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Summary The complexity of physics-based modeling of fluid flow in hydraulically fractured unconventional reservoirs, together with the abundant data from repeated factory-style drilling and completion of these resources, has prompted the development and application of data-driven statistical models for predicting hydrocarbon production performance. More recently, machine learning algorithms have been widely studied in developing data-driven prediction models for unconventional reservoirs. These models often require a large amount of high-quality training data with sufficient range to avoid excessive extrapolation and produce reliable predictions. Unlike statistical models, physics-based models represent causal relations between input and output variables to provide predictions beyond available data. While a detailed physics-based description of fluid flow in unconventional reservoirs is not yet available, approximate physical flow functions have been proposed to capture the general production behavior of unconventional wells. These physical functions can be augmented with the available data to improve data-driven methods by constraining the models to adhere to the general production trends. In this paper, we develop a physics-constrained data-driven model by embedding physical flow functions into neural network models. Since the performance of the physics-constrained model depends on the relevance of the embedded physics, a sizeable residual prediction error is expected if the collected data do not sufficiently match the embedded model. The residual model typically represents errors in the description of inputs or any missing physical phenomenon. We compensate for such errors through residual learning, where an auxiliary neural network is designed to learn the complex relationship between the input parameters (such as formation and completion properties) and the expected prediction residuals. The new physics-guided deep learning (PGDL) model augments any physics-constrained prediction model with residual learning to increase its prediction accuracy. Several synthetic and actual field data sets, from the Bakken play, are used to demonstrate the performance of the PGDL model.

Summary Constructing reliable data-driven models to predict well production performance (e.g., estimated ultimate recovery, cumulative production, production curves, etc.) for unconventional reservoirs requires large amounts of data. However, when considering unconventional reservoirs in their early stages of development, where data and the wells drilled are limited, one may benefit from leveraging available data and/or pretrained models from other more developed fields. Transfer learning, the process of storing knowledge gained while solving one problem (source data) and applying it to solve a different but related problem (target data), provides a workflow for alleviating data needs in training a data-driven model in fields with limited data. However, a pitfall in the application of transfer learning is the possibility of negative transfer, that is, transferring incorrect or irrelevant knowledge to the target data. In particular, the black-box nature of most data-driven models, e.g., neural networks, support vector machines, and random forest, makes it difficult to completely interpret the contribution of different source models used for knowledge transfer. Hence, ranking the viability of source models for transfer learning can reduce the risk of negative transfer and improve the prediction performance. In this paper, we illustrate the impact of negative transfer and how it can be identified, and present a new approach for ranking multiple source models based on their positive transfer contribution. Finally, we propose a framework to build a reliable model to predict well production performance by combining multiple sources of information into one network to be transferred and retrained with limited data in fields at their early stages of development.

Given sufficiently extensive data, deep-learning models can effectively predict the behavior of unconventional reservoirs. However, current approaches in building the models do not directly reveal the causal effects of flow behavior, underlying physics, or well-specific correlations; especially when the models are trained using data from multiple wells of a large field. Field observations have indicated that a single reservoir does not have similar production behaviors. This makes pre-filtering the data to build local models that capture region specific correlations more pertinent than a single global model that will provide averaged-out predictions from different correlations. In this work, we investigate a sophisticated network architecture to expedite the clustering process by training the global model. We utilize attention-based (transformer) neural networks for the input data before mapping to the target variable to extract the attention scores between well properties and the production performance. We leverage the interpretability from these attention-based models to improve the prediction performance for data-centric models derived from clustered datasets. We show the benefits of building local models that are more accurate as they learn correlations that are more region/data specific. Specifically, by utilizing the attention mechanism, we can separate and curate data subsets to train local models, improving the prediction performance by reducing the variability in the entire field.

Neural network predictive models are popular for production forecasting in unconventional reservoirs. They have the ability to learn complex input-output mapping between well properties and observed production responses from the large amount of data collected in the field. Additionally, the flow behavior in hydraulically fractured unconventional reservoirs is not well understood making such statistical models practical. Variants of neural networks have been proposed for production prediction in unconventional reservoirs, offering predictive capability of varying levels of granularity, accuracy and robustness against noisy and incomplete data. Neural network predictive models that incorporate physical understanding are especially useful for subsurface systems as they provide physically sound predictions. In this work, we propose a new Dynamic Physics-Guided Deep Learning (DPGDL) model that incorporates physical functions into neural networks and uses residual learning to compensate for the imperfect description of the physics. The new formulation allows for dynamic residual correction, avoids unintended bias due to less-than-ideal input data, and provides robust long-term predictions. The DPGDL model improves upon a static formulation by utilizing a masked loss function to enable learning from wells with varying production lengths and by improving the results when partially-observed timesteps are present. We also develop a new sequence-to-sequence residual model to correct additional biases in the long-term predictions from the physics-constrained neural networks. Several synthetic datasets with increasing complexity as well as a field dataset from Bakken are used to demonstrate the performance of the new DPGDL model.

When a limited number of wells are drilled at the early stages of developing unconventional fields, the available data is insufficient for developing data-driven models. To compensate for the lack of data in new fields, transfer learning may be adopted by using a previously learned model/knowledge from similar fields (source data) to build a predictive model for the new field. To be effective, transfer learning requires the source and target fields to have similarities and to ensure relevant information/knowledge is transferred. The transfer of irrelevant knowledge may impede the training process and lead to a negative knowledge transfer. When multiple source data are available, it is important to identify each source data's relevance and potential contribution to the target data. We introduce a framework to rank different source datasets and determine their capability for transfer learning. The methodology relies on using knowledge learned from datasets with similar features to the target dataset. This methodology helps circumvent the data needs for training while ascertaining that the right knowledge is transferred when developing new fields. Additionally, the framework allows for combining relevant features from multiple source models (with similar ranks). It allows for transferring the knowledge learned from mature fields to improve the performance of deep learning proxy models for new fields with similar features.

Predictive models that incorporate physical information or constraints are used for production prediction in subsurface systems. They come in many flavors; some include additional terms in the objective function, some directly embed physical functions and some use neural network layers to explicitly perform physical computations. In unconventional reservoirs that are characterized by tight fractured formations, a detailed and reliable description of the flow and transport processes is not yet available. Existing physics-based models use overly simplifying assumptions that may result in gross approximations. In physics-constrained neural network models, the network predictive performance can be degraded when the embedded physics does not represent the relationship within the observed data.We propose dynamic residual learning to improve the predictions from a physics-constrained neural network, whereby an auxiliary neural network component is introduced to compensate for the imperfect description of the constraining physics. When a dataset cannot be fully represented by a trained physics-constrained model, the predictions come with a large error or residual when compared to the ground truth. A deep neural network utilizing a masked loss function to enable learning from wells with varying production lengths is employed to learn the complex spatial and temporal correspondence between the well properties such as formation and completion parameters to the expected residuals. The new formulation allows for dynamic residual correction, avoids unintended bias due to less-than-ideal input data, and provides robust long-term predictions when partially-observed timesteps are present. The proposed method results in a final prediction that combines the prediction from the physics-constrained neural network with the predicted residual from the auxiliary neural network component. Several synthetic datasets with increasing complexity as well as a field dataset from Bakken are used for demonstration.

The machine learning method, now widely used for predicting well performance from unconventional reservoirs in the industry, generally needs large data sets for model development and training. The large data sets, however, are not always available, especially for newly developed unconventional plays. The objective of this work is to develop an innovative machine learning method for predicting well performance in unconventional reservoirs with a relatively small data set.For a small training data set, the corresponding machine learning model can significantly suffer from so-called overfitting meaning that the model can match the training data but has poor predictivity. To overcome this, our new method averages predictions from multiple models that are developed with the same model input, but different initial guesses of model parameters that are unknowns in a machine learning algorithm and determined in the model training. The averaged results are used for the final model prediction. Unlike traditional ensemble learning methods, each prediction in the new method uses all the input data rather than its subset. We mathematically prove that the averaged prediction provides less model uncertainty and under certain conditions the optimum prediction. It is also demonstrated that the method practically minimizes the overfitting and gives relatively unique prediction. The usefulness of the method is further confirmed by its successful application to the data set collected from less than 100 wells in an unconventional reservoir. Sensitivity results with the trained machine learning model show that the model results are consistent with the domain knowledge regarding the production from the reservoir.

Summary Prediction of well production from unconventional reservoirs is often a complex problem with an incomplete understanding of physics and a considerable amount of data. The most effective way for dealing with it is to use the gray-box approach that combines the strengths of physics-based models and machine learning (ML) used for dealing with certain components of the prediction where physical understanding is poor or difficult. However, the development of methodologies for the incorporation of physics into ML is still in its infancy, not only in the oil and gas industry, but also in other scientific and engineering communities, including the physics community. To set the stage for further advancing the use of combining physics-based models with ML for predicting well production, in this paper we present a brief review of the current developments in this area in the industry, including ML representation of numerical simulation results, determination of parameters for decline curve analysis (DCA) models with ML, physics-informed ML (PIML) that provides an efficient and gridless method for solving differential equations and for discovering governing equations from observations, and physics-constrained ML (PCML) that directly embeds a physics-based model into a neural network. The advantages and potential limitations of the methods are discussed. The future research directions in this area include, but are not limited to, further developing and refining methodologies, including algorithm development, to directly embed physics-based models into ML; exploring the usefulness of PIML for reservoir simulations; and adapting the new developments of how the physics and ML are incorporated in other communities to the well-production prediction. Finally, the methodologies we discuss in the paper can be generally applied to conventional reservoirs as well, although the focus here is on unconventional reservoirs.

In an unconventional reservoir, rock matrix has a much larger storage capacity for hydrocarbon and significantly lower permeability than the natural and hydraulic fractures. It acts as a bottleneck for hydrocarbon flow from the reservoir to the production well during production and is a key parameter for controlling the well performance over a long period of time. A new laboratory technology is developed to accurately and efficiently measure the matrix permeability. We have developed the Aramco Nano Permeameter (ANP), a new laboratory technology for measuring the stress-dependent source rock permeability. While the conventional laboratory methods can only measure one permeability data point with one test run, ANP, based on the nonlinear solution to the gas flow equation, measures the rock matrix permeability for a non-fractured sample as a function of stress using a single test run and thus is very efficient. Permeability as a function of pore pressure at a given confining stress is measured with ANP for several Eagle Ford rock samples without fractures. The permeability curve shows complex behavior: permeability initially decreases with increasing pore pressure, as a result of Knudsen diffusion effect, and then increases with pore pressure owing to the mechanical deformation. The measured permeability curves are verified by comparing them with permeability values measured with other methods for selected pore pressures. The high measurement efficiency of ANP is also demonstrated. In summary, ANP is a laboratory method that is based on a theoretical idea that is significantly different from those currently used by the industry and thus provides a high measurement efficiency that the conventional methods cannot achieve.

The physics of fluid flow and transport processes in hydraulically fractured unconventional reservoirs are not well understood. As a result, the predicted production behavior using conventional simulation often does not agree with the observed field performance data. The discrepancy is caused by potential errors in the simulation model and the physical processes that take place in complex fractured rocks subjected to hydraulic fracturing. Additionally, other field data such as well logs and drilling parameters containing important information about reservoir condition and reservoir characteristics are not conveniently integrated into existing simulation models. In this paper, we discuss the development of a deep learning model to learn the errors in simulation-based performance prediction in unconventional reservoirs. Once trained, the model is expected to forecast the performance response of a well by augmenting physics-based predictions with the learned prediction errors from the deep learning model. To learn the discrepancy between simulated and observed production data, a simulation dataset is generated by using formation, completion, and fluid properties as input to an imperfect physics-based simulation model. The difference between the resulting simulated responses and observed field data, together with collected field data (i.e. well logs, drilling parameters), is then used to train a deep learning model to learn the prediction errors of the imperfect physical model. Deep convolutional autoencoder architectures are used to map the simulated and observed production responses into a low-dimensional manifold, where a regression model is trained to learn the mapping between collected field data and the simulated data in the latent space. The proposed method leverages deep learning models to account for prediction errors originating from potentially missing physical phenomena, simulation inputs, and reservoir description. We illustrate our approach using a case study from the Bakken Play in North Dakota.

Transfer learning is a machine learning concept whereby the knowledge gained (e.g., a model developed) in one task can be transferred (applied) to solve a different but related task. In the context of unconventional reservoirs, the concept can be used to transfer a machine learning model that is learned from data in one field (or shale play) to another, thereby significantly reducing the data needs and efforts to build a new model from scratch. In this work, we study the feasibility of developing deep learning models that can capture and transfer common features in a rich dataset pertaining to a mature unconventional play to enable production prediction in a new unconventional play with limited available data. The focus in this work is on method development using simulated data that correspond to the Bakken and Eagle Ford Shale Plays as two different unconventional plays in the US. We use formation and completion parameter ranges that correspond to the Bakken play with their simulated production responses to explore different approaches for training neural network models that enable transfer learning to predict production responses of input parameters corresponding to the Eagle Ford play (previously unseen input parameters). We explore different schemes by accessing the internal components of the model to extrapolate and categorize salient features that are represented in the trained neural network. Ultimately, our goal is to use these new mechanisms to enable effective sharing and reuse of discovered features from one unconventional well to another. To extract salient trends from formation and completion input parameters and their corresponding simulated production responses, we use deep learning architectures that consist of convolutional encoder-decoder networks. The architecture is then trained with rich simulated data from one field to generate a robust mapping between the input and the output feature spaces. The "learned" parameters from this network can then be "transferred" to develop a different predictive model for another field that may lack sufficient historical data. The results show that using standard training approaches, a neural network model that is trained with sufficiently large data samples from Bakken could produce reliable prediction models for typical wells that may be found in that field. The same neural network, however, could not produce reliable predictions for a typical Eagle Ford well. Furthermore, we observe that a neural network trained with insufficient data samples from Eagle Ford produces a poor prediction model for typical wells that may be found in Eagle Ford. However, when extrapolated feature components of the Bakken neural network were integrated into the training process of the Eagle Ford neural network, the resulting predictions for typical Eagle Ford wells improved significantly. Moreover, we observe that the ability to transfer learning can improve when specialized training strategies are adopted to enable transfer learning. Using several numerical experiments, the paper presents and assesses various transfer learning strategies to predict the production performance of unconventional wells in a new area with limited information by integrating knowledge from more mature plays.

Gravitational fingering often occurs for water flow in unsaturated porous media. This paper reviews a recent effort in developing a macroscopic theory to describe the gravitational fingering flow of water in homogeneous and unsaturated soils, based on the optimality principle that water flows in unsaturated soils in such a manner that the generated flow patterns correspond to the minimum global flow resistance. The key difference between the new theory and the conventional unsaturated flow theories is that the hydraulic conductivity in the new theory is not only related to water saturation or capillary pressure, but also proportional to a power function of water flux, because the water flux is closely related to the fingering flow patterns and the power function allows for large hydraulic conductivities at locations where water fluxes are large as well to minimize the global flow resistance. The resultant relationship for the fraction of fingering flow zone is compared with that obtained from a parallel effort based on the fractal nature of fingering flow patterns. The relationships from the two efforts are found to be essentially identical for gravity-dominated water flow in unsaturated soils and can both be expressed as a power function of the water saturation. This work also demonstrates that the theoretical values for the exponent of the power function vary in a relatively narrow range between 0.75 and 0.80 for most soils, which is supported by observations from previous field tests. This remarkable finding makes it easy to apply the new theory to field sites where experimental data are not readily available for estimating the exponent value. The potential limitations of the theory and the suggested future research topics in the area are also discussed.

Summary Hydraulic fracturing has been widely used in stimulating tight carbonate reservoirs to improve oil and gas production. Improving and maintaining the connectivity between the natural and induced microfractures in the far-field and the primary fracture networks are essential to enhancing the well production rate because these natural and induced unpropped microfractures tend to close after the release of hydraulic pressure during production. This paper provides a conceptual approach for an improved hydraulic fracturing treatment to enhance the well productivity by minimizing the closure of the microfractures in tight carbonate reservoirs and enlarging the fracture aperture. The proposed improved fracturing treatment was to use the mixture of the delayed acid-generating materials along with microproppants in the pad/prepad fluids during the engineering process. The microproppants were used to support the opening of natural or newly induced microfractures. The delayed acid-generating materials were used in this strategy to enlarge the flow pathways within microfractures owing to degradation introduced under elevated temperatures and interaction with the calcite formation. The feasibility of the proposed approach is evaluated by a series of the proof-of-concept laboratory coreflood experiments and numerical modeling results. First, one series of experiments (Experiments 1–3) was designed to investigate the depth of the voids on the fracture surface generated by the solid delayed acid-generating materials under different flow rates of the treatment fluids and different temperatures. This set of tests was conducted on a core plug assembly that was composed of half-core Eagle Ford Sample, half-core hastelloy core plug, and a mixture of solid delayed acid-generating materials [polyglycolic acid (PGA)] along with small-sized proppants sandwiched by two half-cores. Surface profilometer was used to quantify the surface-etched profile before and after coreflood experiments. Test results have shown that PGA materials were able to create voids or dimples on the fracture faces by their degradation under elevated temperature and the chemical reaction between the generated weak acid and the calcite-rich formation. The depth of the voids generated is related to the treatment temperature and the flow rate of the treatment fluids. Experiment 4 was conducted using two half-core splits to quantify the improvement factor of the core permeability due to the treatment with mixed sand and PGA materials. Simulations of fluid flow through proppant assembly (inside of the microfractures) using the discrete element method (DEM)–lattice Boltzmann method (LBM) coupling approach for three different scenarios (14 cases in total) were further conducted to evaluate the fracture permeability and conductivity changes under different situations such as various gaps between proppant particulates and different depths of voids generated on fracture faces: (1) fluid flow in a microfracture without proppant, (2) fluid flow in a microfracture with small-sized proppants, and (3) fluid flow in a microfracture supported by small-sized proppants and generated voids on the fracture walls. The simulation results show that with proppant support (Scenario 2), the microfracture permeability can be increased by tens to hundreds of times in comparison to Scenario 1, depending on the gaps between proppant particles. The permeability of proppant-supported microfracture (Scenario 3) can be further enhanced by the cavities created by the reactions between the generated acid and calcite formation. This work provides experimental evidence that using the mixture of the solid delayed acid-generating materials along with microproppants or small-sized proppants in stimulating tight carbonate reservoirs in the pad/prepad fluids during the engineering process may be able to effectively improve and sustain permeability of flow pathways from microfractures (either natural or induced). These findings will be beneficial to the development of an improved hydraulic fracturing treatment for stimulating tight organic-rich carbonate reservoirs.

Understanding geometrical and topological properties of the pore space in permeable media is of paramount importance, particularly in oil and gas production. Pore space characteristics such as pore sizes and their probability distributions, as well as pore's connectivity are main factors in the modeling of fluid flow and chemical transport in soils and rocks. A common method to determine the pore size is to convert an implemented pressure via either the Young-Laplace or Kelvin equation by assuming a specific pore shape. Simple geometries such as cylindrical and slit-shaped have been frequently used in the literature, particularly to represent pores and to derive theoretical models estimating permeability from pore-throat size distribution. In this study, we clarify the relationship between pore diameter (d) and pore width (w), two terms interchangeably used in the literature. The former corresponds to a cylindrical pore, while the latter to a slit-shaped one. We emphasize that d = 2w, in contrast to previously published studies claiming that the diameter of a cylindrical pore is equal to the distance between sides of a slit-shaped pore (i.e., d = w). In addition, we discuss that comparing/combining pore size distribution derived from mercury intrusion porosimetry and that determined from nitrogen adsorption isotherm is not supported, unless the effect of hysteresis is trivial, as most probably the former represents pore-throat while the latter pore-body size distributions.

Organic-rich shales have pore size on nanometer scale and permeability on the order of nano-Darcy. These properties give rise to significant challenges in understanding and modeling flow processes during the hydrocarbon production from shale reservoirs. During production, light hydrocarbons move from nanopores in the rock matrix to fractures generated by hydraulic fracturing to the well. Diffusion becomes a key mechanism in controlling hydrocarbon transport within matrix and from matrix to fractures. However, reliable experimental data for hydrocarbon diffusion coefficients in organic-rich shales are still lacking in the literature. This study presents experimental measurements of in situ methane diffusion coefficients in shales using a pulse-field-gradient nuclear magnetic resonance method. This method measures the diffusion coefficient at equilibrium state and thus eliminates the possibility of fluid flow effects in laboratory measurement generated from pressure or concentration gradient. The measured methane diffusion coefficients in shales are two orders of magnitude smaller than those in the bulk state in the pressure range from 75 to 6000 psi. The measured data can be used to more accurately evaluate and model the production from shale reservoirs.

One characteristic of unconventional shale rock is the abundance of nanoscale pores and pore throats. For many shale reservoirs, these are the dominant factors controlling the total reserve, production rate, and overall production. Accordingly, many new phenomenon related to nanopore physics need to be considered for shale reservoir. A key mechanism controlling hydrocarbon gas transport from pores to fractures in shale reservoirs is molecular diffusion. As a result, the diffusion coefficient of light hydrocarbon becomes an important parameter in reservoir simulation to estimate production rate, especially for the long-term or late time production. The diffusion coefficient is also a key parameter in nuclear magnetic resonance (NMR) logging for fluid typing in determining hydrocarbon-in-place. Diffusion in nanopore systems is complicated by two important factors. First, the gas molecules collide more with pore surfaces than with each other; therefore, simple diffusion theory based on gas molecule collision is not applicable. Second, the occurrence of capillary condensation in small pores or pore throats and the adsorption to the pore surface makes the hydrocarbon transport a mixed process of liquid diffusion and gas diffusion in the reservoir. We derived a theoretical model for mixed phase diffusion under fast exchange for shale gas reservoirs. We obtained that the effective diffusion coefficient of mixed fluid is a fractional average of the liquid and gas diffusivity. We verified this model using NMR to measure n-hexane diffusion in a well-characterized hierarchical carbon with both nanometer pores and micrometer pores so that both gas and liquid can be prepared to exist in the sample simultaneously. We found that the diffusion coefficient of hexane in these hydrophobic nanopores is approximately one magnitude of order larger than the bulk liquid value. The effective diffusion coefficient in this study can be used in reservoir simulation and interpretation of NMR logs for shale gas reservoirs.

Summary When drilling through naturally fractured formations, the existence of natural fractures affects the fluid diffusion and stress distribution around the wellbore and induces degradation of rock strength. For chemically active formations, such as shale, the chemical–potential difference between the drilling mud and the shale–clay matrix further complicates the nonmonotonic coupled pore–pressure processes in and around the wellbore. In this work, we apply a recently formulated theory of dual–porosity/permeability porochemoelectroelasticity to predict the time evolution of mud–weight windows, while calculating stresses and pore pressure around an inclined wellbore drilled in a fractured shale formation. The effects of natural–fracture geometric and spatial distributions coupled with the chemical activity are considered in the wellbore–stability analysis. To account for the degrading effect of the fractured shale matrix on the bulk rock strength, a modified Hoek–Brown (MHB) criterion is developed to more closely describe the in–situ state of stress effects on the compressive shearing strength at great depth. Compared with the original Hoek–Brown (HB) failure criterion, the MHB criterion considers the influence of the intermediate principal stress and thus shows better agreement with true–triaxial data for various rocks at varying stress levels. The MHB criterion converges to the original HB criterion when the confining in–situ stresses are equal. Two field case studies indicate that this novel integrative methodology is capable of predicting the operational drilling–mud–weight windows used in these two cases. Another advantage of this newly developed technique is that it can be used as a back–analysis tool to estimate the fracture–matrix permeability from field operational data.

The pressure pulse-decay permeability (PDP) measurement is a well-established technique to measure the permeability of tight rock samples such as shale. The conventional applications of the PDP measurement almost exclusively treat shale samples as a single-continuum system, even though the gas flow in some shale samples may be more accurately characterized by a dual-continuum, which is due to the large range of pore size distribution and chemical/mineralogical difference between organic and inorganic matters. However, studies about measurements of flow parameters for dual-continuum shale rock samples are very limited in literature. Liu et al. (2016) proposed a new analytical technique to characterize the dual-continuum behavior of a test sample using the PDP measurement with the same upstream and downstream reservoir volumes. In this study, a more general analytical technique is proposed and allows for using different upstream and downstream reservoir volumes in the PDP setup. With this new technique, all the existing PDP systems in laboratories can be conducted to characterize the dual-continuum behavior of a test sample without the need of modifying the upstream and downstream reservoir volumes, and the measured flow parameters of samples can be used as input parameters in the reservoir simulation of the dual-continuum system. The validity and practical usefulness of the new technique is demonstrated by the successful identification and characterization of the dual continuum behavior of test samples in laboratory.

Elastic properties of rocks, including Young’s modulus and Poisson’s ratio, are usually obtained from the uniaxial compressive strength (UCS) test, while tensile strength is obtained from direct or indirect (Brazilian) tensile test. In this paper, we developed an analytical model as well as an improved test procedure, called modified Brazilian tensile (MBT) test, which can simultaneously measure the tensile strength, Young’s modulus and Poisson’s ratio in a single test by attaching two strain gauges at the center of each end face of the specimen. To validate the proposed model, both the UCS and modified Brazilian tensile tests were conducted using two types of aluminum alloy (AL 6061 and AL 7075). Results showed that the Young’s modulus obtained from UCS tests and MBT tests are within the range of experimental error. Poisson’s ratios determined from the two test methods were consistent. The proposed model was further validated with Colton sandstones. The Young’s modulus and the Poisson’s ratio obtained from the UCS test and the MBT test agreed well. We also conducted numerical modeling for further comparison, and the results also verified the reasonableness of the proposed model.

A reservoir-geomechanics coupled simulation tool is required in the interpretation and prediction of stimulation and production performance of unconventional reservoirs in a physically rigorous manner. One such a coupled simulation tool developed at Lawrence Berkeley National Laboratory (LBNL), TOUGH2-FLAC3D, has been extensively adopted in many scientific research and practical application projects in last two decades. In TOUGH2's most often used equation of state (EOS), EOS4, the vapor pressure is used as a primary variable, however, the vapor pressure lowering effect is not the primary interest in a typical reservoir flow simulation. Instead, the temperature should be a natural and physically correct primary variable, considering the convenience of model input, and the understanding and interpretation of simulation results. In this work, the vapor pressure is replaced by temperature in the EOS implementation. To be consistent with the change of primary variable, the Jacobian matrix is modified correspondingly and illustrated using a case of two-phase flow in one grid block. The development work was verified in three well-defined problems that are related to fluid diffusion, thermal conduction, thermal fluid conduction and convection, respectively, through comparing the modeling results with the corresponding analytical solutions.

Summary Robust production forecasting allows for optimal resource recovery through efficient field management strategies. In hydraulically fractured unconventional reservoirs, the physics of fluid flow and transport processes is not well understood and the presence of and transitions between multiple flow regimes further complicate forecasting. An important goal for field operators is to obtain a fast and reliable forecast with minimal historical production data. The abundance of wells drilled in fractured tight formations and continuous data acquisition effort motivate the use of data-driven forecast methods. However, traditional data-driven forecast methods require sufficient training data from an extended period of production for any target well, which may have limited practical use when the effective production life of wells is relatively short. In this paper, a deep recurrent neural network (RNN) model is developed for long-term production forecasting in unconventional reservoirs. As input data, the model takes completion parameters, formation and fluid properties, operating controls, and early (i.e., 3–6 months) production response data. The model is trained on a collection of historical production data across multiple flow regimes, control settings, and the corresponding well properties from multiple shale plays. The proposed RNN model can predict oil, water, and gas production as multivariate time series under varying operating controls. Once the forecast model is trained, it can be used to obtain a one-step forecast by feeding the model with input well properties, operating controls, and a short initial production. The long-term forecast is obtained by either recursively feeding the model with forecast results from the preceding timesteps or by training the model for multistep ahead predictions. Unlike other applications of RNN that require a long history of production data for training, our model employs transfer learning by combining early production data from the target well with the long-term dynamics captured from historical production data in other wells. We illustrate our approach using synthetic data sets and a case study from Bakken Play in North Dakota.

Summary Hydraulic fracturing has been widely used for unconventional reservoirs, including organic-rich carbonate formations, for oil and gas production. During hydraulic fracturing, massive amounts of fracturing fluids are pumped to crack open the formation, and only a small percentage of the fluids are recovered during the flowback process. The negative effects of the remaining fluid on the formation, such as clay swelling and reduction of rock mechanical properties, have been reported in the literature. However, the effects of the fluids on source-rock properties—especially on microstructures, porosity, and permeability—are scarcely documented. In this study, microstructure and mineralogy changes induced in tight carbonate rocks by imbibed fluids and the corresponding changes in permeability and porosity are reported. Two sets of tight organic-rich carbonate-source-rock samples were examined. One sample set was sourced from a Middle East field, and the other was an outcrop from Eagle Ford Shale that is considered to be similar to the one from the Middle East field in terms of mineralogy and organic content. Three fracturing fluids—2% potassium chloride (KCl), 0.5 gal/1,000 gal (gpt) slickwater, and synthetic seawater—were used to treat the thin section of the source-rock and core samples. Modern analytical techniques, such as scanning electron microscopy (SEM) and energy-dispersive spectroscopy (EDS), were used to investigate the source-rock morphology and mineralogy changes before and after the fluid treatment, at the micrometer scale. Permeability as a function of effective stress was quantified on core samples to investigate changes in flow properties caused by the fracturing-fluid treatments. The SEM and EDS results before and after fracturing-fluid treatments on the source-rock samples showed the microstructural changes for all three fluids. For 2% KCl and slickwater fluid, reopening of some mineral-filled natural fractures was observed. The enlargement of the aperture for pre-existing microfractures was slightly more noticeable for samples treated with 2% KCl compared with slickwater at the micrometer scale. In one sample, dissolution of organic matter was captured in the slickwater-fluid-treated rock sample. Mineral precipitation of sodium chloride (NaCl) and generation of new microfractures were observed for samples treated with synthetic seawater. The formation of new microfractures and the dissolution of minerals could result in increases in both porosity and permeability, whereas the mineral deposition would result in permeability decrease. The overall increase in absolute gas permeability was quantified by the experimental measurements under different effective stress for the core-plug samples. This effect on absolute-gas-permeability increase might have an important implication for hydrocarbon recovery from unconventional reservoirs. This study provides experimental evidence at different scales that aqueous-based fracturing fluid might potentially have a positive effect on gas production from organic-rich carbonate source rock by increasing absolute gas permeability through mineral dissolution and generation of new fractures or reopening of existing microfractures. This observation will be beneficial to the future use of freshwater- and seawater-based fluids in stimulating gas production from organic-rich carbonate formations.

Shale matrix permeability is one of the most important parameters for characterizing a source rock reservoir and for predicting hydrocarbon production. The low permeability value and the presence of induced fractures during core retrieval and transportation make the accurate measurement of the true permeability values for source rocks a significant challenge for the industry. The steady state flow method and the transient pressure pulse decay method on core plug samples mainly measure the permeability of fractures when fractures are present. While the Gas Research Institute (GRI) method that uses pressure decay on crushed rock samples was designed to overcome this difficulty associated with the induced fractures, its measurement results are reported to be sensitive to the particle size of crushed rock samples and also need correction of Knudsen diffusion effect. Moreover, the GRI method is limited to the unconfined stress condition. This work develops a practical method to measure the matrix permeability values from fractured source rock samples by extending the commonly used pressure pulse decay method. A source rock sample with fractures can be more accurately described by a dual-continuum system consisting of a fracture continuum and a matrix continuum. During the pulse decay test, the initial flow across the source rock sample is dominated by the fracture continuum because it has much higher permeability values than those for the rock matrix. Thus, the initial gas pressure signals from the test are used to estimate the fracture permeability. During the late-stage of a pulse decay test, the flow process within the rock sample is controlled by the rock matrix. The observed pressure signals at this stage are used for estimating matrix permeability. The method is based on the analytical solution to gas flow in the fractured rock sample and relatively simple to apply in practice. Both fracture and matrix permeability's dependence on the effective stress can be assessed with this method.

In a shale gas reservoir, the rock matrix has a relatively large porosity and gas in place, but extremely low permeability. Thus, the rock matrix is a bottleneck for shale gas flow from the reservoir to hydraulic fractures and then to the production well. We speculate that the next big thing after hydraulic fracturing for unconventional resources development is to enhance the matrix permeability in an economically feasible way. Consequently, the efficient and accurate characterization of rock matrix permeability in the laboratory is a critical task. The current laboratory techniques for source rock permeability measurement follow a "point-by-point" approach. They need multiple test runs to obtain a permeability-pressure curve, because they can only measure one permeability data point for one test run, and are thus time consuming. The root cause of this "point-by-point" approach is that these laboratory techniques are based on linearized gas flow theory requiring only small pore pressure disturbances to the experiment system. Liu et al. (2019) and this work introduce a new methodology that is based on the nonlinear gas flow theory and allows for direct measurement of the permeability-pressure curve with a single test run. This makes the approach highly time efficient. The feasibility and validity of the methodology are demonstrated in this work based on laboratory measurement results and their consistency with theoretical expectations and other independent measurements. The observed permeability exhibits a complex relationship with pore pressure as a result of the combined effects of Knudsen diffusion and mechanical deformation. For a given confining pressure, the observed permeability initially decreases with pore pressure because of Knudsen diffusion and then increases with pore pressure owing to the mechanical deformation. A rock sample with a lower permeability corresponds to a stronger Knudsen diffusion effect and weaker mechanical diffusion effect. This complex behavior highlights the need to accurately and efficiently measure the combined effects that may have important impacts on shale gas production.

Light hydrocarbons produced from unconventional tight shale reservoirs with matrix permeability in nano-Darcy range accounts for more than half of the petroleum production in the United States in the past several years. This has been enabled mainly by the drilling of long horizontal wells coupled with extensive hydraulic fracturing. A typical fracturing job for a horizontal well requires two to five million gallons of water which imposes significant challenges in many areas of the world that lack water resources. In addition, treatment and disposal of produced fracturing fluids can be expensive and may negatively impact the environment. Here we show a ‘water-free’ stimulation method to produce light hydrocarbons from the extremely tight reservoirs using electromagnetic (EM) waves to heat the formation and elevate pore-water pressure. We demonstrated in the laboratory that microwave heating pulverized shales and other tight rocks without confinement and generated extensive fractures within shales with 15 MPa isotropic confinement pressures. Our calculation indicates that for typical shale reservoirs pore-water pressure can increase to 90 MPa or higher that is sufficient to stimulate the formation for production with a less than 100 °C temperature increase of the reservoir. Using a simplified coupled model of EM heating and thermal diffusion, we estimated that with practically reasonable amount of power input the EM heating can stimulate a sufficiently large volume of tight reservoirs to produce light hydrocarbons.

Pulse-decay permeability (PDP) measurement is a widely used technique to measure the permeability of tight rocks such as shales. However, the PDP measurement is so sensitive to gas leakage of the system that the leakage would significantly affect the experimental results. To address the impact of the gas leakage, this paper develops an analytical solution of the PDP measurement with gas leakage that applies to both fractured and un-fractured core samples. The PDP measurement on a fractured core sample can be treated as a two-stage pressure transient process that are dominated by gas flow in a fracture and the flow between the fracture and the matrix, respectively. The analytical solution shows that the linearity of curve of logarithm of the normalized pressure difference (between the upstream and downstream reservoirs in the PDP system) versus time in the first-stage would break up when gas leakage occurs, so does the linearity of logarithm of the pressure decline curve in the second-stage. For an un-fractured core sample, the analytical solution for the PDP measurement with gas leakage is similar to the first-stage process for a fractured core sample. Based on these observations, an effective method to detect and correct the impacts of leakage on the PDP measurements is proposed using the analytical solution. The practical usefulness of the method is demonstrated by its successful applications to simulated PDP permeability measurements for several core samples.

Permeability measurements show that unconventional rock is considerably stress sensitive because the matrix permeability is likely controlled by micro cracks and bedding structures in unconventional reservoirs. While there are a number of laboratory studies in the literature on the dependency of core-scale permeability on effective stress for unconventional rocks, how to determine the corresponding large-scale stress-dependency relationship (of more interest to practical applications) from the laboratory measurements has not been systematically investigated. This work proposes a method to estimate such a large-scale relationship from laboratory measurements. Based on the stochastic approach commonly used for parameter upscaling, we derived relationships between the large-scale effective permeability and the stress for the two- and three-dimensional isotropic porous media. The development is based on the empirical observation that at core scale permeability is an exponential function of effective stress. The developed large-scale relationships can be written in terms of the same mathematical form as the local-scale relationship except parameters in the large-scale relationships correspond to effective ones. The effective stress sensitivity parameter (that characterizes the stress-dependency) is simply the expected value of that at the local scale, or the arithmetic average of local values, for the two-dimensional flow problem and a function of effective stress for the three-dimensional problem. Because of its dominant two-dimensional flow along beddings (resulting from the fact that vertical permeability is significantly smaller than the horizontal one), the relationship for the two-dimensional flow case is valid for unconventional rocks. Nevertheless, we demonstrate that for typical local-scale parameter values from unconventional rocks (e.g., Barnett shale and a carbonate source rock), the relationships obtained for two- and three-dimensional problems give the essentially same results.

Summary This work proposes an innovative laboratory method to measure shale gas permeability as a function of pore pressure, a key parameter for characterizing and modeling gas flow in a shale gas reservoir. The development is based on a solution to 1D gas flow under certain boundary and initial conditions. The details of the theoretical background, including formulations to estimate gas permeability and conceptual design of the test setup, are provided. The advantages of our approach, surpassing the currently available ones, include that it measures gas permeability (as a function of pressure) with a single test run and without any presumption regarding the form of parametric relationship between gas permeability and pore pressure. In addition, our approach allows for estimating both shale permeability and porosity at the same time from the related measurements. Numerical experiments are conducted to verify the feasibility of the proposed methodology.

Understanding porous media properties and their scale dependence have been an active subject of research in the past several decades in hydrology, geosciences and petroleum engineering. The scale dependence of flow in porous media is attributed to small- and large-scale heterogeneities, such as pore size distribution, pore connectivity, long-range correlations, fractures and faults orientations, and spatial and temporal variations. The main objective of this study was to investigate how permeability (k) and formation factor (F) vary with sample dimension at small scales by means of a combination of pore-network modeling and percolation theory. For this purpose, the permeability and formation factor were simulated in twelve three-dimensional pore networks with different levels of pore-scale heterogeneities. Simulations were carried out at five different network sizes, i.e., 1130, 2250, 3380, 4510 and 6770 µm. Four theoretical models were developed based on percolation theory to estimate the scale dependence of permeability and formation factor from the pore-throat radius distribution. In addition, two other theoretical scale-dependent permeability models were proposed to estimate permeability at different scales from the pore-throat radius distribution and/or formation factor. Comparing theoretical estimations with numerical simulations showed that the proposed models estimated the scale dependence of permeability and formation factor reasonably. The calculated relative error (RE) ranged between −3.7 and 3.8% for the permeability and between 0.21 and 4.04% for the formation factor in the studied pore-networks.

Halite cementation is a major exploration risk in hydrocarbon reservoirs. Halite-cemented reservoir zones are characterized by extremely low porosity and permeability due to partial or complete occlusion of the pore space. Despite being a key process that affects the quality of the productive formation, a quantitative analysis of the physical processes responsible for halite cementation is still missing in the scientific literature. Brine reflux caused by temperature and density gradients is one of the main physical mechanisms responsible for the intrusion of salt in the pores of a productive formation. Physically, the dissolution of salt by the resident brine creates a zone of higher density which may give rise to the development of flow instabilities. In this work, we present a quantitative methodology for estimating the distribution of halite-cemented zones by numerically simulating unstable flows for different flow and rock parameters. The main non-dimensional parameter, the Rayleigh number, that governs the flow is identified. The impact of the Rayleigh number on finger distribution is investigated using a statistical methodology to obtain a finger spacing distribution. Finally, a simple relationship is developed between finger spacing and the Rayleigh number that may be used to predict finger spacing.

Mechanical properties of rocks/soils are key inputs in the design and analysis of surface structures (e.g., slope, foundation) and underground excavations (e.g., tunnel, cavern, borehole, and fracture) in earth engineering practice. Brazilian disc test has been extensively used to measure tensile strength for various rocks. In this study, we propose to measure Young’s modulus, Poisson’s ratio and tensile strength in one Brazilian test through making two additional measurements, i.e., two relative displacements using LVDT, or normal strains by pasting two strain gauges, which are perpendicular to each other, at the center of the disc’s side faces. The analytical solutions of the equivalent strains calculated from LVDT measurements or measured directly by strain gauges are derived from elasticity theory. The analytical solutions are verified with measurements in a numerical model. New formulae for calculating Young’s modulus and Poisson’s ratio from two measured strains are provided and their insensitivity to gauge size is illustrated.

A systematic method has been proposed to estimate the two-phase flow properties of horizontal fractures under normal deformation condition. Based on Gaussian aperture distributions and the assumption of local parallel plate model, a simple model was obtained in closed form to predict the capillary pressure-saturation relationships for both wetting and non-wetting phases. Three conceptual models were also developed to characterize the relative permeability behaviors. In order to investigate the effect of normal deformation on two-phase flow properties, the normal deformation could be represented with the maximum void space closure on the basis of penetration model. A rigorous successive random addition (SRA) method was used to generate the aperture-based fractures and a numerical approach based on invasion percolation (IP) model was employed to model capillary-dominated displacements between wetting and non-wetting phases. The proposed models were partially verified by a laboratory dataset and numerical calculations without consideration of deformation. Under large normal deformations, it was found that the macroscopic model is in better agreement with simulated observations. The simulation results demonstrated that the two-phase flow properties including the relationships between capillary pressure, relative permeability and saturation, phase interference, phase structures, residual-saturation-rated parameters and tortuosity factor, were highly sensitive to the spatial correlation of aperture distribution and normal deformation.

Hydraulic fracturing has been widely used in stimulating unconventional reservoirs, including tight carbonate formations, to improve oil and gas production. The stimulation process requires massive volumes of fracturing fluid to crack the formation; however, only a small percentage of the fluid is recovered during the fluid flow back process. Where the remaining fluids reside in the formation is still not clear. This work strives to use microscale radiographic imaging to study the fluid uptake pathways. The spontaneous imbibition of fracturing fluid into organic-rich carbonate source rock was experimentally investigated on the microscopic scale. A thin-section sample, with a dimension of 22×11×3.3 mm (length × width × thickness), was sliced using a trim saw and attached onto a glass slide with epoxy. This sample was composed of two distinguished zones, an organic matter-rich zone and a calcite-rich zone. Iodide containing aqueous-based fluid was used as the source fluid to treat the thin section rock sample from one end. The spontaneous imbibition test was conducted for 100 minutes with one radiographic image taken per minute to capture the dynamic fluid front. The iodide containing aqueous-based fluid was used in this study to enhance the contrast in microscale radiographic imaging. Microfractures were observed by radiographic imaging in the thin-section sample with 5.48 μm and 2.79 μm resolutions before the fluid treatment, both in the organic matter-rich zone and the calcite-rich zone. Three fluid uptake features have been revealed in this dynamic fluid imbibition study: (1) the fluid moved very fast and reached the other end of the sample in less than 4 minutes in the microfractures within the organic matter-rich zone; (2) the fluid moved very fast and reached the other end of the sample in less than 4 minutes in microfractures within the calcite-rich zone; and (3) in a calcite-rich matrix, the water front progressed very slowly, to about 120 μm penetration in 100 minutes. The fast water uptake through microfractures in the organic-rich zone and fracture networks in the calcite-rich zone correspond to imbibition-controlled transport in the strongly water-wet pore space. The slow water uptake through the calcite-rich matrix could be a combination of weakly water-wet imbibition and slow flow process due to large viscous flow resistance (or small permeability) in small-sized pores. During the slick water fracturing process in unconventional reservoirs, only a small percentage of fracturing fluids is generally recovered. Where the remaining fluids reside in the formation is still an open question in the industry. This study experimentally reveals that the imbibition into the rock matrix is much slower than into microfractures. Therefore, it is very likely that natural and induced microfractures are the major areas where the fluids remain after the flow back.