A new theoretical interpretation of Archie’s saturation exponent

This paper describes the extension of the concepts of connectedness and conservation of connectedness that underlie the generalized Archie's law for n phases to the interpretation of the saturation exponent. It is shown that the saturation exponent as defined originally by Archie arises naturally from the generalized Archie's law. In the generalized Archie's law the saturation exponent of any given phase can be thought of as formally the same as the phase (i.e. cementation) exponent, but with respect to a reference subset of phases in a larger n-phase medium. Furthermore, the connectedness of each of the phases occupying a reference subset of an n-phase medium can be related to the connectedness of the subset itself by Gi = GrefSini. This leads naturally to the idea of the term Sini for each phase i being a fractional connectedness, where the fractional connectednesses of any given reference subset sum to unity in the same way that the connectednesses sum to unity for the whole medium. One of the implications of this theory is that the saturation exponent of any phase can be now be interpreted as the rate of change of the fractional connectedness with saturation and connectivity within the reference subset

Archie's law – a reappraisal

When scientists apply Archie's first law they often include an extra parameter a, which was introduced about 10 years after the equation's first publication by Winsauer et al. (1952), and which is sometimes called the “tortuosity” or “lithology” parameter. This parameter is not, however, theoretically justified. Paradoxically, the Winsauer et al. (1952) form of Archie's law often performs better than the original, more theoretically correct version. The difference in the cementation exponent calculated from these two forms of Archie's law is important, and can lead to a misestimation of reserves by at least 20 % for typical reservoir parameter values. We have examined the apparent paradox, and conclude that while the theoretical form of the law is correct, the data that we have been analysing with Archie's law have been in error. There are at least three types of systematic error that are present in most measurements: (i) a porosity error, (ii) a pore fluid salinity error, and (iii) a temperature error. Each of these systematic errors is sufficient to ensure that a non-unity value of the parameter a is required in order to fit the electrical data well. Fortunately, the inclusion of this parameter in the fit has compensated for the presence of the systematic errors in the electrical and porosity data, leading to a value of cementation exponent that is correct. The exceptions are those cementation exponents that have been calculated for individual core plugs. We make a number of recommendations for reducing the systematic errors that contribute to the problem and suggest that the value of the parameter a may now be used as an indication of data quality

The Porosity and Permeability of Binary Grain Mixtures

The processes that control binary mixing of two sizes of grains have been investigated theoretically and validated by comparison with experimental data. These seemingly simple experiments are difficult to carry out with the degree of precision needed to test the models. We have developed a methodology allowing porosity and permeability to be measured to within ± 4.415% and ± 4.989% (at a flow rate of 5.13 cm3/s) of each value, respectively. Theoretical considerations recognise mixing processes: (1) an interstitiation process whereby small grains fit between larger grains and (2) a replacement process whereby large grains replace smaller grains and the porosity associated with them. A major result of this work is that the theoretical models describing these two processes are independent of grain size and grain shape. The latter of these two findings infers that the models developed in this work are applicable to any shape of grain or type of packing, providing that a representative porosity of each size of grain pack is known independently, either experimentally or theoretically. Experimental validation has shown that the newly developed relationships for porosity described measurements of porosity for near-ideal binary mixtures extremely well, confirming that porosity is always reduced by binary mixing, and that the degree of reduction depends upon the size of the ratio between the two grain sizes. Calculation of permeability from the packing model has also been done. Six different permeability estimation methods have been used. It was found that the most accurate representations of the experimental permeability were obtained (1) when the exact RGPZ (Revil, Glover, Pezard, Zamora) method was used with the porosity mixing models developed in this work and (2) when the exact RGPZ method was used with the weighted geometric mean to calculate a representative grain size

Measurements of the relationship between microstructure, pH and the streaming and zeta potentials of sandstones

A large number (1253) of high-quality streaming potential coefficient (Csp) measurements have been carried out on Berea, Boise, Fontainebleau, and Lochaline sandstones (the latter two including both detrital and authigenic overgrowth forms), as a function of pore fluid salinity (Cf) and rock microstructure. All samples were saturated with fully equilibrated aqueous solutions of NaCl (10- 5 and 4.5 mol/dm3) upon which accurate measurements of their electrical conductivity and pH were taken. These Csp measurements represent about a fivefold increase in streaming potential data available in the literature, are consistent with the pre-existing 266 measurements, and have lower experimental uncertainties. The Csp measurements follow a pH-sensitive power law behaviour with respect to Cf at medium salinities (Csp=-1.44×10-9Cf-1.127, units: V/Pa and mol/dm3) and show the effect of rock microstructure on the low salinity Csp clearly, producing a smaller decrease in Csp per decade reduction in Cf for samples with (i) lower porosity, (ii) larger cementation exponents, (iii) smaller grain sizes (and hence pore and pore throat sizes), and (iv) larger surface conduction. The Csp measurements include 313 made at Cf> 1 mol/dm3, which confirm the limiting high salinity Csp behaviour noted by Vinogradov et al., which has been ascribed to the attainment of maximum charge density in the electrical double layer occurring when the Debye length approximates to the size of the hydrated metal ion. The zeta potential (ζ) was calculated from each Csp measurement. It was found that ζ is highly sensitive to pH but not sensitive to rock microstructure. It exhibits a pH-dependent logarithmic behaviour with respect to Cf at low to medium salinities (ζ= 0.01133 log 10(Cf) + 0.003505 , units: V and mol/dm3) and a limiting zeta potential (zeta potential offset) at high salinities of ζo=-17.36±5.11 mV in the pH range 6–8, which is also pH dependent. The sensitivity of both Csp and ζ to pH and of Csp to rock microstructure indicates that Csp and ζ measurements can only be interpreted together with accurate and equilibrated measurements of pore fluid conductivity and pH and supporting microstructural and surface conduction measurements for each sample

A new theoretical interpretation of Archie’s saturation exponent

This paper describes the extension of the concepts of connectedness and conservation of connectedness that underlie the generalized Archie’s law for n phases to the interpretation of the saturation exponent. It is shown that the saturation exponent as defined originally by Archie arises naturally from the generalized Archie’s law. In the generalized Archie’s law the saturation exponent of any given phase can be thought of as formally the same as the phase (i.e. cementation) exponent, but with respect to a reference subset of phases in a larger n-phase medium. Furthermore, the connectedness of each of the phases occupying a reference subset of an n-phase medium can be related to the connectedness of the subset itself by Gi = GrefS ni i . This leads naturally to the idea of the term S ni i for each phase i being a fractional connectedness, where the fractional connectednesses of any given reference subset sum to unity in the same way that the connectednesses sum to unity for the whole medium. One of the implications of this theory is that the saturation exponent of any phase can be now be interpreted as the rate of change of the fractional connectedness with saturation and connectivity within the reference subset

Comment on “Examination of a Theoretical Model of Streaming Potential Coupling Coefficient”

Recently Luong and Sprik published an article that compared measurements that had been made on 20 samples of saturated rock with a number of empirical models and the Glover et al.’s 2012 theoretical model for zeta potential and streaming potential coefficient. They found that none of the empirical models could reproduce the streaming potential coefficient measurements which had been made in the presence of low pore fluid salinities, and the theoretical method could only do so if a constant zeta potential was invoked. This contribution in the form of a comment (i) indicates at least three possible errors in modelling that contribute to the mismatch between the theoretical model and the data at low salinities, and (ii) carries out individual modelling on all of the samples of the Luong and Sprik’s 2014 dataset, showing that the Glover et al.’s 2012 theoretical model matches the data well when the zeta potential is allowed to vary and a good match can only be obtained with a constant zeta potential if an unrealistic value of zeta potential offset is used

Synthetic Fractal Modelling of Heterogeneous and Anisotropic Reservoirs for use in Simulation Studies: Implications on their Hydrocarbon Recovery Prediction

Optimising production from heterogeneous and anisotropic reservoirs challenges the modern hydrocarbon industry because such reservoirs exhibit extreme inter-well variability making them very hard to model. Reasonable reservoir models can be obtained using modern statistical techniques, but all of them rely on significant variability in the reservoir only occurring at a scale at or larger than the inter-well spacing. In this paper we take a different, generic, approach. We have developed a method for constructing realistic synthetic heterogeneous and anisotropic reservoirs which can be made to represent the reservoir under test. The main physical properties of these synthetic reservoirs are distributed fractally. The models are fully controlled and reproducible and can be extended to model multiple facies reservoir types. This paper shows how the models can be constructed and how they have been tested. Varying the fractal dimension and anisotropy factor of each of these physical properties can tell us how sensitive the reservoir is to uncertainties in its heterogeneity and anisotropy as well as how poroperm cross-plot shapes are controlled. Initial reservoir simulation results of the tested models with this approach show that heterogeneity in the reservoir's physical parameters has a little effect on high and moderate porosity and permeability reservoirs. The effect is more pronounced in the models representing tight reservoirs. The production from more heterogeneous reservoirs lasts a little longer, but eventually declines faster. This may be attributed to the fact that water channelling is more significant as heterogeneity increases

Permeability Prediction and Diagenesis in Tight Carbonates Using Machine Learning Techniques

Machine learning techniques have found their way into many problems in geoscience but have not been used significantly in the analysis of tight rocks. We present a case study testing the effectiveness of artificial neural networks and genetic algorithms for the prediction of permeability in tight carbonate rocks. The dataset consists of 130 core plugs from the Portland Formation in southern England, all of which have measurements of Klinkenberg-corrected permeability, helium porosity, characteristic pore throat diameter, and formation resistivity. Permeability has been predicted using genetic algorithms and artificial neural networks, as well as seven conventional ‘benchmark’ models with which the machine learning techniques have been compared. The genetic algorithm technique has provided a new empirical equation that fits the measured permeability better than any of the seven conventional benchmark models. However, the artificial neural network technique provided the best overall prediction method, quantified by the lowest root-mean-square error (RMSE) and highest coefficient of determination value (R2). The lowest RMSE from the conventional permeability equations was from the RGPZ equation, which predicted the test dataset with an RMSE of 0.458, while the highest RMSE came from the Berg equation, with an RMSE of 2.368. By comparison, the RMSE for the genetic algorithm and artificial neural network methods were 0.433 and 0.38, respectively. We attribute the better performance of machine learning techniques over conventional approaches to their enhanced capability to model the connectivity of pore microstructures caused by codependent and competing diagenetic processes. We also provide a qualitative model for the poroperm characteristics of tight carbonate rocks modified by each of eight diagenetic processes. We conclude that, for tight carbonate reservoirs, both machine learning techniques predict permeability more reliably and more accurately than conventional models and may be capable of distinguishing quantitatively between pore microstructures caused by different diagenetic processes

Increased Radon Exposure From Thawing of Permafrost Due To Climate Change

Radon is a natural radioactive gas accounting for approximately one in 10 lung cancer deaths, with substantially higher death rates in sub-Arctic communities. Radon transport is significantly reduced in permafrost, but permafrost is now thawing due to climate change. The effect of permafrost thawing on domestic radon exposure is unknown. Here we present results from radon transport modeling through soil, permafrost, and model buildings either with basements or built on piles. We find that permafrost acts as an effective radon barrier, reducing radiation exposure to a tenth of the background level while producing a ten-fold increase in the radon activity behind the barrier. When we model thawing of the permafrost barrier, we find no increase in radon to the background level for buildings on piles. However, for buildings with basements, the radon increases to over one hundred times its initial value and can remain above the 200 Bq/m3 threshold for up to 7 years depending on the depth of the permafrost and the speed of thawing. When thawing speed is taken into account, radiations remain higher than the threshold for all scenarios where 40% thawing occurs within 15 years. This new information suggests that a significant sub-Arctic population could be exposed to radon levels dangerous to health as a result of climate change thawing of permafrost, with implications for health provision, building codes, and ventilation advice

Effect of a Pore Throat Microstructure on Miscible CO2 Soaking Alternating Gas Flooding of Tight Sandstone Reservoirs

Miscible CO2 soaking alternating gas (CO2-SAG) flooding is an improved version of CO2 flooding, which compensates for the insufficient interaction of CO2 and crude oil in the reservoir by adding a CO2 soaking process after the CO2 breakthrough (BT). The transmission of CO2 in the reservoir during the soaking process is controlled by the pore throat structure of the formation, which in turn affects the displacement efficiency of the subsequent secondary CO2 flooding. In this work, CO2-SAG flooding experiments at reservoir conditions (up to 70 °C, 18 MPa) have been carried out on four samples with very similar permeabilities but significantly different pore size distributions and pore throat structures. The results have been compared with the results of CO2 flooding on the same samples. It was found that the oil recovery factors (RFs) when using CO2-SAG flooding are higher than those when using CO2 flooding by 8–14%. In addition, we find greater improvements in the RF for rocks with greater heterogeneity of their pore throat microstructure compared with CO2 flooding. The CO2 soaking process compensates effectively for the insufficient interaction between CO2 and crude oil because of premature CO2 BT in heterogeneous cores. Moreover, rocks with a more homogeneous pore throat microstructure exhibit a higher pressure decay rate in the CO2 soaking process. The initial rapid pressure decay stage lasts for 80–135 min (in our experimental cores), accounting for over 80% of the total decay pressure. Rocks with the larger and more homogeneous pore throat microstructure exhibit smaller permeability decreases because of asphaltene precipitation after CO2-SAG flooding, possibly because the permeability of rocks with a more heterogeneous and smaller pore throat microstructure is more susceptible to damage from asphaltene precipitation. However, the overall permeability decline is 0.6–3.6% higher than that of normal CO2 flooding because of the increased time for asphaltene precipitation. Nevertheless, the corresponding permeability average decline per 1% oil RF is 0.11–0.34%, which is lower than that for CO2 flooding, making the process worthwhile. We have shown that CO2-SAG flooding has the potential to improve oil RFs with relatively less damage to cores, especially for cores with small and heterogeneous pore throat microstructures, but for which severe wettability changes due to the CO2 soaking process can become significant