Pore-Scale Investigation of the Electrical Property and Saturation Exponent of Archie’s Law in Hydrate-Bearing Sediments

Characterizing the electrical property of hydrate-bearing sediments is essential for hydrate reservoir identification and saturation evaluation. As the major contributor to electrical conductivity, pore water is a key factor in characterizing the electrical properties of hydrate-bearing sediments. The objective of this study is to clarify the effect of hydrates on pore water and the relationship between pore water characteristics and the saturation exponent of Archie’s law in hydrate-bearing sediments. A combination of X-ray computed tomography and resistivity measurement technology is used to derive the three-dimensional spatial structure and resistivity of hydrate-bearing sediments simultaneously, which is helpful to characterize pore water and investigate the saturation exponent of Archie’s law at the micro-scale. The results show that the resistivity of hydrate-bearing sediments is controlled by changes in pore water distribution and connectivity caused by hydrate formation. With the increase of hydrate saturation, pore water connectivity decreases, but the average coordination number and tortuosity increase due to much smaller and more tortuous throats of pore water divided by hydrate particles. It is also found that the saturation exponent of Archie’s law is controlled by the distribution and connectivity of pore water. As the parameters of connected pore water (e.g., porosity, water saturation) decrease, the saturation exponent decreases. At a low hydrate-saturation stage, the saturation exponent of Archie’s law changes obviously due to the complicated pore structure of hydrate-bearing sediments. A new logarithmic relationship between the saturation exponent of Archie’s law and the tortuosity of pore water is proposed which helps to calculate field hydrate saturation using resistivity logging data.

Characterization of Fluid Drainage Mechanism at Core and Pore Scales: an NMR Capillary Pressure–Based Saturation Exponent Prediction

Capillary pressure (Pc) and electrical resistivity index (RI) curves are used in many reservoir engineering applications. Drainage capillary pressure curve represents a scenario where a non-wetting phase displaces a wetting phase such as (i) during gas injection (ii) gas storage in reservoirs (e.g. aquifer or depleted hydrocarbon reservoirs). The gas used for injection is typically natural gas, N2, or CO2. Gas storage principally used to meet requirement variations, and water injection into oil-wet reservoirs are drainage processes. Resistivity index (RI) curve which is used to evaluate the potential of oil recovery from a reservoir, is also an important tool used in log calibration and reservoir fluid typing. The pore drainage mechanism in a multimodal pore system is important for effective recovery of hydrocarbon reserves; enhance oil recovery (EOR) planning and underground gas storage. The understanding of pore structure and drainage mechanism within a multimodal pore system during petrophysical analysis is of paramount importance to reservoir engineers. Therefore, it becomes inherent to study and establish a way to relate these special core analyses laboratory (SCAL) methods with quick measurements such as the nuclear magnetic resonance (NMR) to reduce the time requirement for analysis. This research employed the use of nuclear magnetic resonance (NMR) to estimate saturation exponent (n) of rocks using nitrogen as the displacing fluid. Different rock types were used in this study that cover carbonates, sandstones, and dolomites. We developed an analytical workflow to separate the capillary pressure curve into capillary pressure curve for macropores and a capillary pressure curve for the micropores, and then used these pore scale Pc curves to estimate an NMR - capillary pressure - based electrical resistivity index - saturation (NMR-RI-Sw) curve for the rocks. We predicted the saturation exponent (n) for the rock samples from the NMR-RI-Sw curve. The NMR-based saturation exponent estimation method requires the transverse (T2) relaxation distribution of the rock - fluid system at various saturations. To verify the reliability of the new workflow, we performed porous plate capillary pressure and electrical resistivity measurements on the rock samples. The reliability of the results for the resistivity index curve and the saturation exponent was verified using the experimental data obtained from the SCAL method. The pore scale Pc curve was used to ascertain the drainage pattern and fluid contribution of the different pore subsystems. For bimodal rock system, the drainage mechanism can be in series, in parallel, or in series - parallel depending on the rock pore structure.

SATURATION EXPONENT AS A FUNCTION OF RESERVOIR HETEROGENEITY AND WETTABILITY IN THE TAMBAREDJO OIL FIELD, SURINAME

This research proposed an alternative method for determining the saturation exponent (n) by finding the best correlations for the heterogeneity index using available core data and considering wettability changes. The log curves of the variable n were estimated, and the effect on the water saturation (Sw) calculations and the Stock Tank Oil Initially In Place (STOIIP) in the Tambaredjo (TAM) oil field was analyzed. Core data were employed to obtain the relationship between n and heterogeneity using cross-plots against several heterogeneity indices, reservoir properties, and pore throat size. After filtering the data, the clay volume (Vcl), shale volume, silt volume, basic petrophysical property index (BPPI), net reservoir index, pore grain volume ratio, and rock texture were defined as the best matches. Their modified/improved equations were applied to the log data and evaluated. The n related to Vcl was the best selection based on the criteria of depth variations and logical responses to the lithology. The Sw model in this field showed certain log readings (high resistivity [Rt] reading ≥ 500 ohm.m) that infer these intervals to be probable inverse-wet (oil-wet). The cross-plots (Rt vs. Vcl; Rt vs. density [RHOB]; Rt vs. total porosity [PHIT]) were used to discard the lithologies related to a high Rt (e.g., lignites and calcareous rocks) and to correct Sw when these resulted in values below the estimated irreducible water saturation (Swir). The Sw calculations using the Indonesian equation were updated to incorporate n as a variable (log curves), comparing it with Sw from the core data and previous calculations using a fixed average value (n = 1.82) from the core data. An integrated approach was used to determine n, which is related to the reservoir’s heterogeneity and wettability changes. The values of n for high Rt (n > 2) intervals ranged from 2.3 to 8.5, which is not close to the field average n value (1.82). Specific correlations were found by discriminating Swir (Swir < 15%), (Swir 15%–19%), and Swir (> 19%). The results showed that using n as a variable parameter improved Sw from 39.5% to 36.5% average in the T1 and T2 sands, showing a better fit than the core data average and increasing the STOIIP estimations by 6.81%. This represents now a primary oil recovery of 12.1%, closer to the expected value for these reservoirs. Although many studies have been done on n determination and its effect on Sw calculations, using average values over a whole field is still a common practice regardless of heterogeneity and wettability considerations. This study proposed a method to include the formation of heterogeneity and wettability changes in n determination, allowing a more reliable Sw determination as demonstrated in the TAM oil field in Suriname.

Mass Balance Threshold Matching of Geoelectric and Seismic Data – A case study from Ketzin

&lt;p&gt;Seismic and geoelectric/electro-magnetic methods are used as complementary tools for the identification of fluid/gas effects in underground storage and production scenarios. Both methods generally have very different resolution. Seismic tends to be acquired by much more dense geometrical layouts and the geoelectric or electro-magnetic acquisition being a potential field method shows information integrated over spatial distances. These inherent scale and design dependent differences require spatial tuning in joint inversion approaches and careful matching in independent interpretations of both methods. We present results matching seismic and electrical resistivity tomography (ERT) results from two repeat surveys acquired during CO&lt;sub&gt;2&lt;/sub&gt; storage operations at the Ketzin pilot site in Germany. The approach is based on data acquired in 2009 and 2012, at different stages of total injected CO&lt;sub&gt;2&lt;/sub&gt; volume. Volumes of injected mass are obtained from the averaged acoustic impedance change (seismic) in the vicinity of the injection well and compared to volumes inferred from the ERT cross-well acquisition. The results are compared radially with increasing distances from the injection location. Seismically derived masses of injected CO&lt;sub&gt;2&lt;/sub&gt; are used as a benchmark for a threshold-driven workflow analyzing the electric resistivity model. The cross-well ERT results have been obtained in a quadrant of the seismic survey acquisitions. Assuming radial symmetry for the ERT makes it possible to compare individual mass balances in the near-vicinity of the injection well. Archie's equation is used to obtain saturations from the tomographic geoelectric models. The sensitivities of parameters relevant in determining the mass of injected CO&lt;sub&gt;2&lt;/sub&gt; is analyzed. Variations in saturation exponent&lt;!-- K&amp;#246;nnten wir den auch &amp;#8216;saturation exponent&amp;#8217; nennen? Das ist eher der bekanntere Begriff. --&gt;&lt;!-- Reply to Conny Schmidt-Hattenberger (01/19/2021, 00:10): &quot;...&quot; Angepasst --&gt; n, baseline resistivity R&lt;sub&gt;0&lt;/sub&gt;, and porosity &amp;#934; enable specifying applicable ranges of the parameters and determining the investigation radii compared to the seismic derived benchmark. This is done for individual threshold levels for saturations derived from the ERT field data. Seismically and ERT obtained masses match comparatively well and subtle variations of the sensitive parameters are capable in explaining differences for individual investigation volumes. Applicable investigation radii lie between 20-100 m. A 10% in- or decrease of the mean parameters is able to match the seismic derived mass in this range. Above a threshold of 10% for the saturations, the derived mass decreases more rapidly showing a larger deviation from the seismic derived mass. Both methods underestimate the total injected mass. This is not surprising as there are both fluid related processes and structural heterogeneities not accounted for in either. Results of surface-downhole measurements support the findings and show applicability of the developed approach. The threshold-based approach may support the monitoring concept of a CO&lt;sub&gt;2&lt;/sub&gt; storage site and provides a basis for quantitative evaluation of its containment, as investigated in the frame of the EU project SECURe.&lt;!-- Abhaengig von moeglichen Ergebnissen aus den Surface-Downhole Messungen. --&gt;&lt;!-- @Dennis: Werden wir hier evtl. noch eine Abbildung haben, die diese Feststellung illustriert (f&amp;#252;r EGU-Pr&amp;#228;sentation oder Poster)? Ansonsten k&amp;#246;nnen wir den Satz auch weglassen. --&gt;&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;

A quantitative interpretation of the saturation exponent in Archie’s equations

Saturation exponent is an important parameter in Archie’s equations; however, there has been no well-accepted physical interpretation for the saturation exponent. We have theoretically derived Archie’s equations from the Maxwell–Wagner theory on the assumption of homogeneous fluid distribution in the pore space of clay-free porous rocks. Further theoretical derivations showed that the saturation exponent is in essence the cementation exponent for the water–air mixture and is quantitatively and explicitly related to the aspect ratio of the air bubbles in the pores. The results have provided a theoretical backup for the empirically obtained Archie’s equations and have offered a more physical and quantitative understanding of the saturation exponent.

Effects of Foam Microbubbles on Electrical Resistivity and Capillary Pressure of Partially Saturated Porous Media

Laboratory measurements of capillary pressure (Pc) and the electrical resistivity index (RI) of reservoir rocks are used to calibrate well logging tools and to determine reservoir fluid distribution. Significant studies on the methods and factors affecting these measurements in rocks containing oil, gas, and water are adequately reported in the literature. However, with the advent of chemical enhanced oil recovery (EOR) methods, surfactants are mixed with injection fluids to generate foam to enhance the gas injection process. Foam is a complex and non-Newtonian fluid whose behavior in porous media is different from conventional reservoir fluids. As a result, the effect of foam on Pc and the reliability of using known rock models such as the Archie equation to fit experimental resistivity data in rocks containing foam are yet to be ascertained. In this study, we investigated the effect of foam on the behavior of both Pc and RI curves in sandstone and carbonate rocks using both porous plate and two-pole resistivity methods at ambient temperature. Our results consistently showed that for a given water saturation (Sw), the RI of a rock increases in the presence of foam than without foam. We found that, below a critical Sw, the resistivity of a rock containing foam continues to rise rapidly. We argue, based on knowledge of foam behavior in porous media, that this critical Sw represents the regime where the foam texture begins to become finer, and it is dependent on the properties of the rock and the foam. Nonetheless, the Archie model fits the experimental data of the rocks but with resulting saturation exponents that are higher than conventional gas–water rock systems. The degree of variation in the saturation exponents between the two fluid systems also depends on the rock and fluid properties. A theory is presented to explain this phenomenon. We also found that foam affects the saturation exponent in a similar way as oil-wet rocks in the sense that they decrease the cross-sectional area of water available in the pores for current flow. Foam appears to have competing and opposite effects caused by the presence of clay, micropores, and conducting minerals, which tend to lower the saturation exponent at low Sw. Finally, the Pc curve is consistently lower in foam than without foam for the same Sw.