We present a novel sampling algorithm for characterization and uncertainty quantification of heterogeneous multiple facies reservoirs. The method implements a Bayesian inversion framework to estimate physically plausible porosity distributions. This inversion process incorporates data matching at the well locations and constrains the model space by adding
The proposed workflow uses an ensemble-based Markov Chain Monte Carlo approach combined with sampling probability distributions that are physically meaningful. Moreover, the method targets geostatistical modeling to specific zones in the reservoir. Accordingly, it improves fulfilling the inherent stationarity assumption in geostatistical simulation techniques. Parameter sampling and geostatistical simulations are calculated through an inversion process. In other words, the models fit the known porosity field at the well locations and are structurally consistent within main reservoir compartments, zones, and layers obtained from the seismic impedance volume. The new sampling algorithm ensures that the automated history matching algorithm maintains diversity among ensemble members avoiding underestimation of the uncertainty in the posterior probability distribution.
We evaluate the efficiency of the sampling methodology on a synthetic model of a waterflooding field. The predictive capability of the assimilated ensemble is assessed by using production data and dynamic measurements. Also, the qualities of the results are examined by comparing the geological realism of the assimilated ensemble with the reference probability distribution of the model parameters and computing the predicted dynamic data mismatch. Our numerical examples show that incorporating the seismically constrained models as prior information results in an efficient model update scheme and favorable history matching.
Sidahmed, Anas (University of Alberta) | Nouri, Alireza (University of Alberta) | Kyanpour, Mohammad (RGL Reservoir Management Inc.) | Nejadi, Siavash (University of Alberta) | Fermaniuk, Brent (RGL Reservoir Management Inc.)
Canada has enormous oil reserves which ranks third worldwide with proven oil reserves of 171 billion barrels. Alberta alone contributes with 165.4 billion barrels found in oil sands. However, the oil in oil sands is extremely viscous, and only 10% is recoverable through open-pit mining. In-situ thermal recovery methods such as Steam-Assisted Gravity Drainage (SAGD) have been developed and adopted as an efficient means to unlock the oil sands reserves.
Different reservoir geological settings and long horizontal wells impose limitations and operational challenges on the implementation of SAGD technology. Wellbore trajectory excursions or undulations- unintentionally generated trajectory deviations due to suboptimal drilling operations- are some of the complications that lead to non-uniform steam chamber conformance, high cumulative Steam-Oil Ratio (cSOR) and low bitumen recovery.
Conventional dual-string completion scheme (a short tubing landed at the heel, and a long tubing landed at the toe) has been widely adopted in most of the SAGD operations. Such configurations allow steam injection at two points: the toe and the heel sections of the horizontal well. However, these completions have demonstrated poor efficiency when reservoir/well complications exist. Tubing-deployed Flow Control Devices (FCD's) have been introduced to offer high flexibility in delivering specific amounts of steam to designated areas (such as low permeability zones) and ensure uniform development of steam chamber in the reservoir. The work in this thesis presents the results of a numerical effort for optimizing the design of Outflow Control Devices (OCD's) in SAGD wells for different scenarios of well pair trajectory excursions.
A coupled wellbore-reservoir SAGD simulation model was constructed to optimize the placement and number of ports in every single OCD. Three different cases were generated from the constructed basic SAGD model with each case having a specific well pair trajectory which causes variable lateral distances between the well pair.
Results of the optimized OCD's cases demonstrate a higher SAGD efficiency compared to their corresponding conventional dual-string cases. Those enhancements resulted in a higher steam chamber conformance, a higher cumulative oil production, and an improved Net Present Value (NPV).
Nejadi, Siavash (University of Calgary) | Hubbard, Stephen M. (University of Calgary) | Shor, Roman J. (University of Calgary) | Gates, Ian D. (University of Calgary) | Wang, Jingyi (University of Calgary)
Steam chamber conformance in Steam Assisted Gravity Drainage (SAGD) influences the efficiency and economic performance of bitumen recovery. Conventional SAGD well completion designs provide limited control points in long horizontal well pairs leading to development of a non-ideal steam chambers. Developing advanced wellbore completions and optimizing downhole tool settings is critical to achieve optimal steam distribution in heterogeneous reservoirs for optimal recovery.
This paper presents a workflow to optimize SAGD well completion design by using flow control devices (FCDs). Optimum FCD placement, and specifications are determined in consideration of reservoir heterogeneity. Uncertainties in spatial distribution of facies and rock types, reservoir rock and fluid properties are represented by multiple equiprobable deterministic and stochastic geological realizations using Monte-Carlo simulation. The methodology is based on constrained nonlinear optimizationtomaximize the net present value (NPV) as the objective function. A coupled wellbore/reservoir simulation model of a well pad is implemented in the study, and the efficacy of different scenarios with varied well designs are assessed from evaluating bitumen production, steam injection, and well completion expenses.
Results indicate superior performance of the wells equipped with FCDs compared to conventional concentric and parallel dual string well completion designs. For the cases examined, this translates to an average 7% increase of the expected NPV for different well completion designs when using FCDs. Furthermore, results show using zonal isolation in the well design is essential for compartmentalized reservoirs such aspoint bar deposits with their significant heterogeneity.
Advanced wellbore completions provide sufficient tools to constrain steam injection and liquid production into and from different well segments, and manage steam chamber conformance along the horizontal well pairs, improve production efficiency, increase bitumen recovery, and reduce operating costs.
A novel workflow is presented to optimize advanced wellbore completions utilizing flow control devices. This integrated assisted optimization approach considers uncertainties in geological properties, and determines the optimal FCD parameters and well completion design with acceptable computational effort. This integrated workflow allowed us to undertake a thorough evaluation of the key subsurface uncertainties, and design an overall development plan. The probabilistic nature of the results legitimize quantifying the uncertainties and identify associated risks for different completion strategies.
Advancements in horizontal-well drilling and multistage hydraulic fracturing have enabled economically viable gas production from tight formations. Reservoir-simulation models play an important role in the production forecasting and field-development planning. To enhance their predictive capabilities and to capture the uncertainties in model parameters, one should calibrate stochastic reservoir models to both geologic and flow observations.
In this paper, a novel approach to characterization and history matching of hydrocarbon production from a hydraulic-fractured shale is presented. This new methodology includes generating multiple discrete-fracture-network (DFN) models, upscaling the models for numerical multiphase-flow simulation, and updating the DFN-model parameters with dynamic-flow responses. First, measurements from hydraulic-fracture treatment, petrophysical interpretation, and in-situ stress data are used to estimate the initial probability distribution of hydraulic-fracture and induced-microfracture parameters, and multiple initial DFN models are generated. Next, the DFN models are upscaled into an equivalent continuum dual-porosity model with analytical techniques. The upscaled models are subjected to the flow simulation, and their production performances are compared with the actual responses. Finally, an assisted-history-matching algorithm is implemented to assess the uncertainties of the DFN-model parameters. Hydraulic-fracture parameters including half-length and transmissivity are updated, and the length, transmissivity, intensity, and spatial distribution of the induced fractures are also estimated.
The proposed methodology is applied to facilitate characterization of fracture parameters of a multifractured shale-gas well in the Horn River basin. Fracture parameters and stimulated reservoir volume (SRV) derived from the updated DFN models are in agreement with estimates from microseismic interpretation and rate-transient analysis. The key advantage of this integrated assisted-history-matching approach is that uncertainties in fracture parameters are represented by the multiple equally probable DFN models and their upscaled flow-simulation models, which honor the hard data and match the dynamic production history. This work highlights the significance of uncertainties in SRV and hydraulic-fracture parameters. It also provides insight into the value of microseismic data when integrated into a rigorous production-history-matching work flow.
Advancements in horizontal well drilling and multistage hydraulic fracturing have made gas production from tight formations economically viable. Reservoir simulation models play an important role in the production forecasting and field development planning. To enhance their predictive capabilities and capture the uncertainties in model parameters, stochastic reservoir models should be calibrated to both geologic and flow observations.
In this paper, a novel approach to characterization and history matching of hydrocarbon production from a hydraulic fractured shale gas is presented. This new methodology includes generating multiple discrete fracture network (DFN) models, upscaling the models for numerical multiphase flow simulation, and updating the DFN model parameters using dynamic flow responses. First, measurements from hydraulic fracture treatment, petrophysical interpretation, and in-situ stress data are used to estimate the initial probability distribution of hydraulic and induced micro fractures parameters, and multiple initial DFN models are generated. Next, the DFN models are upscaled into an equivalent continuum dual porosity model using either analytical (Oda) or flow-based techniques. The upscaled models are subjected to the flow simulation, and their production performances are compared to the actual responses. Finally, an assisted history matching algorithm is implemented to assess the uncertainties of the DFN model parameters. Hydraulic fracture parameters including half-length, shape, and conductivity are updated together with the length, conductivity, intensity, and spatial distribution of the induced fractures are optimized in the algorithm.
The proposed methodology is applied to facilitate characterization of fracture parameters of a multi-fractured shale gas well in the Horn River basin. Fracture parameters and stimulated reservoir volume (SRV) derived from the updated DFN models are in agreement with estimates from micro-seismic interpretation and rate transient analysis. The key advantage of this integrated assisted history matching approach is that uncertainties in fracture parameters are represented by the multiple equall-probable DFN models and their upscaled flow simulation models, which honor the hard data and match the dynamic production history. This work highlights the significance of uncertainties in SRV and hydraulic fracture parameters. It also provides insight into the value of micro-seismic data when integrated in a rigorous production history matching workflow.
Productivity in deep-basin tight gas reservoirs can be improved significantly by natural fracture enhanced permeability. Therefore, deviated and horizontal wells are often drilled to intersect highly fractured formations. Unfortunately, fractured reservoirs are highly heterogeneous, often characterized by probability distributions of fracture properties in a discrete fracture network (DFN) model. In addition, the relationship between recovery response and model parameters is vastly non-linear, rendering the process of conditioning reservoir models to both static and dynamic (production) data challenging.
In the current paper, a novel approach is presented for uncertainty assessment and characterization of fractured reservoir model parameters using data from diverse sources. First, Monte Carlo based techniques were used to generate multiple DFN models conditioned to geological and tectonic information, accounting for the uncertainty associated with static data. Next, each model or realization was upscaled for flow simulation. Finally, Ensemble Kalman Filter (EnKF), a data assimilation technique that has been used for assisted history matching, was employed to update the DFN models using production data. In order to ensure positive definiteness of the updated permeability tensors, to reduce the size of model parameter space, and to eliminate the redundancy between parameters for improved convergence, principal component analysis was performed such that only the main principal components of the full permeability tensor and sigma factors were updated through EnKF algorithm.
The qualities of the history-matched models were assessed by comparing the spatial distribution of the updated model parameters with the initial ensemble, as well as the Root Mean Square Error (RMSE) of the predicted data mismatch. The results clearly demonstrate that, characterization of fractured reservoirs combining DFN modeling with updating principal components of the upscaled model parameters through EnKF has the potential to resolve the shortfall of traditional techniques for history matching of such complicated reservoirs. The proposed approach can be used effectively to update reservoir models and optimize development plans in unconventional gas reservoirs using continuous flow and pressure measurements.
Distributed Temperature Sensing (DTS), an optical fiber downhole monitoring technique, provides a continuous and permanent well temperature profile. In SAGD reservoirs, the DTS plays an important role to provide depth- and- time continuous temperature measurement for steam management and production optimization. These temperature observations provide useful information for reservoir characterization and shale detection in SAGD reservoirs. However, use of these massive data for automated SAGD reservoir characterization has not been investigated. The Ensemble Kalman Filter (EnKF), a parameter estimation approach using these real-time temperature observations, provides a highly attractive algorithm for automatic history matching and quantitative reservoir characterization.
Due to its complex geological nature, the shale barrier exhibits as a different facies in Sandstone reservoirs. In such reservoirs, due to non-Gaussian distributions, the traditional EnKF underestimate the uncertainty and fails to obtain a good production data match. We implemented discrete cosine transform (DCT) to parameterize the facies labels with EnKF. Furthermore, to capture geologically meaningful and realistic facies distribution in conjunction with matching observed data, we included fiber-optic sensor temperature data.
Several case studies with different facies distribution and well configurations were conducted. In order to investigate the effect of temperature observations on SAGD reservoir characterization, the number of DTS observations and their locations were varied for each study. The qualities of the history-matched models were assessed by comparing the facies maps, facies distribution, and the Root Mean Square Error (RMSE) of the predicted data mismatch.
Use of temperature data in conjunction with production data demonstrated significant improvement in facies detection and reduced uncertainty for SAGD reservoirs. The RMSE of the predicted data is also improved. The results indicate that the assimilation of DTS data from nearby steam chamber location has a significant potential in significant reduction of uncertainty in steam chamber propagation and production forecast.
The Ensemble Kalman Filter (EnKF) is a Monte-Carlo based technique for assisted history matching and real time updating of reservoir models. However, it often fails to detect facies boundaries and proportions as the facies distributions are non-Gaussian, while prior knowledge of the data is usually insufficient.
It is common to represent distinct facies with categorical indicators, which are intrinsically non-Gaussian. We implemented discrete cosine transform (DCT) to parameterize the facies indicators. This methodology was promising for simple and two facies models. For more complex models, though observed data were matched, it failed to reproduce realistic facies distribution corresponding to the prior variogram and facies proportion.
In this paper a new step is proposed to be included in the history matching of complex reservoirs using EnKF: realizations exhibiting the largest mismatch in terms of production data, experimental variogram, and histogram are discarded after the first few update steps, and a probability map for facies modeling is derived using the remaining ensemble members. Probability field (P-Field) simulation is performed subsequently using the facies probability map to generate a new set of realizations replacing the discarded members. The new realizations are updated again from the beginning using EnKF.
Several case studies with different facies distribution and well configurations were conducted. Initial ensembles were created using known facies classification at the well locations and populating binary facies data throughout reservoir using numerous variogram models and prior facies proportions. The regenerated
realizations are closer to the true reservoir state since they already take into account the first few set of production data.
The qualities of the history-matched models were assessed by comparing the experimental variograms of facies distribution and facies propositions of the final ensemble, as well as the Root Mean Square Error (RMSE) of the predicted data mismatch.
Combination of DCT-EnKF and regenerating new realizations using P-Field simulation demonstrates reasonable improvement and reduction of uncertainty in facies detection. Incorporating the new step in the procedure assists filter to preserve the reference distribution and experimental variogram for complex reservoirs.
The Ensemble Kalman Filter (EnKF) has gained popularity over recent years as a Monte-Carlo based technique for assisted history matching and real time updating of reservoir models. The EnKF procedure utilizes an ensemble of model states (e.g. realizations of reservoir properties such as porosity and permeability) to approximate the covariance matrices used in the updating process. EnKF works efficiently with Gaussian variables and linear dynamics, but it often fails to preserve the reference probability distribution of the model parameters and to achieve an acceptable production data match where the system dynamics are strongly nonlinear, especially of the type related to multiphase flow, or if non-Gaussian prior models are used.
In order to alleviate these drawbacks, we investigated various weighted averaging techniques for computing the ensemble mean by introducing a weighting factor to each ensemble; two new formulations were implemented. The first weighting factor was calculated based on the mismatch in entropy of the model parameters, a normalized measure of the spread of a given probability distribution. The second weighting factor was computed using the forecast mismatch. In addition, both weights could be applied at a single updating step for reducing the forecast mismatch and maintaining the prior distribution simultaneously.
The performance of traditional EnKF and these weighted EnKF methods were evaluated by performing various simulation studies with different reservoir heterogeneity. The qualities of the final matching results were assessed by computing the experimental histogram and variograms of the final ensemble, as well as the Root Mean Square Error (RMSE) of the predicted data mismatch.
The results reveal that reasonable improvement in the efficiency of the EnKF is achieved by suggested weighted techniques. The RMSE of the predicted data is improved, and the quantity of spurious model parameters is reduced at each updating step. Taking advantage of the entropy based weighting factor assists the filter to preserve the reference distribution. The improvement indicates that the Entropy weighted EnKF (EWEnKF) has a significant potential to resolve the shortfall of traditional EnKF in reservoir characterization and history matching of challenging reservoirs with non-Gaussian distributions.