A crm, system and method for multiphase solutions for core analysis

Abstract

The invention provides CRM, system and method for estimating a residual saturation and for estimating a time duration to achieve a predetermined production or estimating a production given a predetermined time duration in a core analysis and / or a reservoir matrix block system, wherein estimating the residual saturation uses a trendline method relating steady state average saturation and inverse rotational speed squared, and estimating a time duration or production comprises estimating a wetting fluid transient state saturation profile to be a compression of a steady state profile of the corresponding system.

Description

[0001]A CRM, SYSTEM AND METHOD FOR MULTIPHASE SOLUTIONS FOR CORE ANALYSIS Background Multiphase flow in porous media may be characterised by saturation functions describing how fluids interact relative to their single-phase behaviour. This governs force-flux relations, fluid distributions and flow, storage, and production and must be taken into account in models describing hydrocarbon production, CO2 and hydrogen storage and trapping in porous formations. Saturation functions are measured as part of special core analysis. Centrifuge experiments are conducted on core plugs and provide information for calculating capillary pressure- and relative permeability saturation functions, wettability (indexes), residual saturations and capillary desaturation behaviour. After spontaneous imbibition or spontaneous drainage, the core can be placed in a centrifuge which exerts gravitational forces on the core by rotation to perform forced displacement. High density fluid will seek to bypass low density fluid towards the outer radius. Depending on boundary conditions (whether the core is surrounded by the dense or light fluid), this either forces high density fluid into or out of the core (respectively). The outlet side of the core may be described having a zero capillary pressure boundary condition. This capillary end effect may cause fluid accumulation of the displaced phase. Capillary forces resist the displacement, and a balance is reached with the gravitational forces at a specified rotational speed. Varying the rotational speed results in different amounts of fluid production which only depends on the capillary pressure function as the unknown. Since the capillary pressure distribution is exactly known at equilibrium, the capillary pressure function can be calculated if the in-situ saturation distribution is measured (but that requires specialized equipment and typically only average saturation data is collected). During the centrifuge test, higher speeds exert stronger gravitational forces on the fluids, resulting in large Bond numbers (ratio of gravitational to capillary forces). It may not be desirable to initiate capillary desaturation, where the residual saturation begins to reduce. Contrarily, it can be advantageous to know when the residual saturation is obtained or be able to estimate it accurately before it becomes altered. Residual saturation is the saturation where a fluid loses connectivity and can no longer flow. Obtaining this saturation is challenging as the capillary end effect causing outlet fluid accumulation theoretically only vanishes at infinite rotational speed. However, in practice there are limitations on the actual speed that can or should be applied during experiments. Practical speed limitations include maintaining core integrity and avoiding unrepresentative capillary desaturation. In particular, in tight or strongly wetted media the capillary forces are strong and more challenging to overcome. It is an object of the invention to provide computer readable media having instruction thereon which, when executed on a processor perform the tasks of accurately calculating a residual saturation in a core sample, and optionally said computer readable media having further instructions which interact with a centrifuge experiment assembly and control a rotational speed of said assembly and / or control a timing of speed variation of said assembly. It is a further object of the invention to provide a system having the computer readable media. It is a yet further object of the invention to provide a method for accurately calculating a residual saturation in a core sample, and optional for controlling a rotational speed of said assembly and / or controlling a timing of speed variation of said assembly. It is an object of the invention that the computer readable media, system and method herein overcome some of the above-described challenges. Summary of the Invention According to a first aspect of the invention, there is provided a computer readable medium for measuring a residual saturation of a core sample comprising instructions that, when executed on a processor, perform the tasks of: obtaining wetting fluid production against rotational speed at the plurality of rotational speeds; calculating a steady state average saturation at each of the plurality of rotational speeds, using the obtained wetting fluid production against rotational speed at the plurality of rotational speeds; calculating a trendline representing a relationship between the steady state average saturation and inverse rotational speed squared; extrapolating the trendline to a steady state average saturation value representing infinite rotational speed, the value of said steady state average saturation value representing the residual saturation of the core sample from which the production data was obtained. The computer readable medium may comprise further instructions that, when executed on a processor, perform the tasks of: plotting at least three data points corresponding to steady state average saturation values at corresponding highest rotational speeds in the plurality of rotational speeds; and calculating a line of best fit through the at least three data points; in order to perform the task of calculating the trendline representing a relationship between steady state average saturation and inverse rotational speed squared. The computer readable medium may comprise further instructions that, when executed on a processor, perform the tasks of: identifying a plateau in the relationship between wetting fluid production against time at each rotational speed; and using the wetting fluid production value corresponding to the plateau for each rotational speed to calculate the corresponding average wetting fluid saturation associated with each rotational speed; in order to perform the task of retrieving a steady state average saturation at each of the plurality of rotational speeds. The computer readable medium may comprise further instructions that, when executed on a processor, performs the task of calculating a speed required to achieve residual saturation using the trendline. The computer readable medium may comprise further instructions that, when executed on a processor, performs the task of comparing datapoints with the trendline to identify capillary desaturation, wherein datapoints falling below the trendline indicate capillary desaturation. The computer readable medium may comprise further instructions that, when executed on a processor, perform the task of calculating at least one parameter for use in reservoir engineering, the at least one parameter comprising: a quantity of recoverable oil / gas; an amount of storable CO2; using the calculated residual saturation. According to a second aspect of the invention, there is provided a system for measuring a residual saturation of a core sample comprising: a processor; a storage module; and a calculation module comprising the computer readable medium of the first aspect of the invention. The system may further comprise a measuring module to measure wetting fluid production against rotational speed at a plurality of rotational speeds; wherein the measured data of wetting fluid production against rotational speed at a plurality of rotational speeds is stored in the storage module. The calculation module may be further configured to measure a level of consistency around the trendline to determine whether the measured data is within a threshold level of consistency. The measuring module may further comprises a centrifuge experiment assembly. The centrifuge experiment assembly may be for a forced imbibition experiment. The centrifuge experiment assembly may be for a forced drainage experiment. According to a third aspect of the invention there is provided a method for estimating a residual saturation comprising: obtaining centrifuge production data at a plurality of rotational speeds; retrieving a steady state average saturation at each of the plurality of rotational speeds; calculating a trendline representing a relationship between the steady state average saturation and inverse rotational speed squared; extrapolating the trendline to a steady state average saturation value representing infinite rotational speed, the value of said steady state average saturation value representing the residual saturation of a core sample from which the production data was obtained. Calculating the trendline representing a relationship between steady state average saturation and inverse rotational speed squared may comprise: plotting at least three data points corresponding to steady state average saturation values at corresponding highest rotational speeds in the plurality of rotational speeds; and calculating a line of best fit through the at least three data points. Obtaining centrifuge production data at a plurality of rotational speeds may comprise: obtaining data for a relationship between wetting fluid production against time at the plurality of rotational speeds. The data of wetting fluid production against time may be obtained by performing a centrifuge experiment. The centrifuge experiment may be a forced imbibition experiment. The centrifuge experiment may be a forced drainage experiment. Retrieving a steady state average saturation at each of the plurality of rotational speeds may comprise: identifying a plateau in the relationship between wetting fluid production against time at each rotational speed; and using the wetting fluid production value corresponding to the plateau for each rotational speed to calculate the corresponding average wetting fluid saturation associated with each rotational speed. The method of the third aspect may further comprise using the trendline to calculate a speed required to achieve residual saturation. The method of the third aspect may further comprise comparing datapoints with the trendline to identify capillary desaturation, wherein datapoints falling below the trendline indicate capillary desaturation. According to a fourth aspect of the invention there is provided a computer readable medium for estimating a time duration to achieve a predetermined production or estimating a production given a predetermined time duration in a core analysis and / or a reservoir matrix block system, the computer readable medium with instructions that, when executed on a processor perform the task of: providing at least one wetting fluid steady state saturation profile of the system, said at least one wetting fluid steady state saturation profile being invariant; estimating a wetting fluid transient state saturation profile to be a compression of the at least one steady state profile and thereby solving associated differential equations using associated boundary conditions and initial conditions of the corresponding system. A core analysis experiment method associated with the system may comprise: core flooding; spontaneous imbibition; gravity drainage; and / or centrifuge. The associated differential equation may be a mass balance equation according to: ^^ ^^^^^^^^= − ^^^^^^^^, ( ^^ = ^^, ^^) integrated to be evaluated on an average saturation over the core; and wherein the boundary conditions and saturation profile are used to determine a pressure drop across the core for different speeds. The at least one wetting fluid steady state saturation profile may be assumed to be invariant within the system. The computer readable medium of the fourth aspect may further comprise instructions that, when executed on a processor perform the tasks of: determining one of the desired production or the predetermined time duration; and using said one of the determined production or the predetermined time duration in the equation: ^^ = ^^ ^^ + ^^ ln(1 − ^^)wherein a and b are parameters that are dependent on the specific core analysis experiment methods, the initial state, applied conditions corresponding to the specific core analysis experiment methods, system parameters; and wherein X is a scaled production and / or pressure drop; to calculate an estimate of the other of the time duration to achieve the predetermined production or the production at the given time duration, respectively. The scaled production may have a value between 0 and 1, 0 representing a start of a new experimental setting and 1 representing equilibrium of the new experimental setting; the computer readable medium having further instruction that, when executed on a processor perform the tasks of setting the scaled production to a value between 0.9 and 0.999 to provide a time scale for when each experimental setting has completed its production. The specific core analysis experiment methods may be a centrifuge experiment; wherein wherein ^^ is porosity, Δ ^^^^is a change in saturation production, ^^ is core length, ^^ is absolute permeability, ^^ is rotation speed of the centrifuge experiment, ^^^^is arm length (distance to core centre), Δ ^^ is fluid density difference, ^^^^∗^^is initial fractional distance from an outlet of an end effect, ^^ is a mobility ratio, ^^∗^^is oil mobility at the residual saturation, and ^^^^^^ ^^ ^^is characteristic flow function value of ∗ ^^∗^^^^1 the end effect profile and wherein ^^^^ is the equilibrium end position of the end effect profile. According to a fifth aspect of the invention there is provided a system for estimating a time duration to achieve a predetermined production or estimating a production given a predetermined time duration in a core analysis and / or a reservoir matrix block system, comprising: a processor; a storage module; and a calculation module comprising the computer readable medium of the fourth aspect. According to a sixth aspect of the invention there is provided a method for estimating a time duration to achieve a predetermined production or estimating a production given a predetermined time duration in a core analysis and / or a reservoir matrix block system comprising: identifying at least one wetting fluid steady state saturation profile of the system; assuming said at least one wetting fluid steady state saturation profile to be invariant; estimating a wetting fluid transient state saturation profile to be a compression of the at least one steady state profile and thereby solving associated differential equations using associated boundary conditions and initial conditions of the corresponding system. A core analysis experiment method associated with the system may comprise: core flooding; spontaneous imbibition; gravity drainage; and / or centrifuge. The associated differential equation may be a mass balance equation according to: ^^ ^^^^^^^^= − ^^^^^^^^,(^^ = ^^, ^^)integrated to be evaluated on an average saturation over the core; and wherein the boundary conditions and saturation profile are used to determine a pressure drop across the core for different speeds. The at least one wetting fluid steady state saturation profile may be assumed to be invariant within the system. The method of the sixth aspect may further comprising: determining one of the desired production or the predetermined time duration; and using said one of the determined production or the predetermined time duration in the equation: ^^ = ^^ ^^ + ^^ ln(1 − ^^)wherein a and b are parameters that are dependent on the specific core analysis experiment methods, the initial state, applied conditions corresponding to the specific core analysis experiment methods, system parameters; and wherein X is a scaled production and / or pressure drop; to calculate an estimate of the other of the time duration to achieve the predetermined production or the production at the given time duration, respectively. The scaled production may have a value between 0 and 1, 0 representing a start of a new experimental setting and 1 representing equilibrium of the new experimental setting; further comprising setting the scaled production to a value between 0.9 and 0.999 to provide a time scale for when each experimental setting has completed its production. The specific core analysis experiment methods may be a centrifuge experiment; wherein wherein ^^ is porosity, Δ ^^^^is a change in saturation production, ^^ is core length, ^^ is absolute permeability, ^^ is rotation speed of the centrifuge experiment, ^^^^is arm length (distance to core centre), Δ ^^ is fluid density difference, is initial fractional distance from an outlet of an end effect, ^^ is a mobility ratio, ^^∗^^is oil mobility at the residual saturation, and ^^^^^^ ^^ ^^is characteristic flow function value of the end effect profile and wherein ^^^^∗^^ is the equilibrium end position of the end effect profile. Brief Description of the Drawings Fig.1 is a flowchart of a method for estimating a residual saturation; Fig.2a shows an experimental setup of a centrifuge experiment; Fig.2b shows an enlargement of a core holder of the centrifuge experiment; Fig.2c shows a graphical representation of a centrifuge experiment; Fig.3 is a graphical representation of a relationship between water production against time at a plurality of rotational speeds; Fig.4 shows a graphical representation of the average saturation- inverse square rotational speed trendline; Fig.5a shows an equilibrium saturation profile depending on rotational speed for primary drainage; Fig.5b shows a graphical representation of the average saturations plotted against inverse square rotational speed for primary drainage data; Fig.5c is an enlargement of a section of fig.5b; Fig.6a shows an equilibrium saturation profile depending on rotational speed for secondary drainage; Fig.6b shows a graphical representation of the average saturations plotted against inverse square rotational speed for secondary drainage data; Fig.6c is an enlargement of a section of fig.6b; Fig.7 shows a graphical representation of steady state average saturations against inverse square rotational speed from real experiment data from a forced imbibition centrifuge experiment; Fig.8 shows a graphical representation of steady state average saturations against inverse square rotational speed from real experimental data from a secondary drainage centrifuge experiment; Fig.8b is a schematic diagram of a system for measuring a residual saturation of a core sample according to the invention; Fig.9a shows a graphical representation of scaled production against scaled time; Fig.9b shows a graphical representation of scaled production against scaled time; Fig.10 shows a method for estimating a time duration to achieve a predetermined production or estimating a production given a predetermined time duration in a core analysis and / or a reservoir matrix block system; and Fig.11 is a schematic diagram of a system for estimating a time duration to achieve a predetermined production or estimating a production given a predetermined time duration in a core analysis and / or a reservoir matrix block system. Definitions Unless otherwise defined, all terms of art, notations and other scientific terms or terminology used herein are intended to have the meanings commonly understood by those of skill in the art to which this invention pertains. In some cases, terms with commonly understood meanings are defined herein for clarity and / or for ready reference, and the inclusion of such definitions herein should not necessarily be construed to represent a substantial difference over what is generally understood in the art. In this text, the term ‘residual saturation’ refers to a saturation wherein fluid loses connectivity and can no longer flow. In this text, the term ‘primary drainage’ refers to the process of displacing wetting fluid (e.g., water) from a porous rock sample (core) initially fully saturated with said wetting fluid where the displacing fluid is non-wetting (e.g., oil or gas). During primary drainage, the wetting fluid is forced into the pore space of the rock sample by increasing the rotation speed of the centrifuge and displaces mobile wetting fluid from the core. The process continues until all of the mobile non-wetting fluid is displaced and the rock is completely saturated with the non-wetting fluid except for the residual saturation of wetting fluid. In this text, the term ‘steady state average saturation’ or ‘equilibrium average saturation’ refers to the spatially averaged fluid saturation (e.g., water, oil, or gas) in a porous rock sample (core) that has reached a stable state under centrifugal force, wherein the saturation does not change with time. In this text, the term ‘forced imbibition’ refers to a laboratory process that involves displacing non-wetting fluid (e.g., oil) with wetting fluid (e.g., water) using centrifuge after spontaneous imbibition (capillary uptake of wetting fluid) has occurred. Sufficiently high centrifuge speed allows displacing the mobile content of non-wetting fluid such that the residual saturation of non-wetting fluid is reached in the core. In this text, the term ‘secondary drainage’ or ‘SD’ refers to the process after full primary drainage and imbibition cycles, when the core sample is initially saturated with wetting fluid (e.g., water) and residual non-wetting fluid. During secondary drainage, the wetting fluid is first displaced spontaneously with non-wetting fluid by capillary forces and then by forced displacement using centrifuge. After sufficient displacement has occurred, the wetting fluid becomes immobile and wetting phase residual saturation is obtained in the core. Detailed Description Estimating residual saturation Residual saturation is the saturation where a fluid loses connectivity and can no longer flow. Obtaining this saturation can be challenging. For example, as the capillary end effect causing outlet fluid accumulation theoretically only vanishes at infinite rotational speed. Practical speed limitations prevent obtaining a speed which is fast enough to obtain the residual saturation. Practical speed limitations may include maintaining core integrity and avoiding unrepresentative capillary desaturation. Figure 1 is a flow chart of a method 1 for accurately estimating a residual saturation. The method starts at step 10, wherein centrifuge production data is obtained. The production data may be obtained from prior experimental data or by performing new centrifuge experiments. In a centrifuge experiment, a cylindrical core is filled with wetting fluid and the core is rotated at a plurality of predetermined rotational speeds. The wetting fluid is pushed out by non-wetting fluid present in the core as a result of the centrifugal force. As the rotational speed is increased, the centrifugal force increases leading to a greater production of wetting fluid out of the core. Figure 2a show an experimental setup 200a of a centrifuge experiment. The experimental setup 200a comprises a centrifuge assembly having a rotor 202 connected to a core holder 204 and production detection device. The production detection device in figure 2a is a line scan camera 208 and the light source 210. With reference to figure 2b, the core holder 204 has a liquid production receptacle 212, a sleeve 214, a first end but 216, a second end butt 218, a spacer 220, a sidearm 222 and a sleeve pressure support 224. A core plug 226 is held within the sleeve 214. The centrifuge assembly may have a plurality of core holders to hold a corresponding plurality of core plugs. The centrifuge technique consists of rotating the core plugs 226 at increasing rotational speeds to measure fluid production. Measurements are preferably made with two or more fluids in the pore space. Core holders 204 can be configured for drainage or imbibition tests with a denser phase, for example water, changing places with a less dense phase, for example oil or gas. Fluid production is measured as a steady state average saturation is reached or can be estimated at every rotational speed. Equilibrium / steady state saturation is determined when fluid production ceases at each rotational speed. This method enables measurement of small increments of fluid production. Production volumes can be measured with an automated data acquisition system such as the line scan camera 208. Figure 2c shows a graphical representation 200b of a centrifuge experiment. Multiphase flow of oil (o) and water (w) is considered in a core aligned along a rotating axis x, overlapping the centrifuge arm. The core is an incompressible, homogeneous porous medium and the fluids are immiscible and incompressible. The invention described herein follows from the same assumptions that are normally applied to model these experiments. These assumptions include: constant fluid and rock properties, the same capillary pressure function during the duration of the experiment, that steady state production is achieved or can be estimated at each rotation speed. The constant fluid properties include fluid densities. The rock properties include permeability and porosity. The residual saturation should remain a constant throughout the duration of the method 1 i.e. capillary desaturation should not have occurred. Thus, if there is a deviation from the trend line, this provides an indication of capillary desaturation. Using the above assumptions that are normally applied to model these experiments, the method ensures there are no significant limitations in applying the method of the invention to estimate the residual saturation. Using the above assumptions that are normally applied to model these experiments allows the method 1 to be applied in all cases of adequate rotational speed as outlined herein. The system is described by the following mass conservation equations: ( 1) and Darcy’s law in a rotating system: ( 2) The term ω2x denotes gravitational acceleration induced by circular rotation at angular rotational speed ω at a distance x from the rotation centre. ϕ is porosity, sisaturation, ui Darcy velocity, K absolute permeability, λi mobility, kri relative permeability, μi viscosity and pi pressure of phase i. x increases outwards. Let the core be defined over r1<x<r2where r1is closest to the rotation axis and L=r2-r1is the core length. Volume conservation and capillary pressure constraints state that: ( 3) Solving the stated equations with representative initial and boundary conditions results in solutions of saturation and pressure as function of position and time. Centrifuge is applied to cause forced displacement. A typical initial condition is a uniform saturation corresponding to zero capillary pressure which correlates with the start of primary drainage or the saturation following spontaneous imbibition or spontaneous secondary drainage. For drainage, an oil-water interface giving a zero capillary pressure boundary condition is placed at x=r2 and oil has hydrostatic pressure outside the core. Increasing the rotational speed causes oil to enter at x=r1 and water to leave at x=r2resulting in increased capillary pressure in the core. For imbibition, an oil-water interface is located at x<r1 and water has hydrostatic pressure outside the core. Increased rotation causes water to enter at x=r2and oil to be produced into the water phase at x=r1 where the capillary pressure is zero. In both cases, a zero capillary pressure boundary condition at the outlet is applied and both capillary pressures are set to zero there for reference. A phase bypassing the core and being exposed to the opposite core side, i.e., the core inlet, has hydrostatic pressure and phase continuity with the core at said core inlet. The other phase does not have pressure continuity there and its pressure changes according to capillary pressure as a function of saturation. These boundary conditions for drainage may be described as: ( 5) For imbibition the boundary conditions may be described as: ( 7) At equilibrium, fluxes of both phases are zero and the gravitational and capillary forces balance. Pressure distributions vary as: ( 8) Subtracting the water pressure distribution from the oil pressure distribution gives the capillary pressure distribution: ( 9) Applying the boundary conditions gives the following equilibria for drainage and imbibition: ( 10) Higher rotational speed ω gives stronger positive capillary pressure for drainage and stronger negative capillary pressure for imbibition, while keeping a zero capillary pressure at the producing side. Capillary pressure and saturation are related by a function Pcimb(sw) or Pcdr(sw). The capillary pressure distribution can thus be inverted to give saturations distributions and average saturation: ( 11) With further reference to figure 1, the method advances to step 20 wherein a steady state average saturation at each of the plurality of rotational speeds is retrieved. This may be achieved by calculating a relationship between water production against time at the plurality of rotational speeds. Wherein the relationship between water production against time plateaus, this is taken as the steady state average saturation at the corresponding rotational speed. A graphical representation 300 of the relationship between water production against time at the plurality of rotational speeds is given in figure 3. Plateaus at three highest rotational speeds in the experiment are shown at points 302, 304 and 306 on the graph 300. The plateau at rotational speed 1800 rotations per minute (RPM) is shown at 302, the plateau at rotational speed 2500RPM is shown at 304, and the plateau at rotational speed 3000RPM is shown at 306. Each rotational speed increase in the graph 300 is indicated with a vertical dashed line. Average saturation was measured once capillary equilibrium was reached at each rotational speed. The water production corresponding to the 1800 RPM plateau is around 0.27 (as a fraction of the pore volume) and occurs on approximately day 88 of the experiment. The water production corresponding to the 2500RPM plateau is around 0.365 and occurs on approximately day 105 of the experiment. The water production corresponding to the 3000RPM plateau is around 0.52 and occurs on approximately day 129 of the experiment. A time to reach equilibrium was dependent on the wettability preference and absolute permeability of the core samples, and spinning time varied from a few days to over a month at some rotational speeds. As shown in the graph 300, a more distinct plateau is observed at the higher rotational speeds. With further reference to figure 1, the method progresses to step 30 wherein a trendline for the relationship between the measured average saturation against an inverse of the square of the rotational speed is calculated. The linear trend is valid once the core saturation profile contains the residual saturation. Figure 4 shows a graphical representation 400 of the average saturation- inverse square rotational speed trendline. The average saturation values obtained from step 20 of the method are plotted against an inverse of the square of their corresponding rotational speed. For example, point A may be the measured average saturation corresponding to rotational speed 3000RPM, point B may be the measured average saturation corresponding to rotational speed 2500RPM, and point C may be the measured average saturation corresponding to rotational speed 1800RPM, from the values given in graph 300 of figure 3. With further reference to figure 1, the method advances to step 40 wherein the trendline is extrapolated to a steady state average saturation value representing infinite rotational speed. This is the steady state average saturation value wherein the inverse square rotational speed is equal to zero. Thus, and with further reference to figure 4, the line is extrapolated to where it intercepts with the y-axis of graph 400. In graph 400, the trendline 402 intercepts the y-axis at Swr. With further reference to figure 1, the method advances to step 50 wherein the extrapolated intercept value represents a residual saturation of the core sample from which the experimental data was obtained. The above solution can be supported by a mathematical approximation as shown below. Firstly, a simplifying assumption that gravitational acceleration is uniform for a n speed and approximated as ω21 give x≈ω2rm(where ^^^^= 2 ( ^^1+ ^^2)is the mid position of the core). The mean relative error in gravity acceleration can be defined as (ω2x-ω2rm) / (ω2rm)<L / (2rm), which can be minimised using short cores compared to centrifuge arm length. Less than 10% local error is achieved if, for example, L<0.03 m and rm>0.15 m. Repeating the derivation above through equations (1) to (11) with the uniformity assumption leads to the following equilibrium distribution of capillary pressure for drainage: The relation (11) still holds for calculating water saturation distribution and average saturation but is now based on capillary pressures in (12). A distance y of a capillary pressure can be expressed from the outlet. For two different rotational speeds ωa, ωbthe positions ya,ybof that capillary pressure are related, only by the rotational speed: This states that the profile is compressed according to the squared rotational speed and that the compression is the same for all capillary pressures. Equivalently, the saturation profile is compressed uniformly and maintains its shape. Saturations and capillary pressures are uniquely related by the function Pc (sw). It is then assumed that there is a capillary pressure Pc*at which sw≈swr. The rotational speed is deemed to be sufficiently high that this capillary pressure exists in the core in the range of x*>x≥r1. The average saturation in the core swav can then be written as the spatially weighted sum of the residual saturation swrand the average saturation of the end effect profile ^^^^^^^,^^^^^^^. More simply it can be phrased as: where Y* is the scaled distance of the capillary pressure Pc* (and the residual saturation) from the outlet. Based on (13), that scaled position is a constant divided by the squared rotational speed ω. The average saturation can then be written as: ( 16) The above equation (16) demonstrates that plotting steady state average saturation against squared inverse rotational speed 1 / ω2yields a straight line where the intercept at 1 / ω2=0 is the residual saturation swr. According to a second aspect of the invention, there is provided a computer readable medium for measuring a residual saturation of a core sample comprising instructions that, when executed on a processor, perform the tasks of method 1. Figure 8b is a schematic diagram of a system 900 for measuring a residual saturation of a core sample according to the invention. The system 900 has a processor P, a storage module SM, and a calculation module CM. The calculation module CM has the computer readable medium described above having instruction for carrying out steps 10, 20, 30, 40, 50 and 60 of the method described above. The CRM and system 900 are configured to carry out the method of the invention described herein. The invention described herein follows from theory under the same assumption that are normally applied to model these experiments. These assumption include: constant fluid and rock properties, the same capillary pressure function during the duration of the experiment, that steady state production is achieved or can be estimated at each rotation speed. The constant fluid properties include fluid densities. The rock properties include permeability and porosity. The residual saturation remains a constant throughout the duration of the method 1. In other words, capillary desaturation has not occurred and, thus, if there is a deviation from the trend line, this provides an indication of capillary desaturation. Using the above assumptions that are normally applied to model these experiments, the method ensures there are no significant limitations in applying the method of the invention to estimate the residual saturation. Using the above assumptions that are normally applied to model these experiments allows the method 1 and associated system 900 to be applied in all cases of adequate rotational speed as outlined herein. Example 1 The above method was tested using simulation data. A simulation was carried out using a two-phase core flooding simulator software. The two-phase core flooding simulator software used was Sendra®. Sendra® software is a two-phase core flooding simulator designed to simulate and verify special core analysis laboratory (SCAL) experiments. It covers all common experimental approaches including unsteady-state and steady-state flow experiments, single- and multi-speed centrifuge experiments, as well as porous plate experiments. Sendra® can be utilised for oil-water experiments as well as gas-oil or gas-water experiments, for both imbibition and drainage processes. Figure 5a shows an equilibrium saturation profile 500a, wherein a saturation profile is how the saturations are distributed along the core at a given time, depending on rotational speed for primary drainage resulting from a primary drainage Sendra® simulation experiment. The simulation experiment was carried out for a rotational speed range of = 10 ^^1.5rads-1(where ^^ = 1: 15 is the curve number) and for assumed uniform gravity. The simulation experiment was then repeated across the same rotational speed range as above for non-uniform gravity cases wherein ^^^^= 0.15 and 0.75, wherein ^^^^= ( ^^1+ ^^2) and ^^ is the centrifuge arm length. For the above simulation experiments including the uniform gravity case and the two non-uniform gravity cases, the average saturations were plotted against inverse square rotational speed to give rise to graph 500b in figure 5b. As is demonstrated in figure 5b, for all of the gravity cases, the data points fall on a straight line at high rotational speed. The straight lines can be extrapolated to an intercept that is equal to the residual saturation. Thus, the validity of the intercept method is demonstrated by the simulation experiments. Furthermore, the simulation experiments demonstrate that the method described herein is applicable to non-uniform gravity scenarios. In the simulation experiments of example 1, trendlines were regressed based on 8 data points with highest rotational speed and extrapolated to higher and lower speeds. Trendline 502 represents the relationship between average water saturation against inverse square rotational speed for the uniform gravity case. Trendline 504 represents the relationship between average water saturation against inverse square rotational speed for the non-uniform gravity case wherein ^^ ^^^^= 0.15. Trendline 506 represents the relationship between average water saturation against inverse square rotational speed for the non-uniform gravity case ^^ wherein ^^^^= 0.75. Figure 5c shows an enlargement of a section of the graph 500b showing the 8 highest rotational speed data points a-h. The table below shows numbers based on linear regression of saturation based on all data points with rotational speed ^^ ≥ 226 rads-1(where the residual saturation exists in the core) for the experiment of example 1 wherein the water production phenomenon is through primary drainage. Table 1 Table 1 shows various measurement values demonstrating the accuracy of each of the trendline fit for the above simulation experiment and method. The trendline fit for the uniform case is described by a coefficient of determination (R2) values equal to 1.000and a root mean square error (RMSE) of 4.6e-6. For the extreme ^^ non-uniform gravity case where2^^^^= 0.75the R was 0.999 and the RMSE was 6.4e-4. These values indicate a more significant, but still very low, error when gravity is non-uniform. The difference between the intercept and the residual saturation was zero to four decimals with uniform gravity, and -0.0016 for the extreme non-uniform gravity case. Example 2 A further simulation experiment was carried out for secondary drainage using the Sendra® software. Figure 6a shows the equilibrium saturation profile depending on rotational speed for secondary drainage resulting for the Sendra® simulation experiment wherein a rotational speed range was = 10 ^^1.5rads-1(where ^^ = 1: 15 is the curve number). In a first experiment, uniform gravity was assumed. The simulation was then repeated for non-uniform gravity cases. For the non-uniform gravity cases 1 ^^^^= 0.15 and 0.75, wherein ^^^^= 2(^^1+ ^^2)and ^^ is the centrifuge arm length in a similar manner to the experiment for primary drainage. For the above simulation experiments including the uniform gravity case and the two non-uniform gravity cases, the average saturations were plotted against inverse square rotational speed to give rise to figure 6b. As is demonstrated in figure 6b, for all of the gravity cases, the data points fall on a straight line at high rotational speed. The straight lines can be extrapolated to an intercept that is equal to the residual saturation. Thus, the validity of the intercept method is demonstrated by the simulation experiments for secondary drainage. Furthermore, the simulation experiment demonstrate that the method described herein is applicable to non-uniform gravity scenarios. In the experiments of example 2, the lines were regressed based on 8 data points i-q with highest rotational speed and extrapolated to higher and lower speeds. The table below shows numbers based on linear regression of saturation based on of all data points with rotational speed ^^ ≥ 226 rads-1(where the residual saturation exists in the core) for the experiment of example 2 wherein the water production phenomenon is through secondary drainage. Table 2 Table 2 shows various measurement values demonstrating the accuracy of each of the trendline fit for the above simulation experiment 2 and method. The trendline fit for the uniform case is described by a coefficient of determination (R2) values equal to 1.000 and an RMSE of 3.7e-6. For the extreme non-uniform gravity case where L / rm = 0.75 the R2was 0.999 and the RMSE was 4.7e-4. These values indicate a more significant, but still very low, error when gravity is non-uniform. The difference between the intercept and the residual saturation was zero with uniform gravity, and -0.0012 for the extreme non-uniform gravity case. At lower speeds the average saturation points fall below the straight lines. Example 3 In a further experiment, real experimental data from a secondary drainage centrifuge experiment was used in the method herein. In this real experimental data, composite exponential correlations were used to determine the equilibrium production for each speed. Based on this data, equilibrium average saturations were plotted against inverse square rotational speed to give rise to graph 700 in figure 7. The data at the four highest rotational speeds q-t were used in the forced imbibition data to create regression line 702. As shown in the graph 700, the four highest rotational speeds q-t align very well with the linear behaviour of the regression line 702. In the forced imbibition experiment the regression line 702 was determined with R2= 0.997 and an intercept (1 minus residual oil saturation) of 0.858 (i.e., sor=0.142). Example 4 In a further experiment, real experiment data from a forced imbibition centrifuge experiment was used in the method herein. In this real experimental data, composite exponential correlations were used to determine the equilibrium production for each speed. Based on this data, equilibrium average saturations were plotted against inverse square rotational speed to give rise to graph 800 in figure 8. Similarly to example 3, the data at the four highest rotational speeds u-y were used in the secondary drainage data to create regression line 802. Only the highest rate point u in the secondary drainage data appears to deviate significantly from the linear behavior of the regression line 802, while the others align very well. This deviation may be a result of inaccuracy or capillary desaturation. For SD the regression line 802 for secondary drainage was slightly less accurately determined than the regression line 702 for forced imbibition data with R2= 0.942 (0.983 excluding the last point) with an intercept of 0.0687 corresponding to the residual water saturation. In both examples 3 and 4, the experimental points that are not on the line show less change in saturation with speed than the extended line, in agreement with the model. The method indicates that when the residual saturation appears in the core the data become linear. The method described herein provides the benefit that of estimating a residual saturation of a core sample with integration or iterative calculations, providing a simplicity to the method which can be applied by a user without theoretical or technical expertise. Since the method focuses on estimating the residual saturation and not on other parameters, less uncertainty can be achieved. In contrast, with other methods such as numerical history matching, all the data must match and there may be uncertainty in all estimated input parameters. Thus, the method herein resolves the problem of the previous methods of finding the residual saturation wherein it can be unclear how many possible explanations exist for the residual saturation. Furthermore, the method can provide a quality check on the measured data in the form of the level of consistency around the trendlines. Yet further the measure can be used to obtain the residual saturation whilst preventing capillary desaturation and / or too high rates since the start of these phenomenon can be observed by data points falling below the resultant trendline, at which point the centrifuge experiment can be ceased to protect the integrity of the core sample. Another benefit to the method for estimating the residual saturation is that the method can also be used to directly determine the speed required to sufficiently reach said residual saturation without directly subjecting the core sample to said speed. The residual saturation estimated by the method described herein can then be used to calculate other important parameters for use in reservoir engineering such as how much oil / gas can be recovered, how much CO2 can be stored, reserve estimates, and initial experimental conditions. Furthermore, measurements of the residual saturation can be used in real time when carrying out a core analysis experimentation by identifying when a next speed in the experiment should be set and additionally what next speed to use. Interpreting transient core analysis data In another aspect of the invention, a method is provided for approximate solutions for how production varies as a function of time. This is achieved by considering driving forces and mobilities of different parts of a core and evaluating how displacement occurs. This can be used to determine timescale trends in the shape of production profiles. Different types of core analysis experiments provide different type of data, however, most core analysis experiments provide a production as a function of time. Core flooding also provides a pressure drop as a function of time. Common core analysis experiments that apply to both simple core plugs that can be tested in the lab, and also larger matrix blocks that can be found in the reservoir include core flooding, spontaneous imbibition, gravity drainage and centrifuge. All of these core analysis experiments have an interplay between competing mechanisms. In core flooding, there is typically attractive forces from injecting a fluid into the core which applies a pressure drop. This pressure drop is resisted by capillary forces that try to trap one of the present fluids. For spontaneous imbibition, a capillary force tries to take up a high-density fluid which is resisted by gravity. This can apply to production of oil and gas, hydrogen storage, and CO2. For gravity drainage, it is gravity that causes the production and capillary forces that resist the production which act to keep fluid inside the reservoir. Again, this can apply to production of oil and gas, hydrogen storage, and CO2provided compressibility is accounted for. For centrifuge as described above, gravity forces are manipulated by changing the speed of rotation, and the production is resisted by the capillary forces in the system. For each case, considering the described competing forces, the method estimates the effect of moving out of an initial state e.g., a previous steady state or the path towards a steady state, by changing a magnitude of one of the competing forces and predicting how the system will respond. In the example of a centrifuge, this can be a response to changing the rotation speed. In the example of core flooding then it can be a response to changing an injection rate. A main assumption of the method of the present invention is that each system has well defined steady state fluid profiles which are substantially compressions of the same identical profile. For some of the systems the invariance of the steady state profiles is exact or it follows theoretically by making reasonable approximations. The method generalises for the case where the invariant profile is not within the system. Thus, the method is substantially valid, i.e., a good approximation, to the more general case. However, provided the profile is directly compressed and with the assumption that it is compressed during the production, then the solutions will be sufficient. Figure 10 shows a method for estimating a time duration to achieve a predetermined production or estimating a production given a predetermined time duration in a core analysis and / or a reservoir matrix block system. At 110, at least one wetting fluid steady state saturation profile of the system is identified. At 120, it is assumed that said at least one wetting fluid steady state saturation profile is invariant. At 130, a wetting fluid transient state saturation profile is estimated to be a compression of the at least one steady state profile. At 140, associated differential equations are solved using associated boundary conditions and initial conditions of the corresponding system. In particular, the method 100 is for estimating a time duration to achieve a predetermined production or estimating a production given a predetermined time duration in a core analysis and / or a reservoir matrix block comprising: determining one of the desired production or the predetermined time duration; and using said one of the determined production or the predetermined time duration in the equation: ^^ = ^^ ^^ + ^^ ln(1 − ^^) ( 17) wherein a and b are parameters that are dependent on a specific fraction and rate considered through the initial and equilibrium state, and X is a scaled production and / or a pressure drop; to calculate an estimate of the other of the time duration to achieve the predetermined production or the production at the given time duration, respectively. The method assumes that the saturation profile of the system is invariant and is compressed when a larger external force is applied. A pure compression, meaning the shape is invariant, is proven theoretically and applies from one steady state to another. The method assumes that this also is the case between steady states, i.e. during the transient / production phase. This implies that the resulting correlation for how production changes with time can be applied from any time after a change in the external force is made. It can be applied immediately (initial time), even if the previous production state had not reached equilibrium, or it can be applied from a time after the change was made. The correlation can then be used to extrapolate production into future time and estimate the production after infinite time and the time scale required to achieve most of that production. For centrifuge, the parameter a is defined as: ( 18) Wherein ^^ is porosity, Δ ^^^^is a change in saturation production, ^^ is core length, ^^ is absolute permeability, ^^ is the rotation speed of the centrifuge experiment, ^^^^is arm length (distance to core centre), Δ ^^ is fluid density difference, ^^^^∗^^is the initial fractional distance from the outlet of the end effect, ^^ is the mobility ratio, ^^∗^^is the oil mobility at the residual saturation, and ^^^^^^ ^^ ^^is the characteristic flow function value of the end effect profile. ( 19) wherein ^^^^∗^^is the equilibrium fractional distance from the outlet of the end effect. The analytical solution that uses equation 17 is derived for transient production after the rotation speed is increased starting from an arbitrary initial state towards equilibrium. It is assumed that outlet profiles compress also during the transient stage. The two regions have fixed mobilities, while the regions occupy different lengths with time. As shown by equation 17, the method provides a relationship between time as a function of production and has a linear term and a logarithmic term, the logarithmic term dominating late time behaviour. With reference to figure 9a, the solution of equation ( 17) is plotted as X(T) in for different values. All solutions converge to the same unit slope curve at early times. Their later behavior depends strongly on ^^Δ. When ^^Δ→0, only the linear term is significant, and production is linear. Generally, the second term in ( 17) will begin to deviate from zero and add additional scaled time compared to the straight-line curve. From the definition of ^^Δ, and that ^^^^∗^^< ^^^^∗^^and ^^ > 0, the magnitude of ^^Δis related to mobility ratio M as: ( 20) At large mobility ratios the production is more linear. This happens when the invading phase (oil) has higher mobility than the displaced profile (the end effect). A mobility ratio greater than 1 may be expected since the end effect profile includes mobilities less than the end point mobility of oil. However, if water has much higher mobility than oil it can dominate the end effect mobility and give ^^ < 1. In that case the production rate declines with time and the decline from the initial rate is more if the mobility ratio is less. As a special case, = 1 which results if ^^ = 1 or if both the initial and final front positions are close to the outlet ( ^^^^∗^^≈ ≈ 1). Then ( 17) simplifies to exponential production: ( 21) which is given by the black curve in figure 9. In all cases, the production terminates as X→1 and the ln term approaches infinite time. With further reference to figure 5a and figure 6a, at the sufficiently high speed of 226 rads-1, residual water saturation is obtained at ^^ = ^^1and at even higher speeds, larger portions of the core are occupied with this saturation. At the higher speeds, the entire saturation profile is compressed equally towards the outlet. At lower speeds, only parts of the profile are equally compressed. Equation ( 17) is supported by the following mathematical derivation: Introduce first the scaled distance from the outlet ^^, and then scale this variable by the location of the front capillary pressure ^^^^∗to get variable ^^: ( 22) The positions closest to the inlet ^^1are defined over ^^∗ > ^^ > 1 and have (by assumption) constant saturation ^^^^ ^^, while the positions closest to the outlet ^^2are defined over 1 > ^^ > 0 where the capillary pressure distribution in terms of ^^ changes as: ^^^^(^^)= ^^ ^^^^∗,(0 < ^^ < 1)( 23) The capillary pressure thus changes linearly with ^^ from its max value ^^^^∗at the front ^^ = 1 to 0 at ^^ = 0, regardless of where the front ^^∗is. The saturation distribution, which is uniquely related to the capillary pressure, is thus also an invariant function of ^^. Adding Darcy’s law ( 2) for both phases gives an expression for total velocity which can be expressed with water- and capillary pressure gradients: ( 24) After expressing position as ^^, ^^^^on the left side of the front (low x) is given by: ( 25) where ^^∗^^is the oil mobility at ^^^^= ^^^^ ^^(also corresponding to the capillary pressure) ^^^^∗, which is constant in this region relative to the front position ^^∗. This expression is solved with respect to ^^^^^^^^: ( 26) As all the parameters in the expression are constants or functions of time (but not Z) it can be integrated directly to find the pressure difference over this region at an assumed total velocity: ( 27) where ^^^∗^= ^^^^(^^∗)and ^^^^1= ^^^^( ^^1). From this ^^^^can be expressed as function of the pressure difference across the region: ( 28) or in a simplified form: ^^^^= ^^1(^^ ^∗^− ^^^^1)^^ ^^∗ + ^^2, ^^1=^^, ^^2= ^^ ^^∗^^^^^^^2^^ ( ^^∗− 1) ^^^ ^^( 29) The constants ^^1and ^^2are positive. Considering next the total velocity expression on right side of the front (high x) and solving for the water pressure gradient: ( 31) To find the pressure difference over this region an integration over the pressure gradient is performed: ( 32) where ^^^^2= ^^^^( ^^2)and ^^^∗^= ^^^^( ^^∗). Since saturation has a unique spatial function of Z, the three integrals in ( 33) are constants and from their definition (mobilities and that capillary pressure increases away from the outlet during drainage), they are positive. To simplify the notation, ( 33) can be written as: ^^^^2− ^^^∗^= − ^^∗^^^^^^3+ ^^4+ ^^∗^^5( 33) The total velocity can be expressed as: ( 34) The total velocity is uniform across the system, which means it must be identical in the two regions (on opposite sides of the front) at all times (although it can change with time). Setting the expressions of ^^^^in ( 29) and ( 34) equal is expressed as: ( 35) Solving for the water pressure at the front gives: ( 36) The water pressure at the boundaries is known from the drainage boundary conditions and assumptions of high rotation speed. Firstly, ^^^^2= 0 (by reference) while ^^^^1is determined by the hydrostatic oil pressure and the capillary pressure at the inlet (which equals ^^^^∗): The expression of ^^^∗^is applied in either of the total velocity expressions resulting in: By setting ^^^^= 0, the equilibrium position ^^^^∗^^at the given rotation speed can be determined: Which gives a more simplified expression for the total velocity: M is defined as the ratio of end point oil mobility to the average total mobility of the end effect profile. As long as the current front position ^^∗is greater than the equilibrium position ^^^^∗^^, the velocity stays positive, and oil displaces water in positive x-direction. Integrating the water transport equation (1) and using that only one phase flows at each boundary, the average saturation is related to the total velocity by: ^^ ^^ ^^ =^^^^ ^^, ^^ ^^− ^^ ^^ ( 42) Then the relation between average saturation and front position in (14) gives: ( 43) where Δ ^^^^is the difference between the end effect average saturation ^^^^^^^,^^^^^^^(redefined above wrt a ^^ integral) and the residual water saturation ^^^^ ^^(obtained when the end effect is displaced). Combining Feil! Fant ikke referansekilden. with Feil! Fant ikke referansekilden. defines a differential equation relating ^^∗and ^^: = ^^Δ ^^^^^^ ( 44) After separation and integration while using that the front is at an initial position ^^^^∗^^at t=0 results in an expression of time t as function of the current position of the front ^^∗: ( 45) Define the scaled variable X as the scaled position of the front starting at 0 in the initial position (in) and ending at 1 in the equilibrium position (eq). The linear relations between ^^∗, ^^∗and average saturation ^^^^, ^^ ^^from (14) and (15) gives: ( 46) The solution ( 45) can then be expressed as: ( 47) Further, when ^^ ≈ 0, ≈ ^^. The terms can be grouped to those that are proportional to X at low X and to those that are not, and then write the solution as follows: ( 49) The method of providing an analytical transient solution is able to predict similar timescales and trends in time scale for example with rotation speed and viscosity as numerical simulations. The method of providing an analytical transient solution addresses the challenge related to centrifuge and core analysis in general of maximizing collection of valuable information within limited time. Often the steady state data gives the most relevant information as it allows interpretation with analytical methods depending on limited model parameters. However, rather than waiting for measurements to stabilise correlations can extrapolate limited data to predict the steady state values. Each system has very well-defined steady state fluid profiles and are basically compressions of the same identical profile and can be seen in figures 5a and 5b. With reference to figures 5a and 5b, for the high saturations, a higher speed simply compresses each saturation profile. For the lower saturation profiles, each saturation needs to have entered the core before it is compressed. Thus, the method is mainly valid when the entire profile has entered the core. However, from the state wherein there is an initial profile in the system and then that is displaced by a profile that is entering the system, having a varying mobility because the saturation is changing. It can be approximated to have a relatively constant mobility to provide a good approximation. The dashed line represents 226 rads-1. Each of the profiles to the right, replicate the 226 rads-1profile, however they have been compressed towards the right side. Thus, they have substantially identical shape, just squeezed towards the right side. This is also the case with the saturation profiles on the left side. However, the left side profiles go outside of the system. The method described herein focuses on what happens to the profiles that are limited to within the core. The 226 rads-1saturation profile is the first saturation profile wherein the lowest saturation appears in the core. Thus, the further right-side saturation profiles comprise the lowest residual saturation. Thus, on the right side of the 226 rads-1saturation profile the entire profile will be compressed, whereas on the left side of the 226 rads-1saturation profile only part of the profile is compressed, while the lowest saturations will still change. There will be lower saturations that are entering the core. In the example of figure 5a, the lowest saturation on that profile is just below 0.8. For the next rotation speed, new saturations are observed including those outside of the compression of that profile. Under the assumptions that the profile is compressed while it is moving from one state to the next, and considering the boundary conditions. and all the properties of the system, for example the saturation functions, viscosities, an approximate solution is achieved that doesn't make any further assumptions. The only main assumption of the method described herein is how the profile is moving. The method has been found to very well characterise the profile and describe an average behaviour. Although some deviations for some of the saturations may be observed, the average behaviour of the profile should be expected to move as described by this solution. The scaled production has a value between 0 and 1, 0 representing a start of a new experimental setting and 1 representing equilibrium of the new experimental setting; further comprising setting the scales production to 0.995 to provide a time scale for when each experimental setting has completed its production. At late times, the logarithmic term denominates and causes production to become exponential. This has the substantial effect of taking infinite time to complete the production. In practice however it takes finite time to complete almost all of the production. Thus, an experimental timescale ^^^^ ^^ ^^is also presented by the method of this invention for which 99.5% of scaled production is completed. ^^^^ ^^ ^^can be used to determine how long it will take for production to stabilise at a given experimental setting. A time scale ^^^^ ^^ ^^can be evaluated for when each experimental setting in practice has completed its production, by setting X=0.995 in equation ( 17) which results in: ( 50) As seen in figure 9b the solution predicts that the displacement of the end effect profile under constant driving force (rotation speed) results in a production profile vs time where the shape depends on the mobility ratio with clear limiting shapes. In one extreme, at high (displacing) oil mobility, the production rate is constant with time, while in the other case of high (displaced) end effect mobility, the production rate declines with time, more rapidly than exponential production. In comparison, during co-current spontaneous imbibition, the mobility ratio between the imbibing profile and the displaced non-wetting phase yields constant rate with time if the mobility ratio is 1, increasing rate if it is great than 1 and declining rate if it is less than 1 with a square root of time production profile as a limit. As discussed above, X defines the scaled production, such that when X is equal to 0 then this represents a start at the previous experimental setting. With further reference to figure 3, in the rotational speed section of 1800 RPM is starts to flatten out around 90 days. Thus, a new production period is starting at this point and X is equal to 0, and there is a new rotation speed of 2500 RPM. When the new equilibrium state is reached the production X is equal to 1. Thus, X represents a scaled production for given experimental settings. When new experimental settings are commenced, before an equilibrium is reached at these new equilibrium settings and the experiment is stopped, the corresponding scaled production X will have a value less than one. For example, assume a previous value of say 0.28, then the new value after a given elapsed time can be calculated. The scaled production value X can be utilised to later calculate a capillary pressure of the system. An aspect of the invention comprises a computer readable medium for estimating a time duration to achieve a predetermined production or estimating a production given a predetermined time duration in a core analysis and / or a reservoir matrix block system, the computer readable medium with instructions that, when executed on a processor perform method 100. Figure 11 is a schematic diagram of a system 1000 for estimating a time duration to achieve a predetermined production or estimating a production given a predetermined time duration in a core analysis and / or a reservoir matrix block system. The system 1000 has a processor P, a storage module SM and a calculation module CM. The calculation module CM comprising the computer readable medium with instructions that, when executed on a processor perform method 100. The CRM and system 1000 are configured to carry out the method of the invention described herein. Having described preferred examples of the invention it will be apparent to those skilled in the art that other embodiments incorporating the invention may be used. These and other examples of the invention illustrated above are intended by way of example only and the actual scope of the invention is to be determined from the appended claims. Statements of Invention 1. A computer readable medium for measuring a residual saturation of a core sample comprising instructions that, when executed on a processor, perform the tasks of: obtaining wetting fluid production against rotational speed at the plurality of rotational speeds calculating a steady state average saturation at each of the plurality of rotational speeds, using the obtained wetting fluid production against rotational speed at the plurality of rotational speeds; calculating a trendline representing a relationship between the steady state average saturation and inverse rotational speed squared; extrapolating the trendline to a steady state average saturation value representing infinite rotational speed, the value of said steady state average saturation value representing the residual saturation of the core sample from which the production data was obtained. 2. The computer readable medium of claim 1, comprising further instructions that, when executed on a processor, perform the tasks of: plotting at least three data points corresponding to steady state average saturation values at corresponding highest rotational speeds in the plurality of rotational speeds; and calculating a line of best fit through the at least three data points; in order to perform the task of calculating the trendline representing a relationship between steady state average saturation and inverse rotational speed squared. 3. The computer readable medium of claim 1 or claim 2, comprising further instructions that, when executed on a processor, perform the tasks of: identifying a plateau in the relationship between wetting fluid production against time at each rotational speed; and using the wetting fluid production value corresponding to the plateau for each rotational speed to calculate the corresponding average wetting fluid saturation associated with each rotational speed; in order to perform the task of retrieving a steady state average saturation at each of the plurality of rotational speeds comprises. 4. The computer readable medium of any preceding claim, comprising further instructions that, when executed on a processor, performs the task of calculating a speed required to achieve residual saturation using the trendline. 5. The computer readable medium of any preceding claim, comprising further instructions that, when executed on a processor, performs the task of comparing datapoints with the trendline to identify capillary desaturation, wherein datapoints falling below the trendline indicate capillary desaturation. 6. The computer readable medium of any preceding claim, comprising further instructions that, when executed on a processor, perform the task of calculating at least one parameter for use in reservoir engineering, the at least one parameter comprising: a quantity of recoverable oil / gas; an amount of storable CO2; using the calculated residual saturation. 7. A system for measuring a residual saturation of a core sample comprising: a processor; a storage module; and a calculation module comprising the computer readable medium of any of claims 1 to 6. 8. The system of claim 7 further comprising a measuring module to measure wetting fluid production against rotational speed at a plurality of rotational speeds; wherein the measured data of wetting fluid production against rotational speed at a plurality of rotational speeds is stored in the storage module. 9. The system of claim 7 or 8, wherein the calculation module is further configured to measure a level of consistency around the trendline to determine whether the measured data is within a threshold level of consistency. 10. The system of claim 9, wherein the measuring module further comprises a centrifuge experiment assembly. 11. The system of claim 10, wherein the centrifuge experiment assembly is for a forced imbibition experiment. 12. The system of claim 10, wherein the centrifuge experiment assembly is for a forced drainage experiment. 13. A method for estimating a residual saturation comprising: obtaining centrifuge production data at a plurality of rotational speeds; retrieving a steady state average saturation at each of the plurality of rotational speeds; calculating a trendline representing a relationship between the steady state average saturation and inverse rotational speed squared; extrapolating the trendline to a steady state average saturation value representing infinite rotational speed, the value of said steady state average saturation value representing the residual saturation of a core sample from which the production data was obtained. 14. The method of claim 13, wherein calculating the trendline representing a relationship between steady state average saturation and inverse rotational speed squared comprises: plotting at least three data points corresponding to steady state average saturation values at corresponding highest rotational speeds in the plurality of rotational speeds; and calculating a line of best fit through the at least three data points. 15. The method of claim 13 or claim 14, wherein obtaining centrifuge production data at a plurality of rotational speeds comprises: obtaining data for a relationship between wetting fluid production against time at the plurality of rotational speeds. 16. The method of claim 15, wherein the data of wetting fluid production against time is obtained by performing a centrifuge experiment. 17. The method of claim 16, wherein the centrifuge experiment is a forced imbibition experiment. 18. The method of claim 16, wherein the centrifuge experiment is a forced drainage experiment. 19. The method of any of claims 13 to 18, wherein retrieving a steady state average saturation at each of the plurality of rotational speeds comprises: identifying a plateau in the relationship between wetting fluid production against time at each rotational speed; and using the wetting fluid production value corresponding to the plateau for each rotational speed to calculate the corresponding average wetting fluid saturation associated with each rotational speed. 20. The method of any of claims 13 to 19, further comprising using the trendline to calculate a speed required to achieve residual saturation. 21. The method of any of claims 13 to 20, further comprising comparing datapoints with the trendline to identify capillary desaturation, wherein datapoints falling below the trendline indicate capillary desaturation. 22. A computer readable medium for estimating a time duration to achieve a predetermined production or estimating a production given a predetermined time duration in a core analysis and / or a reservoir matrix block system, the computer readable medium with instructions that, when executed on a processor perform the task of: providing at least one wetting fluid steady state saturation profile of the system, said at least one wetting fluid steady state saturation profile being invariant; estimating a wetting fluid transient state saturation profile to be a compression of the at least one steady state profile and thereby solving associated differential equations using associated boundary conditions and initial conditions of the corresponding system. 23. The computer readable medium of claim 22, wherein a core analysis experiment method associated with the system comprises: core flooding; spontaneous imbibition; gravity drainage; and / or centrifuge. 24. The computer readable medium of claim 22 or claim 23, wherein the associated differential equation is a mass balance equation according to: ^^ ^^^^^^^^= − ^^^^^^^^,(^^ = ^^, ^^)integrated to be evaluated on an average saturation over the core; and wherein the boundary conditions and saturation profile are used to determine a pressure drop across the core for different speeds. 25. The computer readable medium of any of claims 22 to 24, wherein the at least one wetting fluid steady state saturation profile is assumed to be invariant within the system. 26. The computer readable medium of any of claims 22 to 25, further comprising instructions that, when executed on a processor perform the tasks of: determining one of the desired production or the predetermined time duration; and using said one of the determined production or the predetermined time duration in the equation: ^^ = ^^ ^^ + ^^ ln(1 − ^^)wherein a and b are parameters that are dependent on the specific core analysis experiment methods, the initial state, applied conditions corresponding to the specific core analysis experiment methods, system parameters; and wherein X is a scaled production and / or pressure drop; to calculate an estimate of the other of the time duration to achieve the predetermined production or the production at the given time duration, respectively. 27. The computer readable medium of claim 26, wherein the scaled production has a value between 0 and 1, 0 representing a start of a new experimental setting and 1 representing equilibrium of the new experimental setting; the computer readable medium having further instruction that, when executed on a processor perform the tasks of setting the scaled production to a value between 0.9 and 0.999 to provide a time scale for when each experimental setting has completed its production. 28. The computer readable medium of claim 26 or 27, wherein the specific core analysis experiment methods is a centrifuge experiment; wherein wherein ^^ is porosity, Δ ^^^^is a change in saturation production, ^^ is core length, ^^ is absolute permeability, ^^ is rotation speed of the centrifuge experiment, ^^^^is arm length (distance to core centre), Δ ^^ is fluid density difference, ^^^^∗^^is initial fractional distance from an outlet of an end effect, ^^ is a mobility ratio, ^^∗^^is oil mobility at the residual saturation, and ^^^^^^ ^^ ^^is characteristic flow function value of the end effect profile and wherein ^^^^∗^^ is the equilibrium end position of the end effect profile. 29. A system for estimating a time duration to achieve a predetermined production or estimating a production given a predetermined time duration in a core analysis and / or a reservoir matrix block system, comprising: a processor; a storage module; and a calculation module comprising the computer readable medium of any of claims 22 to 28. 30. A method for estimating a time duration to achieve a predetermined production or estimating a production given a predetermined time duration in a core analysis and / or a reservoir matrix block system comprising: identifying at least one wetting fluid steady state saturation profile of the system; assuming said at least one wetting fluid steady state saturation profile to be invariant; estimating a wetting fluid transient state saturation profile to be a compression of the at least one steady state profile and thereby solving associated differential equations using associated boundary conditions and initial conditions of the corresponding system. 31. The method of claim 30, wherein a core analysis experiment method associated with the system comprises: core flooding; spontaneous imbibition; gravity drainage; and / or centrifuge. 32. The method of claim 30 or claim 31, wherein the associated differential equation is a mass balance equation according to: ^^ ^^^^^^^^= − ^^^^^^^^,(^^ = ^^, ^^)integrated to be evaluated on an average saturation over the core; and wherein the boundary conditions and saturation profile are used to determine a pressure drop across the core for different speeds. 33. The method of any of claims 30 to 32, wherein the at least one wetting fluid steady state saturation profile is assumed to be invariant within the system. 34. The method of any of claims 30 to 33, further comprising: determining one of the desired production or the predetermined time duration; and using said one of the determined production or the predetermined time duration in the equation: ^^ = ^^ ^^ + ^^ ln(1 − ^^)wherein a and b are parameters that are dependent on the specific core analysis experiment methods, the initial state, applied conditions corresponding to the specific core analysis experiment methods, system parameters; and wherein X is a scaled production and / or pressure drop; to calculate an estimate of the other of the time duration to achieve the predetermined production or the production at the given time duration, respectively. 35. The method of claim 34, wherein the scaled production has a value between 0 and 1, 0 representing a start of a new experimental setting and 1 representing equilibrium of the new experimental setting; further comprising setting the scaled production to a value between 0.9 and 0.999 to provide a time scale for when each experimental setting has completed its production. 36. The method of claim 34 or 35, wherein the specific core analysis experiment methods is a centrifuge experiment; wherein wherein ^^ is porosity, Δ ^^^^is a change in saturation production, ^^ is core length, ^^ is absolute permeability, ^^ is rotation speed of the centrifuge experiment, ^^^^is arm length (distance to core centre), Δ ^^ is fluid density difference, ^^^^∗^^is initial fractional distance from an outlet of an end effect, ^^ is a mobility ratio, ^^∗^^is oil mobility at the residual saturation, and ^^^^^^ ^^ ^^is characteristic flow function value of the end effect profile and wherein ^^ ^^ ^^= is the equilibrium end position of the end effect profile.

Claims

143165 / LMA P A T E N T C L A I M S 1. A computer readable medium for measuring a residual saturation of a core sample comprising instructions that, when executed on a processor, perform the tasks of: obtaining wetting fluid production against rotational speed at the plurality of rotational speeds calculating a steady state average saturation at each of the plurality of rotational speeds, using the obtained wetting fluid production against rotational speed at the plurality of rotational speeds; calculating a trendline representing a relationship between the steady state average saturation and inverse rotational speed squared; extrapolating the trendline to a steady state average saturation value representing infinite rotational speed, the value of said steady state average saturation value representing the residual saturation of the core sample from which the production data was obtained.

2. The computer readable medium of claim 1, comprising further instructions that, when executed on a processor, perform the tasks of: plotting at least three data points corresponding to steady state average saturation values at corresponding highest rotational speeds in the plurality of rotational speeds; and calculating a line of best fit through the at least three data points; in order to perform the task of calculating the trendline representing a relationship between steady state average saturation and inverse rotational speed squared.

3. The computer readable medium of claim 1 or claim 2, comprising further instructions that, when executed on a processor, perform the tasks of: identifying a plateau in the relationship between wetting fluid production against time at each rotational speed; andusing the wetting fluid production value corresponding to the plateau for each rotational speed to calculate the corresponding average wetting fluid saturation associated with each rotational speed; in order to perform the task of retrieving a steady state average saturation at each of the plurality of rotational speeds comprises.

4. The computer readable medium of any preceding claim, comprising further instructions that, when executed on a processor, performs the task of calculating a speed required to achieve residual saturation using the trendline.

5. The computer readable medium of any preceding claim, comprising further instructions that, when executed on a processor, performs the task of comparing datapoints with the trendline to identify capillary desaturation, wherein datapoints falling below the trendline indicate capillary desaturation.

6. The computer readable medium of any preceding claim, comprising further instructions that, when executed on a processor, perform the task of calculating at least one parameter for use in reservoir engineering, the at least one parameter comprising: a quantity of recoverable oil / gas; an amount of storable CO2; using the calculated residual saturation.

7. A system for measuring a residual saturation of a core sample comprising: a processor; a storage module; and a calculation module comprising the computer readable medium of any of claims 1 to 6.

8. The system of claim 7 further comprising a measuring module to measure wetting fluid production against rotational speed at a plurality of rotational speeds; wherein the measured data of wetting fluid production against rotational speed at a plurality of rotational speeds is stored in the storage module.

9. The system of claim 7 or 8, wherein the calculation module is further configured to measure a level of consistency around the trendline to determine whether the measured data is within a threshold level of consistency.

10. The system of claim 9, wherein the measuring module further comprises a centrifuge experiment assembly.

11. The system of claim 10, wherein the centrifuge experiment assembly is for a forced imbibition experiment.

12. The system of claim 10, wherein the centrifuge experiment assembly is for a forced drainage experiment.

13. A method for estimating a residual saturation comprising: obtaining centrifuge production data at a plurality of rotational speeds; retrieving a steady state average saturation at each of the plurality of rotational speeds; calculating a trendline representing a relationship between the steady state average saturation and inverse rotational speed squared; extrapolating the trendline to a steady state average saturation value representing infinite rotational speed, the value of said steady state average saturation value representing the residual saturation of a core sample from which the production data was obtained.

14. The method of claim 13, wherein calculating the trendline representing a relationship between steady state average saturation and inverse rotational speed squared comprises: plotting at least three data points corresponding to steady state average saturation values at corresponding highest rotational speeds in the plurality of rotational speeds; and calculating a line of best fit through the at least three data points.

15. The method of claim 13 or claim 14, wherein obtaining centrifuge production data at a plurality of rotational speeds comprises: obtaining data for a relationship between wetting fluid production against time at the plurality of rotational speeds.

16. A computer readable medium for estimating a time duration to achieve a predetermined production or estimating a production given a predetermined time duration in a core analysis and / or a reservoir matrix block system, the computer readable medium with instructions that, when executed on a processor perform the task of: providing at least one wetting fluid steady state saturation profile of the system, said at least one wetting fluid steady state saturation profile being invariant; estimating a wetting fluid transient state saturation profile to be a compression of the at least one steady state profile and thereby solving associated differential equations using associated boundary conditions and initial conditions of the corresponding system.

17. The computer readable medium of claim 16, wherein a core analysis experiment method associated with the system comprises: core flooding; spontaneous imbibition; gravity drainage; and / or centrifuge.

18. The computer readable medium of claim 16 or claim 17, wherein the associated differential equation is a mass balance equation according to: ^^ ^^^^^^^^= − ^^^^^^^^, ( ^^ = ^^, ^^) integrated to be evaluated on an average saturation over the core; and wherein the boundary conditions and saturation profile are used to determine a pressure drop across the core for different speeds.

19. The computer readable medium of any of claims 16 to 18, wherein the at least one wetting fluid steady state saturation profile is assumed to be invariant within the system.

20. The computer readable medium of any of claims 16 to 19, further comprising instructions that, when executed on a processor perform the tasks of: determining one of the desired production or the predetermined time duration; and using said one of the determined production or the predetermined time duration in the equation: ^^ = ^^ ^^ + ^^ ln(1 − ^^)wherein a and b are parameters that are dependent on the specific core analysis experiment methods, the initial state and / or further states, applied conditions corresponding to the specific core analysis experiment methods, system parameters; and wherein X is a scaled production and / or pressure drop; to calculate an estimate of the other of the time duration to achieve the predetermined production or the production at the given time duration, respectively.

21. The computer readable medium of claim 20, wherein the scaled production has a value between 0 and 1, 0 representing a start of a new experimental setting and 1 representing equilibrium of the new experimental setting; the computer readable medium having further instruction that, when executed on a processor perform the tasks of setting the scaled production to a value between 0.9 and 0.999 to provide a time scale for when each experimental setting has completed its production.

22. The computer readable medium of claim 20 or 21, wherein the specific core analysis experiment methods is a centrifuge experiment; whereinwherein ^^ is porosity, Δ ^^^^is a change in saturation production, ^^ is core length, ^^ is absolute permeability, ^^ is rotation speed of the centrifuge experiment, ^^^^is arm length (distance to core centre), Δ ^^ is fluid density difference, ^^^^∗^^is initial fractional distance from an outlet of an end effect, ^^ is a mobility ratio, ^^∗^^is oil mobility at the residual saturation, and ^^^^^^ ^^ ^^is characteristic flow function value of the end effect profile and wherein ^^^^ ^^is the equilibrium end position of the end effect profile.

23. A system for estimating a time duration to achieve a predetermined production or estimating a production given a predetermined time duration in a core analysis and / or a reservoir matrix block system, comprising: a processor; a storage module; and a calculation module comprising the computer readable medium of any of claims 16 to 22.

24. A method for estimating a time duration to achieve a predetermined production or estimating a production given a predetermined time duration in a core analysis and / or a reservoir matrix block system comprising: identifying at least one wetting fluid steady state saturation profile of the system; assuming said at least one wetting fluid steady state saturation profile to be invariant;estimating a wetting fluid transient state saturation profile to be a compression of the at least one steady state profile and thereby solving associated differential equations using associated boundary conditions and initial conditions of the corresponding system.

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