer Pipe Arrangement for Acoustic Drill String Telemetry

Drill string acoustic telemetry is an effective transmission method to retrieve downhole data. Finite-difference simulations produce the comb-filter-like channel response (patterns of pass bands and stop bands) due to the presence of coupling joints in the metallic drill string. Practical pipes used for drilling deep wells have slight variation in length. The selection and arrangement of downhole pipes is important for improving the transmission efficiency of extensional waves transmitted through the drill string. Downhole drill string channel is studied using the transmission coefficients calculated from the transmission matrix method, and the resultant transfer function produces identical results similar to the finite-difference simulations. Reciprocity of the drill string structure is proved by comparing the pass band responses using the ascend-only (AO) and descend-only pipe arrangements. Transferred energies calculated up to 180 pipes of random length at the end of the drill strings using transmission coefficients for the three different pipe arrangements, namely, AO, descend-then-ascend, and ascend-then-descend (ATD), are compared to find the optimal pipe arrangement for single measurement. For the situations when pipes are distributed in sets, multiple measurements are required. In this paper, two sets of AO and two sets of ATD arrangements are analyzed for multiple measurements. ATD and nxATD arrangements are proposed as optimal pipe arrangements to produce the best possible telemetry performance in terms of optimal acoustic energy transfer via one- and two-way acoustic communication for single and multiple measurements, respectively.

Downhole pipe selection and arrangement for acoustic drillstring telemetry

Drillstring acoustic telemetry is an effective transmission method to retrieve downhole data. In this paper, finite-difference algorithm is used for acoustic wave propagation prediction along the drillstring. An impulse excitation signal of time duration 30.87 μs is transmitted from the downhole and the wave displacement at the receiver is found using finite-difference algorithm. The resultant impulse and frequency responses are plotted and compared for different segments. It is found that the selection and arrangement of downhole pipes plays a vital role in improving the transmission efficiency of extensional waves transmitted through the drillstring for acoustic telemetry, particularly in the high-frequency bands. In order to find the optimal pipe arrangement order, 4 segments of drillstring with lengths d11to d14 (in increasing length between 9.3434 m and 9.8185 m) are arranged in all 24possible permutations. The energy of the frequency response is found for each of the six pass bands for the twenty four arrangements. It is concluded from the findings that placing the shortest pipe at the downhole first, followed by the longest pipe, then the next longest pipe and so on, produces the best possible telemetry performance in terms of optimal acoustic energy transfer.

Optimization of acoustic communication for industrial drilling

Drill string acoustic telemetry is an effective transmission method to retrieve downhole data in drilling applications. In practice, pipes used for drilling deep wells have slight variation in length. The arrangement of downhole pipes plays a vital role for improving the transmission efficiency of extensional waves transmitted through the drill string. Finite-difference modeling produce the comb-filter-like channel response (patterns of pass bands and stop bands) due to the presence of coupling joints in the metallic drill string. In this paper, channel response of the 3rd to 6th pass bands for 4 different pipe arrangements, namely, ascend-only, descend-then-ascend, ascendthen-descend and descend-only, are compared for finding the optimal pipe arrangement. Drill pipes and joints with dimensions scaled down to (1/24.2)th of the actual drill string dimensions are used to set up an experimental measurement system for 8 pipes. Channel response measurements are taken from the experimental setup by arranging the 8 pipes in the orders mentioned above. It is concluded from the findings that the ascend-then-descend pipe arrangement produces the best possible telemetry performance in terms of maximum acoustic energy transfer.

Comparison of precipitable water vapor derived from GPS and radiosonde data for Singapore

The objective of this study is to retrieve the Precipitable water vapor (PWV) by analyzing the wet tropospheric delay measurements from the NTUS receiver, and from radiosonde data at Singapore. This paper describes the procedures and results of the analysis of these concurrent measurements, meteorological data.

Performance of channel coding and equalization for acoustic telemetry along drill strings

Real-time telemetry during drilling thousands of meters below the surface plays a key role in efficient utilization of oilfields. Current mud-pulse commercial systems are limited to only a few bits per second (bps). In this paper, we are interested in acoustic data transmission through the steel body of the drill string. We propose trellis coded modulation (TCM) coupled with multicarrier modulation. To cope with the intersymbol interference (ISI) and any synchronization issues at the receiver, joint carrier-phase synchronization and decision feedback equalization is used. In addition, weights based on the knowledge of the signal-to-noise-ratio (SNR) at different passbands are incorporated into the modified Viterbi decoder to improve the bit-error rate (BER). By using a realistic model of a 1-km-drill string channel, the BER performance of the acoustic system is demonstrated while achieving a signaling rate of 400 bps, about two orders of magnitude higher than current state-of-art mud-pulse telemetry systems. In addition, our results demonstrate that the decision feedback equalizer (DFE) is vastly less power-hungry than orthogonal frequency division multiplexing (OFDM).

Design of coded digital telemetry system for acoustic downhole channel with drilling noise

Logging-while-drilling (LWD) and measurement-while-drilling (MWD) applications have prompted the development of acoustic telemetry for retrieving downhole data. In this paper, a multilevel frequency shift keying (ML-FSK) modulation transceiver with pseudo-coherent differential energy detection is proposed and optimized for such acoustic telemetry applications. The motivation of employing the proposed multilevel FSK transceiver is its ability to cancel the effect of large drilling noise (drill bit noise and surface noise) with a low-complexity transceiver architecture, and its relative ease of dealing with oscillator or clock drifts caused by the harsh operating environment. To achieve better bit error rate (BER) over non-coherent demodulation while retaining the drilling noise cancellation capability, the receiver is modified to a pseudo-coherent demodulator. To further improve robustness, forward error correction (FEC) coding is applied and several coding options are evaluated over realistic acoustic drill string channel in the presence of drilling noise. The drill string channel investigated is made up of 110 segments, spans 1.011 km in length, has a characteristic comb-filter channel structure, with four pass bands (2nd, 3rd, 4th and 5th) used for telemetry.