Modeling of Hydraulic Fracturing and Design of Online Optimal Pumping Schedule for Enhanced Productivity in Shale Formations

In hydraulic fracturing, the proppant-filled fracture length at the end of pumping strongly influences the fluid conductivity of natural oil and gas. Therefore, it is very important to regulate proppant bank height and suspended proppant concentration across the fracture to increase the recovery of shale hydrocarbon. From a control engineering viewpoint, hydraulic fracturing has been traditionally viewed as an open-loop problem. Well logs and mini-frac test results are interpreted prior to operation in order to obtain petrophysical and rock-mechanical properties of the formation. The operation is designed based on the properties and then is conducted accordingly. However, the open-loop operation may lead to poor performance if there are large disturbances and plant-model mismatch. In this research, a model predictive control framework is developed for the design of pumping schedules to regulate the spatial variation of proppant concentration across the fracture at the end of pumping for both of conventional and unconventional reservoirs. To this end, we initially focus on the development of a first-principle model of hydraulic fracturing process to obtain fundamental understanding of the proppant bank formation mechanism and its relationship to manipulated input variables such as proppant concentration and flow rate of the injected fracturing fluids by considering a single fracture. Then, a model-based feedback controller is developed to achieve the uniform proppant bank height and suspended proppant concentration along the fracture at the end of pumping for both of conventional and unconventional reservoirs by explicitly taking into account the desired fracture geometry, type of the fracturing fluid injected, total amount of injected proppant, actuator limitations, and safety considerations. Then, we extend this study to multi-stage hydraulic fracturing, where in each stage, multiple simultaneously propagating fractures are generated. In multi-stage hydraulic fracturing treatments, simultaneously propagating multiple fractures with close spacing often induce non-uniform fracture development due to “stress shadow effects”. In order to mitigate these undesired stress-shadow effects, we propose a model-based design technique by utilizing the limited entry design technique to compute the flow rate of fracturing fluids and the perforation conditions which will promote equal distribution of fracturing fluids to achieve uniform growth of multiple fractures. Then, a model-based feedback controller is developed to achieve a uniform proppant bank height in simultaneously propagating multiple fractures at the end of pumping by handling the undesired stress-shadow effects using the optimal perforation conditions. In hydraulic fracturing, higher fracturing fluid injection rates can trigger increased stress, thereby creating more microseismic events; particularly, simultaneously occurring multiple microseismic events can reduce measurement errors. This suggests a new state and output estimation scheme that utilizes the dependence between the fracturing fluid injection rate (i.e., manipulated input) and measurement errors. Motivated by this, we improve our control framework for measurement uncertainty reduction while achieving the original control task of proppant bank height control in hydraulic fracturing. Specifically, the developed model-based feedback control system regulates the uniformity of proppant bank height along the fracture length and achieve accurate state and output estimation by manipulating the fracturing fluid pumping schedule that includes the fracturing fluid injection rate and proppant concentration at the wellbore. In some of the unconventional reservoirs, natural fractures (discontinuities in shale rock formations) are commonly observed using advanced fracture diagnostic techniques such as microseismic monitoring, core samples and outcrops. In naturally fractured unconventional reservoirs, naturally present fractures will interact with hydraulic fractures and divert fracture propagation. Because of complex fracture growth, the ultimate goal of hydraulic fracturing operation in naturally fractured unconventional reservoirs should be changed from achieving a desired fracture geometry to maximizing the total fracture surface area (TFSA) for given fracturing resources, as it will allow more drainage area available for oil recovery. To further consider the interaction between hydraulic fractures and natural fractures, we develop a model-based pumping schedule that maximizes the TFSA by utilizing a recently developed unconventional complex fracture propagation model called Mangrove describing complex fracture networks in naturally fractured unconventional reservoirs

Incorporation of Sustainability and Economic Considerations in Process Control of Hydraulic Fracturing in Unconventional Reservoirs

Typically, the term shale oil refers to natural oil trapped in rock of low porosity and ultralow permeability. What has made the recovery of shale oil and gas economically viable is the extensive use of hydraulic fracturing. Research on the relationship between the distribution of propping agent, called proppant, and well performance indicates that uniformity of proppant bank height and suspended proppant concentration across the fracture at the end of pumping determines the productivity of produced wells. However, it is important to note that traditional pumping schedules have not considered the environmental and economic impacts of the post-fracturing process such as treatment and reuse of flowback water from fractured wells. Motivated by this consideration, a control framework is proposed to integrate sustainability considerations of the post-fracturing process into the hydraulic fracturing process. In this regard, a dynamic model is developed to describe the flow rate and the concentration of total dissolved solids (TDS) in flowback water from fractured wells. Then, a thermal membrane distillation (TMD) system is considered for the removal of TDS. A multi-objective problem is formulated to optimize the entire superstructure that consists of hydraulic fracturing, storage, transportation, and water treatment, minimizing annualized cost from recovered water per period and the water footprint of the process. The capabilities of the proposed approach are illustrated through the simulation of different scenarios that are performed to examine the effects of water availability on the productivity of stimulated wells. Finally, the impact of flowback water generation is evaluated using TRACI, a tool for the reduction and assessment of chemical and other environmental impacts

Mathematical model of linear and non-linear proppant concentration increase during hydraulic fracturing – a solution for sequential injection of a number of proppant types

It is known that much of the technology aimed at intensifying fluid inflow by means of hydraulic fracturing involves the use of proppant. In order to transport and position grains in the fracture, a uniform supply of proppant with a given concentration into the fracturing fluid is ensured. The aim of the operation is to eliminate the occurrence of distortions in the injection program of proppant HF. A mathematically accurate linear increase of concentration under given conditions is possible only if the transient concentration is correctly defined. The proposed approach allows to correctly form a proppant HF work program for both linear and non-linear increase in proppant concentration. The scientific novelty of the work lies in application of a new mathematical model for direct calculation of injection program parameters, previously determined by trial and error method. A mathematical model of linear and non-linear increase of proppant concentration during HF was developed. For the first time, an analytical solution is presented that allows direct calculation of parameters of the main HF stages, including transient concentrations for given masses of the various types of proppant. The application of the mathematical model in formation of a treatment plan allows maintaining correct proppant mass distribution by fractions, which facilitates implementation of information and analytical systems, data transfer directly from a work program into databases. It is suggested to improve spreadsheet forms used in production, which would allow applying mathematical model of work program formation at each HF process without additional labour costs. The obtained mathematical model can be used to improve the software applied in the design, modelling and engineering support of HF processes

Integration of Pumping Profile Design and Water Management Optimization for Shale Gas Production Systems

Unconventional shale gas production in the United States has been largely improved due to the development of hydraulic fracturing technology. However, the shale gas production system is generally complex; further, such enhanced levels of production have generated great concerns on its accompanying environmental implications, especially regarding shale gas water management. To handle the complexity associated with shale gas production system and identify the sustainable water management strategy, many optimization-based approaches have been developed. However, few of them considered the hydraulic fracturing operation as a dynamic process, where the pumping profile directly determines the volume of freshwater consumed and affects the production rates of both shale gas and wastewater. Considering the significant spatiotemporal variation in water footprint of hydraulic fracturing, those obtained planning and operational decisions of shale gas production system could be suboptimal and thus need to be updated when well development strategy changes. From another perspective, one problem could be that the pumping profile is generally designed to only maximize well productivity, without considering the impact of water management. To handle these challenges, the overall objective of this research is to develop a framework for the integration of pumping profile design and water management optimization to achieve the economically viable and environmentally sustainable water management strategy along with maximizing shale gas production. To this end, we initially focus on the development of a novel controller design framework for hydraulic fracturing while explicitly taking into account the associated post-fracturing water management. In particular, a dynamic input-output model is developed to estimate the characteristics of shale gas wastewater produced; and, a mapping-based technique is proposed to estimate the total annual cost of wastewater management and total revenue from shale gas. This framework is demonstrated to be capable to balance the trade-offs between hydraulic fracturing and water management by manipulating the pumping profile. Subsequently, we further extend this study by considering the following practical considerations. First, to better understand the significant spatiotemporal variation in water footprint associated with shale gas well development, the real water-use and flowback and produced (FP) water production data for individual shale gas wells drilled in the Eagle Ford and Marcellus shale regions are collected and analyzed. Herein, a typical model of shale gas production system is utilized to demonstrate how the variation in water recovery ratio can affect the optimal design and operation decisions. Second, to better describe the complex shale gas production system, an optimization model for shale gas supply chain network (SGSCN) incorporating of hydraulic fracturing water cycle is developed. Herein, capacity planning for both large-scale conventional facility and small-scale modular device is considered to achieve a flexible and efficient water management strategy. Third, to better integrate the optimization of shale gas production system and control of hydraulic fracturing, an online integrated scheduling and control framework with two feedback loops is proposed. Herein, the offset-free model predictive control (MPC) scheme is designed to compensate for plant-model mismatch

Incorporation of Sustainability and Economic Considerations in Process Control of Hydraulic Fracturing in Unconventional Reservoirs

Typically, the term shale oil refers to natural oil trapped in rock of low porosity and ultralow permeability. What has made the recovery of shale oil and gas economically viable is the extensive use of hydraulic fracturing. Research on the relationship between the distribution of propping agent, called proppant, and well performance indicates that uniformity of proppant bank height and suspended proppant concentration across the fracture at the end of pumping determines the productivity of produced wells. However, it is important to note that traditional pumping schedules have not considered the environmental and economic impacts of the post-fracturing process such as treatment and reuse of flowback water from fractured wells. Motivated by this consideration, a control framework is proposed to integrate sustainability considerations of the post-fracturing process into the hydraulic fracturing process. In this regard, a dynamic model is developed to describe the flow rate and the concentration of total dissolved solids (TDS) in flowback water from fractured wells. Then, a thermal membrane distillation (TMD) system is considered for the removal of TDS. A multi-objective problem is formulated to optimize the entire superstructure that consists of hydraulic fracturing, storage, transportation, and water treatment, minimizing annualized cost from recovered water per period and the water footprint of the process. The capabilities of the proposed approach are illustrated through the simulation of different scenarios that are performed to examine the effects of water availability on the productivity of stimulated wells. Finally, the impact of flowback water generation is evaluated using TRACI, a tool for the reduction and assessment of chemical and other environmental impacts

Economic Model-Based Controller Design Framework for Hydraulic Fracturing to Optimize Shale Gas Production and Water Usage

As water issues associated with hydraulic fracturing have received much attention, several optimization approaches have been developed for effective water management. However, most of them have not considered pumping schedules for hydraulic fracturing, which determine the productivity of a shale well as well as the total amount of freshwater required. Motivated by this consideration, a novel model-based control framework is proposed for hydraulic fracturing to maximize the net profit from shale gas development which simultaneously minimizes the total cost associated with water management. The framework is as follows; initially a reduced-order model and a Kalman filter are developed based on the simulation data generated from a high-fidelity hydraulic fracturing model to correlate the pumping schedule and the final fracture geometry. Then, a numerical reservoir simulator and mixed-integer nonlinear programming model are used to generate two maps describing the revenue from selling shale gas produced and cost from managing wastewater recovered, respectively. Finally, by applying a data-based dynamic input-output model to connect the two maps, a model predictive control system is formulated. The proposed control framework enables 62% of the generated wastewater to be reused through the application of thermal membrane distillation technology in treatment process and results in a 11% reduction in overall freshwater consumption, while maintaining the productivity of shale wells at its theoretical maximum

Hybrid Modeling Approaches Integrating Physics-Based Models with Machine Learning for Predictive Control of Biological and Chemical Processes

Recently, there has been growing interest in data-based modeling as the amount of data available has increased tremendously. One such method is Dynamic Mode Decomposition with Control technique, which builds temporally local linear models using data. But its limited domain of applicability (DA) hinders its use for prediction purposes. To overcome this challenge, we proposed an algorithm that utilizes multiple "local" training datasets, and it was applied successfully to hydraulic fracturing. Although data-based modeling offers simplicity and ease of construction, it lacks robustness and parametric interpretability, unlike first-principles modeling. To balance the advantages and disadvantages of data-based models and first-principles models, hybrid modeling was proposed using artificial neural networks (ANNs). Since then, Machine Learning (ML) has advanced where deep neural networks (DNNs) with more than three layers can be trained to approximate any function accurately. In this work, we proposed a deep hybrid modeling (DHM) framework that integrates first-principles with DNNs and successfully applied it to two complex processes, i.e., hydraulic fracturing and full-scale fermentation reactor. Similarly, Universal Differential Equations (UDEs) was proposed in ML where DNNs are represented as ODEs and solved using ODE solvers. We utilized UDEs to successfully build a DHM using simulation and experimental data for batch production of ϐ-carotene. One limitation of DHM is that its DA is affected by the DNN within it, and its accuracy is high within its DA. Therefore, it is important to consider its DA when designing a model-based controller. To this end, we proposed a Control Lyapunov-Barrier Function (CLBF)-MPC to stabilize and ensure that the closed-loop system stays within DA of DHM. Theoretical guarantees were provided for the CLBF-MPC controller, and it was successfully implemented on a CSTR. The idea of integrating physics with ML can be extended to Reinforcement Learning (RL). In case when model-based controller design is not possible, we proposed a model-free Deep RL (DRL) controller that utilizes prior knowledge in its reward function to quicken the learning process. This DRL controller was successfully applied to hydraulic fracturing wherein Nolte’s law was included in the reward function for fast convergence

Development of advanced mathematical models for analysis of hydraulic channel fracturing technique

The channel fracturing technique is a Schlumberger's recent development in the area of hydraulic fracture stimulations, which allows for discontinuous proppant placement within the fracture opening. The discontinuous placement of proppant creates a highly conductive network of interconnected open channels, which can significantly increase the overall fluid conductivity of the fracture. Modelling, analysis and prediction of the fluid conductivity of openings created using the channel fracturing technique is of a great interest in both industrial and research contexts. Subsequently, the main objective of this research is to study the channel fracturing technique. Specific aims include the investigation of the effects of different confining stress, proppant placement patterns, and mechanical properties of the rock formation and proppant on the enhancement of the fluid conductivity. The general methodology adopted in this thesis is based on the Distributed Dislocation Technique, which is a powerful analytical tool for the analysis of fracture problems. To meet the main objective, a number of nonlinear mathematical models were developed to predict the fluid conductivity. These models are presented in separate chapters of this thesis. A number of case studies were considered for typical combinations of mechanical properties of rock and proppant, proppant placement patterns as well as confining stress conditions. It was demonstrated that an appropriate selection of proppant and its placement pattern within the openings can significantly increase the well production rates, which is essentially the ultimate goal of hydraulic fracture stimulations. From practical point of view, the outcomes of this thesis can provide a valuable guidance for designing efficient proppant injection schedules and selecting a suitable proppant type in order to maximise the well productivity, decrease environmental impact as well as to reduce the overall cost of oil and gas recovery, which are currently the main concerns for the relevant industries and government organisations. The main body of the thesis represents a compendium of papers submitted to or published in international journals or conference proceedings. These papers are united by the same topic as well as the research methodology mentioned above. The percentage and contribution of the candidate are specified in the Statement of Authorship for each article with more than one author.Thesis (MPhil.) -- University of Adelaide, School of Mechanical Engineering, 201

Automatic hydraulic fracturing design for low permeability reservoirs using artificial intelligence

The hydraulic fracturing technique is one of the major developments in petroleum engineering in the last two decades. Today, nearly all the wells completed in low permeability gas reservoirs require a hydraulic fracturing treatment in order to produce at an economical level. This study presents a new methodology, applicable to tight gas reservoirs, for designing hydraulic fractures.;This study is intended to develop an automatic hydraulic fracture design tool to help users design fracture jobs without being an expert in the art and science of hydraulic fracturing. This process is composed entirely of an integration of several artificial intelligence techniques.;The methodology consists of three modules: formation stress determination, optimum treatment design and net treatment pressure prediction. The first module combines the classic approach of stress calculations with a fuzzy lithology identification system to better characterize the reservoir and estimate the stress profile. The result of this module is essential for the fracture treatment design. The second module incorporates an optimization system composed of neural networks and a genetic algorithm to search for the optimum treatment design. The third, and final, module is designed to predict the net treating pressure expected during fracturing. A one-dimensional vector quantization technique samples and extracts the main characteristic of the pressure profile. The net treatment pressure neural network generates the main features of the pressure profile and then reconstructs the entire signal.;The methodology was integrated in a computer program aimed to help petroleum engineers design optimum treatment schedules and predict net treatment pressure for hydraulic fracturing. This tool is designed to reduce the engineering time for designing optimum treatment schedules

Reducing the environmental impact of hydraulic fracturing pumps

This thesis was previously held under moratorium from 01/12/16 to 01/12/21The current approach to hydraulic fracturing requires large amounts of industrial hard-ware to be transported, installed and operated in temporary locations. Typically 70% of the mass of this equipment is comprised of the fleet of truck-mounted pumps required to provide the high pressures and flows necessary for well stimulation. The established design of these pumps were developed for the shale gas extraction industry in North America, where the environmental, geological, regulatory and social constraints are very different from Europe. Consequently the engineering choices made in the current pump designs did not focus on minimising the physical and environmental footprint of the operation. These aspects are of paramount importance for the emerging hydraulic fracturing industry in Europe, so it is timely to address these factors when considering the design of future high-pressure pumps for European shale resources. This thesis develops and applies a methodology for environmental optimisation of the key mechanical design parameters for the high-pressure pumps that are central to hydraulic fracturing operations. Before describing the optimisation methodology the thesis provides an overview of the industrial plant required to carry out a hydraulic fracturing operation, and an estimate of the functional requirements (i.e. pressure and flow) of the equipment. The computational model, central to the optimisation process, is validated by using field data from a hydraulic fracturing site in North America and an experimental test rig. The optimisation analysis concludes that reducing the plunger diameter and running the pump at higher angular velocity, with lower forces, can increase pump efficiency by up to 4.6%. Furthermore the modification of the pump’s parameters would result in several environmental benefits beyond the obvious economic gains of lower fuel con-sumption. Previous studies have shown that over 90% of the emissions of CO2 and other pollutants that occur during a hydraulic fracturing operation are associated with the pumps and their prime movers. Consequently, any increase in pumping efficiency will also reduce the greenhouse gas emissions and improve local air quality (CO2, NOx and other pollutants). Additionaly, the reduction in plunger diameter will reduce the amplitude of fatigue stresses and so increase the life of the units and allow their overall mass to be reduced. More reliable pumps could decrease the number of standby (i.e. backup) units necessary, and so reduce procurement costs and site traffic, including the overall site footprint. The concluding system optimisation study suggests that the highest level of direct on-site emission is due to the inefficient and asynchronous operation of multiple frac-truck assemblies. Reducing the number of frac-truck assemblies subsequently affects pump traffic lowering the nuisance effects to the local community such as noise, road damage and road traffic risk.The current approach to hydraulic fracturing requires large amounts of industrial hard-ware to be transported, installed and operated in temporary locations. Typically 70% of the mass of this equipment is comprised of the fleet of truck-mounted pumps required to provide the high pressures and flows necessary for well stimulation. The established design of these pumps were developed for the shale gas extraction industry in North America, where the environmental, geological, regulatory and social constraints are very different from Europe. Consequently the engineering choices made in the current pump designs did not focus on minimising the physical and environmental footprint of the operation. These aspects are of paramount importance for the emerging hydraulic fracturing industry in Europe, so it is timely to address these factors when considering the design of future high-pressure pumps for European shale resources. This thesis develops and applies a methodology for environmental optimisation of the key mechanical design parameters for the high-pressure pumps that are central to hydraulic fracturing operations. Before describing the optimisation methodology the thesis provides an overview of the industrial plant required to carry out a hydraulic fracturing operation, and an estimate of the functional requirements (i.e. pressure and flow) of the equipment. The computational model, central to the optimisation process, is validated by using field data from a hydraulic fracturing site in North America and an experimental test rig. The optimisation analysis concludes that reducing the plunger diameter and running the pump at higher angular velocity, with lower forces, can increase pump efficiency by up to 4.6%. Furthermore the modification of the pump’s parameters would result in several environmental benefits beyond the obvious economic gains of lower fuel con-sumption. Previous studies have shown that over 90% of the emissions of CO2 and other pollutants that occur during a hydraulic fracturing operation are associated with the pumps and their prime movers. Consequently, any increase in pumping efficiency will also reduce the greenhouse gas emissions and improve local air quality (CO2, NOx and other pollutants). Additionaly, the reduction in plunger diameter will reduce the amplitude of fatigue stresses and so increase the life of the units and allow their overall mass to be reduced. More reliable pumps could decrease the number of standby (i.e. backup) units necessary, and so reduce procurement costs and site traffic, including the overall site footprint. The concluding system optimisation study suggests that the highest level of direct on-site emission is due to the inefficient and asynchronous operation of multiple frac-truck assemblies. Reducing the number of frac-truck assemblies subsequently affects pump traffic lowering the nuisance effects to the local community such as noise, road damage and road traffic risk