BR122020017677B1 - METHOD FOR ANALYZING A ROCK SAMPLE - Google Patents

Abstract

Methods and systems for estimating the conductivity of clayey mineral systems and for applying the estimates in large-scale analyses. The conductivity of clay can be estimated by building a molecular model of an anhydrous clay with a neutral charge and then assigning an ion substitution charge density to the model of the clay structure. Counter ions are inserted for charge neutrality and water molecules are added to the model to reflect a selected level of hydration. After assignment of force field coefficients, molecular dynamics simulation provides data from which diffusion coefficients can be estimated. The application of the Nernst-Einstein relation to the diffusion coefficients of the counterions gives the ionic conductivity of the clayey system. This conductivity can be used to derive a formation factor and can be applied in direct numerical simulation analysis.

Description

CROSS-REFERENCE TO RELATED ORDERS

[001] This application claims benefit of US Patent Application Serial No. 14/566,520 filed on December 10, 2014 and entitled "Conductivity Estimation for Nanoporous Materials", which is incorporated herein by reference in its entirety.

STATEMENT ON FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[002] The United States Government has rights in this invention pursuant to Contract No. DE-AC04-94AL85000 between the United States Department of Energy and Sandia Corporation, for the operation of Sandia National Laboratories.

FUNDAMENTALS OF THE INVENTION

[003] This invention is in the field of analyzing rock samples to determine petrophysical properties.

[004] As is fundamental in the oil and gas industry, knowledge of the material properties of underground rock formations is important for assessing hydrocarbon reservoirs on Earth and for formulating a development strategy in relation to these reservoirs. A wide variety of tools and techniques for obtaining this information are well known in the art and range from analyzing seismic data, obtaining and analyzing core samples from formations of interest, and various indirect measurements of the Earth that are obtained during the drilling process. .

[005] A common technique for analyzing a subsurface formation is resistivity recording along a hole in the formation. Conventional resistivity logging measures the electrical response of the formation surrounding the borehole, typically to derive a value called the "formation factor", which is the ratio of the resistivity of the rock containing fluid to the resistivity of the fluid itself. According to the well-known Archie Relation, the formation factor is just a function of the rock pore geometry, and can be correlated to the porosity by means of an exponent known as the cementation exponent. As a result, analysis of a conventional resistivity log can provide important information about the porosity or water saturation of the formation of interest. Furthermore, resistivity records in combination with the appropriate interpretation of rock physics can provide information about the permeability of the formation.

[006] Although the Archie Relation is commonly used to interpret the electrical response from records and core samples, it was originally formulated based on a series of experimental measurements. It has been noted, however, that the Archie Relationship is only valid for petrophysically simple rock formations, examples of which include clean sands. It was also observed that Archie's Relation is not valid for scaly sands, namely sands containing clay minerals. A conventional approach to analyzing resistivity recordings from flaky sands is referred to in the art as the Waxman-Smits method. However, this approach is somewhat limited in practice, as it requires knowledge of the clay mineral's cation exchange capacity in flaky sand, in order to correlate resistivity with water saturation and porosity.

[007] The presence of clay within a rock sample has been found to complicate the interpretation of electrical data obtained from logs and core samples. One of the reasons for this is that the electrical properties of clay minerals (also referred to here as "clays") are not well understood. In this regard, interpretation of the electrical properties (and associated properties such as cation exchange capacity) of clays as measured in the laboratory has proven difficult. This complicated interpretation of clay electrical data also arises from the structure of typical clays that are at the "nanoscale", which is much smaller than that of sands and which makes clays less amenable to atomic resolution experiments and analyses. Furthermore, the crystalline structure of clay minerals is often quite irregular, such as consisting of thin plates that are not oriented parallel to each other, with oddly shaped boundaries and unusually shaped pores. Furthermore, impurities that are often present in clays, particularly on the outer surfaces of the plates, can displace other atoms by substitution and change the charge distribution in the clay material. In general, these nanoscale crystal size complexities, the disorder of crystals and plates, and the complex composition of clay minerals make direct measurement of petrophysical properties in clays very difficult.

[008] Direct numerical simulation of material properties from digital rock images is a recent technology for determining the material properties of rock samples. According to this approach, an X-ray tomographic image is taken of a rock sample to produce a representative digital image volume of that sample. A computational experiment is then applied to the digital image volume to simulate the physical mechanisms from which the physical properties of the rock can be measured. Rock properties such as porosity, absolute permeability, relative permeability, formation factor, elastic modulus and the like can be determined using direct numerical simulation.

[009] Specifically, direct numerical simulation of electrical properties from digital rock images is performed by approximating or solving relevant electrical equations, such as the Laplace equation with variable coefficients and relevant boundary conditions. This approach assumes, however, that the electrical properties of the constituent materials within the rock are known. For example, solid grains (eg quartz) can be considered as non-conductors, clay fractions as partially conductive, and pore fluids such as saline as the most conductive phase in the simulation. Although this assignment of conductive properties is well understood for solid grains and pore fluids, a physical basis for the assignment of conductive properties to clays has not been established. As such, the use of assumed values for clay conductivity leads to uncertainties in conventional simulations of the electrical response of clay-bearing sands.

[0010] Still as a background, molecular dynamics simulation ("MD") refers to a computational method of describing the evolution, over time, of a finite molecular or atomic system, based on an approximate expression ( i.e., a "force field") that determines the potential energy experienced by each atom in the system. In a conventional MD simulation, data such as coordinates, velocities and forces for each atom under the force field are stored at periodic time intervals. This data is then used to calculate instantaneous and time-averaged properties, such as atomic or molecular trajectories, atomic or molecular density profiles in one or two dimensions), interatomic structure (e.g., a radial distribution function), coefficients diffusion, vibrational structure, and the like.

BRIEF SUMMARY OF THE INVENTION

[0011] Embodiments of this invention provide a method and system for accurately estimating the electrical response of clay minerals and sands containing clay minerals.

[0012] Embodiments of this invention provide such a method and system for performing direct numerical simulation measurement of petrophysical properties in a sample of a subsurface formation that includes clay minerals.

[0013] The embodiments of this invention provide such a method and system for applying measurements, such as direct numerical simulation measurement of the electrical response, of a nanoscale material such as a clay mineral or sands containing clay minerals, to a characterization in large-scale training.

[0014] Embodiments of this invention provide such a method and system to provide a formation factor estimate for composite formations including nanoscale components such as clays.

[0015] Other objects and advantages provided by embodiments of this invention will become apparent to those skilled in the art with reference to the following specification together with the drawings thereof.

[0016] Embodiments of this invention can be implemented in a method of simulating the electrical response of a clay mineral component and a system for performing such simulation. A model of a molecular clay system is constructed as a multilayer structure corresponding to a clay mineral analogous to the clay of interest, with multivalent cations of a selected species embedded in the structure with a selected charge density, and with an amount of layers of water inserted into the space between the layers in the structure, according to a selected water saturation. Force field parameters representing interatomic forces and simulation variables corresponding to the desired simulation conditions, such as pressure, temperature, volume and the like, are assigned to the model constructed from clay. Molecular dynamics simulation is then performed to determine the ion diffusion coefficients between layers in the clay system. Application of the Nernst-Einstein Relation yields an estimate of clay ion conductivities.

[0017] According to other embodiments of the invention, a method and corresponding system are provided for performing direct numerical simulation of a rock containing clay fractions. A three-dimensional (3D) volume image of a rock sample is obtained by X-ray tomography, followed by segmentation of the volume to differentiate the phases of non-conductive rock fractions (e.g. quartz), partially conductive fractions (e.g. clay), and the pore space. Conductive properties are assigned to each segmented phase, and numerical simulation is performed to evaluate the electrical response of the volume. From the simulated response, one or more electrical properties of the rock sample containing corresponding clay are estimated.

[0018] According to other embodiments of the invention, a model of a molecular fluid system is constructed and populated with water of the desired density, with interstitially selected counterions placed in the model structure at the desired charge concentration. Force field coefficients are assigned to the model, and molecular dynamics simulation is performed to determine the fluid conductivity of the fluid volume as a reference. A formation factor for a clay bearing material is then calculated from a ratio of the volume conductivity of the reference fluid model to the simulated ion conductivities of the clay system.

BRIEF DESCRIPTION OF THE VARIOUS VIEWS OF THE DRAWINGS

[0019] Figure 1 is an electrical diagram, in schematic form, of a networked computer system programmed to perform various processes in the modeling and simulation of oil and gas reservoirs, in accordance with the embodiments of the invention.

[0020] Figure 2 is a flowchart illustrating a process for estimating the ionic conductivity of a clay mineral system, in accordance with the embodiments of the invention.

[0021] Figure 3 is a flowchart illustrating the construction of a molecular model of a clay mineral system in the process of Figure 2, in accordance with an embodiment of the invention.

[0022] Figures 4a to 4g are schematic diagrams illustrating molecular models of clay mineral systems at various stages of the process of Figure 3.

[0023] Figure 5 is a flowchart illustrating a formation factor estimation process for a clay mineral system, in accordance with an embodiment of the invention.

[0024] Figures 6a and 6b are an X-ray microtomography image and a segmented representation, respectively, of a sample of a composite formation including a clay component, for analysis in accordance with embodiments of the invention.

[0025] Figure 6c is a graph of the formation factor for three different clay-bearing sands using direct numerical simulation, in accordance with an embodiment of the invention.

[0026] Figure 7 is a flowchart illustrating a process of performing direct numerical simulation on a sample of a composite formation as shown in Figures 6a and 6b, for use in connection with records and resistivity measurements, in accordance with an embodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

[0027] This invention will be described in connection with one or more of its embodiments, namely as implemented in a method and system for developing clay mineral simulations, particularly for use in connection with direct numerical simulation, as it is contemplated that this invention will be especially beneficial in such an application. However, it is contemplated that embodiments of this invention may provide significant benefits and advantages in a wide range of applications beyond those described herein. Accordingly, it is to be understood that the description which follows is provided by way of example only, and is not intended to limit the true scope of this invention as claimed.

[0028] In recent years, clays and shales have become important formations in the development and production of oil and gas. It was observed that some of these clays have substitutive impurities, such as aluminum atoms that replace silicon atoms in the crystalline structure, or magnesium or iron atoms that replace aluminum atoms in the crystalline structure. These cationic impurities alter the charge balance of the clay crystal structure in such a way that adsorbed extra-structure ions are required to maintain charge neutrality. These adsorbed extrastructure ions are present on the outer surfaces of the clay, and are not part of the clay structure per se.

[0029] As described above, resistivity records provide important information about the fluid content, fluid volume and pore structure of subsurface formations. However, the presence of clay components in the formation clouds the relationship between resistivity and the physical properties of interest, as empirical and physics-based approximations of clay behavior present large uncertainties. An improved understanding of the physical mechanisms involved in the conductivity behavior of clay minerals would therefore also be desirable.

[0030] Embodiments of this invention provide tools and techniques to gain a better understanding of the physical mechanisms underlying the behavior of clay minerals in subsurface formations. Furthermore, as will be described below, these tools and techniques allow for larger scale analysis of clay bearing formations in order to provide improved accuracy in an efficient manner.

COMPUTERIZED SYSTEM

[0031] In accordance with embodiments of this invention, it is contemplated that these tools and techniques will be implemented, at least in part, by a computerized system, considering the nature and extent of the necessary calculations. Figure 1 illustrates an example implementation of an embodiment of the invention, in the form of computer system 20, which performs the operations described in this specification to efficiently run a simulation of the behavior of a clay mineral, particularly for conductivity estimation purposes. of one or more clays, and in some embodiments to estimate the conductivity and other petrophysical properties of a rock sample including a clay component through direct numerical simulation. In this example, system 20 may be realized via a computer system including workstation 21 connected to server 30 via a network. Of course, the particular architecture and construction of a computer system useful in connection with this invention could vary widely. For example, system 20 may be realized by a single physical computer, such as a conventional workstation or personal computer, or, alternatively, by a computer system implemented in a distributed manner across multiple physical computers. Consequently, the generalized architecture illustrated in Figure 1 is provided by way of example only.

[0032] As shown in Figure 1 and as mentioned above, system 20 includes workstation 21 and server 30. Workstation 21 includes central processing unit 25, coupled to the system bus BUS. Also coupled to a BUS system bus is the input/output interface 22, which refers to those interface features through which peripheral I/O functions (e.g., keyboard, mouse, display, etc.) interact with the other constituents of the workstation 21. The central processing unit 25 refers to the data processing capability of the workstation 21 and, as such, may be implemented by one or more CPU cores, co-processing circuits and similar. The particular construction and capacity of the central processing unit 25 are selected in accordance with the application needs of the workstation 21, such needs including, at a minimum, performing the functions described in this specification, and also including other functions that may be performed by system 20. In the architecture of system 20 according to this example, system memory 24 is coupled to the system bus BUS, and provides desired type memory resources useful as data memory for storing input data and the results of processing executed by central processing unit 25, as well as program memory for storing the computer instructions to be executed by central processing unit 25 in carrying out these functions. Of course, this memory arrangement is just one example, it being understood that system memory 24 may implement such data memory and program memory in separate physical memory resources, or distributed wholly or partially outside of workstation 21. Furthermore, as shown in Figure 1, the workstation 21 can also receive from the imaging system 28, via the input/output function 22, data in the form of a digital image volume representative of a sample of Rocha 28 from sensors and transducers implanted in wells in the production field. These measurement entries can be stored in a memory resource accessible to the workstation 21, either locally or via the network interface 26.

[0033] The network interface 26 of the workstation 21 is a conventional interface or adapter through which the workstation 21 accesses network resources on a network. As shown in Figure 1, the network resources that the workstation 21 has access to through the network interface 26 include the server 30, which resides on a local area network, or a wide area network, such as an intranet, a virtual private network or the Internet and which are accessible to the workstation 21 via one of these networking arrangements and corresponding wired or wireless communication facilities (or both). In this embodiment, the server 30 is a computer system, of a conventional architecture similar, in a general sense, to that of the workstation 21 and, as such, includes one or more central processing units, system buses and memory resources. , network interface functions, and the like. According to this embodiment of the invention, the server 30 is coupled to the program memory 34, which is a computer-readable medium that stores executable computer program instructions, in accordance with which the operations described in this specification are carried out by the control system. analysis 20. In this embodiment of the invention, these computer program instructions are executed by the server 30, for example in the form of an interactive application, upon input data communicated from the workstation 21, to create output data and results. which are communicated to workstation 21 for display or output by I/O peripherals in a form useful to the human user of workstation 21. Furthermore, library 32 is also available to server 30 (and perhaps workstation 21). library 21 on the local area network or wide area network) and stores such archival or reference information as may be useful on the system 20. The library 32 may reside on another local area network or, alternatively, be accessible over the Internet or another wide area network. It is contemplated that the library 32 may also be accessible to other associated computers on the general network.

[0034] Of course, the particular memory resource or location where the measurements, library 32 and program memory 34 physically reside can be implemented in various locations accessible to the system 20. For example, these data and program instructions can be stored in local memory resources within the workstation 21, within the server 30, or in network accessible memory resources for these functions. Furthermore, each of these data and program memory resources may be distributed among multiple locations, as is known in the art. It is contemplated that those skilled in the art will be readily able to implement the storage and retrieval of measurements, models and other applicable information useful in connection with this embodiment of the invention, in a manner suitable for each particular application.

[0035] According to this embodiment of the invention, by way of example, the system memory 24 and the program memory 34 store computer instructions executable by the central processing unit 25 and the server 30, respectively, to perform the functions described in this specification. These computer instructions may be in the form of one or more executable programs, or in the form of source code or higher-level code from which one or more executable programs are derived, assembled, interpreted or compiled. Any of several computer languages or protocols can be used, depending on how the desired operations are to be performed. For example, these computer instructions for creating the model in accordance with the embodiments of this invention can be written in a conventional high-level language such as JAVA, FORTRAN or C++, either as a conventional linear computer program or organized for execution. in an object-oriented way. These instructions can also be incorporated into a higher-level application. More specifically, it is contemplated that simulation of the behavior of the modeled subsurface volume may be performed, in part, by means of a computer simulation application or software package, an example of which is the molecular dynamics computer software package of Massively Parallel Atomic/Molecular Simulator (LAMMPS) available from Sandia National Laboratories, using a general force field structure suitable for molecular simulations, an example of which is the CLAYFF framework described in Cygan et al., "Molecular Models of Hydroxide, Oxide, and Clay Phases and the Development of a General Force Field", J. Phys. chem. B, Vol. 108 (2004), pp. 1255 - 1266, incorporated herein by reference. In any case, it is contemplated that those skilled in the art referring to this description will be readily able to carry out, without undue experimentation, this embodiment of the invention in a manner suitable for the desired installations. Such executable computer programs for carrying out embodiments of this invention may be installed as residents on system 20 as described above or, alternatively, may be in the form of an executable web-based application that is accessible to server 30 and client computer systems, as a workstation 21 for receiving input from the client system, executing algorithm modules on a web server, and providing output to the client system in a convenient display or printed form. Alternatively, these computer-executable software instructions may be resident elsewhere on the local area network or wide area network, or for download from higher-level or local servers via information encoded in an electromagnetic carrier signal. through some network interface or input/output device. Computer-executable software instructions may have originally been stored on removable or other non-volatile computer-readable storage medium (e.g., a DVD disc, flash memory, or the like), or capable of being downloaded as encoded information in an electromagnetic carrier signal, in the form of a software package from which computer executable software instructions have been installed by the system 20 in conventional manner for installing software.

ESTIMATE OF IONIC CONDUCTIVITY OF A CLAY MINERAL

[0036] Figure 2 illustrates the generalized operation of the system 20 in the execution of a simulation to estimate the conductivity of a modeled clay mineral system, typically corresponding to a component of a subsurface formation of interest in the exploration and production of oil or gas , according to an embodiment of the invention. As mentioned above, it is contemplated that the various steps and functions in this process may be performed by one or more of the computing resources in system 20 executing computer program instructions residing in available program memory, in conjunction with user input as appropriate. As mentioned above, it is contemplated that system 20 will be programmed, in accordance with embodiments of this invention, with computer programs that, when executed by computing resources in system 20, will perform the various processes described in this specification for simulating the conductivity of systems of clay mineral as specified by various physical parameter values and relationships.

[0037] Although the following description presents an example of this operation as performed at workstation 21 in the network arrangement of system 20 shown in Figure 1, it is evident that the particular computing component used to perform particular operations can vary widely depending on of system implementation. As such, the following description is not intended to be limiting, particularly in identifying those components involved in a specific operation. Accordingly, it is believed that those skilled in the art will readily understand from this specification the manner in which these operations can be performed by computational resources in these various implementations and embodiments. Accordingly, it is contemplated that reference to the execution of certain operations by the system 20 will be sufficient to allow skilled readers to readily implement the embodiments of this invention, without undue experimentation.

[0038] As shown in Figure 2, an initial step in estimating the conductivity of a clay mineral system in accordance with the embodiments of this invention is the construction of a molecular model of the clay system, in process 40. For the purposes of this description, the use of the term "molecular" in connection with models of clay systems and conductivity estimation in this description is intended to refer to models and simulations in which individual atoms, ions and molecules are represented; in this context, the term "molecular" is intended to include atomic and ionic species as well as molecules.

[0039] Referring now to Figures 3 and 4a to 4g, the operation of process 40 in building the molecular model of the clay mineral system to be simulated in accordance with an embodiment of the invention will be described in greater detail. Construction process 40 begins with process 50, in which an analogous anhydrous clay structure is constructed, in this example arranged according to a unit cell model. This analogous anhydrous clay structure is constructed to reflect the attributes of the clay mineral system being modeled.

[0040] Figure 4a illustrates an example of such an anhydrous clay analogue, from which a model of a smectite (swelling) clay will be constructed in accordance with this embodiment of the invention. The clay analogue shown in Figure 4a is based on muscovite as a clay analogue to modeled smectite clay. Muscovite is referred to as a "2-1" layer aluminosilicate, in that each layer 65 of the clay consists of two tetrahedral sheets of silicate on each side of an octahedral sheet of hydroxyl aluminate (herein referred to as the octahedral sheet of aluminum). According to this example, this muscovite structure is then modified by removing potassium ions from the octahedral sheet, and replacing aluminum atoms in the tetrahedral sheets with silicon atoms. This structure remains charge neutral and, in its anhydrous form, provides the structure of a pyrophyllite clay. Figure 4a illustrates the structure of this pyrophyllite clay for portions of a pair of parallel clay layers 65, each including two silicate sheets 60 on either side of a single octahedral aluminum sheet 62. The unit cell 64 is shown in Figure 4a and serves as the basis for the model of this clay mineral system; the chemical formula for cell unit 64 in this example is Si8Al4O20(OH)4. The aluminum (Al), oxygen (O), hydrogen (H) and silicon (Si) atoms in the pyrophyllite clay model are labeled in Figure 4a. As evident from this example of Figure 4a, parallel layers 65 are separated from one another by "interlayer" space 63 (ie, the gallery space between layers 65 in the structure); as will be described below, hydration of this clay structure will swell the volume of the clay, since one or more layers of water will be inserted into this interlayer space 63 between these parallel layers 65 of the structure.

[0041] Figure 4b illustrates the unit cell structure for a different analogous clay mineral, namely kaolinite. Kaolinite is a "1-1" clay, in that a layer 65' (and therefore a unit cell 64') of this clay includes a silicate sheet 60 and an octahedral aluminum sheet 62. As known in the art , kaolinite is not a smectite clay (i.e. it does not have a permanent structural negative charge), and as such will not swell between its layers 65' after hydration. Rather, the edges (i.e., ends) of 65' kaolinite layers are reactive, and as such, are the sites of interaction with water and oil molecules.

[0042] It is contemplated that embodiments of this invention can be used to simulate conductivity in these, and other, clay structures. For the purposes of this description, the clay structure of Figure 4a will be discussed by way of example. It is contemplated that those skilled in the art to which this specification pertains will readily be able to apply the methods and systems described herein, without undue experimentation, to the kaolinite clay of Figure 4b and to other clays of interest.

[0043] Referring again to Figure 3, and in accordance with this embodiment, once the unit cell structure is defined in process 40, process 51 is then performed to orthogonalize the unit cell 64 into a regular structure, with coordinates assigned to each of the atoms to indicate their positions in a coordinate system. Orthogonalization process 51 is optional, as the subsequent simulation processes described herein may be applied to the original mineral symmetry structure system (ie, which may be non-orthogonal). However, it is contemplated that subsequent processing is more conveniently applied to orthogonal model systems such as produced by process 51. After orthogonalization in accordance with this embodiment, unit cell 64 is expanded into a "supercell" in process 52. This supercell created in process 52 is made up of a number of unit cells 64, and is of a sufficient size for the simulation processes described herein. For example, unit cell 64 of Figure 4a can be expanded in process 52 into a supercell of sixty-four unit cells, arranged 8 x 4 x 2 in x, y and z directions (according to the orientation of Figure 4-A), respectively. The number of unit cell repetitions in each direction can naturally vary, according to the desired simulation. Each of the atoms in the supercell representation will be given coordinates representing its position in the coordinate system.

[0044] In process 54, according to this embodiment of the invention, ions of a selected species are replaced in the supercell structure, according to the desired charge density of the clay to be simulated. In this embodiment of the invention, a montmorillonite smectite clay must be simulated. As such, magnesium ions are replaced by aluminum ions in the octahedral sheet 62 of the supercell structure, typically at random. As is known in the art, the charge of magnesium ions (Mg2+) differs from that of the aluminum ions (Al3+) being replaced, which results in negatively charged sites at the supercell sites where magnesium ions reside. Figures 4c and 4d illustrate examples of montmorillonite smectite clay supercells based on the structure of Figure 4a, in which magnesium ions are randomly replaced by aluminum ions at two different charge concentrations; these views of Figures 4c and 4d are plan views relative to the sectional view of Figure 4a, and as such, the interlayer space 63 between the parallel layers of clay is not visible. Although the placement of these substituted ions is random, this placement is preferably controlled in order to avoid creating nearest neighbor Mg-O-Mg interactions. Figure 4c illustrates a relatively low charge example, where the net charge density of the supercell following the 54 replacement process is -0.375e per unit cell, where e represents the elementary electron charge; Negatively charged sites 66 are illustrated in this Figure 4c at locations corresponding to the positions of the substituted magnesium ions. Figure 4d illustrates a high charge example, in which the net charge density of the supercell following the ion replacement process 54 is -0.750e per unit cell, which is twice the density of negatively charged sites 66 as in example from Figure 4c. As part of the 54 ion replacement process, the supercell model is further modified by inserting counterions into the interlayer region to render the supercell charge neutral. In this example, sodium or calcium counterions are used, although other kinds of counterions could alternatively be used. In the examples of Figures 4c and 4d (that is, with different degrees of charge density), the resulting unit cell chemical formulas resulting from process 54, using sodium counterions, are Na0, 375Si8Al3,625Mg0,375O20(OH) 4 and Na0.75Si8Al3.25Mg0.75o20(OH)4, for cases of low and high charge density, respectively.

[0045] In process 56, the clay model supercell structure is then hydrated by introducing water molecules into the space between clay layers in the supercell structure. For the example of the montmorillonite clay structure of Figure 4a, the hydration process 56 separates the clay layers 2-1 by inserting water molecules into the interspace 63 between the layers 65. In this embodiment of the invention, the introduction of molecules of water in the process 56 inserts these water molecules in the form of an integer number of layers of water molecules, according to the desired water concentration to be simulated. For example, one, two or three layers of water can be inserted into the interspace 63, producing stoichiometric ratios of 3.9, 7.9 and 11.8 water molecules per unit cell, respectively. In one example, the process 56 is carried out by moving the counterions (Na+, Ca+2) inserted in the process 54 into interlayer spaces 63, at locations above or below the corresponding negatively charged sites 66 as the case may be, then followed by filling the remaining volume of interlayer spaces 63 with the corresponding number of water molecules at the desired concentration. This insertion of water molecules has the effect of increasing the separation between parallel layers of the 2-1 clay structure and as such is representative of the clay swelling expected for smectite clays of this type.

[0046] Figures 4e to 4g illustrate the clay supercell model of Figure 4a after the hydration process 56, with varying numbers of layers of water inserted between layers 65. Figure 4e illustrates the arrangement of the clay supercell with a layer of water 67 (1) inserted between parallel layers 65 of clay structure 2-1. As is evident from Figure 4e, sodium counterions (Na+) are trapped within layers of water 67 (1). The resulting separation between adjacent parallel layers 65 defines the layer pitch d(1) for the case of a layer of water 67(1). For purposes of this description, "pitch" refers to the combined thickness of a layer 65 and its adjacent interlayer spacing 63; this clay layer pitch can be regarded as equivalent to the basal d spacing as measured experimentally by X-ray powder diffraction methods. Figure 4f illustrates the supercell arrangement with two layers of water 67(2) inserted between each pair of layers clay 2-1 parallels 65; the layer pitch d(2) in this case is greater than the layer pitch d(1) for the single water layer case of Figure 4e. Figure 4g illustrates the supercell arrangement with three layers of water 67 (3) between each pair of adjacent parallel layers 65; the layer step d(3) in this case of three layers of water is again larger than the step d(2) for the case of two layers of water.

[0047] As shown in Figures 4e to 4g as mentioned above, counterions (eg Na+) are trapped within the inserted water layers 67. The number and charge density of these counterions are determined by the number of substitutions (Mg2+ in this example) in clay layers 65 in the anhydrous structure defined in process 50 and, as such, does not vary with the number of water layers 67 inserted in the supercell representation. Because counterions (Na+ or Ca2+, as the case may be) are located within layers of water 67, these counterions will be mobile under the appropriate stimulus (although it is believed that interactions between water molecules and neighboring counterions will cause movement of both). As such, it is this movement of these counterions that gives rise to the electrical conductivity observed in clay in response to an applied potential. Simulating the ionic conductivity of this clay structure in accordance with the embodiments of this invention will thus determine the movement of these counterions to estimate the ionic conductivity of the clay mineral system.

[0048] The coordinates of the atoms in the supercell structure after the hydration process 56 has expanded the separation between adjacent layers 65, including coordinates for the counterions, are then stored as a representation of the molecular model constructed in the appropriate format within the system memory 20. Construction of the molecular model of the clay system to be simulated in process 40 is then complete. Although the supercells in Figures 4e to 4g represent models of finite size, in common practice periodic boundary conditions are used to efficiently represent an infinite number of repeating supercell units in the x, y, and z directions. This way, long-range electrostatic interactions will be properly included in subsequent MD simulations, as described below.

[0049] Returning to Figure 2, process 42 is then performed on the molecular model constructed in process 40. Process 42 assigns force field parameters to the constituents (atoms, molecules) of the constructed model and their interactions with each other. According to this embodiment of the invention, the force field working structure for clays known as "CLAYFF", described in the article by Cygan et al. incorporated by reference above, allows great flexibility in specifying interaction parameters between the atoms and molecules in the hydrated montmorillonite clay supercell model constructed in process 40. In this embodiment of the invention, the assignment of these parameters in process 42 is contemplated to be performed by the system 20 within the simulation software environment, such as within the LAMMPS molecular dynamics computer software package referred to above.

[0050] The values of the force field parameters and the simulation variables are assigned to the constituents of the model built in process 42. As described in the Article by Cygan et al., the force field parameters include: • Representations of atoms in the model as point loads at locations within a coordinate system, with complete translational freedom within the model structure; • Energies for each atom-atom interaction in the system, including those for long-range electrostatic interactions (Coulomb's law), and short-range interactions (van der Waals forces), and cutoff distances for them; and • Bond angles, bond lengths, etc. for hydroxyl groups and water molecules.

[0051] In addition, process 42 can also assign values to certain simulation variables according to the desired conditions of the simulation to be performed, for example, including: • Boundary conditions representative of pressure, temperature and volume; • Thermodynamic set of parameters; and • Other coefficients pertinent to molecular dynamics simulation, as will be understood by those skilled in the art with reference to this specification.

[0052] Once assigned, optimization of the parameters in the force field work structure can be carried out as desirable, and according to conventional techniques as described in Article by Cygan et al. incorporated herein by reference. This optimization can be performed, for example, to provide an energy minimized structure as described in this article. The application of these force field coefficients in process 42 can result in changes in the coordinate positions of the various constituents of the supercell model; for example, it was observed that layer steps d(1), d(2), d(3) have a slight temperature dependence.

[0053] After assigning the force field coefficients in process 42, the system 20 executes the program instructions to perform molecular dynamics (MD) simulation process 44. As described above, the MD simulation software packages suitable for use in process execution 44 are known in the art. An example of such a suitable MD software package is the LAMMPS software package available from Sandia National Laboratories, as mentioned above.

[0054] According to the embodiments of this invention, the MD simulation process 44 evaluates the dynamics of the constituents of the supercell molecular model built in process 40, under the values of the force field parameters and simulation variables as assigned in the process 42. A useful approach to the MD 44 simulation process is to evaluate both short-range and long-range interactions (ie, the appropriate and applicable equations of motion) between model components over a number of time intervals within a selected time interval, to derive the positional coordinates, velocities, and forces of these constituents during that interval.

[0055] In an example according to an embodiment of the invention, short-range (van der Waals) interactions were evaluated in short time intervals (e.g. 0.5 fsec) with a cut-off distance (e.g. 10, 0 Â) applied by these short-range forces, and these interactions are ignored in the simulation. In these simulations, periodic boundary conditions were applied, and long-range electrostatic interactions evaluated over longer time intervals (for example, 1.0 fsec), using a particle-particle-mesh (PPPM) summation algorithm, such as as described in Plimpton et al., "Ewald Mesh Particle and rRESPA for Parallel Molecular Dynamics Simulations", Proceedings of the Eighth SIAM Conference on Parallel Processing for Scientific Computing (1997), incorporated herein by reference. In this example, the model systems were thermally equilibrated using an initial 50 psec simulation on the microcanonical set (i.e., particle number, volume, and potential energy) with velocity rescaling according to the desired temperature, followed by a simulation of 50 additional psec on canonical set (ie particle number, volume and Nose-Hoover thermostat temperature). Following these initial simulations, a simulation of production over a much longer period of time (e.g., 2500 psec) was performed on the isothermal-isobaric set (i.e., particle number, pressure, and temperature, with the pressure Nose-Hoover barostat set to zero). In this simulation, the supercell volume was allowed to change only in the z direction (ie, perpendicular to the clay layers in Figures 4e to 4g).

[0056] The results of process simulation 44 are then used for process 46, in which self-diffusion coefficients D of selected molecules and atoms are calculated by system 20. Process 46 in this embodiment of the invention is based on the movement of atoms and molecules of interest during a selected time period during the simulation. In the smectite clay simulation described above, diffusion coefficients D for sodium (Na+) or calcium (Ca+2) counterions, depending on which are present, and water molecules in the embedded water layers 67 are based on on the position coordinates of these atoms and molecules over an evaluation time series within a selected time interval of the MD simulation of process 44. For the example of the 2500 psec production simulation on the isothermal-isobaric set referred to above, the process 46 can be based on the coordinates of atoms and molecules stored in system 20's memory every 2.0 fsec towards the final 2000 psec of this 2500 psec simulation.

[0057] Based on these stored coordinate positions of the ions and molecules of interest, self-diffusion coefficients D are calculated in process 46 from the mean-square-displacement of these ions and water molecules in the xy plane parallel to the basal surface: where the brackets <> denote a set average of the x and y displacement of the ion or molecule at a given time t. Displacement in the z-direction is set to zero in this example, as there is negligible diffusion in that direction (ie, just random motion, due to kinetic energy occurring in the z-direction in process simulation 44). The average ensemble shift over time is evaluated for each of the selected counterions and water molecules in the water layers 67 in the interlayer space 63 of the supercell structure subjected to simulation, for example, over just one subinterval of time in which the simulation was performed. In the example described above, molecule and ion displacement was evaluated across the subrange of 200 psec to 800 psec points in the 2000 psec range for which the coordinates were stored, in order to avoid the effects of short range non-linear motion (i.e. i.e. rotation). From these results, appropriate regression analysis (eg, least squares) can be performed to recover the displacement slope as a function of simulation time, and thus the self-diffusion coefficient D for each species.

[0058] Alternatively, the diffusion coefficients for the ion and molecule species of interest in bulk fluids or in fluid-only simulations can be calculated in process 46, for example, by directly calculating the diffusion coefficient D from the three-dimensional trajectory of ions and molecules: where the brackets <> denote a set average of the displacement of the ions or molecules over the time interval from start time t0 to time t. As such, this expression calculates the diffusion coefficient from the mean square displacement of the ions and molecules as determined by the MD 44 simulation process.

[0059] According to embodiments of the present invention, once the self-diffusion coefficients D for the species of interest are determined in process 46, ion conductivities of these species in the modeled clay system are calculated, for example, by system 20, in case 48, by applying the Nernst-Einstein relation. Discussion of the Nernst-Einstein relationship can be found in Bockris et al, Modern Electrochemistry 1: Ionics, 2nd ed. (Plenum Press, New York, 1998), pp. 456 - 458, incorporated herein by reference. More specifically, according to embodiments of the invention, the ionic conductivity of the i-index counterion species (referring to one of Na+ or Ca2+ included in the model according to the example described above) embedded in layers of water 67 can be calculated from its self-diffusion coefficient Di as follows: where zi is the ionic valence of counterion i, ci is the ionic concentration of counterion i, F is the Faraday constant, R is the gas constant, and T is the temperature. In the same way, the molar ionic conductivity Ài can be calculated:

[0060] According to the embodiments of this invention, therefore, the ionic conductivity in a modeled clay mineral system can be estimated based on a molecular model of that clay system. This simulation process can be quickly repeated for different species of counterions, varying levels of hydration (i.e. different numbers of layers of water 67 between layers of clay 65), varying physical conditions (e.g. temperature, pressure, etc.) .), and varying charge densities, and the like. The analysis of the results from the resulting sets can provide information about the conductivity mechanisms, and can also help the experimental confirmation of the simulation results. Furthermore, the ability of this simulation tool to estimate conductivity under a wide range of conditions can develop empirical relationships that are useful in understanding the petrophysical properties of subsurface formations.

ESTIMATE OF THE FORMATION FACTOR OF A CLAY MINERAL SYSTEM

[0061] As mentioned above, a petrophysical property that is often of particular interest in connection with the analysis of resistivity records, as commonly obtained in the exploration and production of oil and gas reservoirs, is referred to as the "formation factor" . The common definition of formation factor is the ratio of the resistivity of the formation rock to the resistivity of the fluid itself.

[0062] Figure 5 is a flowchart of this process of estimating the formation factor of a given clay mineral system. As shown in Figure 5, the ionic conductivity for this clay mineral system is determined by system 20 in process 100, in accordance with the process described above in connection with Figure 2. However, to derive the formation factor, the conductivity of fluid volume is also required. According to this embodiment of the invention, this bulk conductivity is estimated similarly to the ionic conductivity of the clay system, starting with process 70.

[0063] In process 70, a molecular model of a bulk solution (ie, charge neutral) representative of the desired fluid is constructed. For example, the process 100 described above is applied to a model where Na+ or Ca2+ cations were entrained in the injected water layers 67 along with Cl- anions to maintain charge neutrality. In this example, the molecular model of a bulk solution contains 4096 water molecules, four sodium (Na+) or calcium (Ca2+) cations, and four or eight Cl- anions (as the case may be), in a cube of approximately 50Â on one side. The molar cation concentration in this modeled bulk solution is therefore about 0.05.

[0064] Alternatively, if the corresponding volume solution modeled in Process 70 does not include anions and therefore has a net positive charge, a charge compensation background can be entered into the model to maintain charge neutrality.

[0065] Processes 72 to 76 are then performed on the molecular model of the bulk solution constructed in Process 70, similarly to Processes 42 to 46 described above for the clay mineral system. In summary, the force field parameters assigned to molecules and cations in the process volume solution model 72 specify parameters such as the location of atoms within a coordinate system and energies of molecules and atoms, and simulation parameters include representative boundary conditions of pressure, temperature and volume, thermodynamic set of parameters and the like. In process 74, a molecular dynamics (MD) simulation is performed by the system 20 on this molecular model based on specified force field coefficients, to determine the positions of water molecules and cations over simulation time, e.g. storing the location of each molecule and cation at a sampling frequency of 2 psec over a simulation interval of 10 nsec, under constant pressure and constant temperature simulation conditions. In process 76, self-diffusion coefficients are calculated for the cations and water molecules in the modeled bulk solution, based on the locations stored at sample times within the MD simulation of process 74. In this process 76, the self-diffusion coefficients can be calculated similarly as in process 46 described above, based on the mean-squared shift in the x-y plane or based on a set average from the ion trajectory in three dimensions.

[0066] Examples of the diffusion coefficient values calculated for a molecular volume solution model according to the approach of processes 70 to 76 were observed according to the results reported for the diffusion coefficients of sodium and calcium solutions in dilution infinite.

[0067] In process 78, the self-diffusion coefficient for the cation in the bulk solution model, at the temperature applied as a boundary condition in process 72, is then applied to the Nernst-Einstein relation to determine the conductivity of the solution, as described above. This calculated conductivity in process 78 constitutes the volume thus provides an estimate of the volume conductivity of the fluid in the clay mineral system, from which the formation factor F of the process clay mineral system 100 can be determined from a conventional way, in process 80: where oi is the ionic conductivity of the counterion in the modeled clay system determined in process 100, and ob is the volume conductivity of a volume solution calculated in process 78. As is known in the art and as described above, the factor of formation F provides a good measure of the porosity in the formation structure, from which other important petrophysical properties can be determined, such as permeability.

[0068] Consequently, this embodiment of the invention provides the ability to estimate the formation factor value from a clay mineral system from modeling and simulating the relevant mechanisms at the molecular level. This molecular-level analysis allows the precise analysis of nanoscale formation components beyond the capability of conventional approaches such as the Archie Relationship and others.

DIRECT NUMERICAL SIMULATION OF FORMATIONS INCLUDING A CLAY COMPONENT

[0069] The ability to accurately estimate the conductivity of clay minerals provided by embodiments of the invention, as described above, can be useful in a wide variety of petrophysical analyses, particularly considering the current importance of rock formations containing hydrocarbons that contain sands carrying clay. Furthermore, it is also contemplated that understanding the physical mechanisms operating at the molecular level in these nanoscale materials will be particularly useful in the design and analysis of production technologies. Other analytical tools and techniques are also contemplated to be enhanced by the conductivity estimation techniques of embodiments of this invention.

[0070] One such analytical tool and technique that can be improved by an accurate estimation of the conductivity of clay mineral systems is direct numerical simulation, particularly as applied to subsurface formations that include both a rock phase and quartz, as in a sandstone, and a clay mineral phase. As known in the art, clay components in formations of this type are typically formed by a series of broadly parallel plates; for example, the clay mineral kaolinite is typically in the form of "leaflets" sandwiched between solid quartz grains and pore space. As discussed above in connection with the Background of the Invention, conventional resistivity records interpreted in accordance with the Archie Relation are based on solid grains exhibiting effectively zero conductivity, while the fluid in the pore space exhibits high conductivity. In those formations where this assumption is valid, the measured resistivity will give a good indication of formation porosity. However, as is known in the art, clay components in the formation will also exhibit conductivity, but to a lesser extent less than that of the pore fluid yet significantly greater than that of solid quartz grains. Conventional resistivity analysis will therefore give a generally ambiguous result when applied to a formation that includes clay components, since the resistivity will depend not only on the porosity exhibited by the pore fluid, but also on the extent to which the clay components are present and their conductivity.

[0071] According to an embodiment of the invention, the existence of an accurate estimate for the conductivity of clay components in a composite formation can be used when determining the electrical response through direct numerical simulation of a volume image of a rock . Referring now to Figure 7, the general process of estimating material properties using digital numerical simulation in accordance with embodiments of this invention will be described.

[0072] The estimation process begins with the sample preparation process 200, in which a specimen is obtained from the formation of interest, and a sample of that specimen prepared for analysis. The training specimen can be acquired in one of several conventional ways. In the context of the oil and gas industry, the test piece will typically be derived from drilling exploration or production wells and as such may come from whole core samples, sidewall core samples, upwelling samples and drilling; alternatively, the specimen can be produced from a laboratory-generated synthetic rock sample, such as a sand pack or cement pack. In accordance with embodiments of this invention, the rock from which the specimen is obtained may not always be highly consolidated, as it will include a combination of rock (e.g., sandstone) together with clays, and other granular material or sedimentary. As such, the preparation process 200 must be carried out in such a way that it does not significantly impair the structure of the formation to be represented by the sample.

[0073] In process 202, the imaging system 28 (Figure 1) obtains two-dimensional (2D) or three-dimensional (3D) images, or other appropriate image representations, of the rock sample prepared in process 200. These images and representations obtained in process 202 include details of the internal structure of the samples. An example of the imaging device used in process 202 is an X-ray computed tomography (CT) scanner, of a type, construction, or other attribute corresponding to any of a number of X-ray devices capable of producing an image. representative of the internal structure of the sample of the desired resolution. For example, a plurality of two-dimensional (2D) sectional images of the sample may be acquired and routed to computer system 20 which then constructs a three-dimensional (3D) digital image volume corresponding to the sample. As discussed above, the system 20 can be constructed in any of a number of ways, for example, as a desktop or workstation computer, a laptop computer, a server computer, a tablet computer, or the like, with sufficient computing power to perform the desired operations.

[0074] Specific conventional techniques for acquiring and processing volumes of 3D digital images of the sample in process 202 include, without limitation, X-ray tomography, X-ray microtomography, X-ray nanotomography, focused ion beam scanning electron microscopy, and Nuclear Magnetic Resonance.

[0075] The image volume produced by the process 202 is typically represented by regular 3D elements called volume elements, or more commonly "voxels", each with an associated numerical value or amplitude, which represents the relative material properties of the sample with image formed at that location of the represented medium. In process 210, the computing device performs segmentation or other image enhancement techniques on the digital image volume of the sample to distinguish and label different components in the image volume. For example, the segmentation process 210 can identify significant elastic components, including pore space and mineralogical components (eg, clays and quartz), that can affect sample characteristics.

[0076] According to this embodiment of the invention, the segmentation process 210 is then performed by the system 20 to identify the significant material phases of the sample represented in the image volume, for example, representing such material constituents as pore space, clay and grain fractions and individual minerals. The particular segmentation algorithm used by the computing device in process 210 can vary according to the desired analysis and rock complexity. The simplest form of segmentation is "limiting", which groups voxels having similar amplitudes to each other. Conventional image processing to improve image volume, to reduce noise, etc. can be included in file 210.

[0077] According to this embodiment of the invention, the segmentation process 210 identifies and distinguishes at least three significant material phases, namely pore space, rock grains and clay minerals. An example of the operation of segmentation process 210 is shown by Figures 6a and 6b. Figure 6a is an example of an X-ray microtomography image of a sandstone rock containing clay mineral components such as kaolinite along with its solid quartz grains. In the image of Figure 6a, the pore space corresponds to the black regions, while the quartz grains and clay components correspond to the varying intermediate shades of gray (the lighter gray tending to indicate the quartz grains). Typically, the spatial resolution of an X-ray microtomography image such as Figure 6a ranges from 1 to 5 microns, which means that the texture, configuration and tissue of clay minerals are not observable at this scale. Furthermore, the brightness varies continuously in the image of Figure 6a, which makes the numerical analysis complex and difficult. Segmentation process 210 operates to distinguish pore space, solid grains and clay components from one another. Figure 6b illustrates an example of the results of the segmentation process 210 applied to the X-ray microtomography image of Figure 6a, where three phases are represented as black for pore space 90, white for quartz or other solid grain material 92 and an intermediate gray for clay components 94. In general, as mentioned above, segmentation process 210 is applied to the 3D image volume acquired in process 202.

[0078] In accordance with this embodiment of the invention, a conductivity estimate for clay components 94 is derived in process 100. As discussed above, it is contemplated that process 100 described above in connection with Figure 5 will provide an excellent conductivity estimate for the clay component 94 in the sample prepared and imaged in processes 200 and 202. However, it is also contemplated that other approaches to measuring and estimating conductivity in the clay component 94 may alternatively be used in connection with this embodiment of the invention; it is expected, however, that conventional approaches to estimating the conductivity of clay mineral systems are less rigorous and will generally provide less accurate conductivity estimates than those described above in connection with embodiments of the invention.

[0079] Based on the conductivity estimate derived in process 100, process 215 is then performed to assign a relative conductivity value w to clay components 94 of the segmented image volume. As discussed above, crystals of quartz 92 (or other solid material) effectively exhibit zero conductivity in conventional resistivity analysis while the fluid in pore space 90 exhibits high conductivity; clay components 94 are normally conductive, as estimated in process 100, but to a lesser extent than the fluid in the pore space 90. According to this embodiment of the invention, the relative conductivity value w assigned to the clay components 94 in-process 215 reflects the estimated conductivity of clay compared to that of the fluid. The formation factor F calculated as described above can be the basis of this relative conductivity value w, for example. This relative conductivity value w is then assigned to each of the voxels representing clay components 94 in the segmented digital image volume from process 210. Of course, if the clay components 94 in the image volume represent more than one species of clay, separate conductivity estimates for these different clay phases can be estimated in process 100, and applied using different relative conductivity values w in process 215.

[0080] In process 220, computing system 20 performs direct numerical simulation to analyze one or more physical properties of the sample, typically through numerical analysis of the segmented digital image volume. Properties that can be determined in process 220 include petrophysical properties of interest that relate directly or indirectly to the conductivity of clay components 94, such as porosity, formation factor, cementing exponent, resistivity index, tortuosity factor, saturation exponent, and the like. These petrophysical properties can be estimated using a suitable discretization of the entire segmented digital image volume or mesh of evolved pore space and clay components, combined with appropriate numerical simulation, for example direct numerical simulation of electrical conductivity to determine the properties rock electrical. Determining some of these petrophysical properties in process 220 may also require numerical simulation using finite element methods, finite difference methods, finite volume methods, Lattice Boltzmann methods, or any other variety of numerical approaches. For example, Figure 6c illustrates formation factor computation for three different clay-bearing sands using direct numerical simulation, where clay 94 components have assigned conductivities.

[0081] According to this embodiment of the invention, therefore, it is contemplated that conventional resistivity records can be extended to more complex formation structures, including formations with clay mineral components, and provide accurate results on important petrophysical properties, such as porosity, water saturation, clay fraction and the like, particularly if conductivity is estimated in accordance with the embodiments of this invention described above. Analysis of the effects of secondary recovery processes on formations for which resistivity records were obtained was also contemplated.

IN CONCLUSION

[0082] As described above, embodiments of this invention provide a method and system for accurately estimating the electrical response of clay minerals and sands containing clay minerals, in a manner that is based on physical mechanisms occurring at the molecular level. The ability to analyze nanoscale materials such as clay minerals in this way is considered useful in a wide range of clay structures beyond the pyrophyllite, montmorillonite and kaolinite examples specifically described above, as the same approach can be applied to a wide variety of molecular models for clay minerals. This capability can provide additional insight into other analytical tools, such as direct numerical simulation measurement of petrophysical properties in a sample of a subsurface formation that includes clay minerals, and formation factor development and analysis for composite formations including nanoscale components. such as clays.

[0083] While this invention has been described in terms of its embodiments, it is of course contemplated that modifications of, and alternatives to, these embodiments, such modifications and alternatives achieving the advantages and benefits of the present invention, will be apparent to those of ordinary rank. persons skilled in the art with reference to this specification and its drawings. It is contemplated that modifications and alternatives are within the scope of the invention as subsequently claimed herein.

Claims (11)

1. A computer-implemented method for analyzing a rock sample comprising a clayey component, the method characterized by comprising: estimating the conductivity of the clayey component in the rock sample; segmenting a digital image volume corresponding to one or more tomographic images of the rock sample, to associate voxels in the digital image volume with pore space, solid material or the clayey component; and assigning a relative conductivity value to voxels corresponding to the clayey component in relation to the conductivity of a fluid occupying the pore space of the sample; determine at least one petrophysical property of the rock sample based on an analysis of a volume representation of the digital image; and evaluating an earth hydrocarbon reservoir based on at least one petrophysical property of the rock sample. 2. Computer-implemented method, according to claim 1, characterized in that the step of estimating the conductivity of the clayey component comprises: constructing a molecular representation of the clayey component, comprising: an anhydrous structure of atoms arranged in a plurality of parallel layers, the anhydrous structure including substitution sites in place of metal atoms in the structure in a concentration corresponding to a selected charge density; counterions of at least one species disposed in an interlayer space between layers of the anhydrous structure, in a concentration corresponding to the selected charge density; and a plurality of water molecules disposed in the interlayer space; assign force field parameters to the molecular representation in combination with boundary conditions corresponding to a selected pressure and temperature condition of the clayey component; operating the computer system to perform a molecular dynamics simulation of the equations of motion over a simulation time interval to determine positional coordinates of counterions in the representation at a plurality of times during the simulation time interval; calculating self-diffusion coefficients for one or more of the counterion species from the positional coordinates at the plurality of times; and calculate ion conductivities for a kind of counter-ions from the self-diffusion coefficients. 3. Computer-implemented method according to claim 2, characterized in that the construction of the molecular representation comprises: defining a unit cell of the representation including atoms corresponding to a portion of at least one layer and including a portion of the interlayer space ; and arranging a plurality of unit cells into a supercell representation of the clay component. 4. Computer-implemented method, according to claim 1, characterized in that it further comprises: acquiring the volume of the digital image of the rock sample, using an X-ray tomography, X-ray micro tomography, nano X-ray tomography, focused ion-beam scanning electron microscopy, nuclear magnetic resonance, or neutron tomography. 5. Computer-implemented method according to claim 4, characterized in that the rock sample comprises one of an entire core, sidewall cores, outcrops, fragments and drill cuttings, laboratory-generated synthetic rock samples , sand packs and cemented packs. 6. Computer-implemented method of operating a computer to calculate a formation factor for a rock system comprising a clay mineral, the method characterized by comprising: constructing a model representation of a molecular fluid system, comprising: a plurality of molecular fluid unit cells filling a selected volume; and localized interstitial ions disposed in the volume in a concentration corresponding to a selected charge density; assign force field parameters to the model representation; operating the computer system to perform a molecular dynamics simulation of the equations of motion over a selected period of time to determine the positional coordinates of a plurality of species in the model representation at a plurality of times in the duration of time; calculating self-diffusion coefficients for one or more of the species from the positional coordinates at the plurality of times; calculate the mass conductivity of the molecular fluid system from the self-diffusion coefficients; determine an ion conductivity for the clay mineral; and calculate the formation factor as a ratio of the total conductivity of the molecular fluid system to the ionic conductivity for the clay mineral; determine at least one petrophysical property of the rock system based on the formation factor; and evaluating an onshore hydrocarbon reservoir based on at least one petrophysical property of the rock system. 7. Computer-implemented method, according to claim 6, characterized in that the determination of an ionic conductivity for the clay mineral comprises: constructing a molecular representation of the clay mineral, comprising: an anhydrous structure of atoms arranged in a plurality of parallel layers, the anhydrous structure including substitution sites in place of metal atoms in the structure in a concentration corresponding to a selected charge density; counterions of at least one species disposed in an interlayer space between layers of the anhydrous structure, in a concentration corresponding to the selected charge density; and a plurality of water molecules disposed in the interlayer space; assign force field parameters to the molecular representation in combination with boundary conditions corresponding to a selected pressure and temperature condition of the clay mineral; operating the computer system to perform a molecular dynamics simulation of the equations of motion over a simulation time interval to determine positional coordinates of counterions in the representation at a plurality of times during the simulation time interval; calculating self-diffusion coefficients for one or more of the counterion species from the positional coordinates at the plurality of times; and calculate ion conductivities for a kind of counter-ions from the self-diffusion coefficients. 8. System for analyzing material samples, the system characterized by comprising: an imaging system configured to produce a representative digital image volume of a material sample; and a computer system coupled to the imaging device and comprising: one or more processors; and one or more memory devices, coupled to one or more processors, storing program instructions that, when executed by the one or more processors, cause the one or more processors to analyze a rock sample comprising a clayey component by performing a plurality of operations comprising: segmenting a digital image volume corresponding to one or more tomographic images of the rock sample, to associate voxels in the digital image volume with pore space, solid material or a clayey component with an estimated conductivity; and assigning a relative conductivity value to voxels corresponding to the clayey component in relation to the conductivity of a fluid occupying the pore space of the sample; determine at least one petrophysical property of the rock sample based on an analysis of a volume representation of the digital image; and evaluating an earth hydrocarbon reservoir based on at least one petrophysical property of the rock sample. 9. System, according to claim 8, characterized in that the plurality of operations further comprises the operation of estimating the conductivity of the clay component by a plurality of operations comprising: building a molecular representation of the clay component, comprising: a anhydrous structure of atoms disposed in a plurality of parallel layers, the anhydrous structure including substitution sites in place of metal atoms in the structure in a concentration corresponding to a selected charge density; counterions of at least one species disposed in an interlayer space between layers of the anhydrous structure, in a concentration corresponding to the selected charge density; and a plurality of water molecules disposed in the interlayer space; assign force field parameters to the molecular representation in combination with boundary conditions corresponding to a selected pressure and temperature condition of the clay mineral; performing a molecular dynamics simulation of the equations of motion over a simulation time interval to determine positional coordinates of counterions in the representation at a plurality of times during the simulation time interval; calculating self-diffusion coefficients for one or more of the counterion species from the positional coordinates at the plurality of times; and calculate ion conductivities for a kind of counter-ions from the self-diffusion coefficients. 10. System for analyzing material samples, the system characterized by comprising: an imaging system configured to produce a digital image volume representative of a material sample; and a computer system coupled to the imaging device and comprising: one or more processors; and one or more memory devices, coupled to one or more processors, storing program instructions that, when executed by the one or more processors, cause the one or more processors to calculate a formation factor for a rock system comprising a clay mineral performing a plurality of operations comprising: constructing a model representation of a molecular fluid system, comprising: a plurality of molecular fluid unit cells filling a selected volume; and localized interstitial ions disposed in the volume in a concentration corresponding to a selected charge density; assign force field parameters to the model representation; performing a molecular dynamics simulation of the equations of motion over a selected period of time to determine the positional coordinates of a plurality of species in the model representation at a plurality of times in the time duration; calculating self-diffusion coefficients for one or more of the species from the positional coordinates at the plurality of times; then calculate the bulk conductivity of the molecular fluid system from the self-diffusion coefficients; determine an ion conductivity for the clay mineral; calculate the formation factor as a ratio of the total conductivity of the molecular fluid system to the ionic conductivity for the clay mineral; determine at least one petrophysical property of the rock system based on the formation factor; and evaluating an onshore hydrocarbon reservoir based on at least one petrophysical property of the rock system. 11. System, according to claim 10, characterized in that the operation of determining an ionic conductivity for the clay mineral comprises: building a molecular representation of the clay mineral, comprising: an anhydrous structure of atoms arranged in a plurality of parallel layers, the anhydrous structure including substitution sites in place of metal atoms in the structure in a concentration corresponding to a selected charge density; counterions of at least one species disposed in an interlayer space between layers of the anhydrous structure, in a concentration corresponding to the selected charge density; and a plurality of water molecules disposed in the interlayer space; assign force field parameters to the molecular representation in combination with boundary conditions corresponding to a selected pressure and temperature condition of the clay mineral; performing a molecular dynamics simulation of the equations of motion over a simulation time interval to determine positional coordinates of counterions in the representation at a plurality of times during the simulation time interval; calculating self-diffusion coefficients for one or more of the counterion species from the positional coordinates at the plurality of times; and calculate ion conductivities for a kind of counter-ions from the self-diffusion coefficients.