Recent studies have indicated that Huff-n-Puff (HNP) gas injection has the potential to recover an additional 30-70% oil from multi-fractured horizontal wells in shale reservoirs. Nonetheless, this technique is very sensitive to production constraints and is impacted by uncertainty related to measurement quality (particularly frequency and resolution), and lack of constraining data. In this paper, a Bayesian workflow is provided to optimize the HNP process under uncertainty using a Duvernay shale well as an example.
Compositional simulations are conducted which incorporate a tuned PVT model and a set of measured cyclic injection/compaction pressure-sensitive permeability data. Markov chain Monte Carlo (McMC) is used to estimate the posterior distributions of the model uncertain variables by matching the primary production data. The McMC process is accelerated by employing an accurate proxy model (kriging) which is updated using a highly adaptive sampling algorithm. Gaussian Processes are then used to optimize the HNP control variables by maximizing the lower confidence interval (μ-σ) of cumulative oil production (after 10 years) across a fixed ensemble of uncertain variables sampled from posterior distributions.
The uncertain variable space includes several parameters representing reservoir and fracture properties. The posterior distributions for some parameters, such as primary fracture permeability and effective half-length, are narrower, while wider distributions are obtained for other parameters. The results indicate that the impact of uncertain variables on HNP performance is nonlinear. Some uncertain variables (such as molecular diffusion) that do not show strong sensitivity during the primary production strongly impact gas injection HNP performance. The results of optimization under uncertainty confirm that the lower confidence interval of cumulative oil production can be maximized by an injection time of around 1.5 months, a production time of around 2.5 months, and very short soaking times. In addition, a maximum injection rate and a flowing bottomhole pressure around the bubble point are required to ensure maximum incremental recovery. Analysis of the objective function surface highlights some other sets of production constraints with competitive results. Finally, the optimal set of production constraints, in combination with an ensemble of uncertain variables, results in a median HNP cumulative oil production that is 30% greater than that for primary production.
The application of a Bayesian framework for optimizing the HNP performance in a real shale reservoir is introduced for the first time. This work provides practical guidelines for the efficient application of advanced machine learning techniques for optimization under uncertainty, resulting in better decision making.
The significant oil reserves related to karst reservoirs in Brazilian pre-salt field adds new frontiers to the development of upscaling procedures to reduce time on numerical simulations. This work aims to represent karst reservoirs in reservoir simulators based on special connections between matrix and karst mediums, both modeled in different grid domains of a single porosity flow model. This representation intends to provide a good relationship between accuracy and simulation time.
The concept follows the Embedded Discrete Fracture Model (EDFM) developed by Moinfar, 2013; however, this work extends the approach for karst reservoirs (Embedded Discrete Karst Model - EDKM) by adding a representative volume through grid blocks to represent karst geometries and porosity. For the extension of EDFM approach in a karst reservoir, we adapt the methodology to four stages: (a) construction of a single porosity model with two grid domains, (b) geomodeling of karst and matrix properties for the corresponding grid domain, (c) application of special connections through the conventional reservoir simulator to represent the transmissibility between matrix and karst medium, (d) calculation of transmissibility between karst and matrix medium.
For a proper validation, we applied the EDKM methodology in a carbonate reservoir with mega-karst structures, which consists of non-well-connected enlarged conduits and above 300 mm of aperture. The reference model was a refined grid with karst features explicitly combined with matrix facies, including coquinas interbedded with mudstones and shales. The grid block of the reference model measures approximately 10 × 10 × 1 meters. For the simulation model, the matrix grid domain has a grid block size of approximately 100 × 100 × 5 meters. The karst grid domain had the same block size as the refined grid. Flow in the individual karst grid domain or matrix grid domain is governed by Darcy's equation, implicitly solved by simulator. However, the transmissibility for the special connections between karst and matrix blocks is calculated as a function of open area to flow, matrix permeability and block center distance. The matrix properties were upscaled through conventional analytical methods. The results show that EDKM had a considerable performance regarding a dynamic matching response with reference model, within a reduced simulation time while maintaining a higher dynamic resolution in the karst grid domain without using an unconstructed grid.
This work aims to contribute to the extension of EDFM approach for karst reservoirs, which can be applied to commercial finite-difference reservoir simulators and it presents itself as a solution to reduce simulation time without disregarding the explicit representation of karst features in structured grids.
Two upscaling exercises performed in 2013-14 and 2017-18 on two onshore green fields with conventional to viscous oil are presented, for which the upscaling tried to compensate the effects of grid coarsening, in particular the increase of numerical dispersion and the decrease of heterogeneity. Our methodology was to adjust the water/oil relative permeabilities called pseudo KRs in the coarse scale simulation, in order to reproduce the behavior in terms of pressure, rates, saturations and concentrations of the fine scale model, which was using microscopic rock KRs based on laboratory data.
As the upscaling depends on the fluid injected, it was done separately for waterflood and polymer flood. When done with polymer flood, the concentration of polymer had to be history matched also mainly by adjusting the Todd-Longstaff mixing parameter in addition to the KRs. As upscaling is case dependent, it was performed on several geological models, varying heterogeneity and grid size, but also rock KRs and even precocity of the polymer flood after some waterflood, to test the robustness of the approach.
It was found that pseudo-KRs for waterflood could be slightly degraded for viscous oils, whereas the upscaling was more neutral for conventional oils. This correlates well with field observation for viscous oils, where water production occurs generally a bit quicker than what numerical simulation predicts when using rock KRs, in absence of upscaling.
For polymer floods, which were considered in secondary or early tertiary mode, pseudo KRs were generally improved, mainly because the polymer steepened the saturation fronts, which can be well represented only with small lateral grid size.
The result of both upscaling exercises was that the increment of polymer flood versus waterflood was noticeably higher when computed on high resolution modelling. This is equivalent to saying that when using pseudo KRs resulting from this high resolution matching, the polymer increment on coarse grid is significantly higher than if computed without pseudo KRs. This improves the economic evaluation of the project, increasing the willingness to de-risk and implement early polymer floods on these fields.
Al-Rudaini, Ali (Heriot-Watt University) | Geiger, Sebastian (Heriot-Watt University) | Mackay, Eric (Heriot-Watt University) | Maier, Christine (Heriot-Watt University) | Pola, Jackson (Heriot-Watt University)
We propose a workflow to optimise the configuration of multiple interacting continua (MINC) models and overcome the limitations of the classical dual-porosity model when simulating chemically enhanced oil recovery processes. Our new approach captures the evolution of the concentration front inside the matrix, which is key to design a more effective chemically enhanced oil recovery projects in naturally fractured reservoirs. Our workflow is intuitive and based on the simple concept that fine-scale single-porosity models capture fracture-matrix interaction accurately and can hence be easily applied in a commercial reservoir simulator. Results from the fine-scale single-porosity system are translated into an equivalent MINC method that yields more accurate results than the classical dual-porosity model or a MINC method where the shells are arbitrarily selected.
Our approach does not require the tuning of capillary pressure curves ("pseudoisation"), diffusion coefficients, MINC shells, or the generation of recovery type curves, all of which have been suggested in the past to model more complex recovery processes. A careful examination of the fine-scale single-porosity model ("reference case") shows that a number of nested shells emerge, describing the advance of the concentration and saturation fronts inside the matrix. The number of shells is related to the required degree of refinement, i.e. the number of shells, in the improved MINC model. Using the results from a fine-scale single-porosity simulation to set up the shells in the MINC model is easy and requires only simple volume calculations. It is hence independent of the chosen simulator.
Our improved MINC method yields significantly more accurate results compared to a classical dual-porosity model, a MINC method with equally sized shells, or a MINC model with arbitrarily refined shells for a number of recovery scenarios that cover a range of matrix wettabilities and permeabilities. In general, improved results can be obtained when selecting five or fewer shells in the MINC. However, the actual number of shells is case-specific. The largest improvement is observed for cases when the matrix permeability is low.
The novelty of our approach is the easy-to-use method to define shells for a MINC model to predict chemically enhanced oil recovery from naturally fractured reservoirs more accurately, especially in cases where the matrix has low permeability. Hence the improved MINC method is particularly suitable to model chemical EOR processes in (tight) fractured carbonates.
Lei, Zhengdong (Research Institute of Petroleum Exploration and Development, PetroChina) | Xie, Qichao (Exploration and Development Research Institute of ChangQing Oilfield Company) | Tao, Zhen (Research Institute of Petroleum Exploration and Development, PetroChina) | He, YouAn (Exploration and Development Research Institute of ChangQing Oilfield Company) | Zhu, Zhouyuan (China university of Petroleum) | Peng, Yan (China university of Petroleum) | Liu, Canhua (China university of Petroleum)
Waterflooding of fractured low permeability reservoirs are often associated with poor sweep and high water cut due to existence of natural fractures, hydraulic fractures, and artificially induced fractures. Therefore, reservoir simulation with coupled geomechanics and dynamic fractures is required for this application. In this work, we present the use of streamline-derived flux information to improve overall waterflooding performance in such complex simulation problems.
This work shows the waterflooding optimization workflow of a fractured low-permeability reservoir in ChangQing Oilfield, China. First, the finite difference simulator considering stress field and geomechanical properties is used to simulate the growth of dynamic fractures. Then, the newly formed fracture properties are included into the dual porosity/permeability reservoir simulation model. Afterwards, streamlines can be traced based on the velocity field of this model, which represent a snapshot of the inter-well fluxes. Finally, with the goal of minimizing field water production, we implement linear programming algorithms to optimize the waterflooding operation by considering the inter-well connectivity and well allocation factors.
Through reservoir simulation coupled with geomechanics, we have found that induced fracture growth rate is relatively limited at reasonable injection rate, which is also validated by field empirical observations. This can avoid fracture propagation and reduce the risk of rapid water breakthrough. We deploy our streamline tracing and linear programming based optimization program to work together with this simulation model. A controlled and cautious increase in injection rate has resulted in a positive production response in 28 producers in the pilot area. Reallocation of water to high-efficiency injectors improves sweep efficiency in the reservoir. Finally, the optimized scenario has resulted in more than 15% incremental swept volume as compared to the basic development case.
This work provides a comprehensive case study for better understanding the impact fracture growth on waterflooding performance in fractured low-permeability reservoirs. It further establishes the workflow of using streamline-based flux information for oil production optimizations in these complex simulation problems.
Integration of time-lapse seismic data into dynamic reservoir model is an efficient process in calibrating reservoir parameters update. The choice of the metric which will measure the misfit between observed data and simulated model has a considerable effect on the history matching process, and then on the optimal ensemble model acquired. History matching using 4D seismic and production data simultaneously is still a challenge due to the nature of the two different type of data (time-series and maps or volumes based).
Conventionally, the formulation used for the misfit is least square, which is widely used for production data matching. Distance measurement based objective functions designed for 4D image comparison have been explored in recent years and has been proven to be reliable. This study explores history matching process by introducing a merged objective function, between the production and the 4D seismic data. The proposed approach in this paper is to make comparable this two type of data (well and seismic) in a unique objective function, which will be optimised, avoiding by then the question of weights. An adaptive evolutionary optimisation algorithm has been used for the history matching loop. Local and global reservoir parameters are perturbed in this process, which include porosity, permeability, net-to-gross, and fault transmissibility.
This production and seismic history matching has been applied on a UKCS field, it shows that a acceptalbe production data matching is achieved while honouring saturation information obtained from 4D seismic surveys.
Nandi Formentin, Helena (Durham University and University of Campinas) | Vernon, Ian (Durham University) | Avansi, Guilherme Daniel (University of Campinas) | Caiado, Camila (Durham University) | Maschio, Célio (University of Campinas) | Goldstein, Michael (Durham University) | Schiozer, Denis José (University of Campinas)
Reservoir simulation models incorporate physical laws and reservoir characteristics. They represent our understanding of sub-surface structures based on the available information. Emulators are statistical representations of simulation models, offering fast evaluations of a sufficiently large number of reservoir scenarios, to enable a full uncertainty analysis. Bayesian History Matching (BHM) aims to find the range of reservoir scenarios that are consistent with the historical data, in order to provide comprehensive evaluation of reservoir performance and consistent, unbiased predictions incorporating realistic levels of uncertainty, required for full asset management. We describe a systematic approach for uncertainty quantification that combines reservoir simulation and emulation techniques within a coherent Bayesian framework for uncertainty quantification.
Our systematic procedure is an alternative and more rigorous tool for reservoir studies dealing with probabilistic uncertainty reduction. It comprises the design of sets of simulation scenarios to facilitate the construction of emulators, capable of accurately mimicking the simulator with known levels of uncertainty. Emulators can be used to accelerate the steps requiring large numbers of evaluations of the input space in order to be valid from a statistical perspective. Via implausibility measures, we compare emulated outputs with historical data incorporating major process uncertainties. Then, we iteratively identify regions of input parameter space unlikely to provide acceptable matches, performing more runs and reconstructing more accurate emulators at each wave, an approach that benefits from several efficiency improvements. We provide a workflow covering each stage of this procedure.
The procedure was applied to reduce uncertainty in a complex reservoir case study with 25 injection and production wells. The case study contains 26 uncertain attributes representing petrophysical, rock-fluid and fluid properties. We selected phases of evaluation considering specific events during the reservoir management, improving the efficiency of simulation resources use. We identified and addressed data patterns untracked in previous studies: simulator targets,
We advance the applicability of Bayesian History Matching for reservoir studies with four deliveries: (a) a general workflow for systematic BHM, (b) the use of phases to progressively evaluate the historical data; and (c) the integration of two-class emulators in the BHM formulation. Finally, we demonstrate the internal discrepancy as a source of error in the reservoir model.
Pathak, Varun (Computer Modelling Group Ltd.) | Hamedi, Yousef (Computer Modelling Group Ltd.) | Martinez, Oscar (Computer Modelling Group Ltd.) | Vermeulen, Stephen (Computer Modelling Group Ltd.) | Kumar, Anjani (Computer Modelling Group Ltd.)
Integrated production systems models are very valuable for predicting the performance of complex systems containing multiple reservoirs and networks. In addition, the value of quantifying uncertainty in reservoirs and production systems is immense as it can build confidence in operational investments. However, traditionally it has been extremely tedious to incorporate uncertainty assessments in the context of integrated production systems modelling. This has been addressed in the current work with the help of a case study.
In the current work, a complex integrated production systems model is presented - from Pre-Salt carbonates reservoir offshore of Brazil. The model includes multiple reservoirs with unique fluid types and complex fluid blending in the production network, multiphase and thermal effects in flowlines and risers, gas separation, gas processing, gas compression, and re-injection for either pressure maintenance or for miscible EOR.
The operational strategies, well placement, and well and network configurations are often based on a single geological realization. With the case study presented in this paper, an integrated way of quantifying geological uncertainty has been presented. A new multi-user, multi-disciplinary tool was used for this study that removed any discontinuities and inconsistencies that typically occur in such projects when multiple standalone tools are used for individual tasks. When quantifying uncertainty on production, the dependence on a single realization was eliminated as uncertain parameters were identified and used for creating robust probabilistic forecasts. Probability distribution curves were generated to represent the uncertainty in overall production from this asset, and the risk associated with operational investments was minimized.
Typically, an end-to-end uncertainty assessment is missing from the traditional Integrated Modelling workflows. With this new approach, the challenge of achieving a truly integrated uncertainty assessment for integrated reservoir and production models has been addressed successfully.
Zhang, Na (Division of Sustainable Development, College of Science and Engineering, Hamad Bin Khalifa University) | Abushaikha, Ahmad Sami (Division of Sustainable Development, College of Science and Engineering, Hamad Bin Khalifa University)
Modelling fluid flows in fractured reservoirs is crucial to many recent engineering and applied science research. Various numerical methods have been applied, including finite element methods, finite volume methods. These approaches have inherent limitations in accuracy and application. Considering these limitations, in this paper, we present a novel mimetic finite difference (MFD) framework to simulate two phase flow accurately in fracture reservoirs.
A novel MFD method is proposed for simulating multiphase flow through fractured reservoirs by taking advantage of unstructured mesh. Our approach combines MFD and finite volume (FV) methods. Darcy's equation is discreted by MFD method, while the FV method is used to approximate the saturation equation. The resulting system of equations is then imposed with suitable physical coupling conditions along the matrix/ fracture interfaces. This coupling conditions at the interfaces between matrix and fracture flow involve only the centroid pressure of fractures, which brings some simplification in analysis. The proposed approach is applicable for three dimensional systems. Moreover, it is applicable in arbitrary unstructured gridcells with full-tensor permeabilities. Some examples are implemented to show the performance of MFD method. The results showed a big potential of our method to simulate the flow problems with high accuracy and application.
Many gas reservoirs at the appraisal stage exhibit evidence of persistent gas saturations below free water levels (FWL's). The amounts of gas contained here may, under some situations, be a sizable fraction of the gas cap volumes. Many engineers appear poorly equipped to include, and model, paleo gas in simulation models. This often results in paleo gas being simply ignored when development plans are being considered. This is unfortunate because paleo gas upon pressure depletion can expand, displacing brine towards well completions. This means that while some additional gas production may occur from the paleo zone, the risk of water production may be significantly underestimated if paleo gas is simply omitted. This work discusses the evidence for paleo gas and shows that it may be described and incorporated in simple simulation models provided the user avoids some common misconceptions. It is demonstrated that under depletion conditions, paleo gas can be entirely visible to material balance pressure responses, while at the same time increasing the risk of produced water volumes. For higher pressure paleo gas reservoirs the common P on Z diagnostic plots can also provide early trends that are frequently misinterpreted. This work quantifies the curvature that can result in such systems, and shows that simulation models inherently predict the expected curvature in P on Z. The approach taken here is by design simplistic and is applicable to scoping evaluations where the paleo gas volumes could be a significant volumetric uncertainty. Where possible, we indicate where additional, or more rigorous, descriptions can be applied.