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Early kick detection and nonlinear behavior of drilling mud

Frank-Michael Jaeger, Dipl-Ing.(TH), Dipl.-Ing.Öc., IBJ Technology DOI: 10.13140/2.1.1444.7683

The following test measurements serve the quantification of resolution and achievable sensitivity of parameters of sound velocity and sound absorption in wellbore fluids. More precisely, these studies refer to tools and methods to identify the flow of liquids or gases, preferably hydrocarbons in the well bore in real time during the drilling. The aim is a way to show with the highly sensitive and robust tools for use in the deep ocean can be realized.

State of the art

The following test measurements serve the quantification of resolution and achievable sensitivity of parameters of sound velocity and sound absorption in wellbore fluids. More precisely, these studies refer to tools and methods to identify the flow of liquids or gases, preferably hydrocarbons in the well bore in real time during the drilling. The aim is a way to show with the highly sensitive and robust tools for use in the deep ocean can be realized. Other known methods for the identification of potential inflows, called also gas kick, rely on density measurements of the drilling mud. Example, the patents US 4492865, US4412130, US 6648083 and US 6768106. A disadvantage which is methods that basing density measurements, that gas must be available in sufficient quantities to influence the density of drilling muds. Also procedures and devices with sound waves are proposed to allow early detection of inflows. A process is revealed in the patent specification US20130341094, which should capture in a drilling fluid with several acoustic sensors on a drill pipe gas bubbles in the longitudinal direction. Connected sensors which are mounted along the drill rod and measure along the drill string with telecommunication lines are necessary. The detection of liquid flows affecting the speed of sound, will not be. The patents US20120298421 and WO20162212A2 a procedure, where a steady influx through does a variety of gas in a borehole acoustic sensors along the length of the drill string, by the acoustic sensors spread out acoustic pulses in the drilling fluid in the longitudinal direction of the drill string and thereby monitor the change of the acoustic characteristics of the drilling muds. The influx of small quantities of formation fluids (such as oil, water and gas) into the hole, the density of drilling mud can reduce and in extreme cases lead to a catastrophic event. The solution to the problem is a measurement of the variable parameters as close as possible in the place of the inflow. This means the measurement device should simply as part of the riser or the mud return line be integrated. The solution to the problem is a measurement of the variable parameters as close as possible in the place of the inflow. This means the measurement device should simply as part of the riser or the mud return line be integrated. The change of parameters of wave velocity and attenuation are features for the drilling mud. The monitoring this parameters should be the basis of an improved method for the early kick detection. Experimental procedure The measurement of sound velocity and attenuation took place at IBJ Technology under realistic conditions with shear stress of the sludge. Shear stresses were realized with a stirrer by alternating circular rotations of the sludge.

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Figure (1) shows the experimental setup with a PC-controlled processor that monitors the variable burst pulse generation. Is the transit time between the transmitter and receiver with a standard deviation of approximately 50 ps with a TDC is determined. The amplitude of the envelope at certain times of the multiple reflections between the transmitter and receiver with an ADC is calculated by determining the damping. In addition,

even the length of multiple reflections is determined. These represent the number of multiple reflections of the ultrasonic signal between the transmitter and the receiver. The distance between of the sensors (piezo-electric disc) is about 42 cm. The distance of the sensor can be adjusted freely. The performance of the system is so designed that can be used also with larger sensor distances. The building is therefore all sizes of sludge return lines or marine risers. Air in the mud can be blown defined via a feeder tube. Figure 1: Apparatus

The raw signal is picked up on the receiver (sensor) and one with a sensitive amplifier for the Fourier Analysis (FFT spectral analysis software) processed. The real time analysis is sufficient to a standard PC. Figure 2 shows exemplary three States a drilling mud.

- no gas bubbles in the drilling mud

- a few gas bubbles in the drilling mud

- many gas bubbles in the drilling mud

Figure 2: Bubbles detection with FFT spectral analysis software

The evaluation is carried out in real time. The portrayal of waterfall is beneficial. Can be presented in either horizontally or vertically.

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Fundamentals of the method

Ultrasound attenuation spectroscopy is a method for characterizing properties of fluids and dispersed paricles. It is also known as acoustic spectroscopy.

The classic ultrasonic spectroscopy is the characterization of ultrasonic answer a material (also liquid) to the low level ultrasonic wave. McClemens [1] describes the relationship between ultrasonic velocity and attenuation spectra as follows: Once the ultrasonic velocity and/or attenuation spectra of an emulsion have been measured it is necessary to convert them into a particle size distribution using an appropriate theory. Theories are based on a mathematical treatment of the physical processes that occur when an ultrasonic wave propagates through an ensemble of particles suspended in a fluid.[2–4] One of the most comprehensive models (Equation 1) is based on multiple scattering theory [5]. (1)

where f (0) and f (π) are the scattering amplitudes of the individual droplets (Equations 2 and 3):

(2) (2) (3) Here K = ( ωωωω/cS + iααααS) is the complex propagation constant, cS is the ultrasonic velocity, ααααS is the attenuation coefficient of the colloidal suspension, k1 is the complex propagation constant of the continuous phase = ( ωωωω/c1 + iαααα1),

φφφφ is the disperse phase volume fraction, ω = 2ππππf is the angular frequency, f is the frequency, r is the droplet radius.

The An terms are the scattering coefficients of the various types of waves scattered from the individual droplets, e.g. monopole (A0), dipole (A1), quadrupole (A2) etc.

Approaches for calculating the scattering coefficients of both fluid and solid particles are available in the literature [6,7]. The most rigorous approach calculates the An terms by solving a series of 6 x 6 complex linear simultaneous equations at each value of n, although simpler analytical expressions are available in the long wavelength limit. [6,7] The values of the scattering coefficients depend on the relative thermophysical properties of the component phases, the ultrasonic frequency used and the size of the emulsion droplets. The terms containing φ in Equation (4)

describe single scattering effects, whilst the terms containing φ2 describe multiple scattering effects. Multiple scattering becomes increasingly important as the concentration of droplets in a colloidal suspension increases. For a colloidal suspension containing polydisperse particles the above equation must be modified (Equation 4):

(4),

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where the subscript j refers to the property with droplet size rj. This equation can be used to relate the ultrasonic properties of a colloidal suspension (velocity and attenuation coefficient) to its thermophysical properties, composition (φ) and particle size distribution.

Recently, it has been shown that the above theory must be modified to take into account interactions due to overlap of viscous [8] and thermal waves [9] generated by the particles. These interactions cause large deviations between the classical multiple scattering theory and experimental measurements at low ultrasonic frequencies, small droplet sizes and high droplet concentrations.

Influence of micro-bubbles In a feasibility study [10], the Radio-frequency (RF) echo signals were synthesized by summing the weighted acoustic responses of a population of microbubbles at known radial distances, as described in Zheng et al [11]. The mechanical response (radial oscillations) of the simulated microbubble (gas filled, lipid coated) to a known ultrasound excitation was predicted using a modified Rayleigh–Plesset model, given by:

(5),

where R1 and R10 represent the instantaneous and equilibrium inner bubble radii, respectively; pL and µL represent the equilibrium density and the shear viscosity of the surrounding liquid, respectively; and p0 and j represent the atmospheric pressure and the polytropic index of the gas, respectively. In this model, the surrounding medium was assumed to be infinite, and the pressure at infinity was assumed to be due to the excitation pulse pi(t). The bubble shell was assumed to be viscous and incompressible; and shell properties, i.e., thickness, shear modulus, and shear viscosity, were represented by ds, GS, and ls, respectively. The outer (R2) and inner radii (R1) of the bubble were related as follows [12]:

(6), where R20 represents the equilibrium outer radius. The pressure at the gas-shell interface (Pg) was governed by changes in the bubble radius and was computed as follows [12]:

(7), The backscattered pressure (Psc) of an oscillating microbubble was computed as follows [13]:

(8),

where r represents the radial distance from the microbubble where the pressure was computed. Another approach for the influence of micro bubbles is found in [14]: “It is important to note that liquid sodium is perfectly opaque, thus making it impossible to optically characterize this presence of bubbles. Moreover, its electric properties, together with the very low values of the radii together with the expected vacuum levels (r 10 µm, void

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fraction 10-6), render most other bubble characterization methods inapplicable. We therefore studied the potential use of acoustic methods. Safety requirements also impose the development of measurement techniques for which no a priori data are necessary. However, the acoustic methods based on the measurement of attenuation or scattering by the bubbles have an ambiguity, since the scattering of a resonant bubble is identical to that of a considerably larger non-resonant bubble. As for propagation velocity measurements, these allow the void fraction to be determined only for a frequency range, which depends on the size of the bubbles which are present. Linear acoustic methods thus appear to be inadequate under these conditions. The dynamic behavior of a bubble in an acoustic field can be described by the modified Rayleigh equation (equation 9) : (9), where ρρρρ is the mass density of the liquid, R is the instantaneous radius of the bubble, R0 is its rest radius, p0 is the static pressure, pv is the saturation vapor pressure, γγγγ is the polytropic gas pressure, σσσσ is the surface tension, and µ is the dynamic viscosity of the liquid. The acoustic field P(t) takes the form p� sin(ωt). This equation is strongly nonlinear, which explains our decision to investigate the nonlinear resonant behavior of bubbles, in order to unambiguously reconstruct the radius histogram of a cloud of bubbles, without the need for any a priori data. From Eq. ( 9), the Minnaert [15] equation can be derived, relating the resonance frequency of a bubble to its radius: (10)

The excitation of a bubble at its resonant frequency (f1) leads to the appearance of multiple and sub-multiple frequencies, such as its harmonics (n.f1) and, eventually, its ultra-harmonics [(2n + 1).f1/2] and sub-harmonic (f1/2). In the case of a bi-frequency excitation (f1 < f2), if f1 corresponds to the bubble’s resonant frequency, the mixing of the different frequencies leads in addition to the appearance of sum and difference frequencies (f2 ± nf1) and, possibly, to various ultra-harmonic and sub-harmonic combinations.

Results of the test procedure Realised building after Figure 1 enables the measurement of medium-sized ultra sonic speed with resolution better 1 x 10-2 m/s, at the same time causes the pulse-stimulating a strong broadband response sound spectrum. In the tested drilling fluids varied subharmonics frequency shares with pronounced resonances can be found. This can be explained in part by the model of parametric resonance. A parametric resonance is above a certain threshold to a sharp increase in amplitude of sub-harmonics (unstable behavior). Migrates growing on this a sequence of integer multiplier of

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multiple and sub-multiple can be amplitudes in the spectrum of response frequencies, such as its harmonics, ultra-harmonics and sub-harmonic. Flow at higher excitation amplitudes gaseous or liquid ingredients in a drilling fluid, the resonance region is increased so that parametric resonance in a wide frequency range are possible. The attenuation of the drilling fluid is characteristically changed. These changes can thus be detected immediately. Particularly significant is that these changes are already visible without a change in the wave velocity can be measured. For the evaluation of the spectrum of a FFT analysis is performed. The analysis can with the known methods are, etc. performed by Hamming. Here are some results are shown as an example:

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Example 1: Mud density: 15.6 lb / gal (base Barite), stirrer 500 rpm Start without agitators, the speed of sound is V = 1421.23 m / s. In-commissioning of the stirrer from 09:04:30 clock. There follows an increase in the speed of sound at 1505.12 m / s. The stirrer is in operation during the experimental period. The gas is introduced into two equal intervals with 30 sec 20cc / min of gas (air). The speed of sound drops to about 1420 m / s. Even after the end of the gas inlet speed of sound falls on this final value. The gas bubbles are initially distributed even in the mud. The high viscosity keeps a part of the bubbles in the mud. Due to the constant movement of the mud with the agitator is mechanically degassing of the drilling mud. The ascent to the output value of the speed of sound occurs abruptly. It turns out that the degassing is faster than the gas solution. Noteworthy is the exact same pattern of waterfall render the FFT analysis.

Figure 3: Relationship between gas bubbles and FFT analysis

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Example 2: Mud density: 12 lb / gal (base Barite), stirrer 500 rpm

Figure4: Relationship between gas bubbles and FFT analysis, multiple injection

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Example3: Mud density: 12 lb / gal (base Barite), stirrer 500 rpm The stirrer is in operation during the experimental period. The apparatus is empty at the beginning (filled with air). The sound transmission is evident in the FFT analysis. 20:22 Uhr was filled with drilling mud.

Figure 5: Relationship between gas bubbles and FFT analysis, filling operation

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View The acoustic attenuation spectroscopy can provide important additional information about the state of drilling muds. Especially with the appearance of several phases and transformations of dissolved gas to gas-free, even the smallest differences in the frequency-dependent attenuation in a very wide frequency range are visible in FFT analysis. An automated image analysis pattern so inexpensive and new monitoring devices for the entire process of production of deep holes in the ocean can be created. This technology is applicable to pipes with the same hardware. IBJ Technology as a partner for all producers of offshore technology available. References [1] D.J. McClements, ‘Ultrasonic Measurements in Particle Size Analysis’, Encyclopedia of Analytical Chemistry Edited by Robert A. Meyers. John Wiley & Sons Ltd, Chichester. ISBN 0471 97670 9 DOI: 10.1002/9780470027318

[2] U. Riebel, F. Loffler, ‘The Fundamentals of Particle Size Analysis by means of Ultrasonic Spectrometry’, Part. Part. Syst. Charact., 6, 135–143 (1989). [3] D.J. McClements, ‘Principles of Ultrasonic Droplet Size Determination’, Langmuir, 12, 3454–3461 (1996). [4] M.J.W. Povey, Ultrasonic Techniques for Fluid Characterization, Academic Press, San Diego, 1997.

[5] P.C. Waterman, R. Truell ‘Multiple Scattering of Waves’, J. Math. Phys., 2, 512–537 (1962). [6] P.S. Epstein, R.R. Carhart, ‘The Absorption of Sound in Suspensions and Emulsions’, J. Acoust. Soc. Am., 25, 553–565 (1953). [7] J.R. Allegra, S.A. Hawley, ‘Attenuation of Sound in Suspensions and Emulsions: Theory and Experiments’, J. Acoust. Soc. Am., 51, 1545–1564 (1972). [8] A.S. Dukhin, P.J. Goetz, ‘Acoustic and Electroacoustic Spectroscopy’, Langmuir, 12, 4998–5003 (1996).

9] Y. Hemar, N. Herrmann, P. Lemarechal, R. Hocquart, F. Lequeux, ‘Effective Medium Model for Ultrasonic Attenuation due to the Thermo-elastic Effect in Concentrated Emulsions’, J. Phys. II France, 7, 637–642 (1997). [10] H. Shekhar , M. M. Doyley, ‘Improving the sensitivity of high-frequency subharmonic imaging with coded excitation: A feasibility study’, Medical Physics, Vol. 39, No. 4, April 2012 [11] Zheng H. R., Mukdadi S., and Shandas R., ‘Theoretical predictions of harmonic generation from submicron ultrasound contrast agents for nonlinear biomedical ultrasound imaging‘, Phys. Med. Biol. 51, 557–573 (2006). 10.1088/0031-9155/51/3/006 [12] Church C. C., ‘ The Effects of an elastic solid-surface layer on the radial pulsations of gas-bubbles‘, J. Acoust. Soc. Am. 97, 1510–1521 (1995). 10.1121/1.412091

[13] Plesset M. S. and Prosperetti A., ‘Bubble dynamics and cavitation‘, Ann. Rev. Fluid Mech. 9, 145–185 (1977). 10.1146/annurev.fl.09.010177.001045 [14] M. Cavaro, C. Payan, J. Moysan and F. Baque, ‘Microbubble cloud characterization by nonlinear frequency mixing‘, J. Acoust. Soc. Am. 129 (5), May 2011 [DOI: 10.1121/1.3565474] [15] M. Minnaert, ‘On musical air bubbles and the sound of running water‘, Philos. Mag. 16 (7), 235–248 (1933).