Decline curves are fast methods to predict production behavior in oil and gas wells. Some of the notable decline curve methods are Arp’s, SEDM (Stretched Exponential Decline Model), Duong’s Model and Weibull decline curves. Available production history data can be used to fit any of these equations and future production decline can thus be extrapolated. However, when limited production data is available during early periods of well history, these equations could be fitted using inaccurate parameters leading to erroneous predictions. Also, the traditional decline curve analysis approach does not account for the complexities related to reservoir description and well completions.
This study utilizes publicly available databases of the Eagle Ford formation to develop a novel predictive modeling methodology linking decline curve model parameters to well completion related variables that allows for the rapid generation of synthetic decline curves at potential new well locations. Modern machine learning algorithms such as Random Forests (RF), Support Vector Machines (SVM) and Multivariate Adaptive Regression Splines (MARS) can then be used to model the well decline behavior. Cross-Validation technique such as
First, production data are fitted to decline curve models to estimate the corresponding model parameters. Next, machine learning models are built for these parameters as a function of initial flow rate, various well completion parameters (i.e., number of hydraulic fracture stages, completed lengths, proppant and fracturing fluid amounts) and well location/depth parameters (i.e., well latitudes, longitudes, total vertical depth of heel and difference between total vertical depths of heel and toe of horizontal wells). These models are used to rapidly predict the decline curves for new or existing wells without the need for costly reservoir simulators. It has been found that accurate prediction of rate decline of new wells can be predicted using this methodology. This method can also predict ultimate recovery of a new well based on data collected from previous wells.
To our knowledge, this is the first time machine learning algorithms have been used to predict the decline curve parameters and examine the relative performance of various decline curve models. The power and utility of our approach are demonstrated by successful prediction of the decline behavior of blind wells that were not incorporated in the analysis. We also examine the relative influences of various well design and location variables to determine the hidden correlations or interactions among them which are hard to decipher with other methods.
Hetz, Gill (Texas A&M University) | Kim, Hyunmin (Texas A&M University) | Datta-Gupta, Akhil (Texas A&M University) | King, Michael J. (Texas A&M University) | Przybysz-Jarnut, Justyna K. (Shell Global Solutions International B. V) | Lopez, Jorge L. (Shell International Exploration & Production Inc.) | Vasco, Donald (Lawrence Berkeley Laboratory)
We present a novel and efficient approach to integrate frequent time lapse (4D) seismic data into high resolution reservoir models based on seismic onset times, defined as the calendar time when the seismic attribute crosses a pre-specified threshold value at a given location. Our approach reduces multiple time- lapse seismic survey data into a single map of onset times, leading to substantial data reduction for history matching while capturing all relevant information regarding fluid flow in the reservoir. Hence, the proposed approach is particularly well suited when frequent seismic surveys are available using permanently embedded sensors.
Our history matching workflow consists of two stages: global and local. At the global stage of history matching, large-scale features such as regional permeabilities, pore volumes, temperature and fluid saturations are adjusted to match seismic and bottomhole pressure data using a Pareto-based multiobjective history matching workflow. Rather than an artificial subdivision of the domain, the history matching regions are naturally defined based on an eigen-decomposition of the grid Laplacian and a spectral clustering of the second eigenvector (fiedler vector). The global updating is followed by local history matching whereby cell permeabilities are adjusted to further refine the history match using semi- analytic, streamline-based model parameter sensitivities. The power and efficacy of our proposed approach is illustrated using synthetic and field applications.
The field example involves steam injection into a heavy oil reservoir at Pad 31 in the Peace River Field (Alberta, Canada) with daily time lapse seismic surveys recorded by a permanently buried seismic monitoring system (
Olalotiti-Lawal, Feyi (Texas A&M University) | Onishi, Tsubasa (Texas A&M University) | Datta-Gupta, Akhil (Texas A&M University) | Fujita, Yusuke (JX Nippon Oil & Gas Exploration Corporation) | Hagiwara, Kenji (JX Nippon Oil & Gas Exploration Corporation)
We present a simulation study of a mature reservoir for CO2 Enhanced Oil Recovery (EOR) development. This project is currently recognized as the world's largest project utilizing post-combustion CO2 from power generation flue gases. With a fluvial formation geology and sharp hydraulic conductivity contrasts, this is a challenging and novel application of CO2 EOR. The objective of this study is to obtain a reliable predictive reservoir model by integrating multi-decadal production data at different temporal resolutions into the available geologic model. This will be useful for understanding flow units, heterogeneity features and their impact on subsurface flow mechanisms to guide the optimization of the injection scheme and maximize CO2 sweep and oil recovery from the reservoir.
Our strategy consists of a hierarchical approach for geologic model calibration incorporating available pressure and multiphase production data. The model calibration is carried out using regional multipliers whereby the regions are defined using a novel Adjacency Based Transform (ABT) accounting for the underlying geologic heterogeneity. To start with, the Genetic Algorithm (GA) is used to match 70-year pressure and cumulative production by adjusting pore volume and aquifer strength. Water injection data for reservoir pressurization prior to CO2 injection is then integrated into the model to calibrate the formation permeability. The fine-scale permeability distribution consisting of over 7 million cells is reparametrized using a set of linear basis functions defined by a spectral decomposition of the grid connectivity matrix (grid Laplacian). The parameterization represents the permeability distribution using a few basis function coefficients which are then updated during history matching. This leads to an efficient and robust workflow for field scale history matching.
The history matched model provided important information about reservoir volumes, flow zones and aquifer support that led to additional insight to the prior geological and simulation studies. The history matched field-scale model is used to define and initialize a detailed fine-scale model for a CO2 pilot area which will be utilized for studying the impact of fine-scale heterogeneity on CO2 sweep and oil recovery. The uniqueness of this work is the application of a novel geologic model parameterization and history matching workflow for modeling of a mature oil field with decades of production history and which is currently being developed with CO2 EOR.
Tanaka, Shusei (Chevron Energy Technology Company) | Kam, Dongjae (Chevron Energy Technology Company) | Xie, Jiang (Chevron Energy Technology Company) | Wang, Zhiming (Chevron Energy Technology Company) | Wen, Xian-Huan (Chevron Energy Technology Company) | Dehghani, Kaveh (Chevron Energy Technology Company) | Chen, Hongquan (Texas A&M University) | Datta-Gupta, Akhil (Texas A&M University)
Rate allocation optimization for water and gas injection/production processes is typically complex, requiring multiple simulations to find the optimal reservoir management strategy for improved economic value of the asset. The objective of this paper is to develop and demonstrate a fast and robust derivative-free workflow which improves economic values via optimizing water and gas flooding rate allocation by streamline-based technique.
Streamline-based rate allocation optimization has been demonstrated to be a powerful tool for application to waterflood operations. However, the utility of the technique has been limited in optimizing the Net-Present-Value (NPV) for improving the economics of these operations. In addition, the theoretical assumptions on physics limit its application to pressure-sensitive secondary or tertiary recovery processes such as gas injection. In the proposed workflow the expected NPV of each injector-producer pairs are evaluated at a given future business decision such as next infill time by using static, dynamic, and economic parameters such as price and discount rate along with time-of-flight. Then new flow rates are allocated based on the performance of the wells ranked by expected NPV to achieve better future economic value.
The proposed workflow was first compared with previous streamline-based rate reallocation technique using series synthetic models. Although all tested methods showed better performance when compared with the base scenario, our proposed approach showed improved performance in terms of NPV, primarily due to proper handling of the reservoir dynamics and economic value in the objective function. The workflow was then benchmarked by a case study of a field subjected to waterflood and gas injection. The results of proposed approach were comparable to the population based derivative-free techniques such as Genetic Algorithm (GA) or Particle Swarm Optimization (PSO) where many simulations are required to achieve a similar outcome.
The proposed workflow was coupled with next generation simulator and applied to various field studies. The method provides the ability to simultaneously control injector and producer flow rates for improving the economic value under multiple constraints. The workflow retains advantages of the conventional streamline-based technique such as fast post processing and ease of application to a broad field studies.
Iino, Atsushi (Texas A&M University) | Vyas, Aditya (Texas A&M University) | Huang, Jixiang (Texas A&M University) | Datta-Gupta, Akhil (Texas A&M University) | Fujita, Yusuke (JX Nippon Oil and Exploration Corporation) | Sankaran, Sathish (Anadarko Petroleum Corporation)
Reliable performance assessment of unconventional reservoirs requires accurate modeling of inter-porosity flow characteristics in hydraulic fractures, microfractures and reservoir rock. In addition, phase behavior in nano-porous rocks plays an important role in reservoir performance. High resolution flow simulation incorporating the complex underlying physics and detailed reservoir heterogeneity is computationally expensive. In this paper, we propose a fast and novel approach for field scale compositional simulation and history matching for unconventional reservoirs.
Our proposed simulation approach is based on a high frequency asymptotic solution of the diffusivity equation in heterogeneous and fractured reservoirs. The high frequency solution leads to the Eikonal equation which is solved for a ‘diffusive time of flight’ (DTOF) that governs the propagation of the ‘pressure front’ in the reservoir. Our approach consists of two decoupled steps: calculation of the DTOF using the Fast Marching Method (FMM) and fully-implicit compositional simulation using DTOF as a spatial coordinate. The computational efficiency is achieved by reducing the 3-D compositional flow equation into 1-D equation using the DTOF as spatial coordinate, leading to orders of magnitude faster computation over full 3-D compositional simulation. The savings in computation time increases significantly with grid refinement and for high resolution models.
We demonstrate the power and utility of our method using synthetic and field applications. The field application involves history matching of three-phase production data from a horizontal well with multi-stage hydraulic fractures in a shale reservoir in East Texas. The properties of individual hydraulic fractures, microfractures and the matrix/fracture geometries and the extent of the stimulated reservoir volume were adjusted through history matching using the Genetic Algorithm with the FMM-based compositional simulation. For the history matching, 2,200 simulation runs were required but completed in four days using the FMM-based simulation, at least an order of magnitude savings in computation time over a commercial finite difference simulator. Multiple history-matched models were generated and used for obtaining the bounds of production forecast.
This study shows the novelty and efficiency of the FMM-based compositional simulation for field-scale modeling of shale reservoirs including phase behavior and multi-continua heterogeneity. It also enables systematic history matching and uncertainty analysis that require large number of simulation runs.
One of the challenges in the development planning of unconventional reservoirs is determining the potential for well interference. It is essential to understand when and how the well performance has been impacted by surrounding wells as this limits the ultimate recovery from a well. Modeling of well interference in unconventional reservoirs is complicated by the complexity and uncertainties in fracture geometry and the impact of natural fractures. We propose a novel and efficient simulation technique to identify well interference and quantify the impact on well performance in unconventional reservoirs.
Our proposed approach relies on the high frequency asymptotic solution of the diffusivity equation leading to the ‘Eikonal Equation’, which describes the propagation of the pressure front and can be efficiently solved using the Fast Marching Method (FMM) including a detailed description of fracture geometry. Thus, our proposed method serves as a bridge between simplified analytical tools and complex numerical simulation. The well interference time can be quickly estimated and the reservoir can be partitioned accordingly based on the competing pseudo steady state drainage volumes amongst the wells. The transient drainage volume evolution within each PSS subdomain associated with any particular well can be used to recast the 3-D diffusivity equation to a 1-D form which can be solved analytically for pressure and rate response. This method allows us not only to compute rigorously the well drainage volume evolution with time but also to assess the potential impact of neighboring wells. The novelty and advantage of this approach is that it provides an intuitive way to characterize well interference and drainage volume connectivity in the reservoir.
We demonstrate the power and versatility of the proposed method using a series of synthetic models. First, a synthetic shale oil reservoir model is used to demonstrate that the FMM can be effectively extended to bounded reservoirs while a series of multi-well scenarios are used to validate the proposed FMM with multi-well drainage volume competition. Next, we apply the above improvements to a large-scale synthetic shale oil model with well interference and performance calculation. Last, we use a simple well spacing optimization example to demonstrate the effectiveness and efficiency of the FMM-based simulation-free workflow.
With the current industry practice of reduced cluster spacing and increased fracturing proppant/fluid volume, the hydraulic fracture treatment tends to generate more complex fracture systems, where an unstructured computational grid, instead of a Cartesian or corner point grid, is preferred to accurately model the fracture geometry. With unstructured grids, the reservoir performance is generally simulated with finite volume simulation, for which one major issue is the potentially heavy computational cost. A novel approach has recently been introduced to provide a rapid simulation of unconventional reservoirs, which first captures the drainage volume during the transient pressure propagation process using the Fast Marching Method (FMM) and then rapidly solves fluid flow equation in an equivalent 1D domain. However, this application is currently limited to calculating the reservoir response with Cartesian or corner-point grids.
In the study, we propose an effective workflow to model and simulate the complex fracture system. The fracture propagation process is first modeled, based on the pre-existing natural fracture information and fracturing treatment data, to generate complex fractures, which can be calibrated against micro-seismic data. A 2.5D perpendicular bisector PEBI grid based on a Voronoi tessellation is then constructed with high resolution near the fractures and with larger cells far from the fractures. Next, the Eikonal equation, which governs the transient pressure propagation process, is solved on the basis of subdivided tetrahedrons using the Fast Marching Method. Solving this pressure propagation equation on the unstructured grid, with high resolution near the fractures, provides more accurate calculation of the travel time (i.e. diffusive time of flight, DToF) and the transient drainage volume. Finally, the fluid flow equation is effectively solved in the transformed 1D domain, where DToF acts as the 1D spatial coordinate.
Complex fracture systems may be developed from fracture propagation models and accurately represented using unstructured grids. The FMM algorithm is studied on unstructured grids with two types of discretization, which are based on Fermat’s principle and Eulerian discretization. The accuracy and convergence characteristics are investigated. The DToF-based fluid flow simulation is validated against finite volume reservoir simulation and can be integrated with industry fracturing modeling software to provide a rapid calculation of reservoir response. Through numerical examples, our proposed workflow is demonstrated to be an efficient approach to model and simulate the complex fracture system in unconventional reservoirs.
Unstructured grids allow better characterization of the transient drainage volume for complex fracture systems while the DToF-based fluid flow simulation provides rapid simulation of the reservoir performance based on the drainage volume. Combining the advantages of unstructured grids and the DToF-based fluid flow simulation, we have developed an effective workflow to model and simulate the complex fracture system. This proposed workflow provides orders of magnitude reduction in computational cost, which is attractive for high-resolution models. The approach is also efficient for calibrating the reservoir and fractures parameters and optimizing the well and hydraulic fracturing design.
Iino, Atsushi (Texas A&M University) | Vyas, Aditya (Texas A&M University) | Huang, Jixiang (Texas A&M University) | Datta-Gupta, Akhil (Texas A&M University) | Fujita, Yusuke (JX Nippon Oil & Gas Exploration Corporation) | Bansal, Neha (Anadarko Petroleum Corporation) | Sankaran, Sathish (Anadarko Petroleum Corporation)
This paper demonstrates the novelty and practical feasibility of the FMM-based multi-phase simulation for rapid field-scale modeling of shale reservoirs with multi-continua heterogeneity.
Modeling of unconventional reservoirs requires accurate characterization of complex flow mechanisms in multi-continua because of the interactions between reservoir rocks, microfractures and hydraulic fractures. It is also essential to account for the complicated geometry of well completion, the reservoir heterogeneity and multi-phase flow effects. Currently, such multi-phase numerical simulation for multi-continua reservoirs needs substantial computational time that hinders efficient history matching and uncertainty analysis. In this paper, we propose an efficient approach for field scale application and performance assessment of shale reservoirs using rapid multi-phase simulation with the Fast Marching Method (FMM).
The key idea of the reservoir simulation using the FMM is to recast the 3-D flow equation into 1-D equation along the ‘diffusive time of flight’ (DTOF) coordinate, which embeds the 3-D spatial heterogeneity. The DTOF is a representation of the travel time of pressure propagation in the reservoir. The pressure propagation is governed by the Eikonal equation which can be solved efficiently using the FMM. The 1-D formulation leads to orders of magnitude faster computation than the 3-D finite difference simulation. The use of FMM-based simulation also enables systematic history matching and uncertainty analysis using population-based techniques that require substantial simulation runs.
We first validate the accuracy and computational efficiency of the FMM-based multi-phase simulation using synthetic reservoir models and comparison with a commercial finite-difference simulator. Next, we apply our proposed approach to a field example in Texas for a multi-stage hydraulically fractured horizontal well. The 3-D heterogeneous reservoir model was built and history matched for oil, gas and water production using the Genetic Algorithm with the FMM-based flow simulation. Multiple history-matched models were obtained to examine uncertainties in the production forecast associated with respect to the properties related to hydraulic fractures, microfractures and the matrix.
Watanabe, Shingo (Texas A&M University) | Han, Jichao (Texas A&M University) | Hetz, Gill (Texas A&M University) | Datta-Gupta, Akhil (Texas A&M University) | King, Michael J. (Texas A&M University) | Vasco, Donald W. (Lawrence Berkeley National Laboratory)
We present an efficient history-matching technique that simultaneously integrates 4D repeat seismic surveys with well-production data. This approach is particularly well-suited for the calibration of the reservoir properties of high-resolution geologic models because the seismic data are areally dense but sparse in time, whereas the production data are finely sampled in time but spatially averaged. The joint history matching is performed by use of streamline-based sensitivities derived from either finite-difference or streamline-based flow simulation. For the most part, earlier approaches have focused on the role of saturation changes, but the effects of pressure have largely been ignored. Here, we present a streamline-based semianalytic approach for computing model-parameter sensitivities, accounting for both pressure and saturation effects. The novelty of the method lies in the semianalytic sensitivity computations, making it computationally efficient for high-resolution geologic models. The approach is implemented by use of a finite-difference simulator incorporating the detailed physics. Its efficacy is demonstrated by use of both synthetic and field applications. For both the synthetic and the field cases, the advantages of incorporating the time-lapse variations are clear, seen through the improved estimation of the permeability distribution, the pressure profile, the evolution of the fluid saturation, and the swept volumes.
Production logs from horizontal wells in shale reservoirs indicate that more than 30% of the perforation clusters do not contribute to production. One major reason is recognized as the stress shadow effect which impedes the propagation of the interior fractures within a single fracture stage. Although limited entry perforations have been successfully introduced in horizontal wells to counteract this completion inefficiency, the complex mechanisms involved have not been fully understood.
In this paper, a fully integrated workflow that incorporates fracture propagation, reservoir flow and wellbore hydraulics has been developed to evaluate the efficiency of limited entry perforations during multiple simultaneous fracture propagation. Darcy–Weisbach and classic orifice flow equations are adopted to describe the wellbore and perforation friction. The coupled reservoir and geomechanics model are solved by finite element code while a cohesive zone model, which accounts for the significant non-linear effects near fracture tip over the conventional linear elastic fracture mechanics, is used to simulate the fracturing process.
During the stimulation of multiple fractures, uneven fluid distribution will be observed once the fractures begin to interfere with each other. Meantime, the difference in perforation pressure loss due to uneven fluid rates will counteract the stress shadow effects and balance fluid distribution. Thus, a larger perforation friction coefficient is favorable but it also causes higher pumping pressure. A novel proppant model is proposed to represent both stress- and time-dependent fracture conductivity change due to proppant degradation in subsequent long-term production. Production simulation results demonstrate that deliberate deployment of limited entry technique can significantly increase production but this benefit is reduced with increased cluster spacing. Sensitivity study indicates that better well performance could be obtained by reducing number of shots in each cluster and increasing number of clusters in each stage. Non-uniform perforation shots distribution is proven to be an effective means to counteract the stress shadow effects while the cluster length is unchanged. Simulation results also indicate how the heterogeneity in reservoir properties affects the performance of limited entry perforations.
The proposed workflow has the advantage to integrate fracturing and production simulation in the same grid system and evaluate performance of different stimulation strategies. The comparison studies can provide critical insights to the application of engineered limited entry.