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Dual Laterolog DLLThe DLL consists of two Laterologs, a deep and shallow investigating device, recorded simultaneously.Deep Laterolog LLdThe LLd is the deepest investigating laterolog.This tool is needed to extend the range of formation conditions in which reliable determintaons of Rt are possible.At the same time it is necessary to obtain good vertical resolution, for which very long guard electrodes are needed (28 feet measured between ends of the guard electrodes).

The same electrode array is used for deep laterolog and shallow laterolog, but the current flows are different.In the LLd (deep) mode,the surveying current Io, that flows from the center electrode, A0, is focused by bucket currents from electrodes A2 and A2'supported by A1 and A1'.The four "A" electrodes are all connected in this mode. The total current returns to the surface fish (electrode).This arrangement provides strong focusing deep into the formation.Current and voltage are used to compute resistvity.Shallow Laterolog (LLs)The shallow Laterolog (LLs) has the same vertical resolution as the deep Laterolog (2 feet), but responds more strongly to the region affected by invasion.In the LLs(shallow) mode the bucking currents flow from A1 to A2 and A1 to A2, reducing the depth of investigation. #the same electrodes are used for the shallow device although in a different way.The total constant current it is generated downhole and applied directly to bucking and measure electrodes.It is split into two components: Ib going to A1 and Io going to Ao; both currents return to A2 producing a shallow Io beamThe electrodes are switched several times per second from one to the other configuration, and the two resistivity traces are produced simultaneously.PrincipleWave TypesThe tool measures the time it takes for a pulse of sound (i.e., and elastic wave) to travel from a transmitter to a receiver, which are both mounted on the tool. The transmitted pulse is very short and of high amplitude. This travels through the rock in various different forms while undergoing dispersion (spreading of the wave energy in time and space) and attenuation (loss of energy through absorption of energy by the formations).Sound energy arrives at the receiver, after passing through the rock, at different times in the form of different types of wave.Because the different types of wave travel with different velocities in the rock or take different pathways to the receiver.First type of wave arrives is the compressional or longitudinal or pressure wave (P-wave).Next wave is the transverse or shear wave (S-wave).Then come Rayleigh waves and Stoneley waves that are associated with energy moving along the borehole wall.Lastly mud waves arrives which is a pressure wave that travels through the mud in the borehole.

The data of interest is the time taken for the P-wave to travel from the transmitter to the receiver. This is measured by circuitry that starts timing at the pulse transmission and has a threshold on the receiver.When the first P-wave arrival appears the threshold is exceeded and the timer stops. Clearly the threshold needs to be high enough so that random noise in the signal dies not trigger the circuit, but low enough to ensure that the P-wave arrival is accurately timed.The data is presented as a slowness or the travel time per foot traveled through the formation, which is called delta t (t or T), and is usually measured in s/ft.Hence we can write a conversion equation between velocity and slowness:

where the slowness, t is in microseconds per foot, and the velocity, V is in feet per second.

The velocity of the compressional wave depends upon the elastic properties of the rock (matrix plus fluid), so the measured slowness varies depending upon the composition and microstructure of the matrix, the type and distribution of the pore fluid and the porosity of the rock. The velocity of a P-wave in a material is directly proportional to the strength of the material and inversely proportional to the density of the material. Hence, the slowness of a P-wave in a material is inversely proportional to the strength of the material and directly proportional to the density of the material, i.e.;

The strength of a material is defined by two parameters Bulk modulusShear modulusThe bulk modulus, K is the extent to which a material can withstand isotropic squeezing.Imagine an amount of material subjected to an isotropic pressure P1. Now let the isotropic pressure increase to a pressure P2. The material will compress from its initial volume v1 to a new smaller volume v2. The bulk modulus is then given by;

where P is the change in pressure, and v is the change in volume. Thus P is the change in pressure that causes v change in volume.

The shear modulus, is the extent to which a material can withstand shearing. Imagine an amount of material subjected to a isotropic pressure P1. Now apply a shear stress (non-isotropic pressure) Ps to one side of the sample. The material will shear to the new shape, and its overall length will increase from its initial length l1 to a new larger length l2.The shear modulus is then given by;

where g is the shear strain. The application of the shear stress Ps causes the development of a shear strain g.

Detailed analysis of the velocity and slowness of P-waves in a material shows that:

Reflection and RefractionThe transmitter emits sound waves at a frequency of about 20-40 kHz, in short pulses, of which there are between 10 and 60 per second depending on the tool manufacturer. The energy spreads out in all directions.Imagine a pulse emanating from a Tx on a sonic tool. It will travel through the drilling mud and encounter the wall of the borehole. The P-wave travels well through the mud at a relatively slow velocity, Vm, as the mud has a low density. The S-wave will not travel through liquid mud. At the interface it is both reflected back into the mud and refracted into the formation. The portion of the P-wave energy that is refracted into the formation travels at a higher velocity, Vf, because the density of the rock is higher.

By using Snells law:

and at the critical angle of refraction, where the refracted wave travels along the borehole wall, R= 90o, so;

The velocity of the refracted wave along the borehole wall remains Vf. Each point reached by the wave acts as a new source retransmitting waves back into the borehole at velocity Vm.

MicrologThe microlog (ML) is a rubber pad with three button electrodes placed in a line with a 1 inch spacing . A known current is emitted from electrode A, and the potential differences between electrodes M1 and M2 and between M2 and a surface electrode are measured.The two resulting curves are called the 2 normal curve (ML) and the 1 inverse curve (MIV). The radius of investigation is smaller for the second of these two curves, and hence is more affected by mudcake. The difference between the two curves is an indicator of mudcake, and hence bed boundaries.The tool is pad mounted, and the distance across the pads is also recorded, giving an additional caliper measurement (the micro-caliper log).

The Proximity LogThe proximity log (PL) was developed from the MLL to overcome problems with mudcakes over 3/8 thick, and is used to measure RXO. The device is similar, except that it is larger than the MLL and the functions of the central electrode and the first monitoring ring electrode are combined into a central button electrode.The tool operates in a similar fashion to the LL3. It has a depth of penetration of 1 ft., and is not affected by mudcake. It may, however, be affected by Rt when the invasion depth is small.

Compensated Neutron Log (CNL)Designed to be sensitive to thermal neutrons, and is therefore affected by the chlorine effect. Two detectors situated 15 in. and 25 in. from the source. Far detector is larger to ensure adequate count rates are observed. Its significant measurement is the difference in thermal neutron population, resulting from neutron capture and neutron scattering.Readings are presented in limestone porosity units. Use very strong source of neutrons to ensure that the measured count rates are sufficiently high.Stronger source permits a deeper depth of investigation and can be used in cased holes. CNL tool is run eccentred in the hole by an arm which presses the tool against the side of the borehole. Insensitive to the type of mud in the hole but implies that the readings are only for one portion of the borehole wall.