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.
Hydraulic fracturing treatment in naturally fractured unconventional reservoirs generally induce complex fracture geometries. Thus an unstructured grid, instead of a Cartesian or corner point grid, is preferred to accurately model the geometry of the fractures and the performance of such reservoirs. The drawback of conventional simulation on unstructured grids is the potentially heavy computational cost. A novel approach has recently been introduced to provide rapid simulation of unconventional reservoirs, which first captures the drainage volume during the transient 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 this study, the FMM based simulation method is extended to unstructured grid. A new mesh generation approach is first presented to discretize the complex fracture network, accounting for both hydraulic fractures and natural fractures. Voronoi cells (or perpendicular bisector, i.e. PEBI grids) are constructed with high resolution near the fractures and with larger cells far from fractures. A force-equilibrium algorithm is adopted here to optimize the mesh quality and reduce highly skewed cells. FMM algorithm is computed on the basis of subdivided triangles, which can provide the diffusive time of flight (DToF) at both Voronoi cell vertices and cell centers. Thus, a more accurate calculation of drainage volume in unconventional reservoir with complex fracture networks can be obtained. Finally, fluid flow is calculated in transformed 1D domain, where DToF acts as the 1D spatial coordinate.
Unstructured grids with good mesh quality are constructed to accurately capture the complex fracture network system. The convergence characteristic of FMM on unstructured grids is investigated. Reservoir simulation is efficiently computed based on the drainage volume information from the unstructured grid system using FMM, and the simulation results are validated with finite-difference based and finite-volume based numerical results. There are three key parts of this proposed approach, which are: (i) good mesh generation technique to capture complex fracture networks, (ii) FMM computation on unstructured grids to provide the drainage volume, and (iii) fluid flow calculation in transformed 1D domain.
We extend the reservoir simulation using FMM in unconventional reservoirs from Cartesian and corner point grid systems to unstructured grids. The proposed approach shows orders of magnitude reduction in simulation time for modeling unstructured grids, bringing typical simulation times of hours or days down to minutes, which is quite attractive for high-resolution models. Through the numerical examples, the proposed method is demonstrated to be an accurate and efficient approach to simulate naturally fractured unconventional reservoirs with unstructured grids.
Modeling of fluid flow in unconventional reservoirs requires accurate characterization of complex flow mechanisms because of the interactions between reservoir rock, microfractures, and hydraulic fractures. The pore-size distribution in shale and tight sand reservoirs typically ranges from nanometers to micrometers, resulting in ultralow permeabilities. In such extremely low-permeability reservoirs, desorption and diffusive processes play important roles in addition to heterogeneity-driven convective flows.
For modeling shale and tight oil and gas reservoirs, we can compute the well-drainage volume efficiently with a fast marching method (FMM) and by introducing the concept of “diffusive time of flight” (DTOF). Our proposed simulation approach consists of two decoupled steps--drainage-volume calculation and numerical simulation with DTOF as a spatial coordinate. We first calculate the reservoir drainage volume and the DTOF with the FMM, and then the numerical simulation is conducted along the 1D DTOF coordinate. The approach is analogous to streamline modeling whereby a multidimensional simulation is decoupled to a series of 1D simulations resulting in substantial savings in computation time for high-resolution simulation. However, instead of a “convective time of flight” (CTOF), a DTOF is introduced to model the pressure-front propagation.
For modeling physical processes, we propose triple continua whereby the reservoir is divided into three different domains: microscale pores (hydraulic fractures and microfractures), nanoscale pores (nanoporous networks), and organic matter. The hydraulic fractures/microfractures primarily contribute to the well production, and are affected by rock compaction. The nanoporous networks contain adsorbed gas molecules, and gas flows into fractures by convection and Knudsen diffusion processes. The organic matter acts as the source of gas. Our simulation approach enables high-resolution flow characterization of unconventional reservoirs because of its efficiency and versatility. We demonstrate the power and utility of our approach with synthetic and field examples.
Downhole-temperature measurement is one of the solutions to understanding downhole-flow conditions, especially in complex well/reservoir domains such as multistage-fractured horizontal wells. In the past, models and methodologies have been developed for fracture diagnosis for multiple-stage-fractured horizontal wells. They are based either on a semianalytical approach for simplicity or on reservoir simulation for generality. The challenges are that semianalytical models are not robust enough to describe complex fracture systems, whereas numerical simulation is computationally expensive and impractical for inversion. To develop a comprehensive approach to translate temperature to flow profile, we adopted the fast marching method (FMM) in simulating both heat transfer and the velocity/pressure field in the interested domain (heterogeneous reservoir with multiple-fractured horizontal wells). FMM is a new approach that is efficient in front tracking. Previous studies show a significant success in the investigation of pressure-depletion behavior and shale-gas production-history match. By the nature of heat transfer in porous media, the thermal-front propagation would lag behind pressure, and the noticeable temperature change in the reservoir only happens near hydraulic/natural fractures. FMM can be used to efficiently track the heat front that is associated with the flow field.
In this study, we solve the thermal model in porous media by transforming the general energy-balance equation into a 1D equation, with the diffusive time of flight (DTOF) as the spatial coordinate system. Besides the diffusive heat conduction, the convection, Joule-Thomson effect, and viscous dissipation are considered in the model. The inner boundary of the model is carefully handled, and the drainage volume of each fracture is calculated to identify different inflow temperature related to flow rate at perforation locations. The model was validated by the finite-difference approach. Examples are presented in the paper to illustrate the application of the new method. The approach can be used to quantitatively interpret temperature measurements to fracture profiles in horizontal wells.
Zhang, Yanbin (Texas A&M University) | Bansal, Neha (Texas A&M University) | Fujita, Yusuke (Texas A&M University) | Datta-Gupta, Akhil (Texas A&M University) | King, Michael J. (Texas A&M University) | Sankaran, Sathish (Anadarko Petroleum Corporation)
Current industry practice for characterization and assessment of unconventional reservoirs mostly uses empirical decline-curve analysis or analytic rate- and pressure-transient analysis. High-resolution numerical simulation with local perpendicular bisector (PEBI) grids and global corner-point grids has also been used to examine complex nonplanar fracture geometry, interaction between hydraulic and natural fractures, and implications for the well performance. Although the analytic tools require many simplified assumptions, numerical-simulation techniques are computationally expensive and do not provide the more-geometric understanding derived from the depth-of-investigation (DOI) and drainage-volume calculations.
We propose a novel approach for rapid field-scale performance assessment of shale-gas reservoirs. Our proposed approach is dependent on a high-frequency asymptotic solution of the diffusivity equation in heterogeneous reservoirs and serves as a bridge between simplified analytical tools and complex numerical simulation. The high-frequency solution leads to the Eikonal equation (Paris and Hurd 1969), which is solved for a “diffusive time of flight” (DTOF) that governs the propagation of the “pressure front” in the reservoir. The Eikonal equation can be solved by use of the fast-marching method (FMM) to determine the DTOF, which generalizes the concept of DOI to heterogeneous and fractured reservoirs. It provides an efficient means to calculate drainage volume, pressure depletion, and well performance and can be significantly faster than conventional numerical simulation. More importantly, in a manner analogous to streamline simulation, the DTOF can also be used as a spatial coordinate to reduce the 3D diffusivity equation to a 1D equation, leading to a comprehensive simulator for rapid performance prediction of shale-gas reservoirs. The speed and versatility of our proposed method makes it ideally suited for high-resolution reservoir characterization through integration of static and dynamic data.
The major advantages of our proposed approach are its simplicity, intuitive appeal, and computational efficiency. We demonstrate the power and utility of our method by use of a field example that involves history matching, uncertainty analysis, and performance assessment of a shale-gas reservoir in east Texas. A sensitivity study is first performed to systematically identify the “heavy hitters” affecting the well performance. This is followed by history matching and an uncertainty analysis to identify the fracture parameters and the stimulated-reservoir volume. A comparison of model predictions with the actual well performance shows that our approach is able to reliably predict the pressure depletion and rate decline.
Identification of channel geometry, facies boundaries, and characterization of channel petrophysical properties are critical for performance predictions of channelized reservoirs. Level set methods have shown great promise to effectively parameterize facies boundaries and allow for changing channel geometry and connectivity during history matching. An outstanding challenge is efficient updating of channel geometry as well as channel petrophysics during history matching. Also, seismic data can provide important information and needs to be used as constraints.
In this paper, a novel two-step history matching workflow is proposed where the channel geometry is modeled using level sets and the internal heterogeneity within the channel facies is modeled using parameterization with linear basis functions, specifically the Grid Connectivity Transform (GCT) basis. Facies boundaries are first represented by the level set function where seismic information is incorporated and the boundaries are gradually moved by solving the level set equation under the seismic constraints. For history matching, Markov Chain Monte Carlo (MCMC) method is employed to minimize production data misfit by adjusting channel geometry and channel petrophysics.
The proposed approach is applied to both 2D and 3D examples. First, we examine the effectiveness of the level set approach by comparison with other approaches for channelized reservoirs, such as Discrete Cosine Transform and Discrete Wavelet Transform. The level set approach is shown to outperform other methods significantly in terms of reproducing channel geometry. Second, we show that the use of seismic constraints helps preserve the structure of facies distributions and geologic realism during history matching. Finally, calibrated facies models are further updated by adjusting the internal channel permeability distributions to fine-tune the history matching. The permeability changes are carried out by perturbing the coefficients of the GCT bases. High and low permeability regions are clearly depicted within the channels and production data misfit is significantly reduced during this second stage. We demonstrate the power and utility of the approach using both 2D and 3D applications.
Previous approaches focused on conditioning channelized models to well data but seismic constraints in level set were not considered. The successful integration of seismic constraints can help not only improve channelized reservoir history matching performance significantly, but also extend applicability of the level set method from simple channelized models to more complicated ones. Also, the GCT approach, for the first time, is shown to capture internal heterogeneity of the channel architecture.
Production performance for unconventional shale reservoirs generally show an early high flow rate followed by a steep decline. Refracturing the underperforming wells is an economical practice to mitigate the flow rate decline and maximize reservoir deliverability, especially at the current low oil price environment. Selecting the correct candidates for refracturing is a crucial step for refracturing jobs. Despite the experience that has been gained in refracturing candidate selection for conventional reservoirs and unconventional tight reservoirs, very little literature is currently available about refracturing candidate selection for multistage hydraulic fractured horizontal wells.
An efficient refracturing candidate selection approach is proposed in this paper based on competition between the produced volume and the drainage volume. The well drainage volume is calculated based on pressure and production data, which measures how much reservoir volume is accessed by the well. Instantaneous Recovery Ratio (IRR), defined as the ratio of produced volume to the drainage volume, is proposed in this paper to measure how quickly or efficiently the accessed volume is being produced. Wells are qualitatively ranked based on their drainage volume and IRR after sufficient production time. Accordingly, well production performance can be compared and refracturing candidates can be selected.
Proposed drainage volume calculation and IRR can efficiently measure the effectiveness of fracture stimulation. The proposed refracturing candidate selection approach is first validated through coupled fluid flow and geo-mechanical simulation, which can account for stress shadow and stress change due to depletion for modeling of the refracturing process. Candidate selection approach is then applied to Eagle Ford shale wells. Results suggest that maximum potential candidate seems to be the well with relatively large drainage volume but with poor depletion rate.
The advantage of the proposed approach is that all calculations are based on pressure and production data, which is purely data driven without any presumptive flow regimes. The result of our refracturing candidate selection criteria is compared to that of previous approaches based on production and completion indices. The proposed approach by this paper can select consistent underperforming wells but additionally can differentiate the wells by giving possible underlining reasons for underperforming. Thus, more appropriate refracturing jobs can be designed accordingly to maximize the chance of refracturing success.
Multistage hydraulically fractured horizontal wells provide an effective means to exploit unconventional reservoirs. The current industry practice in the interpretation of field response often utilizes empirical decline curve analysis or pressure/rate transient analysis (PTA/RTA) for the characterization of these reservoirs and fractures. These analytical tools are based on many simplifying assumptions and cannot provide a detailed description of the evolving reservoir drainage volume from a well, the understanding of which is essential for unconventional reservoir and fracture assessment and optimization.
In our previous study, we developed a novel “data-driven” methodology for the production analysis of shale gas and shale oil reservoirs. The approach is based on the high frequency asymptotic solution of the diffusivity equation in heterogeneous reservoirs. It allows us to determine the drainage volume from a well, and the instantaneous recovery ratio (IRR), which is defined as the ratio of the produced volume to the drainage volume, directly from the production data. In addition, in a manner analogous to the diagnostic plot in PTA, a new w(τ) plot has been proposed to provide better insight into the depletion mechanisms and the fracture geometry.
In the current study, we extend this novel approach to the interpretation of the characteristics of the (potentially) complex fracture systems and drainage volume. We have utilized the w(τ) and IRR plots to the identification of field signatures that imply complex fracture geometry, formation linear flow, partial reservoir completions, fracture interference and compaction effects during production. The w(τ) analysis gives us the fracture surface area and diffusivity information while the IRR analysis provides additional information on fracture conductivity.
The major advantages of this current approach are the model free analysis without presumptions of flow regimes, and a simple and intuitive understanding of the drainage volume and fracture conductivity. The results of the analysis are useful for well and hydraulic fracturing operation design optimization and matrix and fracture parameter estimation.
Unconventional reservoirs such as shale oil and shale gas play a significant role in the US and the world energy market (Holditch, 2013). For these low permeability reservoirs, long horizontal wells with multistage hydraulic fracturing have been proven to be an effective way to stimulate the formation in most cases. However, due to large uncertainty in fracture complexity and reservoir heterogeneity, the characterization of the fracture systems and the prediction of well performance are always of paramount interest.