Schlumberger Doll Research Model Research Articles

Permeability evaluation based on Nuclear Magnetic Resonance analysis for gas hydrate reservoir

Permeability (or hydraulic conductivity) is one of the most important parameters for analyzing hydraulic behavior of underground. For example, in the geotechnical engineering, permeability is necessary to calculate water inflow and draw down of water level during excavation, to predict the deformation time due to the consolidation, and to evaluate the barrier of the ground for radioactive waste disposal. In the petroleum industry, permeability is considered an essential parameter which is directly linked to the productivity of oil and natural gas. Therefore, predicting permeability using wireline logging or logging while drilling (LWD) is required during the assessment of the reservoir. Nuclear Magnetic Resonance (NMR) logging is performed at this point. Low-field NMR measurements are sensitive to the hydrogen proton, 1H, in liquid water but not to the 1 H bond in solid form, making it possible to obtain the bulk water volume. In addition, the hydrogen proton NMR- T2 (transverse or spin-spin) relaxation time distribution is used to infer pore-size information and to estimate permeability [1, 2]. The major methods used for estimating permeability, k, are the Schlumberger Doll Research (SDR) model and Timur-Coates (TC) model [3, 4]:
 Where fNMR is the NMR-estimated (effective) porosity. SDR model uses the averaged value of the T2 distribution plotted on log-scale of time and matches it to the experimental reference permeability with the fitting parameter a [mD/(ms)2]. The TC model seeks to differentiate between the fraction of free (mobile) fluid volume (FFV) and bound fluid volume (BFV) and estimates permeability with FFV/BFV ratio and the material constant c [m2/s2]. The permeability in the research and development of methane hydrate, which is expected to be a next-generation resource, has been estimated using above methods. Methane hydrate is an ice-like solid crystalline structure of water and methane molecules. Because hydrate is solid, NMR is not sensitive, the initial (effective) permeability can be estimated by NMR analyzer. On the other hand, A strong disconnect (up to 2 orders of magnitude) between NMR-based estimates of permeability with those determined from a laboratory study of pressure cores from the same reservoir has further cast uncertainty in the application of borehole NMR data in hydrate evaluation [5, 6]. Recently, authors provided comparisons between NMR-derived values and direct fluid flow estimates of permeability in naturally occurring hydrate-bearing sediment [7, 8]. On the basis of the NMR measurement for hydrate-bearing pressure core sediments, which were recovered from the Gulf of Mexico and Alaska North Slope, the following new hydraulic radius model was proposed [7].
 This equation estimates the specific surface based on the NMR signal and has been shown to successfully estimate the initial permeability of a hydrate reservoir by expressing a hydraulic radius model based on Kozeny's equation [9]. However, the proposed equation is not universal and has been found to overestimate for clayey and silty hydrate free sediment. This study summarizes the methods and parameters used to estimate permeability using NMR signals from hydrate-bearing sediment obtained from logging and laboratory tests for the Gulf of Mexico and Alaska North Slope. In addition, we reports parameters for predicting model for muddy sediments which was recovered from overburden of hydrate-reservoir in the Hyuganada sea in 2022 Japan [10, 11]. When using the hydraulic radius model to predict permeability of hydrate-bearing sediment, reasonable estimates can be obtained by setting the shape factor for grains Cs = 1/2 (for a circular grain) and the shape factor for the flow path cn = 4 (for the cylinder network), respectively. Although, for hydrate free muddy sediment, Cs = 1/3 for parallel plate grain shape and cn = 2 for the fracture network model matched its permeability. Furthermore, the conversion parameter from T2 relaxation time to the pore size for hydrate free muddy sediments r2 = 0.009 (mm/s) was confirmed based on the result of mercury injection capillary pressure analysis, which is lower than r2 = 0.0325 (mm/s) of hydrate-bearing sediments.

CHARACTERISTIC OF PORE STRUCTURE AND FLOW PROPERTY IN SANDSTONES BASED ON LOW FIELD NUCLEAR MAGNETIC RESONANCE

Surface relaxivity is the most significant parameter that converts transverse relaxation time into pore size in porous media. However, the value of surface relaxivity is difficult to obtain. This paper focuses on measuring surface relaxivity to evaluate permeability of two types of sandstones (loose sandstone and tight sandstone), combining the high-speed centrifugation with nuclear magnetic resonance test. The results reveal the surface relaxivities for loose sandstones (1.89-2.20 μm/s) are larger than that for tight sandstones (0.69-0.87 μm/s). The measured surface relaxivity is consistent with that from the method of monolayer water adsorption. During centrifugation, the variation of water content is analyzed, including the pore with different size categories. Based on the measured surface relaxivity, the Schlumberger doll research model is used to estimate the absolute permeability of sandstones.

A Novel Permeability Prediction Model for Deep Coal via NMR and Fractal Theory

A quantitative description of the permeability of deep coal is of great significance for improving coalbed methane recovery and preventing gas disasters. The Schlumberger–Doll research (SDR) model is often used to predict rock permeability, but it has inherent defects in characterizing the pore structure of deep coal. In this study, a permeability model with fractal characteristics (FCP model) is established for deep coal based on nuclear magnetic resonance (NMR). The constants in the SDR model are theoretically explained by the relevant parameters in the FCP model. Centrifugation and NMR experiments were performed to determine the optimal centrifugal force and dual T2 cutoff values. The results show that the coal samples are mainly composed of micrometer and nanometer pores. The adsorption pores account for the largest proportion, followed by the percolation pores and migration pores. In addition, the prediction accuracy of the FCP model is significantly higher than that of the other three models, which provides a fast and effective method for the evaluation of deep coal permeability.

A novel permeability prediction model for coal based on dynamic transformation of pores in multiple scales

Schlumberger-Doll research (SDR) model is popular in predicting rock permeability, however the intrinsic defects constrain its applicability in coal. Pore structure in coal is complicated while SDR model assumes it is homogeneous. To solve this problem, we conducted water flushing experiments to simulate coalbed methane (CBM) drainage process using nuclear magnetic resonance (NMR) on durain (DHB-9-3), clarain (HP-5-3) and semi clarain (MD-6-6). Through comparative analyses on stress sensitivity, adsorption pores in DHB-9-3, non-adsorbed pores in HP-5-3 and seepage pores in MD-6-6 show a greater sensitivity. The non-adsorbed pores, which are responsible for reservoir permeability, become more complicated under increasing effective stress. The fractal dimension of non-adsorbed pores in DHB-9-3 and HP-5-3 increases from 2.93 to 2.97, and from 2.92 to 2.93 in MD-6-6 when the inlet water pressure reduces from 8 MPa to 3 MPa, indicating a more complicated pore geometry and a longer water flow pathway. As a result, the permeability shows a downward trend. A novel coal permeability prediction model is constructed with a factor of fractal dimension embedded in. Compared with SDR model, the new model is verified to have 0.79 times, 0.16 times and 0.08 times less error rates in DHB-9-3, HP-5-3 and MD-6-6, respectively.

Assessment of NMR Logging for Estimating Hydraulic Conductivity in Glacial Aquifers.

Glacial aquifers are an important source of groundwater in the United States and require accurate characterization to make informed management decisions. One parameter that is crucial for understanding the movement of groundwater is hydraulic conductivity, K. Nuclear magnetic resonance (NMR) logging measures the NMR response associated with the water in geological materials. By utilizing an external magnetic field to manipulate the nuclear spins associated with 1 H, the time-varying decay of the nuclear magnetization is measured. This logging method could provide an effective way to estimate K at submeter vertical resolution, but the models that relate NMR measurements to K require calibration. At two field sites in a glacial aquifer in central Wisconsin, we collected a total of four NMR logs and obtained measurements of K in their immediate vicinity with a direct-push permeameter (DPP). Using a bootstrap algorithm to calibrate the Schlumberger-Doll Research (SDR) NMR-K model, we estimated K to within a factor of 5 of the DPP measurements. The lowest levels of accuracy occurred in the lower-K (K <10-4 m/s) intervals. We also evaluated the applicability of prior SDR model calibrations. We found the NMR calibration parameters varied with K, suggesting the SDR model does not incorporate all the properties of the pore space that control K. Thus, the expected range of K in an aquifer may need to be considered during calibration of NMR-K models. This study is the first step toward establishing NMR logging as an effective method for estimating K in glacial aquifers.

A Model for Estimating the Saturation Exponent Based on NMR in Tight Sandy Conglomerate Reservoirs

The electrical resistivity of a porous medium, which is used for water or oil saturation evaluation through combination with Archie’s law, strongly depends on the wettability and geometry of the pore system. In tight sandy conglomerate reservoirs, the pore-throat structure is so complicated that Archie’s equation is non-applicable. Analysis shows that the saturation exponent n is a function of the water saturation $$(S_\mathrm{w})$$ , microstructure, and wettability. Here, a novel method based on nuclear magnetic resonance is proposed to determine the saturation exponent (n) under water- or oil-wet conditions. The Schlumberger Doll Research model is also introduced to estimate and analyze the fluid distribution in an irregular pore space. To validate the model, 21 water-wet core samples from the tight conglomerate reservoir in the Junggar Basin, Northwestern China, were selected to measure the electrical resistivity at varying water saturation levels. The absolute errors between the predicted and measured saturation exponents range from −0.153 to 0.131, and the absolute errors for the water saturation between the predicted and measured values vary from −0.032 to 0.023. These results indicate that the proposed model could be applied to accurately predict the water saturation in tight sandy conglomerate reservoirs.

New insight into the microtexture of chalks from NMR analysis

An integrated petrographical and petrophysical study was carried out on a set of 35 outcrop chalk samples, covering a wide range of lithologies and textures. In this study various chalk rock-types have been characterized, in terms of microtextures and porous network, by integrating both geological, sediment-petrological and petrophysical data, including porosity, permeability, low-field NMR (Nuclear Magnetic Resonance), MICP and specific surface area (BET) measurements. The data allow an in depth understanding of the NMR signal of chalks, with a focus on tight chalks, including all low reservoir quality chalks independently of their sedimentological and/or diagenetic history. The study aims to develop an NMR-based approach to characterize a broad range of chalk samples. The provided laboratory low-field NMR chalk classification can be used as a guide to interpret NMR logging data.Based on the petrographical and petrophysical analysis, 6 groups of samples were identified, each of them characterized by a unique NMR signature: (1) micritic chalks, (2) grainy chalks, (3) cemented chalks, (4) marl-seam chalks, (5) argillaceous chalks and (6) silicified chalk. NMR T2 distributions were linked to pore body size and T2 logarithmic (T2lm) was calculated. It is apparent that tight chalks, whether their characteristics are sedimentological or diagenetic, yield smaller pore body sizes (T2lm < 20 ms), as well as narrower pore throats (average radius < 150 nm) and lower permeability values (typically below 0.2 mD). Grainy chalks possess T2 distributions reflecting larger pore sizes (T2lm > 60 ms) and pore throats (average radius > 290 nm) and higher permeabilities (up to 13 mD). The marl-seam chalk samples yield bimodal T2 distributions, with a first peak related to the micritic matrix pores and a second peak related to intraparticle pores within fossils. For all samples, permeability was inferred from NMR spectra using SDR (Schlumberger Doll Research) model.

Estimation of Permeability from NMR Logs Based on Formation Classification Method in Tight Gas Sands

The Schlumberger Doll Research (SDR) model and cross plot of porosity versus permeability cannot be directly used in tight gas sands. In this study, the HFU approach is introduced to classify rocks, and determine the involved parameters in the SDR model. Based on the difference of FZI, 87 core samples, drilled from tight gas sandstones reservoirs of E basin in northwest China and applied for laboratory NMR measurements, were classified into three types, and the involved parameters in the SDR model are calibrated separately. Meanwhile, relationships of porosity versus permeability are also established. The statistical model is used to calculate consecutive FZI from conventional logs. Field examples illustrate that the calibrated SDR models are applicable in permeability estimation; models established from routine core analyzed results are effective in reservoirs with permeability lower than 0.3 mD, while the unified SDR model is only valid in reservoirs with permeability ranges from 0.1 to 0.3 mD.

Calculating absolute permeability using nuclear magnetic resonance models

1D transverse relaxation measurements were made on fully cylindrical cores of sandstone sediments with varying values of porosity, pore size and magnetic susceptibility. Porosity calculated from amplitudes of transverse relaxation measurements agrees well with porosity determined by independent method. Transverse relaxation measurements within the homogeneous magnetic field can be used for permeability prediction. In the case of sandstone samples with high porosity, a standard calculation scheme from NMR logging in the oil industry yields good results. However, standard SDR (Schlumberger Doll Research) model based on the T2LM cannot be applied for an accurate permeability prediction for samples with low porosity, small pore sizes, clay filling pores, and presence of iron minerals and associated with high internal magnetic field gradients. Therefore, a model theory was developed physically based on Kozeny-Carman equation, which describes the pore radius dependence of the surface relaxivity ρ as both an analytical and a more practicable empirical equation was applied. Regarding corrected ρ values, permeability can be predicted more accurately from the physically based Kozeny-Carman equation than from the logarithmic mean of the T2 distribution. From the relaxation measurements new empirical models with high coefficient of correlation by MLS regression were derived, additionally the coefficients of SDR and Kozeny were reestimated. The prediction models were applied, and the results compared to absolute permeability results from basic core analysis. As expected, the Kozeny model response presented better match to the core permeability values when compared with the optimized SDR.

Determination of permeability index using Stoneley slowness analysis, NMR models, and formation evaluations: a case study from a gas reservoir, south of Iran

In hydrocarbon reservoirs, permeability is one of the most critical parameters with a significant role in the production of hydrocarbon resources. Direct determination of permeability using Stoneley waves has always had some difficulties. In addition, some un-calibrated empirical models such as Nuclear Magnetic Resonance (NMR) models and petrophysical evaluation model (intrinsic permeability) do not provide reliable estimates of permeability in carbonate formations. Therefore, utilizing an appropriate numerical method for direct determination of permeability using Stoneley waves as well as an appropriate calibration method for the empirical models is necessary to have reliable results. This paper shows the application of a numerical method, called bisection method, in the direct determination of permeability from Stoneley wave slowness. In addition, a linear regression (least squares) method was used to calibrate the NMR models including Schlumberger Doll Research (SDR) and Timur–Coates models as well as the intrinsic permeability equation (permeability from petrophysical evaluations). The Express Pressure Tester (XPT) permeability was considered as an option for the reference permeability. Therefore, all permeability models were validated for the Stoneley permeability and calibrated for the empirical models with the XPT permeability. In order to have a quantitative assessment on the results and compare the results before and after the calibration, the Root Mean Squares Error (RMSE) was calculated for each of the used models. The results for the Stoneley permeability showed that, in many points there was not much difference between the Stoneley permeability calculated by the bisection method and the XPT permeability. Comparing the results showed that the calibration of the empirical models reduced their RMSE values. As a result of the calibration, the RMSE was decreased by about 39% for the SDR model, 18% for the Timur–Coates model, and 91% for the petrophysical evaluations model. Presented bisection method calculates permeability directly without of any inversion or external calibration.

A novel model of predicting Archie’s cementation factor from nuclear magnetic resonance (NMR) logs in low permeability reservoirs

The resistivity experimental measurements of core samples drilled from low permeability reservoirs of Ordos Basin, Northwest China, illustrate that the cementation factors are not agminate, but vary from 1.335 to 1.749. This leads to a challenge for the estimation of water and hydrocarbon saturation. Based on the analysis of Purcell equation and assumption that rock resistivity is determined by the parallel connection of numerous capillary resistances, a theoretical expression of cementation factor in terms of porosity and permeability is established. Then, cementation factor can be calculated if the parameters of porosity and permeability are determined. In the field application, porosity can be easily obtained by conventional logs. However, it is a tough challenge to estimate permeability due to the strong heterogeneity of low permeability reservoirs. Thus, the Schlumberger Doll Research (SDR) model derived from NMR logs has been proposed to estimate permeability. Based on the analysis of the theoretical expressions of cementation factor and SDR model, a novel cementation factor prediction model, which is relevant to porosity and logarithmic mean of NMR T2 spectrum (T2lm), is derived. The advantage of this model is that all the input information can be acquired from NMR logs accurately. In order to confirm the credibility of the novel model, the resistivity and corresponding laboratory NMR measurements of 27 core samples are conducted. The credibility of the model is confirmed by comparing the predicted cementation factors with the core analyzed results. The absolute errors for all core samples are lower than 0.071. Once this model is extended to field application, the accuracy of water and hydrocarbon saturation estimation will be significantly improved.

Applicability of Classical Permeability Estimation Models Based on NMR Logging in Tight Sandstones

Permeability cannot be directly predicted from porosity by using a single function in tight sandstones reservoirs due to the extreme heterogeneity. The hydraulic flow unit (HFU) approach and classification scale method (CSM) are available in permeability prediction, while they are all significant time-consuming. In this paper, based on the analysis of the proposed data sets of lab NMR experimental measurements by Xiao et al. (2012; 2013), the applicability of the classical SDR (Schlumberger Doll Research) and Timur-Coates models, which are used to estimate permeability from NMR logging is analyzed. A field example shows that the Timur-Coates model is valuable in tight sandstone permeability estimation once the involved input parameter of irreducible water saturation (Swi) can be accurately calculated without acquiring T2cutoff. While the SDR model is not available because the effects of hydrocarbon to NMR spectra cannot be removed.

Tight-Gas-Sand Permeability Estimation From Nuclear-Magnetic-Resonance (NMR) Logs Based on the Hydraulic-Flow-Unit (HFU) Approach

Summary The crossplot of porosity vs. Klinkenberg permeability (PERM) for 378 core samples, drilled from tight gas sands in the Xujiahe formation of the Anlu region-central Sichuan basin, southwest China, showed that tight-gas-sand permeability cannot be estimated effectively from porosity directly because only a poor relationship can be found between core-derived porosity and permeability because of the strong heterogeneity, especially for reservoirs with dominant microfractures (with porosities lower than 6.5%). However, the problem can be solved by introducing the HFU approach. In this paper, the 378 core samples were divided into five types on the basis of the difference of the flow-zone indicator (FZI), and then relationships of rock porosity and permeability were established for every type of core sample. By virtue of the analysis of the expression of FZI and the classical Schlumberger Doll Research (SDR) Center model, a novel technique used to obtain FZI from NMR logs was proposed and a corresponding model was established. The model parameters were calibrated by use of the laboratory NMR measurements of 54 plug samples taken from the Xujiahe formation. Carried out on the experimental data sets, this procedure can be extended to reservoir conditions to estimate consecutive formation permeability along the intervals through which NMR logs were acquired. The processing results of field examples illustrate that the calculated FZI values from field NMR logs match very well with the core analyzed results; the absolute errors among them are within the scope of 60.15. Moreover, permeability, estimated by use of the proposed technique and the core analyzed results are consistent. However, the calibrated SDR model is exclusive to the cases where formation permeability ranges from 0.2 to 0.4 md. To improve permeability prediction with the SDR model, many more core samples drilled from formations with dominant microfractures needed to be tested for laboratory NMR experiments to calibrate the SDR model for each HFU.