Unleashing the Potential of Relative Permeability Using Artificial Intelligence

One of the most important aspects of any dynamic model is relative permeability. To unlock the potential of large relative permeability data bases, the proposed workflow integrates data analysis, machine learning, and artificial intelligence (AI). The workflow allows for the automated generation of a clean database and a digital twin of relative permeability data. The workflow employs artificial intelligence to identify analogue data from nearby fields by extending the rock typing scheme across multiple fields for the same formation. We created a fully integrated and intelligent tool for extracting SCAL data from laboratory reports, then processing and modeling the data using AI and automation. After the endpoints and Corey coefficients have been extracted, the quality of the relative permeability samples is checked using an automated history match and simulation of core flood experiments. An AI model that has been trained is used to identify analogues for various rock types from other fields that produce from the same formations. Finally, based on the output of the AI model, the relative permeabilities are calculated using data from the same and analog fields. The workflow solution offers a solid and well-integrated methodology for creating a clean database for relative permeability. The workflow made it possible to create a digital twin of the relative permeability data using the Corey and LET methods in a systematic manner. The simulation runs were designed so that the pressure measurements are history matched with the adjustment and refinement of the relative permeability curve. The AI workflow enabled us to realize the full potential of the massive database of relative permeability samples from various fields. To ensure utilization in the dynamic model, high, mid, and low cases were created in a robust manner. The workflow solution employs artificial intelligence models to identify rock typing analogues from the same formation across multiple fields. The AI-generated analogues, combined with a robust workflow for quickly QC’ing the relative permeability data, allow for the creation of a fully integrated relative permeability database. The proposed solution is agile and scalable, and it can adapt to any data and be applied to any field.

Simulation of Immiscible WAG Experiments Performed in Carbonate Rocks: The Impact of Heterogeneity on Hysteresis Phenomenon

Simulation of Water-Alternating-Gas (WAG) Experiments require precise estimation of hysteresis phenomenon in three-phase relative permeability. Most of the research available in the literature are focused on experiments performed on sandstone rocks and the study of carbonate rocks has attracted less attention. In this paper, a recently published hysteresis model by Heriot-Watt University (HWU) was used for simulation of WAG experiments conducted on mixed-wet homogenous carbonate rock. In this study, we simulated immiscible WAG experiments, which were performed under reservoir conditions on mixed-wet carbonate reservoir rock extracted from Abu Dhabi field by using real reservoir fluids. Experiments are performed with different injection scenarios and at high IFT conditions. Then, the results of the coreflood experiments were history matched using 3RPSim to generate two-phase and three-phase relative permeability data. Finally, the hysteresis model suggested by Heriot-Watt University was used for the estimation of hysteresis in relative permeability data. The performance of the model was compared with the experimental data from sandstones to evaluate the impact of heterogeneity on hysteresis phenomenon. It was shown that the available correlations for estimation of three-phase oil relative permeability fail to simulate the oil production during WAG experiments, while the modified Stone model suggested by HWU provided a better prediction. Overall, HWU hysteresis model improved the match for trapped gas saturation and pressure drop. The results show that the hysteresis effect is less dominant in the carbonate rock compared to the sandstone rock. The tracer test results show that the carbonate rock is more homogenous compared to sandstone rock. Therefore, the conclusion is that the hysteresis effect is negligible in homogenous systems.

Generative adversarial networks for modeling reservoirs with permeability anisotropy

The geological model is a main element in describing the characteristics of hydrocarbon reservoirs. These models are usually obtained using geostatistical modeling techniques. Recently, methods based on deep learning algorithms have begun to be applied as a generator of a geologic models. However, there are still problems with how to assimilate dynamic data to the model. The goal of this work was to develop a deep learning algorithm - generative adversarial network (GAN) and demonstrate the process of generating a synthetic geological model: • Without integrating permeability data into the model • With data assimilation of well permeability data into the model The authors also assessed the possibility of creating a pair of generative-adversarial network-ensemble smoother to improve the closed-loop reservoir management of oil field development.

Permeability of Buccal Mucosa

The buccal mucosa provides an alternative route of drug delivery that can be more beneficial compared to other administration routes. Although numerous studies and reviews have been published on buccal drug delivery, an extensive review of the permeability data is not available. Understanding the buccal mucosa barrier could provide insights into the approaches to effective drug delivery and optimization of dosage forms. This paper provides a review on the permeability of the buccal mucosa. The intrinsic permeability coefficients of porcine buccal mucosa were collected. Large variability was observed among the published permeability data. The permeability coefficients were then analyzed using a model involving parallel lipoidal and polar transport pathways. For the lipoidal pathway, a correlation was observed between the permeability coefficients and permeant octanol/water partition coefficients (Kow) and molecular weight (MW) in a subset of the permeability data under specific conditions. The permeability analysis suggested that the buccal permeation barrier was less lipophilic than octanol. For the polar pathway and macromolecules, a correlation was observed between the permeability coefficients and permeant MW. The hindered transport analysis suggested an effective pore radius of 1.5 to 3 nm for the buccal membrane barrier.

A Machine Learning Methodology for Rock-Typing Using Relative Permeability Curves

The determination of the petrophysical rock-types often lacks the inclusion of measured multiphase flow properties as the relative permeability curves. This is either the consequence of a limited number of SCAL relative permeability experiments, or due to the difficulty of linking the relative permeability characteristics to standard rock-types stemming from porosity, permeability and capillary pressure. However, as soon as the number of relative permeability curves is significant, they can be processed under the machine learning methodology stated by this paper. The process leads to an automatic definition of relative permeability based rock-types, from a precise and objective characterization of the curve shapes, which would not be achieved with a manual process. It improves the characterization of petrophysical rock-types, prior to their use in static and dynamic modeling. The machine learning approach analyzes the shapes of curves for their automatic classification. It develops a pattern recognition process combining the use of principal component analysis with a non-supervised clustering scheme. Before this, the set of relative permeability curves are pre-processed (normalization with the integration of irreducible water and residual oil saturations for the SCAL relative permeability samples from an imbibition experiment) and integrated under fractional flow curves. Fractional flow curves proved to be an effective way to unify the relative permeability of the two fluid phases, in a unique curve that characterizes the specific poral efficiency displacement of this rock sample. The methodology has been tested in a real data set from a carbonate reservoir having a significant number of relative permeability curves available for the study, in addition to capillary pressure, porosity and permeability data. The results evidenced the successful grouping of the relative permeability samples, according to their fractional flow curves, which allowed the classification of the rocks from poor to best displacement efficiency. This demonstrates the feasibility of the machine learning process for defining automatically rock-types from relative permeability data. The fractional flow rock-types were compared to rock-types obtained from capillary pressure analysis. The results indicated a lack of correspondence between the two series of rock-types, which testifies the additional information brought by the relative permeability data in a rock-typing study. Our results also expose the importance of having good quality SCAL experiments, with an accurate characterization of the saturation end-points, which are used for the normalization of the curves, and a consistent sampling for both capillary pressure and relative permeability measurements.

An Approach for Exploring the Application of the Flow Zone Index Concept in Describing Petrophysical Properties Using Available SCAL Data Relative Permeability

This paper describes a unique approach for exploring the Flow Zone Index (FZI) concept using available relative permeability data. It proposes an innovative routine for relating the FZI parameter to saturation end-points of relative permeability data and produces a better model for relative permeability curves. In addition, this paper shows distinct wettabilities for various core samples and validated functions between FZI and residual oil saturation (Sor), irreducible water saturation (Swi), maximum oil allowed to flow (Kro, max), maximum water allowed to flow (Krw, max),and mobile/recoverable oil (100-Swi-Sor). The wettability of the core samples were defined using cross-plots of relative permeability of oil (Kro), relative permeability of water (Krw), and water saturation (Sw). After classifying the data sets into their respective wettabilities based on these criteria, a stepwise non-linear regression analysis was undertaken to develop realistic correlations between the FZI parameter, initial water saturation and end-point relative permeability parameters. In addition, a correlation using Corey's type generalised model was developed using relative permeability data, with new power law constants and well defined curves. Other parameters, including Sor, Swi, Kro, max, Krw,max and mobile oil, were plotted against FZI and correlations developed for them showed unique well behaved plots with the exception of the Sor plot. A possible theory to explain this unexpected behaviour of the FZI Vs Sor cross plot was noted and discussed. These derived functions and established relationships between the FZI term and other petrophysical parameters such as permeability, porosity, water saturation, relative permeability and residual oil saturation can be applied to other wells or reservoir models where these key parameters are already known or unknown. These distinctive established correlations could be employed in the proper characterization of a reservoir as well as predicting and ground truthing petrophysical properties.

Closing the Loop on a History Match for a Permian EOR Field Using Relative Permeability Data Uncertainty

Reservoir production forecasts are inherently uncertain due to the lack of quality data available to build predictive reservoir models. Multiple data types, including historical production, well tests (RFT/PLT), and time-lapse seismic data, are assimilated into reservoir models during the history matching process to improve predictability of the model. Traditionally, a ‘best estimate’ for relative permeability data is assumed during the history matching process, despite there being significant uncertainty in the relative permeability. Relative permeability governs multiphase flow in the reservoir; therefore, it has significant importance in understanding the reservoir behavior as well as for model calibration and hence for reliable production forecasts. Performing sensitivities around the ‘best estimate’ relative permeability case will cover only part of the uncertainty space, with no indication of the confidence that may be placed on these forecasts. In this paper, we present an application of a Bayesian framework for uncertainty assessment and efficient history matching of a Permian CO2 EOR field for reliable production forecast. The study field has complex geology with over 65 years of historical data from primary recovery, waterflood, and CO2 injection. Relative permeability data from the field showed significant uncertainty, so we used uncertainties in the saturation endpoints as well as in the curvature of the relative permeability in multiple zones, by employing generalized Corey functions for relative permeability parameterization. Uncertainty in the relative permeability is used through a common platform integrator. An automated workflow generates the first set of relative permeability curves sampled from the prior distribution of saturation endpoints and Corey exponents, called ‘scoping runs’. These relative permeability curves are then passed to the reservoir simulator. The assumptions of uncertainties in the relative permeability data and other dynamic parameters are quickly validated by comparing the scoping runs and historical observations. By creating a mismatch or likelihood function, the Bayesian framework generates an ensemble of history matched models calibrated to the production data which can then be used for reliable probabilistic forecasting. Several iterations during the manual history match did not yield an acceptable solution, as uncertainty in the relative permeability was ignored. An application of the Bayesian inference accelerated by a proxy model found the relative permeability data to be one of the most influential parameters during the assisted history matching exercise. Incorporating the uncertainty in relative permeability data along with other dynamic parameters not only helped speed up the model calibration process, but also led to the identification of multiple history matched models. In addition, results show that the use of the Bayesian framework significantly reduced uncertainty in the most important dynamic parameters. The proposed approach allows incorporating previously ignored uncertainty in the relative permeability data in a systematic manner. The user-defined mismatch function increases the likelihood of obtaining an acceptable match and the weights in the mismatch function allow both the measurement uncertainty and the effect of simulation model inaccuracies. The Bayesian framework considers the whole uncertainty space and not just the history match region, leading to the identification of multiple history matched models.

Development and evaluation of two-parameter linear free energy models for the prediction of human skin permeability coefficient of neutral organic chemicals

The experimental values of skin permeability coefficients, required for dermal exposure assessment, are not readily available for many chemicals. The existing estimation approaches are either less accurate or require many parameters that are not readily available. Furthermore, current estimation methods are not easy to apply to complex environmental mixtures. We present two models to estimate the skin permeability coefficients of neutral organic chemicals. The first model, referred to here as the 2-parameter partitioning model (PPM), exploits a linear free energy relationship (LFER) of skin permeability coefficient with a linear combination of partition coefficients for octanol–water and air–water systems. The second model is based on the retention time information of nonpolar analytes on comprehensive two-dimensional gas chromatography (GC × GC). The PPM successfully explained variability in the skin permeability data (n = 175) with R2 = 0.82 and root mean square error (RMSE) = 0.47 log unit. In comparison, the US-EPA’s model DERMWIN™ exhibited an RMSE of 0.78 log unit. The Zhang model—a 5-parameter LFER equation based on experimental Abraham solute descriptors (ASDs)—performed slightly better with an RMSE value of 0.44 log unit. However, the Zhang model is limited by the scarcity of experimental ASDs. The GC × GC model successfully explained the variance in skin permeability data of nonpolar chemicals (n = 79) with R2 = 0.90 and RMSE = 0.23 log unit. The PPM can easily be implemented in US-EPA’s Estimation Program Interface Suite (EPI Suite™). The GC × GC model can be applied to the complex mixtures of nonpolar chemicals.