A method for resistivity correction of clastic reservoirs

Abstract

The application provides a method for resistivity correction of clastic rock reservoirs, and belongs to the technical field of oil and gas resource reservoir exploration; the method comprises the following steps: S1, standardizing the logging curve of the existing well of the reservoir to be analyzed to obtain a standardized logging curve; S2, based on the standardized logging curve and core data obtained in step S1, a multi-mineral model is used to solve the lithology profile of the reservoir to be analyzed, and the gravel content and the lime content of the reservoir to be analyzed are determined; S3, according to the gravel content and the lime content determined in step S2 and the resistivity to be corrected, the corrected resistivity is obtained according to a resistivity correction formula, and a correction chart is established. Compared with the prior art, the application realizes the resistivity correction of the clastic rock reservoirs containing gravel and lime, and improves the accuracy of the fluid logging interpretation of the complex clastic rock reservoirs.

Description

Technical Field

[0001] This invention belongs to the field of oil and gas resource reservoir exploration technology, specifically relating to a method for resistivity correction of clastic rock reservoirs. Background Technology

[0002] The resistivity method is an electrical exploration method that utilizes the differences in electrical conductivity (expressed as resistivity) between different rocks in the Earth's crust. By observing and studying the distribution patterns of a stable current field artificially established underground, it aims to locate coal and other beneficial minerals, groundwater, and solve related geological problems. The resistivity method is the earliest researched and most widely used method in electrical exploration.

[0003] For example, invention patent CN111255446B discloses a resistivity correction method based on formation simulation. This method establishes a theoretical model of how the resistivity of different lithologies varies with factors including temperature, pressure, and porosity through laboratory testing. It corrects well logging and laboratory measurement data of the rock electrical properties in the test area to the corresponding formation conditions, establishing an effective initial geoelectric model. This invention simulates the temperature and pressure environment at different depths in the test area where the rock samples are located, measures the amplitude and phase of the complex resistivity under different depth conditions, obtains the relationship between rock induced polarization parameters and temperature and pressure, and then corrects existing geoelectric data to obtain an initial geoelectric model for electromagnetic exploration. Its purpose is to solve the mismatch between well logging and laboratory data of rock geoelectricity and exploration conditions, providing important parameter basis for electromagnetic exploration inversion interpretation and evaluation.

[0004] It is evident that how to accurately and efficiently analyze the resistivity of formations is one of the important issues studied by those skilled in the art.

[0005] However, the resistivity of any rock is not fixed and cannot be determined by a single, definitive number. For example, the resistivity of limestone varies considerably. Pure limestone generally has a resistivity above 20,000 ohm-meters, and can exceed 100,000 ohm-meters. However, the resistivity of argillaceous limestone will decrease significantly. In limestone with well-developed fractures, if it is filled with argillaceous material or rich in water within highly mineralized zones, its resistivity will also decrease. Therefore, in environments containing limestone, such as clastic rocks, the requirements for resistivity measurement are relatively higher, necessitating corresponding research.

[0006] For example, the paper "A New Form of the Three-Water Model Based on Complex Resistivity-NMR Co-measurement Experiment" published by Zhang Lihua et al. proposes a new method for calculating cation exchange capacity based on complex resistivity data to address the multi-parameter problem in the application of three-water models in the interpretation of clastic reservoirs. Based on this, a new form of the three-water model is proposed, and a genetic optimization algorithm combining NMR data is used to determine the parameter values ​​of the three-water model. The relative error between the resistivity of the rock sample calculated based on these parameters at 100% water content and the experimentally measured resistivity is 0.3417; this demonstrates the importance of resistivity research in clastic rock environments. Conglomerate and limestone are common in complex clastic reservoirs. The presence of these highly resistive conglomerates and limestones increases the reservoir resistivity, causing some water layers to be classified as oil and gas-bearing reservoirs in pure sandstone oil-water layer evaluation standards. Current well logging curve environmental correction methods often rely on empirical formulas, which have relatively poor correction effects.

[0007] Therefore, providing an effective resistivity correction method to correct the resistivity of gravelly and calcareous clastic reservoirs and improve the accuracy of fluid logging interpretation in complex clastic reservoirs is of great significance in this field. Summary of the Invention

[0008] This invention addresses the lack of a resistivity correction method for complex clastic rock reservoirs in existing technologies by providing a method for resistivity correction of clastic rock reservoirs. This method enables resistivity correction of gravelly and calcareous clastic rock reservoirs, thereby improving the accuracy of fluid logging interpretation in complex clastic rock reservoirs.

[0009] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for resistivity correction of clastic rock reservoirs includes the following steps: S1. Standardize the logging curves of existing wells in the reservoir to be analyzed to obtain standardized logging curves; S2. Based on the standardized logging curves and core data obtained in step S1, the lithological profile of the reservoir to be analyzed is solved using a multi-mineral model to determine the gravel content and ash content of the reservoir to be analyzed. S3. Based on the gravel content and ash content determined in step S2, and the resistivity to be corrected, calculate the corrected resistivity according to the resistivity correction formula and establish a correction chart. The method for solving the multi-mineral model in step S2 is as follows: A system of equations was established using cross-plots of two different porosity logging methods. The resistivity correction formula mentioned in step S3 is: Z(x,y)=1 / (1 / (Rc*y)+1 / (x*(1-y))) Where Z(x,y) is the corrected resistivity curve, Ω·m; Rc is the resistivity value of limestone and conglomerate, and if no experimental analysis value is available, the regional empirical value can be used, Ω·m; x is the resistivity to be corrected, Ω·m; y is the gravel content and lime content of the reservoir, decimal.

[0010] Preferably, the statistical tools used in the standardization process in step S1 include histograms.

[0011] In some embodiments, the standardization process involves placing the standard well curve and the logging curve to be standardized in the same histogram, and shifting the logging curve to be standardized by comparing the abscissa of the curve peaks, so that the abscissa of the peak values ​​of the standard well curve and the logging curve to be standardized are consistent.

[0012] Preferably, the standardized logging curve described in step S1 further requires logging curve environmental correction under the following conditions: ① When the actual measured sonic transit time of the well corresponding to the standardized logging curve is greater than the upper limit of the sonic transit time of the interval to be interpreted; ② The diameter of the well corresponding to the standardized logging curve is enlarged, resulting in a smaller actual test density; ③ When the diameter of the well corresponding to the standardized logging curve increases, resulting in a thicker mud layer between the instrument and the formation.

[0013] It should be noted that the reason for environmental correction under condition ① above is that when the actual measured acoustic transit time is greater than the upper limit of the acoustic transit time of the section to be interpreted, it is generally considered that the wellbore has collapsed. The reason for environmental correction under condition ② above is that the density of drilling mud in the wellbore is generally lower than that of the formation. When the well diameter is enlarged, the actual measured density will be too small. The reason for environmental correction under condition ③ above is that when the wellbore is enlarged, the mud layer between the instrument and the formation thickens, and the mud has a greater impact on the measurement results. Usually, the mud has a high hydrogen index, so the neutron porosity measured when the wellbore is enlarged is greater than the actual neutron porosity of the formation.

[0014] More preferably, the environmental correction for the logging curve in condition ① is acoustic transit time (AC) correction, using the following formula:

[0015] Where: AC and ACc are the acoustic transit time before and after correction, respectively, in μs / ft; RCAL is the theoretical well diameter of the interpreted well section, in inches; CAL is the actual well diameter of the interpreted well section, with x taking a value of 0.2, in inches.

[0016] More preferably, the environmental correction for the logging curve in condition ② is density (DEN) correction, using the following formula: when hour

[0017] when hour

[0018] when hour

[0019] when hour

[0020] when hour

[0021] when hour

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029] Where: CAL is the well diameter, in inches; DEN and DENc are the logging density values ​​before and after correction, in g / cm³, respectively. 3 .

[0030] More preferably, the logging curve environmental correction for condition ③ is a compensated neutron (CNL) correction, using the following formula: when hour:

[0031] when hour:

[0032] Where CNL and CNLc are the logging neutron values ​​before and after correction, respectively; %; and d is the well diameter, in cm.

[0033] It should be noted that although CAL and d are both well diameters, they are in different units for easy distinction.

[0034] Preferably, the cross plot of the porosity logging is selected from neutron-density cross plot, neutron-acoustic cross plot, and acoustic-density cross plot.

[0035] More preferably, the method of solving the multi-mineral model by using the cross-plots of two porosity logging methods to solve the simultaneous equations includes the following cases: (1) The strata are composed of two types of minerals; (2) The strata are composed of three minerals.

[0036] More preferably, when in case (1), the system of equations of the intersection graph is solved directly.

[0037] More preferably, when in case (2), a numerical method is used to solve the system of equations of the intersection graph in matrix form, specifically as follows:

[0038] In the formula: ρ is the density logging response value, g / cm³ 3 φN is the neutron logging response value, %; Δt is the sonic transit time logging response value, μs / ft; ρf is the fluid density, g / cm³. 3 ρ1 is the density of the first mineral, in g / cm³. 3 ρ2 is the density of the second mineral, in g / cm³. 3 ρ3 is the density of the third mineral, in g / cm³. 3 φNf is the fluid neutron value, %; φN1 is the neutron value of the first mineral, %; φN2 is the neutron value of the second mineral, %; φN3 is the neutron value of the third mineral, %; △tf is the fluid acoustic transit time value, μs / ft; △t1 is the acoustic transit time value of the first mineral, μs / ft; △t2 is the acoustic transit time value of the second mineral, μs / ft; △t3 is the acoustic transit time value of the third mineral, μs / ft; φ is the fluid volume, decimal; V1 is the volume of the first mineral, decimal; V2 is the volume of the second mineral, decimal; V3 is the volume of the third mineral, decimal.

[0039] Preferably, the method for establishing the calibration pattern in step S3 is to calculate the resistivity correction value Z by taking the resistivity x to be corrected and the gravel and ash content y according to the resistivity correction formula in step S3, and then forming a three-dimensional calibration pattern.

[0040] Compared with the prior art, the present invention has the following beneficial effects: This invention employs a simple, standardized processing method and provides environmental correction methods and multi-mineral model solution methods applicable to different complex scenarios. It establishes resistivity correction charts for gravelly and calcareous reservoirs in the study area and achieves resistivity correction for gravelly and calcareous clastic reservoirs, thereby improving the accuracy of fluid logging interpretation in complex clastic reservoirs. Attached Figure Description

[0041] Figure 1 This is a schematic diagram illustrating the standardization process of well logging curves according to an embodiment of the present invention; Figure 2 This is a schematic diagram of a lithological profile according to an embodiment of the present invention; Figure 3 This is a three-dimensional resistivity correction diagram according to an embodiment of the present invention; Figure 4 A simplified two-dimensional diagram of resistivity correction according to an embodiment of the present invention. Figure 5 This is a schematic diagram of the well logging curves for a production example in this embodiment of the invention; Figure 6 These are core photographs of a production example in this invention. Figure 7 This is an explanatory diagram of oil saturation from well logging in a production example according to an embodiment of the present invention. Detailed Implementation

[0042] Unless otherwise defined, all technical and scientific terms used in this invention have the same meaning as commonly used in the field to which this invention pertains. For the purposes of interpreting this specification, the following definitions will apply, and where appropriate, terms used in the singular will also include the plural forms, and vice versa.

[0043] Unless the context clearly indicates otherwise, the terms “a” and “an” as used herein include plural references.

[0044] As used herein, the term "about" indicates a range of ±20% of the following value. In some embodiments, the term "about" indicates a range of ±10% of the following value. In some embodiments, the term "about" indicates a range of ±5% of the following value.

[0045] The numerical ranges used in this article should be understood as including all numbers within that range. For example, the range 1 to 20 should be understood to include any number, combination of numbers, or subrange from the following group: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, or 20.

[0046] As used herein, the terms “comprises” or “comprising” mean “including, but not limited to”. This term is intended to be open-ended to specify the presence of any of the stated features, elements, integers, steps, or components, but does not exclude the presence or addition of one or more other features, elements, integers, steps, components, or groups thereof. Therefore, the term “comprising” includes the more restrictive terms “consisting of” and “substantially consisting of”. In one embodiment, the term “comprising” as used throughout the application, particularly in the claims, may be replaced by the term “consisting of”.

[0047] As used herein, the terms “optional,” “any,” “arbitrary,” or “any one” mean that the event or situation described below may, but does not have to, occur, including the circumstances in which the event or situation occurs or does not occur. As used herein, “an” and “a” refer to one or more grammatical objects.

[0048] The term “and / or” as used herein should be understood to mean any one of the options or any combination of two or more of the options.

[0049] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. Unless otherwise specified in the embodiments, conventional conditions or conditions recommended by the manufacturer shall apply. All reagents or instruments without specified manufacturers are commercially available conventional products. Numerous specific details are provided in the following detailed embodiments to better illustrate the invention. The specific embodiments described herein are for illustrative purposes only and are not intended to constitute any limitation on the invention. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concept of the invention. Such structures and techniques have also been described in many publications.

[0050] Example: A method for resistivity correction in clastic rock reservoirs In step S1: Based on the statistical data of multiple wells in the reservoir to be analyzed, the logging curves are standardized and necessary environmental corrections are performed.

[0051] Mathematical statistical methods such as histograms are used to standardize the logging curves of the reservoir to be analyzed. Figure 1 This diagram illustrates the standardization process of well logging curves for the reservoir being analyzed using histograms. (For example...) Figure 1 As shown, Figure 1The upper blue curve is the histogram of the standard well curve distribution, and the red curve is the histogram of the curve to be standardized. By comparing peak values, the curve to be standardized is shifted to match the peak values ​​of the standard well curve distribution. The standardized logging curve obtained after standardization is shown below. Figure 1 As shown in the lower part.

[0052] Based on wellbore conditions, necessary logging curve environmental corrections are performed, mainly including: In some embodiments, acoustic time difference (AC) correction is required:

[0053] When CAL > RCAL, ACc = ACc (correction); When CAL < RCAL, ACc = AC (no correction); In the formula: AC and ACc are the sonic transit time difference before and after correction, respectively, in μs / ft; RCAL is the theoretical well diameter of the interpreted well section, in inches; CAL is the actual well diameter of the interpreted well section, with x taking the value of 0.2, in inches.

[0054] When the actual measured acoustic transit time is less than the upper limit of the section to be interpreted, the corrected result is still the actual value; however, when the actual value is greater than the upper limit, it is considered that the wellbore has collapsed, and the above formula is used for correction.

[0055] In some embodiments, density DEN correction is required: The density of drilling mud in wellbore is generally lower than that of the formation. When the well diameter is increased, the actual measured density will be underestimated. Therefore, the following correction formula can be used to correct this: when hour

[0056] when hour

[0057] when hour

[0058] when hour

[0059] when hour

[0060] when hour

[0061] Where: CAL is the well diameter; DEN and DENc are the logging density values ​​before and after correction, respectively.

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] In some embodiments, compensating neutron CNL correction is required: As the wellbore diameter increases, the mud layer between the instrument and the formation thickens, increasing the mud's influence on the measurement results. Typically, the mud has a high hydrogen index, therefore the apparent neutron porosity measured during diameter enlargement is greater than the actual neutron porosity of the formation; conversely, when the wellbore diameter d < 20 cm, it is slightly greater than the actual neutron porosity. The following empirical formulas can be used to correct the wellbore diameter for neutron logging curves: when hour: ; when hour: ; Where: CAL is the well diameter; CNL and CNLc are the logging neutron values ​​before and after correction, respectively; %; and d is the well diameter, cm.

[0070] Next, proceed to step S2.

[0071] In step S2: using the standardized logging curves and core data, the lithological profile of the reservoir to be analyzed is solved using a multi-mineral model, thereby determining the clay content, sand content, porosity, gravel content, and ash content of the reservoir to be analyzed.

[0072] The multi-mineral model processing method is as follows: In some embodiments, when the formation consists of two minerals, the lithology and porosity can be determined by solving a system of simultaneous equations using cross plots of two porosity logging methods (neutron-density cross plot, neutron-acoustic cross plot, and acoustic-density cross plot).

[0073] In some embodiments, when there are three minerals, a numerical method is used to write the system of simultaneous equations in matrix form:

[0074] In the formula: ρ is the density logging response value, g / cm³ 3 φN is the neutron logging response value, %; Δt is the sonic transit time logging response value, μs / ft; ρf is the fluid density, g / cm³. 3 ρ1 is the density of the first mineral, in g / cm³. 3 ρ2 is the density of the second mineral, in g / cm³. 3 ρ3 is the density of the third mineral, in g / cm³. 3 φNf is the fluid neutron value, %; φN1 is the neutron value of the first mineral, %; φN2 is the neutron value of the second mineral, %; φN3 is the neutron value of the third mineral, %; △tf is the fluid acoustic transit time value, μs / ft; △t1 is the acoustic transit time value of the first mineral, μs / ft; △t2 is the acoustic transit time value of the second mineral, μs / ft; △t3 is the acoustic transit time value of the third mineral, μs / ft; φ is the fluid volume, decimal; V1 is the volume of the first mineral, decimal; V2 is the volume of the second mineral, decimal; V3 is the volume of the third mineral, decimal.

[0075] In some embodiments, errors in measurement, selection of mineral parameters, and the approximation inherent in the logging response equation itself can all lead to erroneous results. Therefore, in addition to making appropriate choices in the solution method, certain constraints must be added during the solution process, such as ensuring that the solved values ​​V1, V2, V3 are greater than or equal to 0 and less than 1. The mineral composition parameters in the matrix are selected with appropriate values ​​based on the mineral assemblage of the interpreted layer.

[0076] Figure 2 This is a schematic diagram of a lithological profile according to an embodiment of the present invention. By solving a system of equations simultaneously, the total porosity value is made to match the core porosity value, and the final lithological profile obtained is as follows: Figure 2 The rightmost channel in the diagram shows the gravel content in the green filler.

[0077] Next, proceed to step S3.

[0078] In step S3: Based on the gravel and ash content obtained in the above steps and the resistivity obtained from experimental analysis or the empirical value of the resistivity in the region, the corrected resistivity is obtained according to the resistivity correction formula and a correction chart is established.

[0079] The calculation formula is as follows: Z(x,y)=1 / (1 / (Rc*y)+1 / (x*(1-y))) Where Z(x,y) is the corrected resistivity curve, Ω·m; Rc is the resistivity value of limestone and conglomerate, and if no experimental analysis value is available, the regional empirical value can be used, Ω·m; x is the resistivity to be corrected, Ω·m; y is the gravel content and lime content of the reservoir, decimal.

[0080] A three-dimensional resistivity correction plot is established based on the above formula, as follows: Figure 3 As shown. Figure 3 To provide a three-dimensional resistivity correction chart according to an embodiment of the present invention, the resistivity correction value z is obtained by using the resistivity to be corrected x and the gravel and ash content y according to the formula.

[0081] In practical calibration processes, to facilitate operation, two-dimensional resistivity calibration charts are established based on different ash contents, such as... Figure 4 As shown. Figure 4 This is a simplified two-dimensional resistivity correction chart according to an embodiment of the present invention. The horizontal axis represents the resistivity to be corrected, and the corrected resistivity is obtained according to different gravel contents.

[0082] By correcting the resistivity of the reservoir to be analyzed using the above method, oil and gas can be identified based on the corrected resistivity using the pure sandstone oil-water layer evaluation standard.

[0083] Production Examples like Figure 5 The logging curve at 4909 meters shows conglomerate characteristics, while the core sampling section from 4905 to 4910 meters consists of gray medium-gray sandstone, conglomerate sandstone, and conglomerate. Figure 6 The oil-bearing grade is oil-immersed sands, and the original well logging interpretation concluded it as an oil and gas reservoir. After lithological profile processing, the ash content is 47-53%, as shown in the resistivity correction chart (…). Figure 4 The original resistivity was corrected from 3.6 Ω·m to 1.86 Ω·m, and this was reflected in the well logging oil saturation interpretation chart. Figure 7 The data points in the image were corrected from the red star points representing oil and gas layers to the blue box points representing water layers. The interpretation conclusion was that the water layer was indeed a water layer, and subsequent testing confirmed that the water layer was indeed a water layer, thus verifying the rationality of the resistivity correction.

[0084] Finally, it should be noted that the above content is only used to illustrate the technical solution of the present invention, and is not intended to limit the scope of protection of the present invention. Simple modifications or equivalent substitutions made by those skilled in the art to the technical solution of the present invention do not depart from the essence and scope of the technical solution of the present invention.

Claims

1. A method for resistivity correction in clastic rock reservoirs, characterized in that, Includes the following steps: S1. Standardize the logging curves of existing wells in the reservoir to be analyzed to obtain standardized logging curves; S2. Based on the standardized logging curves and core data obtained in step S1, the lithological profile of the reservoir to be analyzed is solved using a multi-mineral model to determine the gravel content and ash content of the reservoir to be analyzed. S3. Based on the gravel content and ash content determined in step S2, and the resistivity to be corrected, calculate the corrected resistivity according to the resistivity correction formula and establish a correction chart. The method for solving the multi-mineral model in step S2 is as follows: A system of equations was established using cross-plots of two different porosity logging methods. The resistivity correction formula mentioned in step S3 is: Z(x,y)=1 / (1 / (Rc*y)+1 / (x*(1-y))) Where Z(x,y) is the corrected resistivity curve, Ω·m; Rc is the resistivity value of limestone or conglomerate, and if no experimental analysis value is available, the regional empirical value can be used, Ω·m; x is the resistivity to be corrected, Ω·m; and y is the gravel content or lime content of the reservoir, expressed as a decimal.

2. The method according to claim 1, characterized in that, The statistical tools used in the standardization process described in step S1 include histograms.

3. The method according to claim 1, characterized in that, The standardized logging curves described in step S1 still require logging curve environmental correction under the following conditions: ① When the actual measured sonic transit time of the well corresponding to the standardized logging curve is greater than the upper limit of the sonic transit time of the interval to be interpreted; ② The diameter of the well corresponding to the standardized logging curve is enlarged, resulting in a smaller actual test density; ③ When the diameter of the well corresponding to the standardized logging curve increases, resulting in a thicker mud layer between the instrument and the formation.

4. The method according to claim 3, characterized in that, The environmental correction for the logging curve under condition ① is acoustic transit time correction, using the following formula: ACc=AC-a×((CAL-RCAL) / 12)×168; Where: AC and ACc are the acoustic time difference before and after correction, respectively, in μs / ft; RCAL is the theoretical well diameter of the interpreted well section, in inches; CAL is the actual well diameter of the interpreted well section, with a value of 0.

2.

5. The method according to claim 3, characterized in that, The environmental correction for the logging curve under condition ② is density correction, using the following formula: when hour when hour when hour when hour when hour when hour Where: CAL is the actual well diameter of the interpreted section, mm; DEN and DENc are the logging density values ​​before and after correction, g / cm³, respectively. 3 .

6. The method according to claim 3, characterized in that, The logging curve environmental correction for condition ③ is a compensated neutron correction, using the following formula: when hour: when hour: Where CNL and CNLc are the logging neutron values ​​before and after correction, respectively; %; and CAL is the actual well diameter of the interpreted well section, in cm.

7. The method according to claim 1, characterized in that, The cross plots used in the porosity logging are selected from neutron-density cross plots, neutron-acoustic cross plots, and acoustic-density cross plots.

8. The method according to claim 1, characterized in that, The method of solving the multi-mineral model using a set of equations derived from cross-plots of two porosity logging methods includes the following scenarios: (1) The strata are composed of two types of minerals; (2) The strata are composed of three minerals.

9. The method according to claim 8, characterized in that, In case (1), directly solve the system of equations of the intersection graph.

10. The method according to claim 8, characterized in that, When in case (2), a numerical method is used to solve the system of equations of the intersection graph in matrix form, specifically as follows: In the formula: ρ is the density logging response value, g / cm³ 3 φN is the neutron logging response value, %; Δt is the sonic transit time logging response value, μs / ft; ρf is the fluid density, g / cm³. 3 ρ1 is the density of the first mineral, in g / cm³ 3 ρ2 is the density of the second mineral, in g / cm³. 3 ρ3 is the density of the third mineral, in g / cm³. 3 φNf is the fluid neutron value, %; φN1 is the neutron value of the first mineral, %; φN2 is the neutron value of the second mineral, %; φN3 is the neutron value of the third mineral, %; △tf is the fluid acoustic transit time value, μs / ft; △t1 is the acoustic transit time value of the first mineral, μs / ft; △t2 is the acoustic transit time value of the second mineral, μs / ft; △t3 is the acoustic transit time value of the third mineral, μs / ft; φ is the fluid volume, decimal; V1 is the volume of the first mineral, decimal; V2 is the volume of the second mineral, decimal; V3 is the volume of the third mineral, decimal.

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