We present a novel approach to calculate drainage volume and well performance in shale gas reservoirs using a Fast Marching Method (FMM) combined with a geometric pressure approximation. Our approach can fully account for complex fracture network geometries associated with multistage hydraulic fractures and their impact on the well pressure and rates. The major advantages of our proposed approach are its simplicity, intuitive appeal and computational efficiency. For example, we can compute and visualize the time evolution of the well drainage volume for multimillion cell geologic models in seconds without resorting to reservoir simulation. A geometric approximation of the drainage volume is then used to compute the well rates and the reservoir pressure.
The speed and versatility of our proposed approach makes it ideally suited for parameter estimation via inverse modeling of shale gas performance data. We utilize experimental design to perform the sensitivity analysis to identify the ‘heavy hitters' and a genetic algorithm to calibrate the relevant fracture and matrix parameters in shale gas reservoirs by history matching of production data. In addition to the production data, microseismic information is utilized to help us constrain the fracture extent and orientation and to estimate the stimulated reservoir volume (SRV). The proposed approach is applied to a fractured shale gas well. The results clearly show reduced uncertainty in the estimated fracture parameters and SRV, leading to improved forecasting and reserve estimation.
We present the development and field application of a workflow for multiscale reservoir-model calibration that seamlessly integrates production data into the reservoir description from the facies to the grid-cell scale. To start with, the permeability field is parameterized using a novel grid-connectivity-based transformation basis that can be applied with any model geometry, including unstructured and corner-point grids. The parameterization basis functions emerge from spectral decomposition of the grid-connectivity Laplacian and are related to the structural harmonics of the grid. To reconcile data with model resolution during history matching, we first use the coarsest-scale basis functions to identify the large-scale variability. Additional smaller-scale basis elements are then adaptively incorporated to successively refine the model to a level supported by data resolution. During refinement, the inclusion of more detailed basis functions into the parameterization is determined by generic modal frequency when the prior model is unavailable or by using prior information when available. In the final step of the workflow, a streamline-based inversion is performed to locally adjust the reservoir model at grid-cell resolution along preferential-flow paths defined during the coarser-scale parameterization.
We demonstrate the suitability and effectiveness of the developed workflow through application to an offshore turbidite reservoir with frequent well intervention, including shut-ins and recompletions. The static model has over 300,000 cells, a complex channelized interpretation with faults, four injector/producer pairs with deviated wells, and over eight years of production history, including water cut and pressure data. The grid-connectivity-based parameterization effectively updates the prior regional permeability at scales and in locations warranted by the data, while preserving the geologic continuity and avoiding ad hoc redefinition of regions given the sparse well pattern. The multiscale calibrated-permeability field indicates flow communication previously unrecognized in static geologic interpretation or manual history matching.
The concept of depth of investigation is fundamental to well test analysis. Much of the current well test analysis relies on solutions based on homogeneous or layered reservoirs. Well test analysis in spatially heterogeneous reservoirs is complicated by the fact that Green's function for heterogeneous reservoirs is difficult to obtain analytically (Deng and Horne 1993). In this paper, we introduce a novel approach for computing the depth of investigation and pressure response in spatially heterogeneous and fractured reservoirs.
In our approach, we first present an asymptotic solution of the diffusion equation in heterogeneous reservoirs. Considering terms of highest frequencies in the solution, we obtain two equations: the Eikonal equation that governs the propagation of a pressure ‘front' and the transport equation that describes the pressure amplitude as a function of space and time. The Eikonal equation generalizes the depth of investigation for heterogeneous reservoirs and provides a convenient way to calculate drainage volume. From drainage volume calculations, we estimate a generalized pressure solution based on a geometric approximation of the drainage volume. A major advantage of our approach is that the Eikonal equation can be solved very efficiently using a class of front tracking methods called the Fast Marching Methods (FMM). Thus, transient pressure response can be obtained in multimillion cell geologic models in seconds without resorting to reservoir simulators.
We first visualize depth of investigation and pressure solution for a homogeneous reservoir with multi-stage transverse fractures and identify flow regimes from pressure diagnostic plot. And then, we apply the technique to a heterogeneous reservoir to predict depth of investigation and pressure behavior. The computation is orders of magnitude faster than conventional numerical simulation and provides a foundation for future work in reservoir characterization and field development optimization.
The ensemble Kalman filter (EnKF) has gained increased popularity for history matching and continuous reservoir-model updating. It is a sequential Monte Carlo approach that works with an ensemble of reservoir models. Specifically, the method uses cross covariance between measurements and model parameters estimated from the ensemble. For practical field applications, the ensemble size needs to be kept small for computational efficiency. However, this leads to poor approximations of the cross covariance and can cause loss of geologic realism from unrealistic model updates outside the region of the data influence and/or loss of variance leading to ensemble collapse. A common approach to remedy the situation is to limit the influence of the data through covariance localization.
In this paper, we show that for three-phase-flow conditions, the region of covariance localization strongly depends on the underlying flow dynamics as well as on the particular data type that is being assimilated in terms of water cut or gas/oil ratio (GOR). This makes the traditional distance-based localizations suboptimal and, often, ineffective. Instead, we propose the use of water- and gas-phase streamlines as a means for covariance localization for water-cut- and GOR-data assimilation. The phase streamlines can be computed on the basis of individual-phase velocities which are readily available after flow simulation. Unlike the total streamlines, phase streamlines can be discontinuous. We show that the discontinuities in water-phase and gas-phase streamlines naturally define the region of influence for water-cut and GOR data and provide a flow-relevant covariance localization during EnKF updating.
We first demonstrate the validity of the proposed localization approach using a waterflood example in a quarter-five-spot pattern. Specifically, we compare the phase streamline trajectories with cross-covariance maps computed using an ensemble size of 2,000 for both water-cut and GOR data. The results show a close correspondence between the time evolution of phase streamlines and the cross-covariance maps of water-cut and GOR data. A small-size industrial reservoir engineering production forecasting with uncertainty quantification (the PUNQ-S3) (Carter 2007) model application shows that our proposed localization outperforms a distance-based localization method. The updated models show improved forecasts while preserving geological realism.
Taware, Satyajit Vijay (Texas A&M University) | Park, Han-young (Texas A&M University) | Datta-Gupta, Akhil (Texas A&M University) | Bhattacharya, Shyamal (Oil & Natural Gas Corp. Ltd.) | Tomar, A.K. (ONGC) | Kumar, Munil (ONGC LTD) | Rao, H.S. (ONGC)
The placement of infill producers and injectors is an important aspect in the overall development strategy of any field and is particularly challenging for mature fields with high levels of water-cut. Previous screening approaches based upon static reservoir quality maps have limited applicability as these do not account for the drainage and swept volumes from existing wells. In contrast, direct application of formal optimization methods such as evolutionary algorithms and adjoint-based methods to high resolution geologic models may better represent reservoir dynamics but can be complex to implement or computationally prohibitive.
We propose a novel method for well placement optimization that relies on streamlines which represents the flow paths in the reservoir and the time of flight which represents the travel time of fluids along streamlines. Specifically, the streamline time of flight from the injectors provides swept volumes for injectors whereas streamline time of flight from producers gives drainage volumes for producers. These quantities can be effectively combined to a ‘total time of flight' to locate the potential regions of unswept and undrained oil in the reservoir. Our approach utilizes a dynamic measure based on the total streamline time of flight combined with static parameters to identify potential locations for infill drilling. Areas having high value of the dynamic measure (sweet spots) are both poorly drained and poorly swept, making them attractive for drilling infill wells.
We show the power and utility of our proposed method on a mature offshore carbonate field in western India. The simulation model was history matched using a hierarchical history matching approach that follows a sequence of calibrations from global to local parameters in coarsened and fine scales. Using our proposed method on the history matched model we obtained a dynamic measure map highlighting areas suitable for drilling infill wells. Finally, we compared the performance of infill wells located using the dynamic measure map with wells located using traditional well placement techniques, for example, oil saturation map from simulation. Our proposed method consistently outperforms the traditional approaches. Subsequent field infill drilling in the field has validated our approach.