System and method for determining properties of drilling mud

Abstract

Systems and methods determine physical properties of drilling mud by modeling velocity and dispersion behavior of drilling mud based on signals received from a downhole fluid cell device. The systems and methods may determine fluid and / or gas properties. The systems and methods may provide enhancement to interpretation of data from logging tools. The systems and methods may be integrated with a drilling control system to design optimum drilling mud and / or provide real-time monitoring and adjustment of drilling mud properties.

Description

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims priority to U.S. Provisional Patent Application No. 63 / 762,715, filed Feb. 25, 2025, the entire content of which is incorporated herein by reference.STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] Not applicable.TECHNICAL FIELD

[0003] The disclosed embodiments relate generally to techniques for optimizing wellbore operations during drilling for and production of hydrocarbons. In particular, the disclosed embodiments relate to techniques to determine properties of the drilling mud.BACKGROUND

[0004] Drilling mud, a crucial component in the oil and gas industry, plays a significant role in various operations such as drilling, completion, production, and shut in. Its functions are manyfold and include, but are not limited to: a) applying hydrostatic pressure to prevent the intrusion of formation fluids into the wellbore; b) managing open fractures during drilling operations; c) removing drill cuttings during drilling and suspending them when drilling is halted; d) cooling the drill bit and clearing cuttings from beneath it during drilling; e) regulating well pressure and stabilizing the formation; and f) cooling and lubricating the wellbore.

[0005] Moreover, drilling mud serves as a conduit from the formation to the tools in the well and to the surface. Understanding the properties of the drilling mud in the well is vital for several reasons, including: a) identifying the points of formation fluid entry into the well and the properties of the formation fluid; b) tracking the loss of drilling mud additives into the formation and pinpointing where these losses occurred; c) assisting both logging while drilling (“LWD”) and wire line (“WL”) logging tools with measurements and interpretation, as drilling mud properties are crucial for interpreting resistivity, dielectric, and acoustic tool measurements.

[0006] There exists a need for methods to determine the properties of drilling mud to enable the above.SUMMARY

[0007] In accordance with some embodiments, a method of determining physical properties of drilling mud is disclosed. These embodiments may include any of the following: a) characterization of drilling mud dispersion behavior; b) determination of fluid / gas properties in drilling mud; c) enhancing data interpretation for wireline and logging-while-drilling logging tools; d) designing engineered drilling mud; e) real-time monitoring and adjustment of drilling mud; and e) integration with drilling control systems.

[0008] In accordance with certain example embodiments, a method for measuring properties of a drilling mud in a borehole in an earth formation may comprise: (a) deploying a fluid cell device into the drilling mud in the borehole; (b) analyzing, by a drilling mud analyzer executing on a processor, measured acoustic signals from the fluid cell device to determine acoustic characteristic data, wherein the acoustic characteristic data is one or more of acoustic wave velocity and acoustic wave attenuation for the drilling mud; (c) selecting, by the drilling mud analyzer, an acoustic model for the drilling mud corresponding to a measured property of the drilling mud, wherein the measured property includes a property of a component suspended in the drilling mud; (d) comparing, by the drilling mud analyzer, the acoustic characteristic data to the acoustic model; and (e) determining, by the drilling mud analyzer, a derived property of the drilling mud from a correspondence of the acoustic characteristic data to the acoustic model.

[0009] In another aspect of the present invention, to address the aforementioned problems, some embodiments provide a non-transitory computer readable storage medium storing one or more programs. The one or more programs comprise instructions, which when executed by a computer system with one or more processors and memory, cause the computer system to perform any of the methods provided herein. For example, the method may comprise: (a) receiving, by a drilling mud analyzer, measured acoustic signals from a fluid cell device deployed in drilling mud in a borehole; (b) analyzing, by the drilling mud analyzer, the measured acoustic signals to determine acoustic characteristic data of the measured acoustic signals, wherein the acoustic characteristic data is one or more of acoustic wave velocity and acoustic wave attenuation for the drilling mud; (c) selecting, by the drilling mud analyzer, an acoustic model for the drilling mud corresponding to a measured property of the drilling mud, wherein the measured property includes a property of a component suspended in the drilling mud; (d) comparing, by the drilling mud analyzer, the acoustic characteristic data to the acoustic model; and (e) determining, by the drilling mud analyzer, a derived property of the drilling mud from a correspondence of the acoustic characteristic data to the acoustic wave model.

[0010] In yet another aspect of the present invention, to address the aforementioned problems, some embodiments provide a computer system. The computer system includes one or more processors, memory, and one or more programs. The one or more programs are stored in memory and configured to be executed by the one or more processors. The one or more programs include an operating system and instructions that when executed by the one or more processors cause the computer system to perform any of the methods provided herein.

[0011] In yet another example embodiment, a system is provided that may comprise a fluid cell device and a computing system. The fluid cell device may comprise: (a) a housing; (b) at least one chamber; and (c) at least one transducer disposed in the at least one chamber, wherein the at least one transducer emits acoustic signals of at least a first frequency and detects measured acoustic signals in response to the acoustic signals that are emitted. The computing system may comprise a drilling mud analyzer executed by a hardware processor that performs a method comprising: (a) analyzing, by a drilling mud analyzer, the measured acoustic signals to determine acoustic characteristic data of the measured acoustic signals, wherein the acoustic characteristic data is one or more of acoustic wave velocity and acoustic wave attenuation for the drilling mud; (b) selecting, by the drilling mud analyzer, an acoustic model for the drilling mud corresponding to a measured property of the drilling mud, wherein the measured property includes a property of a component suspended in the drilling mud; (c) comparing, by the drilling mud analyzer, the acoustic characteristic data to the acoustic model; and (d) determining, by the drilling mud analyzer, a derived property of the drilling mud from a correspondence of the acoustic characteristic data to the acoustic wave model.

[0012] In yet another example embodiment, a method is provided for formulating an engineered drilling mud. The method may comprise: (a) receiving, at a drilling mud analyzer executing on a hardware processor of a computer system, a desired acoustic characteristic for the engineered drilling mud; (b) selecting, by the drilling mud analyzer, an acoustic model corresponding to the desired acoustic characteristic of the engineered drilling mud; (c) outputting, by the drilling mud analyzer, desired properties of the engineered drilling mud derived from the acoustic model, wherein the desired properties include properties of a suspended component of the engineered drilling mud; (d) formulating the engineered drilling mud having the desired properties; and (e) placing the engineered drilling mud in a borehole in an earth formation.

[0013] The foregoing embodiments are non-limiting examples and other aspects and embodiments will be described herein. The foregoing summary is provided to introduce various concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify required or essential features of the claimed subject matter nor is the summary intended to limit the scope of the claimed subject matter.BRIEF DESCRIPTION OF THE DRAWINGS

[0014] FIG. 1A illustrates acoustic wave velocity at different frequencies for solid particles suspended in oil for 1, 5, 10 and 20% volume fractions of solid particles and 0.1, 1.0, 10 and 20 μm particle radius;

[0015] FIG. 1B illustrates acoustic wave velocity at different frequencies for gas bubbles suspended in oil for 1, 5, 10 and 20% volume fractions of gas bubbles and 0.1, 1.0, 10 and 20 μm bubble radius;

[0016] FIG. 1C illustrates acoustic wave velocity at different frequencies for water bubbles suspended in oil for 1, 5, 10 and 20% volume fractions of water bubbles and 0.1, 1.0, 10 and 20 μm bubble radius;

[0017] FIG. 2A illustrates acoustic wave velocity dispersion for solid particles suspended in oil for 1, 5, 10 and 20% volume fractions and 0.1, 1.0, 10 and 20 μm radius of the particles;

[0018] FIG. 2B illustrates acoustic wave velocity dispersion for gas bubbles suspended in oil for 1, 5, 10 and 20% volume fractions and 0.1, 1.0, 10 and 20 μm radius of the bubbles;

[0019] FIG. 2C illustrates acoustic wave velocity dispersion for water bubbles suspended in oil for 1, 5, 10 and 20% volume fractions and 0.1, 1.0, 10 and 20 μm radius of the bubbles;

[0020] FIG. 3 illustrates dependence of velocity difference at 0 and 250 kHz on particle / bubble radius and volume fraction of suspensions of solid particles, gas, and water bubbles in oil;

[0021] FIG. 4A illustrates acoustic wave attenuation at different frequencies for solid particles suspended in oil for 1, 5, 10 and 20% volume fractions of solid particles and 0.1, 1.0, 10 and 20 μm particle radius;

[0022] FIG. 4B illustrates acoustic wave attenuation at different frequencies for gas bubbles suspended in oil for 1, 5, 10 and 20% volume fractions of gas bubbles and 0.1, 1.0, 10 and 20 μm bubble radius;

[0023] FIG. 4C illustrates acoustic wave attenuation at different frequencies for water bubbles suspended in oil for 1, 5, 10 and 20% volume fractions of gas bubbles and 0.1, 1.0, 10 and 20 μm bubble radius;

[0024] FIG. 5 illustrates dependence of acoustic wave attenuation at 250 kHz on particle / bubble radius and volume fraction of suspensions of solid particles, gas, and water bubbles in oil;

[0025] FIG. 6 illustrates a representation of the drilling mud, including the underlying continuous oil phase, water emulsion, solid (barite) particles, and droplets of gas;

[0026] FIG. 7A illustrates dependence of acoustic wave velocity on frequency in the mixtures containing 2 or 3 suspended components;

[0027] FIG. 7B illustrates dependence of acoustic wave attenuation on frequency in mixtures containing 2 or 3 suspended components;

[0028] FIG. 8 illustrates a comparison of acoustic wave velocity modeling at 0 kHz for mixtures containing 2 or 3 components suspended in oil;

[0029] FIG. 9A illustrates a comparison of acoustic wave modeling results with acoustic wave field data for drilling mud;

[0030] FIG. 9B illustrates an acoustic wave velocity difference distribution for the field data at a depth less than 3250 ft.

[0031] FIG. 9C illustrates an acoustic wave velocity difference distribution for the field data at a depth greater than 3250 ft.

[0032] FIG. 9D illustrates acoustic wave velocity difference from the models of FIG. 1A through FIG. 3.

[0033] FIG. 10 illustrates using a fluid cell device in a borehole in accordance with the example embodiments provided herein;

[0034] FIG. 11 illustrates an example method for determining a property of a drilling mud in a borehole using the embodiments described herein;

[0035] FIG. 12 illustrates example methods of using the drilling mud property determined in FIG. 11 in accordance with the embodiments described herein;

[0036] FIG. 13 illustrates an example method of engineering a drilling mud using the embodiments described herein; and

[0037] FIG. 14 illustrates an example system for determining physical properties of drilling mud.

[0038] Like reference numerals refer to corresponding parts throughout the drawings.DETAILED DESCRIPTION OF EMBODIMENTS

[0039] Described below are methods, systems, and computer readable storage media that provide a manner of determining physical properties of drilling mud. In particular, these methods, systems, and computer readable storage media characterize the velocity and attenuation dispersion behavior of drilling mud.

[0040] The velocity and attenuation dispersion behavior refers to the dependence of velocity and attenuation of sound waves in a mixture on frequency. The drilling mud comprises a continuous phase fluid (typically oil or water) with multiple components (solid, fluid, or gas) suspended in it. This method can be used for the following purposes:

[0041] a) Characterizing the acoustic and ultrasonic behavior of drilling mud, which is a multidisperse suspension of gas and water bubbles and solid particles, under varying pressure and temperature conditions, provided the acoustic properties of each drilling mud component at these temperatures and pressures are known.

[0042] b) Identifying the influx of formation fluid into drilling mud in the borehole and determining its properties using fluid cell data.

[0043] c) Detecting the loss of drilling mud components into the formation and assessing their properties using fluid cell data.

[0044] d) Estimating the drilling mud acoustic wave velocity at low (acoustic) frequencies based on fluid cell measurements at high frequencies.

[0045] e) Adjusting the drilling mud composition to ensure its dispersive properties meet both operational and measurement requirements. For instance, creating drilling mud with minimal velocity dispersion allows high-frequency velocity measurements to be directly applied in Stoneley inversion for vertical transverse anisotropy (VTI).

[0046] FIGS. 1A-C illustrate models of acoustic wave velocities of suspensions containing solid, gas, and water particles / bubbles in oil for various suspension volumes (1%, 5%, 10%, and 20%) and particle / bubble sizes (0.1, 1, 10, and 20 μm) within the 0 to 5 MHz range.

[0047] In all cases, the oil is the reference continuous phase. The dynamic viscosity of oil is set at 0.021 Pa-s. The velocities at 0 Hz (seismic frequency) can be determined by Wood's equation:V=1ρ⁢∑i=1NφiKi,(1)where N is the number of components (2 in this case), V and ρ are the velocity at 0 Hz frequency and the density of the mixture, Ki and φi denote the bulk modulus (static bulk modulus) and volume fraction of each component. Since Wood's equation is based on a Reuss average of the bulk moduli, the most significant change in velocity at 0 kHz frequency occurs in the mixture of gas bubbles suspended in oil, with the mixture of solid particles in oil being a distant second, as shown in Table 1.TABLE 1Seismic velocities of different mixtures at 1%and 20% concentration and their difference.SeismicSeismicAbsolutevelocity atvelocity atvalue of the1% volume20% volumedifference,Mixturefraction, m / secfraction, m / secm / secSolid particles in oil1333.11207.5125.6Gas bubbles in oil1217.7618.5599.2Water bubbles in oil1345.11361.716.6One should also recognize that the velocity (the overall change in velocity as a function of increasing frequency) follows a different rule for each mixture. FIGS. 2A-C illustrate models of acoustic wave velocity dispersions for the suspensions of FIGS. 1A-C. As illustrated in FIGS. 2A-C, by subtracting the velocity at 0 Hz from the velocities at other frequencies, the resulting dispersion is greater for solid particles suspended in oil compared to immiscible gas or water suspensions. In addition, as the sizes of the particles increase, the maximum of the dispersion gradient shifts towards lower frequency.This is further demonstrated in FIG. 3, which shows models of the total acoustic wave velocity dispersion between 0 and 250 kHz for various suspension volumes and different particle / bubble sizes. This information can be used to design a drilling mud (type of suspension, chemistry, and particle size) that reduces the dispersion to be within an uncertainty threshold, thereby enabling the measuring of acoustic wave velocity for the drilling mud at 250 kHz with ultrasonic methods to be reflective of acoustic wave velocity for the drilling mud at 0 Hz. The models of FIG. 3 illustrate again that the acoustic wave velocity dispersion is greatest for solid particles suspensions, followed by gas and water suspensions. Since gas is typically not added to drilling mud, and water suspension in oil causes only minor velocity changes (compared to solid particles), one can largely control acoustic wave velocity dispersion by adjusting the size of the solid particles suspended in the continuous oil phase.

[0050] In addition to acoustic wave velocity dispersion, the presence of solid particles or gas bubbles in suspensions also leads to the attenuation of acoustic energy. This attenuation, caused by acoustic scattering, is distinct from the attenuation observed in single-phase fluids, which is mainly due to molecular viscosity and loss of elastic energy via conversion to heat due to internal friction. Furthermore, scattering attenuation can be utilized to determine the properties of materials and the sizes of particles in suspensions.

[0051] FIGS. 4A-C illustrate models of acoustic wave attenuation for suspensions containing solid, gas, and water particles / bubbles in oil for various suspension volumes (1%, 5%, 10%, and 20%) and particle / bubble sizes (0.1, 1, 10, and 20 μm) within the 0 to 5 MHz range. As shown, attenuations for solid and gas suspensions may be several orders of magnitude higher than for water suspensions in oil when compared at the same concentration and particle / bubble sizes. Also shown are the nonlinear characteristics of the attenuation depending on the particle size showing the prediction of attenuation is complicated and depends on many things. But it can be observed that as one increases particle size, attenuation reaches a peak and then starts declining.

[0052] This characteristic is further demonstrated in FIG. 5, which shows the attenuations at 250 kHz for various suspension volumes and different particle / bubble sizes. As shown, the peak of attenuation for different suspensions is reached at different particle / bubble sizes.Calculations to Derive the Models

[0053] In the following section, the calculations are provided that are used to derive the models illustrated in FIGS. 1A-5. The following calculations describe the acoustic wave propagation in a mixture with multiple components (solid, gas or fluid) suspended in it. As each of the suspended components is characterized by its component radius, the developed relationship also allows for the modeling of the particle size distribution of each component.Deriving the Non-Linear Partial Differential Equations

[0054] To derive an analytical equation for the acoustic properties of drilling mud by extending the model proposed by [1], we model the mud as a continuous liquid phase, which can be either water-based or oil-based, containing suspended particles. These suspended particles may include an emulsified liquid phase (e.g., water / oil emulsion in oil / water-based drilling mud), solid particles (such as barite or cuttings), and gas, which may be present in the event of a kick. This approach contrasts with the original analytical model introduced by [1] which only accounted for a single dispersed phase.

[0055] To illustrate the mathematical derivation, we assume, without loss of generality, that the continuous phase is oil, as illustrated in FIG. 6. Additionally, the suspended particles are assumed to be spherical. As they vibrate within the continuous phase, they do not undergo any deformation, and the fluid particles (such as liquid emulsions and gas droplets) do not exhibit internal circulation.

[0056] The mixture, comprising the continuous liquid phase and all suspended particles, is also assumed to form a continuum. Therefore, we can derive a continuity equation for each suspended phase separately by assuming that the particles oscillate in a single direction (e.g., the x-direction) as follows:∂vi⁢ρi∂t+∂∂x(vi⁢ρi⁢vi)=0,(A.1)where vi is the volume fraction of phase i, ρi is the density of phase i, and vi is the velocity of phase i. The subscript i can be replaced by e for emulsion, s for solid, and g for gas and, hence, equation A. 1 represents 3 independent continuity equations.Since the volume fractions of all phases must sum to 1, the continuity equation for the underlying continuous phase is given by:∂(1-ve-vs-vg)⁢ρc∂t+∂∂x[(1-ve-vs-vg)⁢ρc⁢vc]=0,(A.2)where ρc and vc are density and velocity of the underlying continuous phase, respectively.Similarly, we can derive a volume-averaged momentum balance for each one of the phases in suspension, neglecting gravitational effects, and assuming that the dispersion phases only interact with the underlying continuous phase as follows:vi⁢ρi⁢ (∂vi∂t+vi⁢∂vi∂x)=Fi⁢c,(A.3)where Fic stands for force per unit volume exerted by the underlying continuous phase c on the dispersion phase i.Noting that the volume fractions of all phases must sum to 1, by considering Newton's third law, and neglecting the viscous dissipation outside the boundary layers around the particles in suspension, the momentum equation for the underlying continuous phase is given by(1-ve-vs-vg)⁢ρc⁢ (∂vc∂t+vc⁢∂vc∂x)=-∂P∂t-Fec-Fsc-Fgc,(A.4)where P corresponds to the static pressure of the underlying continuous phase.Equations A.1 and A.2 correspond to 4 independent continuity equations and Equations A.3 and A.4 correspond to 4 independent momentum equations in 12 unknowns, namelyxT=[vcvevsvgPvevsvgρcρeρsρg].(A.5)Therefore, we need 4 additional equations of state that relate the density of each one of the phases to the static pressure. These equations of state are linearized in a small neighborhood (in the context of Taylor series) of the local static pressure resulting inρi=ρi0(1+Δ⁢Pκi),(1.6)whereρi0and κi are the density and bulk modulus of phase i at pressure P and ΔP corresponds to a pressure perturbation in a small neighborhood around P. In the specific case of Equation A.6, the subscript i can be replaced by e for emulsion, s for solid, g for gas, and c for the underlying continuous phase resulting in 4 additional equations.The momentum interaction terms Fic still need to be determined. To achieve this, we start from the analytical equation in [4] modeling the unsteady drag on an isolated sphere, FD0, asFD⁢0=6⁢π⁢μ⁢a⁡(1+aiδ)⁢(vi-vc)+3⁢π⁢a2⁢ρc(29⁢ai+δ)⁢D⁡(vi-vc)D⁢t,(A.7)where μ is the viscosity of the continuous phase, αi is the diameter of the isolated sphere of phase i, δ is the unsteady viscous boundary layer thickness surrounding the spherical particleδ=2⁢μρc⁢ω,(A.8)with ω is the angular frequency at which the isolated sphere oscillates, and the material derivative is defined asD⁡(vi-vc)D⁢t=(∂vi∂t+vi⁢∂vi∂x)-(∂vc∂t+vc⁢∂vc∂x).(A.9)However, there is an added mass, or virtual mass effect, due to the extra inertia in the system. This effect arises because the oscillating spheres must displace the underlying continuous phase as they move through it. Hence, it can be shown that, to account for the added mass effect, Equation A.7 can be re-written as followsFD=6⁢π⁢μ⁢a⁡(1+aδ)⁢(vi-vc)+43⁢π⁢a3⁢ρc(C⁡(vi)+9⁢δ4⁢a)⁢D⁡(vι¯⁢vc)D⁢t,(A.10)where the added mass coefficient can be expressed asC⁡(vi)=(1-vi2).(A.11)Linearizing the Partial Differential EquationsEquations A.1 to A.4 and A.6 describe a system of 12 coupled nonlinear partial differential equations involving the 12 variables defined in Equation A.5. To analytically solve this system, we need to further simplify the problem by assuming that all the variables defined in Equation A.5 are perturbed from their steady-state values by an infinitesimal amount. So, first, we assume that the steady-state velocities are all zero:vc0=ve0=vs0=vg0=0.(A.12)Additionally, we arbitrarily assume that the datum pressure is zeroP0=0.(A.13)Note that this does not imply the reference pressure is 0 atm. It is intended solely to simplify the algebra, as all terms directly dependent on the pressure are either derivatives or differences. Therefore, a constant shift does not alter the final results.Hence, the state variables can be written asxT=[Δ⁢vcΔ⁢veΔ⁢vsΔ⁢vgΔ⁢Pve0+Δ⁢vevs0+Δ⁢vsvg0+Δ⁢vgρc0+Δρcρe0+Δρeρs0+Δρsρg0+Δρg].(A.14)Under these conditions, and neglecting second order effects, it is easy to show that Equation A.1 becomesvi0⁢∂Δ⁢ρi∂t+ρi0⁢∂Δ⁢vi∂t+vi0⁢ρi0⁢∂Δ⁢vi∂x=0,(A.15)and Equation A.2 becomes(1-ve0-vs0-vg0)⁢∂Δ⁢ρc∂t-ρc0⁢∂Δ⁢vc∂t+(1-ve0-vs0-v90)⁢ρc0⁢∂Δ⁢vc∂x=0.(A.16)Similarly, Equation A.6 becomesΔ⁢ρi=ρi0⁢Δ⁢Pκi.(A.17)The momentum equation A.3 of the dispersed phase i becomesvi0⁢ρi0⁢∂Δ⁢vi∂x=-vi0⁢∂Δ⁢P∂x+vi0⁢Fic′,(A.18)wherevi0⁢Fic′=-9⁢μ⁢vi02⁢ai2⁢(1+aiδ)⁢(Δ⁢vi-Δ⁢vc)-9⁢vi04⁢ai⁢Δρc[49⁢C⁡(vi0)⁢ai+δ]⁢(∂Δ⁢vi∂x-∂Δ⁢vc∂t),(A.19)and the momentum equation of the underlying continuous phase becomes(1-ve0-vs0-vg0)⁢ρc0⁢∂Δ⁢vi∂t=-(1-ve0-vs0-vg0)⁢∂Δ⁢P∂x-ve0⁢Fec′-vs0⁢Fsc′-vg0⁢Fgc′.(A.20)Equations A.15 to A.20 represent a system of 12 coupled linear partial differential equations. However, for the purposes of this work, we are not focused on solving these equations. Instead, we are interested in the algebraic function that describes the dispersive behavior of the drilling mud slowness.Algebraically Deriving the Dispersion RelationTo derive the algebraic function that describes the dispersive behavior of the drilling mud slowness, we assume that there is a solution to Equations A.15 to A.20 of the form of a Helmholtz plane wave equation such asΔ⁢f=f0⁢ej⁡(ω⁢t+kx),(A.21)where j is the imaginary number (√{square root over (−1)}), f refers to any of the perturbations to the state variables defined asΔ⁢xT=[Δ⁢vcΔ⁢veΔ⁢vsΔ⁢vgΔ⁢PΔ⁢veΔ⁢vsΔ⁢vgΔ⁢ρcΔ⁢ρeΔ⁢ρsΔ⁢ρg],(A.22)andk=ωvw+j⁢α,(A.23)where vw is the acoustic velocity of the drilling mud and α is the attenuation parameter.Now, it is possible to show that by representing each of the variables defined in Equation A.22 with a function similar to the one in Equation A.21, and then substituting them into Equations A.15 to A.20, the system of coupled linear partial differential equations can be transformed into a system of algebraic equations, defined as follows:M⁢Δ⁢x=0,(A.24)where M is a 12 by 12 matrix. From equation A.24, it is evident that the non-trivial solution Δx is in the null space of matrix M and, hence, the condition for which the null space of matrix M is not an empty set can be algebraically found from the solution ofdet⁡(M)=0.(A.25)By setting ω as a constant input in Equation A.21 and assuming k as the independent variable, we can obtain k from Equation A.25. Once k is determined, we can easily calculate vw and α from Equation A.23. To fully understand the dispersive behavior of the drilling mud slowness, we need to solve Equation A.25 for all angular frequencies of interest.Since the analytical solution to Equation A.25 can be obtained using any off-the-shelf symbolic math library, our next step is to correctly define matrix M.It is easy to see that the perturbations applied to the equations of state, as defined by Equation A.17, translate into four rows of matrix M. In this case, these equations are arbitrarily chosen to occupy rows 9 to 12, as follows:M(9:12,:)=[0000-ρc0κc00010000000-ρe0κe00001000000-ρs0κs00000100000-ρg0κg0000001](A.26)where the subscript (9:12,:) indicates that Equation A.26 shows the rows 9 to 12 and all the corresponding columns of matrix M.Next, we need to include the rows of M that contain the continuity equations for the underlying continuous phase (row 5)M(5,:)=
[k⁢(1-ve0-vs0-vg0)⁢ρc00000-ωρc0-ωρc0-ωρc0ω⁡(1-ve0-vs0-vg0)000],(A.27)for the liquid emulsion phase (row 6)M(6,:)=[0kve0⁢ρe0000ωρe0000ω⁢ve000],(A.28)for the dispersed solid phase (row 7)M(7,:)=[00kvs0⁢ρs0000ωρs0000ω⁢vs00](A.29)And for the dispersed gas bubbles (row 8)M(8,:)=[000kvg0⁢ρg0000ωρg0000ω⁢vg0],(A.30)Then, we need to define rows 1 to 4 of matrix M that correspond to the volume-averaged momentum balance for each one of the phases.Equation A.18 translates into 3 independent momentum equations for the liquid emulsion phase (row 2)M(2,:)=[-Ae-j⁢ω⁢BeAe+j⁢ω⁢(Be+ρe0)00jk0000000],(A.31)whereAi=9⁢μ2⁢ai2⁢(1+aiδ),and(A.32)Bi=ρc0 [C⁡(vi0)+94⁢δai],(A.33)and the subscript i can be replaced by e for emulsion, s for solid, and g for gas. For Equation A.31, in particular, i is replaced by e for emulsion.For the suspension of solid particles, Equation A.18 translates into (row 3)M(3,:)=[-As-j⁢ω⁢Bs0As+j⁢ω⁢(Bs+ρs0)0jk0000000],(A.34)for the gas bubblesM(4,:)=[-Ag-j⁢ω⁢Bg00Ag+j⁢ω⁢(Bg+ρg0)jk0000000].(A.35)Finally, Equation A.18 also translates into the momentum for the underlying continuous phase as follows:M(1,:)=[M11M12M13M14M150000000],(A.36)whereM11=j⁢ω⁢ρc0(1-ve0-vs0-vg0)+ve0(Ae+j⁢ω⁢Be)+vs0(As+j⁢ω⁢Bs)+vg0(Ag+j⁢ω⁢Bg),(A.37)M12=-ve0(Ae+j⁢ω⁢Be),(A.38)M13=-vs0(As+j⁢ω⁢Bs),(A.39)M14=-vg0(Ag+j⁢ω⁢Bg),(A.40)M15=jk⁡(1-ve0-vs0-vg0).(A.41)The derivation described above differs from conventional derivations not only because we explicitly derive the equations for four phases instead of just two, but also because our mathematical formulation facilitates extending the model to any number of phases.The solution to Equation A.25 gives us the value of k for which the null space of M is not an empty set and, then, we can calculate the mud slowness from the real part of k asslowness⁢=1ω⁢R⁢e⁡(k),(A.42)and the attenuation from the imaginary part of k asattenuation=Im⁡(k).(A.43)The mud slowness in equation A.42 is the inverse of the acoustic wave velocity. Thus, equations A.42 and A.43, which are derived from the system of equations above, are used to derive the example models of FIGS. 1A-5.Applications of ModelsWe now demonstrate the results of using these relationships shown in the models of FIG. 1A through FIG. 5 for the mixtures containing 2 or 3 suspended components. The properties are reflected in the following table:TABLE 2Material properties, radius of suspended particles andbubbles, and volume fractions used in the modelingof suspensions containing 2 and 3 components. The dynamicviscosity of oil is assumed to be 0.021 Pa-s.BulkDensityModulusRadiusVolumeName(g / cc)(GPa)(um)FractionContinuous0.831.5N / A1 − Vsolid −Phase (Oil)Vwater − VgasSolid3.057457.50.13 or 0Water1.02.21.20.21 or 0Gas0.2050.0631.00.03 or 0FIGS. 7A and 7B illustrate the dependencies of velocity and attenuation on frequency using the models of FIG. 1A through FIG. 5. The velocity curves (FIG. 7A) show that mixtures containing solids (dashed lines) exhibit notable dispersion, while the velocity of the gas and water mixture (solid line) remains relatively stable up to 5 MHz. When it comes to attenuation (FIG. 7B), mixtures with both solid and gas show the highest attenuation, whereas the gas and water mixture demonstrates the lowest attenuation across all frequencies.Additionally, as the number of components in suspension increases, tracking dependencies on different parameters becomes more complex. The results depicted in FIGS. 6A and 6B pertain to a specific case of volumetric concentrations and particle / bubble size. However, the developed models offer comprehensive control over describing the velocity and attenuation of mixtures at various frequencies, provided the properties of the components and the sizes of the suspended particles / bubbles are known. The models also allow one invert for suspension content, particle / bubble sizes, and dispersion characteristics based on velocity and attenuation measurements at a particular frequency or different frequencies.In FIG. 8 we demonstrate consistency with expectations that the foregoing models correctly reproduce velocities at 0 Hz as given by Wood's relationship in equation (1) provided above. The Wood's relationship describes the acoustic wave velocities for a fluid mixture at 0 Hz. The models provided in FIGS. 1A-5 predict an acoustic wave velocity for a fluid mixture at 0 Hz and the predictions of the models correspond with the relationship provided by the Wood's equation.In FIGS. 9A-9D, we compare field data results with the acoustic wave modeling described herein. FIG. 9A shows acoustic wave velocity field data acquired using acoustic devices placed in drilling mud in a borehole of a well. The acoustic wave velocity field data was acquired over an interval of approximately 4300 feet in the borehole. The righthand curve in FIG. 9A represents the acoustic wave velocity measured using a fluid cell device at a “high” frequency of approximately 250 kHz. The lefthand curve in FIG. 9A represents the apparent mud velocity at a “low” acoustic frequency near 1 kHz, derived using a multicomponent inversion from the Stoneley data acquired in the well using an acoustic logging tool. Note that the mud velocities measured at both high and low frequencies show a substantial decrease below 3250 ft, likely due to the influx of gas into the well from the formation.FIGS. 9B and 9C display the distribution of the high and low frequency acoustic wave velocity differences, potentially due to dispersion, measured in the well above 3250 ft (FIG. 9B, a depth less than 3250 ft) and below 3250 ft (FIG. 9C, a depth greater than 3250 ft). FIG. 9D illustrates the velocity differences, as determined from the models of FIGS. 1A-3, for suspensions of solids, water, and gas in oil, as well as solids and water in oil. The components used in the modeling have the properties listed in Table 2. The modeled difference in velocities due to dispersion for the suspension of solids and water in oil uses the volumetric fractions corresponding to the mud in the well according to the mud report. As shown, above 3250 ft the modeled difference of 48 m / sec (in FIG. 9D) is similar to the peak of the velocity difference of 53 m / sec in FIG. 9B. For the interval below 3250 ft, where it is believed there is a gas influx into the borehole and the drilling mud, we treated the depth interval as having an arbitrary constant gas volume fraction of 3%, which is a “best fit” average approximation for a depth range that likely has a gradient in gas volume fraction. The modeled value of 37 m / sec (in FIG. 9D) generally corresponds with the peak difference of 43 m / sec in FIG. 9C. Given that this observed high / low frequency velocity difference in the log of ~10 m / s is accurately modeled by the addition of gas below 3250 ft, and that the modeled velocity absolute values for each frequency are fairly similar to that observed, we interpret that the field data difference is due to velocity dispersion and the model correctly explains the field data.The small differences between the model and field data can also be explained by changes in temperature and pressure that were not accounted for. We also do not have the exact frequency at which the mud cell data were acquired as well as information about solid particle size distribution. An additional problem arises when considering the source of low frequency data, as it was obtained via a multicomponent inversion of Stoneley data, which does not have a unique solution and relies on multiple assumptions. In the next section, we demonstrate how the issues listed here are resolved in this application.The methods described herein utilize measurements acquired by one or more acoustic devices, such as a fluid cell device. Conventional fluid cell devices can be deployed in drilling mud within a borehole and used to acquire acoustic wave velocity measurements. Alternatively, an improved fluid cell device such as that described in co-pending U.S. patent application Ser. No. 19 / 446,705 can be employed. This improved fluid cell device is designed to measure both the acoustic wave velocity and attenuation at high frequency in the drilling mud as well as the drilling mud's density. Additionally, we suggest performing a frequency analysis of the waveform data recorded by the fluid cell device to determine the frequency corresponding to the measured acoustic wave velocity and attenuation. Calibration can be employed to better understand the relationship between the frequencies, velocities and attenuations measured by the fluid cell device for different drilling mud compositions. Multiple fluid cell devices operating at different frequencies can be deployed to gain a better understanding of the drilling mud dispersion behavior, i.e. variation of both velocity and attenuation with frequency. For example, a first fluid cell device can operate at a first frequency providing a first data point along a dispersion curve, a second fluid cell can operate at a second frequency providing a second data point along the dispersion curve, and a third fluid cell can operate at a third frequency providing a third data point along the dispersion curve. Having data at multiple frequencies allows for determining a more accurate dispersion curve.The methods may utilize the following information measured by the fluid cell device: drilling mud density, acoustic wave velocity and attenuation, and the frequency corresponding to this velocity and attenuation (or the frequencies corresponding to different velocities and attenuations if multiple mud cells are employed).While conventional fluid cell devices may be used to acquire the acoustic wave velocity measurements described herein, an example of the improved fluid cell device as described in co-pending U.S. patent application Ser. No. 19 / 446,705 is illustrated in FIG. 10. The example of FIG. 10 illustrates a fluid cell device 1001 that has been lowered into drilling mud 1024 within a borehole 1022 in a formation 1020 of the earth. The fluid cell device 1001 includes a housing 1002, a top pipe 1012 extending from a top of the housing 1002, and a bottom pipe 1013 extending from the bottom of the housing 1002. The top and bottom pipes allow the fluid cell device 1001 to be inserted between sections of pipe in a pipe string, such a drill pipe string. Alternatively, the fluid cell device 1001 could be lowered into the drilling mud 1024 on a wire line or other device. While not shown in FIG. 10, wiring can extend from housing 1002 up through the top pipe 1012 or a wireline to the surface of the borehole. Such wiring can be used to transmit data collected by the fluid cell device to a computing system at the surface for analysis.In the example of FIG. 10, the housing 1002 includes a first chamber 1004 and a second chamber 1006 that are adjacent to each other and that are separated by a plate 1008. In the example of FIG. 10, the first chamber 1004 is located closer to the proximal end of the housing 1002 and the second chamber 1006 is located closer to the distal end of the housing 802. Although the first chamber 1004 is located above the second chamber 1006 in the example of FIG. 10, in other embodiments the first and second chambers can have other orientations such as a horizontal side by side configuration as long as the first and second chambers are adjacent and separated by a plate. Additionally, the housing 1002 has a generally cylindrical shape in the example of FIG. 10. However, in alternate embodiments, the housing can have other shapes.The first chamber 1004 and the second chamber 1006 are in the shape of recesses in the housing 1002 into which the drilling mud 1024 can flow. The first chamber 1004 and the second chamber 1006 may be completely separated by the plate 1008 or the two chambers may be in fluid communication permitting drilling mud to flow between the two chambers. The first chamber 1004 has a first transducer T1 1003 located at a proximal end of the first chamber 1004. At a distal end of the first chamber, the plate 1008 is located with a proximal surface of the plate 1008 facing the first transducer T1 1003. Opposite the proximal surface of the plate 1008 is the distal surface of the plate located at the proximal end of the second chamber 1006 and facing a distal end of the second chamber. Optionally, at the distal end of the second chamber 1006 a second transducer T2 1005 can be located.Consistent with the other embodiments herein, the fluid cell device 1001 collects data relating to the drilling mud 1024 in order to determine properties of the drilling mud 1024. The first transducer T1 1003 can emit an acoustic signal that will pass through drilling mud in the first chamber until it reaches the plate 1008. The acoustic signal will generate reflection and reverberation signals when it impacts the plate 1008. The reflection and reverberation signals can be detected by the first transducer T1 1003. Alternatively or additionally, if the second transducer T2 1005 is present, the second transducer T2 1005 can be used to collect the reflection and reverberation signals.The reflection and reverberation signals can be analyzed by a hardware processor located onboard the fluid cell device. Alternatively, the reflection and reverberation signals can be transmitted via a wired or wireless link to a hardware processor at the surface where they are analyzed. The reflection and reverberation signals can be analyzed to determine one or more properties of the drilling mud, including acoustic wave velocity, impedance, and attenuation. The determination of the drilling mud properties can be used to improve operations associated with the borehole. As one example, the determined drilling mud properties may be used to adjust the composition of the drilling mud. As another example, the determination of the drilling mud properties may be used to adjust drilling equipment in the boreholeReference will now be made to example methods of using the previously described models. In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the present disclosure and the embodiments described herein. However, embodiments described herein may be practiced without these specific details. In other instances, well-known methods, procedures, components, and mechanical apparatus have not been described in detail so as not to unnecessarily obscure aspects of the embodiments.Referring now to FIG. 11, an example method 1100 is illustrated. The example method 1100 may employ aspects of the system illustrated in FIG. 14, which is described further below.In operation 1102, an acoustic device such as a fluid cell device is deployed in drilling mud in a borehole of an earth formation. The deployed fluid cell device may be a conventional fluid cell device or it may be an improved fluid cell device as described above in connection with FIG. 10. In operation 1104, the deployed fluid cell device emits acoustic signals from a transducer and detects measured acoustic signals in response to the emitted acoustic signals.As described further in connection with FIG. 14 below, a computing system can execute a drilling mud analyzer to analyze the measured acoustic signals. The drilling mud analyzer may be one or more software modules or software services. In operation 1106, the drilling mud analyzer determines acoustic characteristic data for the drilling mud from the measured acoustic signals. The acoustic characteristic data may be one or more of acoustic wave velocity, acoustic wave velocity dispersion, and acoustic wave attenuation.In operation 1108, the drilling mud analyzer receives a drilling mud report of measured properties of the drilling mud. The measured properties of the drilling mud report may be gathered by one or more tools placed into the drilling mud in the borehole. As examples, the measured properties may be properties associated with components suspended in the drilling mud, such as solid particles, gas bubbles, and water droplets. The drilling mud reports of the measured properties may be stored as measured data in electronic storage accessible by the drilling mud analyzer.As described previously, the acoustic models provided in FIGS. 1A-5 are based upon particular properties of suspended components in the drilling mud or oil, such as size of the suspended component or volume fraction of the suspended component. Acoustic models, such as those provided in FIGS. 1A-5, may stored in electronic storage and accessed by the drilling mud analyzer. In operation 1110, the drilling mud analyzer selects, from the stored acoustic models, an acoustic model corresponding with the properties in the drilling mud report. For example, if the measured properties of the drilling mud report indicate the presence of water bubbles having a radius of 10 micrometers and a constituting a volume fraction of 10%, the drilling mud analyzer may select an acoustic model corresponding to the measured properties of the water bubbles suspended in the drilling mud. In some instances, the drilling mud analyzer can select multiple acoustic models based upon the measured properties in the drilling mud report.Lastly, in operation 1112, the drilling mud analyzer compares the acoustic characteristic data derived from measured acoustic signals to the selected acoustic model(s). By identifying correspondence between the acoustic characteristic data and the selected acoustic model(s), the selected acoustic model(s) can provide one or more derived properties for the drilling mud. The derived properties may be wave velocity dispersion characteristics, wave velocity attenuation characteristics, further information about the continuous phase fluid, or further information about the suspended components in the continuous phase fluid.Referring now to FIG. 12, a method 1200 is illustrated for using the property or properties derived from the acoustic models in accordance with the method 1100 of FIG. 11. As illustrated in FIG. 12, the property or properties derived from using the acoustic models can be applied to a variety of applications.Characterization of Drilling Mud Dispersion Behavior: Operation 1202 describes a method for characterizing drilling mud dispersion behavior, defined as the dependence of velocity and attenuation on frequency, for in situ downhole conditions. This method utilizes the temperature and pressure dependencies of each drilling mud component or other modeling and experimental techniques, to reconstruct the dispersion behavior based on the modeling described herein and data obtained by the fluid cell device. As explained in connection with operation 1110, one or more acoustic models, such as those illustrated in FIGS. 1A-5, can be selected that correspond with the measured properties of the drilling mud report. Once corresponding acoustic models are selected, the acoustic models can be used to predict the other characteristics of the drilling mud, such as behavior at different frequencies or behavior when the volume concentrations of suspended components changes. Accordingly, by using the property derived by the method of FIG. 11, the drilling mud analyzer can characterize the drilling mud's dispersion behavior.Determination of Fluid / Gas Properties: Operation 1204 describes a method for determining the properties of fluid or gas entering the well, or the components of mud lost into the formation. When the density measured by the fluid cell device significantly deviates from the acoustic models described herein, this method models the loss of drilling mud components into the formation or the influx of gas / fluid from the formation into the well. It also includes ascertaining the volumetric fractions of these “gained” or “lost” components. Surface measurements from drilling mud logging can be used to constrain the inversion. The derived property from the method of FIG. 11 can indicate there has been a change in the suspended components in the drilling mud. The drilling mud analyzer can use the detected change to select an acoustic model that corresponds with the detected change in the suspended components. As illustrated above in connection with FIGS. 9A-9D, a selected acoustic model having a volumetric fraction of 3% gas bubbles corresponded with the acoustic characteristic data gathered by the fluid cell device indicating an influx of that amount of gas into the drilling mud from the formation.Enhance Data Interpretation for WL and LWD Logging Tools: Operation 1206 describes a method for enhancing the interpretation of data from logging tools (LWD and WL) by incorporating the drilling mud measured properties and the drilling mud composition properties derived from the acoustic models described herein. The drilling mud analyzer can incorporate these measured properties and derived properties into the processing workflows of logging data (real time or postprocessing). This method improves the accuracy of resistivity, dielectric, nuclear and acoustic tools by accounting for the state of the drilling mud and its composition during the measurement. For example, the dispersion characteristics of the drilling mud, as detailed previously, can be utilized in Stoneley inversion for Vertical Transverse Isotropy (VTI). For VTI inversion, it is crucial to know the acoustic wave velocity at low frequencies for the drilling mud. By measuring the density and acoustic wave velocity and attenuation at high frequencies using the fluid cell device, one can apply the dispersion relationships of the acoustic models described above in connection with FIGS. 1A-5 to derive the acoustic wave velocity for the drilling mud at low frequencies.Real-Time Monitoring and Adjustment: Operation 1208 describes a method for real-time monitoring and adjustment of drilling mud properties using continuous data from the fluid cell device or devices and inversion to derive properties of the drilling mud based on the relationships provided by the acoustic models described herein. This method includes dynamic adjustments to the composition of the drilling mud based on the real-time measurements and inversions to optimize wellbore stability and efficiency. For example, if the drilling mud analyzer detects an undesirable change in a derived property of the drilling mud in the borehole, this undesirable change can be counteracted by introducing modified drilling mud or modified suspended components into the borehole.Integration with Drilling Control Systems: Operation 1210 describes a system based on the fluid cell measurements and the derived properties from the acoustic models described herein to provide automated feedback and control to a drilling control system. The drilling control system is illustrated and described below in connection with FIG. 14. In this system, the drilling mud analyzer uses the derived properties of the drilling mud composition to generate commands to a drilling control system to adjust drilling parameters such as mud flow rate, pressure, torque, weight on bit and drilling mud composition.Referring to FIG. 13, a method 1300 is provided for designing an engineered drilling mud that provides the necessary dispersion properties, based on the acoustic models described herein. As an example, this method may include reducing the particle size of the solids contained in the drilling mud to minimize dispersion, thereby allowing the fluid cell device measurements of acoustic wave velocities for the drilling mud to be directly used in Stoneley inversions for VTI.In operation 1302 of FIG. 13, the drilling mud analyzer receiving input of a desired acoustic characteristics for a drilling mud that is to be engineered. In operation 1304, the drilling mud analyzer selects an acoustic model or models corresponding with the desired acoustic characteristics. For example, if the received input is for an engineered drilling mud that has a particular wave velocity dispersion or attenuation, the drilling mud analyzer will select from the available acoustic models one or more acoustic models with characteristics matching the desired wave velocity dispersion or attenuation.In operation 1306, the drilling mud analyzer uses the selected acoustic model to output properties of the engineered drilling mud. As examples, the selected acoustic model may be based upon suspended components having a particular size and a particular volume concentration. In operation 1308, the engineered drilling mud is formulated using the particular size and volume concentration of the suspended components on which the selected acoustic model is based. In operation 1310, the engineered drilling mud is placed in the borehole of the well to perform its desired functions. Optionally, as described in operation 1312, an acoustic device may be deployed in the borehole to detect measured acoustic signals to monitor for changes to the engineered drilling mud as described previously.The methods and systems of the present disclosure may be implemented by a system and / or in a system, such as a system 10 shown in FIG. 14. The system 10 may include one or more of a processor 11, an interface 12 (e.g., bus, wireless interface), an electronic storage 13, a memory 14, a graphical display 15, a fluid cell device 17, an optional link to a drilling control system 16, and / or other components. The processor 11 is configured to use machine-readable instructions from electronic storage 13 and to use information from one or more fluid cell devices 17 to determine physical properties of drilling mud.The electronic storage 13 may be configured to include any electronic storage medium that electronically stores information. The electronic storage 13 may store software algorithms, information determined by the processor 11, information received remotely, and / or other information that enables the system 10 to function properly. For example, as indicated by the measured data 104, the electronic storage 13 may store information relating to input measurements from the fluid cell device 17, and / or other information. The electronic storage 13 also may store information relating to physical properties of drilling mud, such as information in drilling mud reports, and / or physical properties of drilling mud that are derived by the acoustic models described herein.The electronic storage 13 may include acoustic models 106, such as the acoustic models described herein and the acoustic models illustrated in FIGS. 1A-5. The electronic storage 13 also may include the drilling mud analyzer 102 described previously. The drilling mud analyzer 102 may be implemented as one or more software modules or may be distributed as one or more software services. The drilling mud analyzer 102 includes instructions executable by the processor 11 for analyzing measured acoustic data, drilling mud properties, and the acoustic models in accordance with the methods and systems described herein.The electronic storage media of the electronic storage 13 may be provided integrally (i.e., substantially non-removable) with one or more components of the system 10 and / or as removable storage that is connectable to one or more components of the system 10 via, for example, a port (e.g., a USB port, a Firewire port, etc.) or a drive (e.g., a disk drive, etc.). The electronic storage 13 may include one or more of optically readable storage media (e.g., optical disks, etc.), magnetically readable storage media (e.g., magnetic tape, magnetic hard drive, floppy drive, etc.), electrical charge-based storage media (e.g., EPROM, EEPROM, RAM, etc.), solid-state storage media (e.g., flash drive, etc.), and / or other electronically readable storage media. The electronic storage 13 may include one or more non-transitory computer readable storage medium storing one or more programs. The electronic storage 13 may be a separate component within the system 10, or the electronic storage 13 may be provided integrally with one or more other components of the system 10 (e.g., the processor 11). Although the electronic storage 13 is shown in FIG. 9 as a single entity, this is for illustrative purposes only. In some implementations, the electronic storage 13 may comprise a plurality of storage units. These storage units may be physically located within the same device, or the electronic storage 13 may represent storage functionality of a plurality of devices operating in coordination.The graphical display 15 may refer to an electronic device that provides visual presentation of information. The graphical display 15 may include a color display and / or a non-color display. The graphical display 15 may be configured to visually present information. The graphical display 15 may present information using / within one or more graphical user interfaces. For example, the graphical display 15 may present information relating to measurements received from the fluid cell device 17, properties determined by the drilling mud analyzer 102, and / or other information.The hardware processor 11 may be configured to provide information processing capabilities in the system 10. As such, the processor 11 may comprise one or more of a digital processor, an analog processor, a digital circuit designed to process information, a central processing unit, a graphics processing unit, a microcontroller, an analog circuit designed to process information, a state machine, and / or other mechanisms for electronically processing information. The processor 11 may be configured to execute one or more machine-readable instructions to facilitate determining physical properties of drilling mud. The machine-readable instructions may include one or more computer program components. The machine-readable instructions may include the drilling mud analyzer 102, and / or other computer program components.It should be appreciated that although computer program components are illustrated in FIG. 14 as being co-located within a single processing unit, one or more of computer program components may be located remotely from the other computer program components. While computer program components are described as performing or being configured to perform operations, computer program components may comprise instructions which may program processor 11 and / or system 10 to perform the operation.While computer program components are described herein as being implemented via processor 11 through machine-readable instructions, this is merely for ease of reference and is not meant to be limiting. In some implementations, one or more functions of computer program components described herein may be implemented via hardware (e.g., dedicated chip, field-programmable gate array) rather than software. One or more functions of computer program components described herein may be software-implemented, hardware-implemented, or software and hardware-implemented.Referring again to machine-readable instructions, the drilling mud analyzer 102 may be configured to perform any of the actions described above to determine physical properties of drilling mud, including one or both of the velocity and attenuation dispersion behavior.In an embodiment, the physical properties of drilling mud determined by processor 11 using drilling mud analyzer 102 may be used to send instructions to drilling control system 16. Drilling control system 16 may adjust drilling parameters such as mud flow rate, pressure, torque, weight on bit and drilling mud composition.The description of the functionality provided by the different computer program components described herein is for illustrative purposes, and is not intended to be limiting, as any of computer program components may provide more or less functionality than is described. For example, one or more of computer program components may be eliminated, and some or all of its functionality may be provided by other computer program components. As another example, processor 11 may be configured to execute one or more additional computer program components that may perform some or all of the functionality attributed to one or more of computer program components described herein.While particular embodiments are described above, it will be understood it is not intended to limit the invention to these particular embodiments. On the contrary, the invention includes alternatives, modifications and equivalents that are within the spirit and scope of the appended claims. Numerous specific details are set forth in order to provide a thorough understanding of the subject matter presented herein. But it will be apparent to one of ordinary skill in the art that the subject matter may be practiced without these specific details. In other instances, well-known methods, procedures, components, and circuits have not been described in detail so as not to unnecessarily obscure aspects of the embodiments.The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in the description of the invention and the appended claims, the singular forms “a,”“an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that the term “and / or” as used herein refers to and encompasses any and all possible combinations of one or more of the associated listed items. It will be further understood that the terms “includes,”“including,”“comprises,” and / or “comprising,” when used in this specification, specify the presence of stated features, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, operations, elements, components, and / or groups thereof.As used herein, the term “if” may be construed to mean “when” or “upon” or “in response to determining” or “in accordance with a determination” or “in response to detecting,” that a stated condition precedent is true, depending on the context. Similarly, the phrase “if it is determined [that a stated condition precedent is true]” or “if [a stated condition precedent is true]” or “when [a stated condition precedent is true]” may be construed to mean “upon determining” or “in response to determining” or “in accordance with a determination” or “upon detecting” or “in response to detecting” that the stated condition precedent is true, depending on the context.Although some of the various drawings illustrate a number of logical stages in a particular order, stages that are not order dependent may be reordered and other stages may be combined or broken out. While some reordering or other groupings are specifically mentioned, others will be obvious to those of ordinary skill in the art and so do not present an exhaustive list of alternatives. Moreover, it should be recognized that the stages could be implemented in hardware, firmware, software or any combination thereof.The foregoing description, for purpose of explanation, has been described with reference to specific embodiments. However, the illustrative discussions above are not intended to be exhaustive or to limit the invention to the precise forms disclosed. Many modifications and variations are possible in view of the above teachings. The embodiments were chosen and described in order to best explain the principles of the invention and its practical applications, to thereby enable others skilled in the art to best utilize the invention and various embodiments with various modifications as are suited to the particular use contemplated.

Claims

1. A method for measuring properties of a drilling mud in a borehole in an earth formation, the method comprising:deploying a fluid cell device into the drilling mud in the borehole, the fluid cell device comprising:a housing;at least one chamber; andat least one transducer disposed in the at least one chamber, wherein the at least one transducer emits acoustic signals of at least a first frequency and detects measured acoustic signals in response to the acoustic signals that are emitted;analyzing, by a drilling mud analyzer executing on a processor, the measured acoustic signals to determine acoustic characteristic data of the measured acoustic signals, wherein the acoustic characteristic data is one or more of acoustic wave velocity and acoustic wave attenuation for the drilling mud;selecting, by the drilling mud analyzer, an acoustic model for the drilling mud corresponding to a measured property of the drilling mud, wherein the measured property includes a property of a component suspended in the drilling mud;comparing, by the drilling mud analyzer, the acoustic characteristic data to the acoustic model; anddetermining, by the drilling mud analyzer, a derived property of the drilling mud from a correspondence of the acoustic characteristic data to the acoustic model.

2. The method of claim 1, wherein the measured property is a volume fraction of one or more of gas bubbles, water droplets, and solid particles suspended in the drilling mud.

3. The method of claim 1, wherein the acoustic characteristic data is acoustic wave velocity at the first frequency and acoustic wave velocity at a second frequency, the method further comprising:calculating, by the drilling mud analyzer, acoustic wave velocity dispersion data from a difference between the acoustic wave velocity at the first frequency and acoustic wave velocity at the second frequency;comparing, by the drilling mud analyzer, the acoustic wave velocity dispersion data to the acoustic model of drilling mud acoustic wave velocity dispersion data; anddetermining, by the drilling mud analyzer, a second derived property of the drilling mud from a second correspondence of the acoustic wave velocity dispersion data to the acoustic wave model.

4. The method of claim 1, further comprising adjusting a composition of the drilling mud in the borehole in response to determining the derived property of the drilling mud.

5. The method of claim 1, further comprising adjusting an operation of a drill using a drill control system in response to determining the derived property of the drilling mud.

6. The method of claim 1, further comprising:analyzing, by the drilling mud analyzer, the measured acoustic signals to determine acoustic wave attenuation data for the drilling mud;comparing, by the drilling mud analyzer, the acoustic wave attenuation data to the acoustic model; anddetermining, by the drilling mud analyzer, a second derived property of the drilling mud from a second correspondence of the acoustic wave attenuation data to the acoustic wave model.

7. The method of claim 1, further comprising incorporating the derived property of the drilling mud with borehole data gathered from a logging tool.

8. A system comprising:a fluid cell device configured to be deployed into a drilling mud in a borehole in an earth formation, the fluid cell device comprising:a housing;at least one chamber; andat least one transducer disposed in the at least one chamber, wherein the at least one transducer emits acoustic signals of at least a first frequency and detects measured acoustic signals in response to the acoustic signals that are emitted; anda computing system, the computing system comprising a drilling mud analyzer executed by a hardware processor that performs a method comprising:analyzing, by a drilling mud analyzer, the measured acoustic signals to determine acoustic characteristic data of the measured acoustic signals, wherein the acoustic characteristic data is one or more of acoustic wave velocity and acoustic wave attenuation for the drilling mud;selecting, by the drilling mud analyzer, an acoustic model for the drilling mud corresponding to a measured property of the drilling mud, wherein the measured property includes a property of a component suspended in the drilling mud;comparing, by the drilling mud analyzer, the acoustic characteristic data to the acoustic model; anddetermining, by the drilling mud analyzer, a derived property of the drilling mud from a correspondence of the acoustic characteristic data to the acoustic wave model.

9. The system of claim 8, wherein the fluid cell device comprises two chambers divided by a plate enabling collection of acoustic reflection data and acoustic reverberation data, and wherein the drilling mud analyzer determines acoustic wave attenuation data from the acoustic reflection data and the acoustic reverberation data.

10. The system of claim 8, wherein the computing system further comprises an electronic storage, the electronic storage comprising:the acoustic model; andthe drilling mud analyzer.

11. The system of claim 8, further comprising a drilling control system, wherein, responsive to the derived property, the drilling control system receives commands from the drilling mud analyzer to control a drill used in drilling the borehole.

12. The system of claim 8, wherein responsive to the derived property, the drilling mud analyzer generates a command to modify a composition of the drilling mud.

13. A computer-readable medium comprising instructions of a drilling mud analyzer that when executed by a hardware processor perform a method comprising:receiving, by the drilling mud analyzer, measured acoustic signals from a fluid cell device deployed in drilling mud in a borehole;analyzing, by the drilling mud analyzer, the measured acoustic signals to determine acoustic characteristic data of the measured acoustic signals, wherein the acoustic characteristic data is one or more of acoustic wave velocity and acoustic wave attenuation for the drilling mud;selecting, by the drilling mud analyzer, an acoustic model for the drilling mud corresponding to a measured property of the drilling mud, wherein the measured property includes a property of a component suspended in the drilling mud;comparing, by the drilling mud analyzer, the acoustic characteristic data to the acoustic model; anddetermining, by the drilling mud analyzer, a derived property of the drilling mud from a correspondence of the acoustic characteristic data to the acoustic wave model.

14. The computer-readable medium of claim 13, wherein the measured property is a volume fraction of one or more of gas bubbles, water droplets, and solid particles suspended in the drilling mud.

15. The computer-readable medium of claim 13, wherein the derived property is a change in volume fraction of one or more of gas bubbles, water droplets, and solid particles suspended in the drilling mud.

16. The computer-readable medium of claim 13, wherein the method further comprises generating a command, by the drilling mud analyzer, to a drilling control system to modify an operation of a drill used to for drilling the wellbore.

17. The computer-readable medium of claim 13, wherein the method further comprises generating a command, by the drilling mud analyzer, to modify a composition of the drilling mud.

18. A method for formulating an engineered drilling mud, the method comprising:receiving, at a drilling mud analyzer executing on a hardware processor of a computer system, a desired acoustic characteristic for the engineered drilling mud;selecting, by the drilling mud analyzer, an acoustic model corresponding to the desired acoustic characteristic of the engineered drilling mud;outputting, by the drilling mud analyzer, desired properties of the engineered drilling mud derived from the acoustic model, wherein the desired properties include properties of a suspended component of the engineered drilling mud;formulating the engineered drilling mud having the desired properties; andplacing the engineered drilling mud in a borehole in an earth formation.

19. The method of claim 18, further comprising:deploying a fluid cell device into the engineered drilling mud in the borehole, the fluid cell device comprising:a housing;at least one chamber; andat least one transducer disposed in the at least one chamber, wherein the at least one transducer emits acoustic signals of at least a first frequency and detects measured acoustic signals in response to the acoustic signals that are emitted.

20. The method of claim 19, further comprising:analyzing, by the drilling mud analyzer, the measured acoustic signals to determine acoustic characteristic data of the measured acoustic signals, wherein the acoustic characteristic data is one or more of acoustic wave velocity and acoustic wave attenuation for the engineered drilling mud;selecting, by the drilling mud analyzer, an acoustic model for the engineered drilling mud corresponding to a measured property of the engineered drilling mud, wherein the measured property includes a property of a component suspended in the engineered drilling mud;comparing, by the drilling mud analyzer, the acoustic characteristic data to the acoustic model; anddetermining, by the drilling mud analyzer, a derived property of the engineered drilling mud from a correspondence of the acoustic characteristic data to the acoustic wave model.

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