Generalized mixture Markov chain Monte Carlo inversion for seismic fluid discrimination

The purpose of the work was to construct petrophysical models of reservoir rocks of different rank: typical and unified. Typical models describe connections between the parameters of individual rocks lithotypes occurring in definite geological conditions and serving as the basis for the development of petrophysical classification of reservoir rocks in the oil geology. The principle of unification provides for creation of the models structure for different reservoir lithotypes both in the geological section and in the area. We have studied petrophysical properties of reservoir rocks of Carboniferous deposits in the central part of the Dnieper-Donets depression. Petrophysical properties of rocks in conditions close to the formational ones and relations between them were studied on a number of samples formed by the core samples of different age. Main geological factors that have an influence on reservoir properties of rocks were taken into consideration. While constructing and analysing of petrophysical models we have used a probable-statistic approach with the use of the correlative-regressive analysis. Result of the work is contained in typical petrophysical models for individual areas and in unified models obtained on consolidated samples for Lower Carboniferous deposits of this region. Characteristic features in variations of petrophysical properties of reservoir rocks of Carboniferous deposits and their models have been ascertained. A conclusion has been made that multidimensional models, in which the depth of occurrence of deposits is one of the parameters that are necessary to consider while constructing petrophysical models, are the most informative for determination of petrophysical properties of the studied deposits, and the models obtained by us are known to be a petrophysical basis for quantitative interpretation of data from geophysical studies in the boreholes of the given region.

In order to model petrophysical properties of hydrocarbon reservoir rocks, the underlying physics occurring in realistic rock pore structures must be captured. Experimental evidence showing variations of wetting occurring within a pore, and existence of the so-called 'non-Archie' behaviour, has led to numerical models using pore shapes with crevices (for example, square, elliptic, star-like shapes, etc.). This paper presents theoretical derivations and simulation results of a new pore space network model for the prediction of petrophysical properties of reservoir rocks. The effects of key pore geometrical factors such as pore shape, pore size distribution and pore co-ordination number (pore connectivity) have been incorporated into the theoretical model. In particular, the model is used to investigate the effects of wettability and saturation history on electrical resistivity and capillary pressure characteristics. The petrophysical characteristics were simulated for reservoir rock samples. The use of the more realistic grain boundary pore (GBP) shape allows simulation of the generic behaviour of sandstone rocks, with various wetting scenarios. The predictions are in close agreement with electrical resistivity and capillary pressure characteristics observed in experiments.

<p>Imaging the subsurface structure through seismic data needs various information and one of the most important information is the subsurface P-wave velocity. The P-wave velocity structure mainly influences on the location of the reflectors during the subsurface imaging, thus many algorithms has been developed to invert the accurate P-wave velocity such as conventional velocity analysis, traveltime tomography, migration velocity analysis (MVA) and full waveform inversion (FWI). Among those methods, conventional velocity analysis and MVA can be widely applied to the seismic data but generate the velocity with low resolution. On the other hands, the traveltime tomography and FWI can invert relatively accurate velocity structure, but they essentially need long offset seismic data containing sufficiently low frequency components. Recently, the stochastic method such as Markov chain Monte Carlo (McMC) inversion was applied to invert the accurate P-wave velocity with the seismic data without long offset or low frequency components. This method uses global optimization instead of local optimization and poststack seismic data instead of prestack seismic data. Therefore, it can avoid the problem of the local minima and limitation of the offset. However, the accuracy of the poststack seismic section directly affects the McMC inversion result. In this study, we tried to overcome the dependency of the McMC inversion on the poststack seismic section and iterative workflow was applied to the McMC inversion to invert the accurate P-wave velocity from the simple background velocity and inaccurate poststack seismic section. The numerical test showed that the suggested method could successfully invert the subsurface P-wave velocity.</p>

Ocean submesoscale dynamics are thought to play a key role in both the climate system and ocean productivity, however, subsurface observations at these scales remain rare. Seismic oceanography, an established acoustic imaging method, provides a unique tool for capturing oceanic structure throughout the water column with spatial resolutions of tens of meters. A drawback to the seismic method is that temperature and salinity are not measured directly, limiting the quantitative interpretation of imaged features. The Markov Chain Monte Carlo (MCMC) inversion approach has been used to invert for temperature and salinity from seismic data, with spatially quantified uncertainties. However, the requisite prior model used in previous studies relied upon highly continuous acoustic reflection horizons rarely present in real oceanic environments due to instabilities and turbulence. Here we adapt the MCMC inversion approach with an iteratively updated prior model based on hydrographic data, sidestepping the necessity of continuous reflection horizons. Furthermore, uncertainties introduced by the starting model thermohaline fields as well as those from the MCMC inversion itself are accounted for. The impact on uncertainties of varying the resolution of hydrographic data used to produce the inversion starting model is also investigated. The inversion is applied to a mid-depth Mediterranean water eddy (or meddy) captured with seismic imaging in the Gulf of Cadiz in 2007. The meddy boundary exhibits regions of disrupted seismic reflectivity and rapid horizontal changes of temperature and salinity. Inverted temperature and salinity values typically have uncertainties of 0.16°C and 0.055 psu, respectively, and agree well with direct measurements. Uncertainties of inverted results are found to be highly dependent on the resolution of the hydrographic data used to produce the prior model, particularly in regions where background temperature and salinity vary rapidly, such as at the edge of the meddy. This further advancement of inversion techniques to extract temperature and salinity from seismic data will help expand the use of ocean acoustics for understanding the mesoscale to finescale structure of the interior ocean.

Until an accurate fluid saturation tool is designed, the lack of a solid link between the petrophysical properties of reservoir rock and fluid is a real problem. The reservoir water saturation models are normally based on the standard Archie model to calculate fluid volumes. However, in tight carbonate reservoirs with heterogeneous wettability this model may present unrealistic results for the fluid volume (e.g., water/oil/gas) estimates. An integrated model using resistivity and NMR logs is introduced to quantify the movability of hydrocarbons in the reservoir transition zone. Pay zones may be missed in low-resistivity reservoirs (i.e., transition zones) due to the high water volume estimated from conventional logs. New synthetic resistivity logs are made in both the invaded and non-invaded zones based on assumptions made on the basis of pore and fluid interaction in the NMR log T2 distribution. The differences between the original and synthetic resistivity logs in connection with other log data are dominant signatures of the fluid volumes and movability in the formation. The new approach is developed on basis of exploration well data from a complex and heterogeneous carbonate reservoir in the Norwegian Barents Sea. The estimated fluid movability results are in agreement with the wireline formation tester (WFT) measurements of the well. This model, in addition to the transition zone, can also be applied for hydrocarbon bearing intervals which contain connate water. This approach shows that the reservoir wettability signature can also be identified by comparing the measured and constructed resistivity logs.

The petrophysical inversion of seismic data is one of the key components of seismic reservoir characterization. The goal of petrophysical inversion is to estimate the petrophysical properties of reservoir rocks, such as porosity, volumes of minerals or lithologies, and water and hydrocarbon saturations, from seismic data. This process can be performed by combining seismic amplitude-variation-with-offset (AVO) modeling and rock-physics relations with deterministic or probabilistic inverse theory methods, either in a two-step approach based on seismic AVO inversion and rock-physics inverse mapping or in a single-loop step that includes both. We present a comprehensive MATLAB library named Geostatistical Petrophysical Inversion. The novelty of the library lies in a single-loop geostatistical inversion method based on probability field simulation and ensemble smoother multiple data assimilation, as well as its implementation for applications to 3D data sets. The library also includes a Bayesian petrophysical inversion based on the two-step approach for comparison. We illustrate the main algorithms, explain the structure of the source codes, and demonstrate the library applications through 1D and 3D examples.

Raising the world's demand for energy accompanied by decrease in the ease of oil exploration and production, has forced the oil industry to investigate novel and advanced techniques for different stages of providing the energy; from early stages of oil exploration to increasing the production from oil reservoirs by secondary or tertiary recovery. A critical phase that plays an important role in simulating oil reservoirs and therefore managing the different field's development plans is reservoir characterization. Poor reservoir characterization may lead to implementation incorrect methods in field development and reservoir management and cause losing unrecoverable sources and costs. Characterization of carbonate rocks is a vital process, because carbonate systems constitute more than half of the oil reservoirs of the world and also most of the reservoirs in the Middle East. On the other hand heterogeneity is a problem that causes these types of reservoirs not to obey from general rules and formula. Due to the need for a comprehensive model for characterizing carbonate reservoirs, a very extensive integrated study of all the methods available for different stages of a reservoir characterization process (reservoir rock typing, rock type prediction, saturation distribution and modeling, dynamic reservoir characterization, absolute permeability and relative permeability prediction) is done in this paper. For providing the best model, geophysical and petrophysical approaches are taken into consideration and are discussed in detail and the best combination and integration of them is presented as a comprehensive model for characterizing heterogeneous carbonate reservoirs. Then using conventional core and different wireline logs and also seismic data, this model is used to characterize numbers of carbonate oil reservoirs of Sarvak formation of Iran. Applying this model can save time of characterizing carbonate reservoirs and lead to best images of petrophysical properties of reservoir rocks and the most accurate reservoir simulation models.

For exploring subsurface resources such as oil or natural gas reservoirs, seismic reflection survey has been widely iplementd in order to image subsurface structures. In recent years, utilization of S-wave or converted wave is required for estimating lithology or petrophysical properties of reservoir rock. However, such an analysis of S-wave seismograms had been relatively difficult. On the other hand, equivalent offset migration (EOM) is one of the prestack time migrations and has been found to be effective method for imaging S-wave information on the common scatter point (CSP) gather with recorded horizontal component in our previous study. Furthermore, S-wave AVO effect has also been confirmed by the amplitude reversal of S-wave event on the CSP gathers. Therefore, we propose the procedure of accurate estimation of densities and shear modulus with S-wave source. First, we conduct numerical experiment with a 2D layer model using horizontal point force to obtain horizontal component seismic data, in which we can get higher S/N data about S-wave. Second, we implement EOM with those data to get CSP gather, and calculate each cross-correlated value versus incident angle as observed waveform information. Third, in contrast, we generate calculated waveform information as a function of incident angle and physical properties with geometrical spreading, radiation pattern and S-wave reflection coefficient. Finally, we can estimate the optimal solutions by minimizing the misfit from the both information.

Objectives/Scope X-ray Micro-Computer Tomography (μ-CT) has been widely adopted in earth science and petroleum engineering due to its non-destructive characteristic. Meanwhile, this three-dimensional-imaging method can be integrated with computer simulation to investigate petrophysical properties of reservoir rocks at pore scales. However, the application of μ-CT is limited by the trade-off between field of view and resolution, and it is challenging to indicate the pore structure of rocks, especially for shale or carbonate rocks. To address this issue, deep-learning-based super-resolution techniques have rapidly developed in the past few years. Methodology In this study, a super-resolution algorithm based on the state-of-the-art (STOA) diffusion model is proposed to generate super-resolved CT images for carbonate rocks. The proposed method adapts denoising diffusion probabilistic models to conditional image generation and performs super-resolution through a stochastic denoising process. Cascaded diffusion model is utilized to increase the training speed and generate high fidelity CT images. This method exhibits superior performance in the resolution-enhancement of CT images at various magnification factors (with a large scaling factor of up to 16) without the occurrence of image-noise and image-blurring issue, and the super-resolved CT images performs well for the calculation of petrophysical properties of carbonate rocks. Results This algorithm is applied to the carbonate rock and the performance of the diffusion model is evaluated by quantitative extraction and qualitative visualization. In addition, this method is compared with other methods, such as GAN, Variational Autoencoder, and Super-Resolution Convolutional Neural Networks (SRCNN). The results indicate that the built model shows excellent potential in enhancing the resolution of heterogeneous carbonate rocks. To be specific, the super-resolved images exhibit clear and sharp edges and a detailed pore network. In addition, it performs well on different upscaling factors (up to 16) and is superior to the existing super-resolution approaches (for both supervised and unsupervised algorithms). This study provides a novel deep-learning-based method using a diffusion model to enhance the resolution of μ-CT images of carbonate rocks (up to 16). Novelty The novelty of this study is three-fold. First, this method belongs to unsupervised learning, indicating that pairs of high-resolution and low-resolution CT images are no longer needed. Second, a large scaling factor (up to 16) is reached without an image-blurring issue, which normally occurs in other deep-learning-based super-resolution algorithms. Third, the quality of super-resolved images is promising and faithful when compared with other generated learning methods, such as Generative Adversarial Networks (GAN).

Chapter 13 - Conclusions (Chapters 9 to 12)

Productive zones or "sweet spots" in unconventional reservoirs depend on their geomechanical and petro-physical rock properties. Machine learning algorithms can significantly improve workflows used for evaluating sweet-spots in such complex reservoirs. The objectives of this paper are to: (i) quantity the effects of rock mechanical properties on fracturing treatments using data analytics and (ii) use regression-based machine learning algorithms and improve sweet-spot assessment in complex mudrock reservoirs. We used a hydraulic fracturing simulator that couples fluid-flow with fracture deformation in discrete fracture networks to model field-scale hydraulic fracturing treatments. First, we selected several geomechanical properties related to rock fracability. We obtained wide variation in aforementioned properties using a quasi-random design approach. Then, we performed 200 slick-water fracturing simulations with quasi-random distribution of design parameters using the hydraulic fracturing simulator. We quantified the performance of fracture treatments by calculating the effective short- and long-term Stimulated Reservoir Volume of the reservoir (SRV). We finally analyzed the results of numerical simulations by applying regression analysis to improve the assessment of sweet-spots in complex reservoirs. The regression analysis involved the following simulation variables: shear modulus, poisson's ratio, fracture friction coefficient, principal horizontal stress anisotropy, fracture toughness, fracture closure stress, shear dilation angle, and initial fracture aperture. The SRV results were analyzed using: linear regression, linear regression with beta coefficients, ridge and lasso regression, and principal component regression algorithms. The regression analysis revealed that linear models can explain 73.1% and 59.2% variance in short- and long-term SRV values, respectively. The ridge and lasso regression and beta linear regression analysis revealed that stress anisotropy, fracture dilation angle, and fracture friction coefficient show the highest effect on the aforementioned SRV values. In all the regression models, shear modulus and critical fracture toughness did not have a significant effect on SRV but these parameters are important as they are correlated to other parameters that directly impact fluid flow. The results of using data analytic approaches demonstrated that factors related to unpropped fracture conductivity play a critical role in success of hydraulic fracturing treatments. We have also introduced and compared the performances of different machine learning algorithms that might be used to assess the impact of geomechanical properties on fracturing treatments. Such supervised and unsupervised machine learning algorithms can help in integrating legacy field data in the analysis of productive zones in complex reservoirs. Such analysis can also be used to develop data-based models that might improve the study of sweet-spot and fracturing treatment performance assessment in complex reservoirs.

This paper was prepared for the 49th Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Houston, Texas, Oct. 6–9, 1974. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract This paper briefly reviews the current status of knowledge on the effect of elevated temperature on pore volume, permeability, electrical resistivity and capillary pressure behavior of reservoir rocks. Various authors have suggested that these effects may be caused by changes in the properties of the rock matrix or the properties of the rock matrix or the fluids or by a change in the wettability of the rock-fluid system. These suggested causes are examined in the light of the similarities and the contradictions in the published results, consider the basic petrophysical relationships and idealized pore geometries. It is concluded that the temperature sensitivity of rock-fluid wettability in explaining the observed temperature effects on petrophysical properties may have been overemphasized in the literature, and in this regard due consideration should be given to the change in fluid viscosity and rock matrix with temperature. Although the explanation of some of the observed effects on rock properties or the extent to which the properties or the extent to which the reported results apply to real reservoirs may be questioned, these effects are important, particularly when dealing with production from deep, hot reservoirs or thermal oil recovery projects. The possible errors in projects. The possible errors in well log analysis and formation evaluation due to the common practice of neglecting temperature effects on some rock properties are pointed out. No results are available on the effects of temperature on the relative permeability to oil in gas-oil and permeability to oil in gas-oil and gas-oil-water systems. Calculations were made to predict these effects. Through hypothetical examples it is shown that the error due to neglecting temperature effects on petrophysical properties may be significant when properties may be significant when predicting performance of primary predicting performance of primary (oil expansion, solution gas) and secondary (water-flood) recovery projects. Introduction The thermal oil recovery techniques have become well accepted in the oil industry during the last two decades.

A two-phase, two-dimensional black oil simulator was developed for simulating reservoir production behavior with simultaneously occurring reservoir formation compaction and ground subsidence at the surface.The flow equations were solved by both alternating direction implicit procedure and strongly implicit procedure. Reservoir compaction was described on the basis of the experimental data reported. The magnitude of areal subsidence at the surface was calculated using reservoir compaction, utilizing the recently developed theory of poroelasticity. poroelasticity. Computer runs were used to generate a variety of data, such as reservoir Pressure variation with oil production, for different reservoir compaction production, for different reservoir compaction coefficients. It was found that the average reservoir pressure increased with the Compaction coefficient pressure increased with the Compaction coefficient for a given cumulative oil production.The model was used for generating the reservoir formation profiles, as well as the ground subsidence bowls for a variety of conditions. It was found that the subsidence behavior strongly depends on the depth of burial. For example, with an increase in the depth, the reservoir bottom surface may actually uplift, while the top surface subsides.The model was also used for studying the effect of subsidence on pressure buildup behavior. The calculated reservoir pressure was higher in a compacting than in a noncompacting reservoir, taking into account the variation of permeability with compaction.Another phase studied was the effect of rebound on reservoir performance when gas is injected into the formation. Even though rebound is small in practice (on the order of 10 percent of subsidence), practice (on the order of 10 percent of subsidence), the effect was clearly evident in the reservoir pressure-production behavior. However, when there pressure-production behavior. However, when there was no rebound, gas injection simply inhibited compaction.Finally, the model was used for simulating the reported oil production and subsidence history of one of the Bolivar Coast oil fields in the Western Venezuela. Fair agreement was obtained between the observed and the predicted behavior. Introduction The phenomenon of ground subsidence associated with production of oil or gas from underground hydrocarbon reservoirs is not common; however, it does present environmental problems in a few oil-producing areas around the world. Notable examples are the Wilmington oil field, below Long Beach, Calif. where almost 30 ft of subsidence have been recorded, and the oil fields near and under Lake Maracaibo in Venezuela, where the surface has subsided as much as 10 ft. Other cases have been reported in Harris County, Tex., in the Niigata district of Japan, and in the Po Delta in Italy.Numerous causes may give rise to ground subsidence, either natural or as a result of man's activities. However, as far as the problem at hand is concerned, the observed land subsidence is considered to be a result of reservoir compaction, resulting from pore pressure decline in reservoirs that meet certain specific geometrical and structural conditions. The changes in the petrophysical properties of reservoir rocks caused by compaction properties of reservoir rocks caused by compaction have been studied to some extent, as well as the influence of such changes on the fluid production behavior of the reservoir. However, very little has been accomplished in relating the compaction of the underground reservoir with the subsidence occurring at the surface. Among the few studies conducted on this problem, the most realistic are those that consider subsidence above a disk-shaped reservoir, in which a uniform pressure reduction has occurred. These studies do not simulate the fluid production behavior of the compacting reservoir as such; this is considered to be known and is used to determine the compaction of the reservoir and the accompanying subsidence. SPEJ P. 411

This study examines the geomechanical effects of depleted oil and gas reservoir rocks during underground hydrogen storage (UHS), with a specific focus on the Red River Formation in North Dakota. As the transition to renewable energy sources accelerates, hydrogen storage in geological formations presents a promising solution for large-scale energy storage. However, numerous challenges and barriers exist that prevent this technology from becoming a widely available decarbonization solution. The UHS process comprises multiple cycles of injection and withdrawal. These cycles may elevate the risk of fracturing or seal integrity failure in certain reservoirs. Furthermore, it is crucial to assess the potential alteration of rocks caused by hydrogen exposure to understand its impact on the mechanical properties of the reservoir rock and caprock. This study investigates the effect of geomechanical change in the mechanical and petrophysical properties of reservoir rock and caprock rocks (Carbonate + Anhydrite), crucial factors for securing subsurface hydrogen containment. Core samples from three wells in the Red River Formation's Zone B were subjected to high-pressure, high-temperature (HPHT) conditions simulating underground storage environments, including 30-day hydrogen exposure at 2000 psi and 140°C. Advanced analytical techniques including Nuclear Magnetic Resonance (NMR) porosity measurements, pulse-decay permeability analysis, and ultrasonic velocity measurements were employed to assess geomechanical changes before and after hydrogen exposure. The results revealed distinct lithological control on hydrogen-rock interactions with favorable implications for storage integrity. Carbonate reservoir samples demonstrated systematic porosity increases ranging from 9.7% to 23.1%, with corresponding permeability enhancements of 12.7% to 25.8%. Despite these petrophysical changes, mechanical properties showed improvement, with dynamic Young's modulus increasing by 1.7% to 11.4% and compressional wave velocities enhancing by 8.6% to 30.1%. Poisson's ratio increased by 3.6% to 13.7%, indicating altered deformation characteristics that remain within acceptable operational ranges. Anhydrite caprock samples exhibited exceptional stability and enhanced sealing capacity under hydrogen exposure. Porosity changes were negligible (±2%), while permeability remained ultra-low with minimal variations (±4.5%). Remarkably, caprock mechanical properties showed significant strengthening, with Young's modulus increasing by 10.4% to 18.3% and compressional wave velocities improving by up to 22.1%. These enhancements indicate improved structural integrity and resistance to deformation under operational pressures. The systematic mechanical property improvements in both reservoir and caprock formations create a geomechanically favorable environment for hydrogen storage operations. These findings advance the understanding of geomechanical processes in UHS and provide crucial insights supporting the safe and efficient implementation of hydrogen storage in depleted carbonate reservoirs with anhydrite seals, particularly in similar geological settings throughout the Williston Basin.

Nuclear Magnetic Resonance (NMR) spectrometry has proved to be a good technique for determining the petrophysical properties of reservoir rocks; such as porosity and pore size distribution. We investigated how pore water rich in divalent ions affect the NMR signal from chalk with two different depositional textures. We compared two cases. The first experiments on outcrop chalk with high salinity brines showed that saturation with divalent ions (Mg2+, Ca2+ and SO42-) cause major shifts in the T2 distribution curve, probably due to precipitation in the pore space. In a second set of experiments, fluid samples where precipitation takes place were found to show shifts in the T2 relaxation curve due to the creation of crystals. We were able to identify how differences in the rock texture and precipitants within the pore space may affect the transverse relaxation time by altering the surface-to-volume ratio of the pore space. The results of this work could benefit the ongoing study on the optimization of the water composition for Enhanced Oil Recovery (EOR) methods and shed light on how it can affect the mechanical and physical properties of the rock.