GANSim-3D for conditional geomodelling: theory and field application

Geomodelling of subsurface reservoirs is important for water resources, hydrocarbon exploitation, and Carbon Capture and Storage (CCS). Traditional geostatistics-based approaches cannot abstract complex geological patterns and are thus not able to simulate very realistic earth models. We present a Generative Adversarial Networks (GANs)-based 3D reservoir simulation framework, GANSim-3D, which can capture geological patterns and relationships between various conditioning data and earth models and is thus able to directly simulate multiple 3D realistic and conditional earth models of arbitrary sizes from given conditioning data. In GANSim-3D, the generator, designed to only include 3D convolutional layers, takes various 3D conditioning data and 3D random latent cubes (composed of random numbers) as inputs and produces a 3D earth model. Two types of losses, the original GANs loss and condition-based loss, are designed to train the generator progressively from shallow to deep layers to learn the geological patterns and relationships from coarse to fine resolutions. Conditioning data can include 3D sparse well facies data, 3D low-resolution probability maps, and global features like facies proportion, channel width, etc. Once trained on a training dataset where each training sample is a 3D cube of a small fixed size, the generator can be used for geomodelling of 3D reservoirs of large arbitrary sizes by directly extending the sizes of all inputs and the output of the generator proportionally. To illustrate how GANSim-3D is used for field geomodelling and also to verify GANSim-3D, a field karst cave reservoir in Tahe area of China is used as an example. The 3D well facies data and 3D probability map of caves obtained from geophysical interpretation are used as conditioning data. First, we create a training dataset consisting of facies models of 64×64×64 cells with a process-mimicking simulation method to integrate field geological patterns. The training well facies data and the training probability map data are produced from the training facies models. Then, the 3D generator is successfully trained and evaluated in two synthetic cases with various metrics. Next, we apply the pretrained generator for conditional geomodelling of two field cave reservoirs of Tahe area. The first reservoir is 800m×800m×64m and is divided into 64×64×64 cells, while the second is 4200m×3200m×96m and is divided into 336×256×96 cells. We fix the input well facies data and cave probability maps and randomly change the input latent cubes to allow the generator to produce multiple diverse cave reservoir realizations, which prove to be consistent with the geological patterns of real Tahe cave reservoir as well as the input conditioning data. The noise in the input probability map is suppressed by the generator. Once trained, the geomodelling process is quite fast: each realization with 336×256×96 cells takes 0.988 seconds using 1 GPU (V100). This study shows that GANSim-3D is robust for fast 3D conditional geomodelling of field reservoirs of arbitrary sizes.

A Statistical Approach to generate ensembles of observation data of precipitation using hindcast data over the Northwest Himalayas

<p>Availability of precipitation data at fine spatial resolution is highly desirable for hydroclimatic studies. Rain gauges are often considered as the primary source of precipitation data due to its reliability. However, due to either physical, climatic or economic constraints, setting up networks of rain gauges becomes unfeasible in many isolated terrains such as the Himalayan region. In the absence of gauge data, other alternate sources of weather information such as Satellite based Precipitation Products (SPPs) and Reanalysis precipitation Datasets (RPDs) are generally used. In this study, we aim to utilise 18 years of precipitation data (2001-2018) derived from the Integrated Multi-Satellite Retrievals for GPM (IMERG) at 10km spatial resolution as input to a Multiple-Point Statistics (MPS) based statistical model to obtain corresponding data for the year 2019 at 10km over the North-west Himalayan region. MPS is capable of generating fine scale data using the available coarse scale hindcast data by reproducing spatially connected spatial patterns. It requires data to be split into two parts. First part is called the training image and it requires both coarse and fine scale data. Second part is called the conditioning data which requires data only at coarse scale for the year 2019. In the attempt of using MPS as the tool for this study, the spatial field of Original IMERG data at 10 km (O_IMERG) is smoothen (S_IMERG) in order to transform the data features to a coarse scale reference data. The reference data used for this purpose is the High Asia Refined analysis (HAR) available at 30km spatial resolution over the South-Central Asia and Tibetan Plateau region. The variograms of both O_IMERG and S_IMERG are used to evaluate error frequency between the two data at specific distances followed by bias correction of S_IMERG. The bias corrected S_IMERG (BCS_IMERG) acts as the conditioning data for the MPS model. Training Image is composed of both BCS_IMERG and O_IMERG. Both the training image (year 2001-2018) and the conditioning data (2019) are provided to the MPS model. In addition to the variable of precipitation, the model also employs static parameters such as locational and topographical variables to help in identification of true patterns between training image and conditioning data. The study is significant in its ability to generate future precipitation information by utilising the available hindcast data observation data (10 km spatial resolution) by overcoming the spatial heterogeneity involved with observation data.</p>

Effects of working memory load and CS-US intervals on delay eyeblink conditioning

Background: Eyeblink conditioning is used in many different species to study motor learning and make inferences about cerebellar function. However, considerable discrepancies in performance between different species combined with evidence that awareness of stimulus contingencies affects performance indicates that eyeblink conditioning in part reflects activity in non-cerebellar regions. This questions whether eyeblink conditioning can be used as a pure measure of cerebellar function in humans. Methods: Here we explored two ways to reduce non-cerebellar influences on performance in eyeblink conditioning: (1) using a short interstimulus interval, and (2) having participants do working memory tasks during the conditioning. Data were analyzed, and the influence of the interstimulus interval and working memory tasks was assessed using a linear mixed effects model. Results: Our results show that subjects trained with a short interstimulus interval (150ms and 250ms) produce few conditioned responses after 100 trials. For subjects trained with a longer interstimulus interval (500ms), those who did working memory tasks produced fewer conditioned responses and had a more gradual learning curve, more akin to those reported in the animal literature. Conclusions: Our results suggest that having subjects perform working memory tasks during eyeblink conditioning can be a viable strategy to reduce non-cerebellar interference in the learning.

Modeling Three-Dimensional Anisotropic Structures of Reservoir Lithofacies Using Two-Dimensional Digital Outcrops

Reservoir heterogeneity is a key geological problem that restricts oil and gas exploration and development of clastic rocks from the early to late stages. Existing reservoir heterogeneity modeling methods such as multiple-point geostatistics (MPS) can accurately model the two-dimensional anisotropic structures of reservoir lithofacies. However, three-dimensional training images are required to construct three-dimensional reservoir lithofacies anisotropic structures models, and the method to use reservoir heterogeneity model of fewer-dimensional to obtain a three-dimensional model has become a much-focused research topic. In this study, the outcrops of the second member of Qingshuihe Formation (K1q2) in the northwestern margin of the Junggar Basin, which are lower cretaceous rocks, were the research target. The three-dimensional reservoir heterogeneity model of the K1q2 outcrop was established based on the unmanned aerial vehicle (UAV) digital outcrops model and MPS techniques, and the “sequential two-dimensional conditioning data” (s2Dcd) method was modified based on a sensitivity parameter analysis. Results of the parametric sensitivity analysis revealed that the isotropic multigrid simulations demonstrate poor performance because of the lack of three-dimensional training images, conditioning data that are horizontally discrete and vertically continuous, and distribution of lithofacies that are characterized by large horizontal continuities and small thicknesses. The reservoir lithofacies anisotropic structure reconstructions performed well with anisotropic multigrids. The simulation sequence of two-dimensional surfaces for generating the three-dimensional anisotropic structure of reservoir lithofacies models should be reasonably planned according to the actual geological data and limited hard data. In additional to this, the conditional probability density function of each two-dimensional training image should be fully utilized. The simulation results using only one two-dimensional section will have several types of noises, which is not consistent with the actual geological background. The anisotropic multigrid simulations and two-dimensional training image simulation sequence, proposed in this paper as “cross mesh, refinement step by step”, effectively reduced the noise generated, made full use of the information from the two-dimensional training image, and reconstructed the three-dimensional reservoir lithofacies anisotropic structures models, thus conforming to the actual geological conditions.

3D Multiple-point Statistics Simulations of the Roussillon Continental Pliocene Aquifer using DeeSse

This study presents a novel workflow to model the internal heterogeneity of complex aquifers using the multiple-point statistics algorithm DeeSse. We illustrate the applicability of this workflow on the Roussillon's aquifer in the region of Perpignan (southern France). This work is part of a project aiming at assessing the groundwater dynamics of this Mediterranean aquifer in the context of a growing population, climate change, and increasing pressure on the freshwater resources. We focus here on the geological heterogeneity of the Continental Pliocene layer because it is expected to influence possible saltwater intrusion process and its corresponding uncertainty quantification. The main aim of the paper is therefore to describe the procedure that is used to model the aquifer heterogeneity with a relatively small number of direct geological observations and a well defined geological concept. When few direct observations are available, the traditional geostatistical approaches cannot be applied easily because variogram inference is difficult. On the opposite, multiple-point statistics simulations can rely on a conceptual geological model. Here, the conceptual model consists not only of a training image displaying the spatial organization of the main sedimentological elements in space, but also in a set of additional information such as general trends and paleo orientations of the sedimentological features. The direct sampling algorithm DeeSse can be used in this context to model the expected heterogeneity. The workflow involves creating 2D non-stationary training images (TI) coupled during simulation with auxiliary information and controlled by hard conditioning data obtained from interpreted electrofacies. To control the non-stationarity, a 3D trend map is obtained by solving numerically the diffusivity equation as a proxy to describe the spatial evolution of the sedimentary patterns, from the source of the sediments to the outlet of the system. A 3D continuous rotation map is estimated from paleo orientations of the fluvial system. Both trend and orientation maps are derived from geological insights gathered from outcrops and general knowledge of processes occurring in these types of sedimentary environments. Finally, the 3D model is obtained by stacking 2D simulations following the paleo-topography of the aquifer. The vertical facies transition between two 2D simulations is controlled by both the hard conditioning data set and by simulating conditional data points from one simulation to another. This process allows to bypass the creation of a 3D training image while preserving the vertical continuity of the sedimentary objects.

Efficient and Scalable Approach to Equilibrium Conditional Simulation of Gibbs Markov Random Fields

We study the performance of an automated hybrid Monte Carlo (HMC) approach for conditional simulation of a recently proposed, single-parameter Gibbs Markov random field. This is based on a modified version of the planar rotator (MPR) model and is used for efficient gap filling in gridded data. HMC combines the deterministic over-relaxation method and the stochastic Metropolis update with dynamically adjusted restriction and performs automatic detection of the crossover to the targeted equilibrium state. We focus on the ability of the algorithm to efficiently drive the system to equilibrium at very low temperatures even with sparse conditioning data. These conditions are the most challenging computationally, requiring extremely long relaxation times if simulated by means of the standard Metropolis algorithm. We demonstrate that HMC has considerable benefits in terms of both computational efficiency and prediction performance of the MPR method.

Embryonic Methamphetamine Exposure Inhibits Methamphetamine Cue Conditioning and Reduces Dopamine Concentrations in Adult N2 Caenorhabditis elegans

Methamphetamine (MAP) addiction is substantially prevalent in today's society, resulting in thousands of deaths and costing billions of dollars annually. Despite the potential deleterious consequences, few studies have examined the long-term effects of embryonic MAP exposure. Using the invertebrate nematode Caenorhabditis elegans allows for a controlled analysis of behavioral and neurochemical changes due to early developmental drug exposure. The objective of the current study was to determine the long-term behavioral and neurochemical effects of embryonic exposure to MAP in C. elegans. In addition, we sought to improve our conditioning and testing procedures by utilizing liquid filtration, as opposed to agar, and smaller, 6-well testing plates to increase throughput. Wild-type N2 C. elegans were embryonically exposed to 50 μM MAP. Using classical conditioning, adult-stage C. elegans were conditioned to MAP (17 and 500 μM) in the presence of either sodium ions (Na+) or chloride ions (Cl-) as conditioned stimuli (CS+/CS-). Following conditioning, a preference test was performed by placing worms in 6-well test plates spotted with the CS+ and CS- at opposite ends of each well. A preference index was determined by counting the number of worms in the CS+ target zone divided by the total number of worms in the CS+ and CS- target zones. A food conditioning experiment was also performed in order to determine whether embryonic MAP exposure affected food conditioning behavior. For the neurochemical experiments, adult worms that were embryonically exposed to MAP were analyzed for dopamine (DA) content using high-performance liquid chromatography. The liquid filtration conditioning procedure employed here in combination with the use of 6-well test plates significantly decreased the time required to perform these experiments and ultimately increased throughput. The MAP conditioning data found that pairing an ion with MAP at 17 or 500 μM significantly increased the preference for that ion (CS+) in worms that were not pre-exposed to MAP. However, worms embryonically exposed to MAP did not exhibit significant drug cue conditioning. The inability of MAP-exposed worms to condition to MAP was not associated with deficits in food conditioning, as MAP-exposed worms exhibited a significant cue preference associated with food. Furthermore, our results found that embryonic MAP exposure reduced DA levels in adult C. elegans, which could be a key mechanism contributing to the long-term effects of embryonic MAP exposure. It is possible that embryonic MAP exposure may be impairing the ability of C. elegans to learn associations between MAP and the CS+ or inhibiting the reinforcing properties of MAP. However, our food conditioning data suggest that MAP-exposed animals can form associations between cues and food. The depletion of DA levels during embryonic exposure to MAP could be responsible for driving either of these processes during adulthood.

Challenges in conditioning a stochastic geological model of a heterogeneous glacial aquifer to a comprehensive soft data set

In traditional hydrogeological investigations, one geological model is often used based on subjective interpretations and sparse data availability. This deterministic approach usually does not account for any uncertainties. Stochastic simulation methods address this problem and can capture the geological structure uncertainty. In this study the geostatistical software TProGS is utilized to simulate an ensemble of realizations for a binary (sand/clay) hydrofacies model in the Norsminde catchment, Denmark. TProGS can incorporate soft data, which represent the associated level of uncertainty. High-density (20 m × 20 m × 2 m) airborne geophysical data (SkyTEM) and categorized borehole data are utilized to define the model of spatial variability in horizontal and vertical direction, respectively, and both are used for soft conditioning of the TProGS simulations. The category probabilities for the SkyTEM data set are derived from a histogram probability matching method, where resistivity is paired with the corresponding lithology from the categorized borehole data. This study integrates two distinct data sources into the stochastic modeling process that represent two extremes of the conditioning density spectrum: sparse borehole data and abundant SkyTEM data. In the latter the data have a strong spatial correlation caused by its high data density, which triggers the problem of overconditioning. This problem is addressed by a work-around utilizing a sampling/decimation of the data set, with the aim to reduce the spatial correlation of the conditioning data set. In the case of abundant conditioning data, it is shown that TProGS is capable of reproducing non-stationary trends. The stochastic realizations are validated by five performance criteria: (1) sand proportion, (2) mean length, (3) geobody connectivity, (4) facies probability distribution and (5) facies probability–resistivity bias. In conclusion, a stochastically generated set of realizations soft-conditioned to 200 m moving sampling of geophysical data performs most satisfactorily when balancing the five performance criteria. The ensemble can be used in subsequent hydrogeological flow modeling to address the predictive uncertainty originating from the geological structure uncertainty.