Multiscale methods have been developed as a robust alternative to upscaling and to accelerate reservoir simulation. In their basic setup, multiscale methods use both a restriction operator to construct a reduced system of flow equations that can be solved on a coarser grid and a prolongation operator to map pressure unknowns from the coarse grid back to the original simulation grid. When combined with a local smoother, this gives an iterative solver that can efficiently compute approximate pressures to within a prescribed accuracy and still provide mass-conservative fluxes. We present an adaptive and flexible framework for combining multiple sets of such multiscale approximations. Each multiscale approximation can target a certain scale; geological features such as faults, fractures, facies, or other geobodies; or a particular computational challenge such as propagating displacement and chemical fronts, wells being turned on or off, and others. Multiscale methods that fit the framework are characterized by three features. First, the prolongation and restriction operators are constructed by use of a nonoverlapping partition of the fine grid. Second, the prolongation operator is composed of a set of basis functions, each of which has compact support within a support region that contains a coarse gridblock. Finally, the basis functions form a partition of unity. These assumptions are quite general and encompass almost all existing multiscale (finite-volume) methods that rely on localized basis functions. The novelty of our framework is that it enables multiple pairs of prolongation and restriction operators—computed on different coarse grids and possibly also by different basis-function formulations—to be combined into one iterative procedure.
Through a series of numerical examples consisting of both idealized geology and flow physics as well as a geological model of a real asset, we demonstrate that the new iterative framework increases the accuracy and efficiency of the multiscale technology by improving the rate at which one converges the fine-scale residuals toward machine precision. In particular, we demonstrate how it is possible to combine multiscale prolongation operators that have different spatial resolution and that each individual operator can be designed to target, among others, challenging grids, including faults, pinchouts, and inactive cells; high-contrast fluvial sands; fractured carbonate reservoirs; and complex wells.
In static reservoir modeling it is common practice to calculate saturations from core plug-derived (not upscaled) Saturation Height Function (SHF) using model-scale (upscaled) porosity and/or permeability values. This incongruence of scale difference may result in erroneous estimates of Hydrocarbons Initially In Place (HCIIP). It is because core plug-derived SHF would not accurately represent saturation from the upscaled porosity and permeability values due to scale difference between core plugs and the layers in the static model.
This article presents a workflow for SHF upscaling (core plug-scale to model-scale) and its impact on GIIP (Gas Initially In Place) for an offshore gas-condensate green field in South East Asia.
The strategy behind the workflow for upscaling the core-derived SHF is to generate a function that preserves HCIIP when using upscaled porosity and permeability values. The original core plug- derived Brooks-Corey SHF equation was used as the starting point for the upscaled SHF. Irreducible Water Saturation (Swi), Capillary Pressure (PCe), and the shape factor (N) were adjusted by minor tweaking of the parameters to obtain the best fit with the upscaled saturations. The adjustments of these parameters accounts for the upscaling.
To demonstrate the accuracy of the upscaled SHF over plug-derived SHF, water saturation (Sw) curves were generated by applying the upscaled porosity and permeability values to both SHFs in a dummy well. Sw curve from upscaled SHF shows a better match (lesser residual value) with the upscaled (weighted average) Sw values at different HAFWL (Height Above Free Water Level) values than core-derived Sw curve. The upscaled SHF shows a slightly longer transition zone & wider spread in Swi for the different porosity & permeability classes. For the field, GIIP estimated using the upscaled SHF is about 1 Tscf (Trillion standard cubic feet) less compared to the GIIP obtained by applying the plug-derived SHF in the same porosity and permeability model. The core plug-derived SHF overestimated GIIP due to upscaling effects on the porosity-permeability transform. In static reservoir modeling, saturation calculations typically use upscaled rock properties as input; be it porosity, permeability or a combination thereof. Hence, the SHF used for this purpose should be also be upscaled. This work has shown that there is indeed an effect, which in this case would have led to an overestimate of GIIP.
Giant reservoirs such as Lula (Santos Oil Basin, Brazil) and Ghawar (Saudi Arabia) have high permeability intervals, known as super-k zones, associated with thin layers. Modeling these small-scale flow features in large-scale simulation models is complex. Current methods are limited by high computational costs or simplifications that mismatch the representation of these features in simulation grid blocks. This work has two purposes: (1) present an upscaling workflow to integrate highly laminated or inter-bedded reservoirs with thin, highly permeable layers in reservoir simulations through a combination of (a) an explicit modeling of super-k layers using
We use the benchmark model UNISIM-II-R, a fine single-porosity grid based on field information from the Brazilian Pre-salt and Ghawar oil fields, as the reference solution to compare the upscaling matching between the three methods. We compare; oil recovery, water cut, average reservoir pressure, waterfront, and the time consumption for simulation. Our proposed parsons dual-medium (PDP) methodology achieved better upscaling matches with the reference model and had minimal time consumption when compared with the representation of super-k layers through an implicit matrix modelling by single porosity flow models (IMP) and through the explicit representation of super-k zones in the fracture system of dual-medium flow models (DFNDP).
This paper recall the Compositional Dual Mesh Method, an extension to the concept of dual mesh for reactive transport modeling. This approach involves two meshes, a low-resolution mesh to resolve the pressure equation and a high-resolution mesh to transport the species and to calculate the geochemical equilibrium. Geochemical equilibrium being very sensitive to the concentration, preserving the fine heterogeneities leads to a more accurate field behavior simulation than conventional approach which consist in performing simulations on a coarser mesh. The method is applied to a simulation of CO2 storage in a geological model representing a fluvial deposit with a complex realistic architecture that keep a high resolution of the heterogeneities.
Optimal acid-injection rate is critical information for carbonate-matrix-acidizing design. This rate is currently obtained through fitting acidizing-coreflood experimental results. A model is needed to predict optimal acid-injection rates for various reservoir conditions.
A wormhole forms when larger pores grow in the cross-sectional area at a rate that greatly exceeds the growth rate of smaller pores caused by surface reaction. This happens when the pore growth follows a particular mechanism, which is discussed in this paper. We have developed a model to predict wormhole-growth behavior. The model uses the mode size in a pore-size distribution--the pore size that appears most frequently in the distribution--to predict the growth of the pore. By controlling the acid velocity inside of it, we can make this particular pore grow much faster than other smaller pores, thus reaching the most-favorable condition for wormholing. This also results in a balance between overall acid/rock reaction and acid flow. With the introduction of a porous-medium model, the acid velocity in the mode-size pore is scaled up to the interstitial velocity at the wormhole tip. This interstitial velocity at the wormhole tip controls the wormhole propagation. The optimal acid-injection rates are then calculated by use of semiempirical flow correlations for different flow geometries.
The optimal injection rate depends on the rock lithology, acid concentration, temperature, and rock-pore-size distribution. All these factors are accounted for in this model. The model can predict the optimal rates of acidizing-coreflood experiments correctly, compared with our acidizing-coreflood experimental results. In addition, on the basis of our model, it is also found that at optimal conditions, the wormhole-propagation velocity is linearly proportional to the acid-diffusion coefficient for a diffusion-limited reaction. This is proved both experimentally and theoretically in this study. Because there is no flow-geometry constraint while developing this model, it can be applied to field scales. Applications are presented in this paper.
Gao, Sunhua (Texas A&M University) | Killough, John E. (Texas A&M University) | He, Jie (Texas A&M University) | Fadlelmula, Mohamed M. (Texas A&M University at Qatar) | Wang, F. Yuhe (Texas A&M University at Qatar) | Fraim, Michael L. (King Fahd University of Petroleum & Minerals)
Numerical modeling of naturally fractured vuggy reservoirs presents many challenges due to the coexistence of three very different kinds of media and their complex interaction on multiple scales. With current computing capabilities, conventional fine-scale single-porosity models are not practical for large-scale reservoir simulation. A multi-continuum reservoir model is presented as an effective approach to modeling fractured vuggy reservoirs on the coarse scale. This model consists of four different porosity systems, i.e. the matrix, fractures, isolated vugs and connected vugs. This study investigates mass exchange between different porosity systems with the final objective of developing new transfer functions that can be used as an application to upscaling fractured vuggy reservoir models.
A well-designed procedure is proposed to obtain the novel transfer functions in multi-continuum fractured vuggy reservoir models. Different realizations of the vug-filled matrix blocks are generated to show the effect of vug fraction, distribution and connectivity on multi-phase fluid flow. For interporosity flow between vugs and the other two media, new formulations of the shape factors that incorporate the effect of vug spatial variation are developed respectively. The dominant mechanisms of multiphase fluid exchange between each two porosity systems (matrix-isolated vugs, fractures-connected vugs) are discussed separately. New transfer functions for multiphase flow in the multi-continuum fractured vuggy model to capture the complex flow mechanisms and emulate the results of the fine-grid model are provided. In addition, a transmissibility multiplier table is introduced as another connection term for the transfer functions to improve the accuracy of upscaling solution. Finally, a new upscaling approach by incorporating the proposed transfer functions into multi-continuum models is presented.
This paper provides a new insight to the complex fluid exchange among three different media in fractured vuggy reservoirs. Results show that the new upscaling methodology helps to reduce the size of simulation model and improve the computational speed significantly, while providing an accurate representation of the fine-scale results.
A new absolute permeability upscaling method based on geological hierarchical models that affect different scales reservoir heterogeneities is presented. Reservoir anisotropy is evaluated via horizontal permeability (Kh) and vertical permeability (Kv). The new approach based on the geologic viewpoint that various geologic hierarchical-elements set result in relevant permeability display of different reservoir scales. For reservoirs, from micro-scale to macro-scale, influencing factors of permeability become abstruse. In conventional scenario, the calculation method based on single-phase numerical simulation test, core analysis and data statistics integrates all these factors as much as possible to upscale permeability. Considering reservoir anisotropy, horizontal permeability (Kh) and vertical permeability (Kv) are studied to show how anisotropy changes according to different reservoir heterogeneities. In the case study of Mackay River Oil Sand Block, Alberta, Canada, database includes regional depositional setting, core, and logging data for more than 20 wells. Generally, reservoir sedimentary setting poses a direct effect on permeability. Local rock bedding affects permeability anisotropy greatly, as well. There is no obvious linear parity between horizontal permeability (Kh) and vertical permeability (Kv) in core-plug. Vertical and lateral grain size variance also alters permeability. The mm-cm scale mud drapes have a worse effect on vertical permeability (Kv) than on horizontal permeability (Kh). Besides, bioturbations in the transitional facies could be favor of permeability. The three factors have non-linear relationship on effecting permeability. The new upscaling model synthesizes all these factors to upscale the permeability for nearly all scales of reservoirs, from the scale of core to lithofacies or even to the entire reservoir. Comparisons study is also conducted between this model and current upscaling algorithms such as arithmetic average, harmonic average, etc. The results showed that the upscaling model of this paper is more reasonable. Meanwhile, reservoir characterization hierarchical models can also be applied to explicate heterogeneity effect on the attribute of reservoir fluid qualitatively. The novelty of this approach lies in solving reservoir fluids' attributes quantitatively through exact heterogeneities analysis.
Multiphase flow in carbonate reservoirs has been a hard problem of scientific research for many years. Accurate flow simulation is essential for the efficient exploitation. In this paper, a coupled triple-continuum and discrete fracture network approach is developed for modeling multiphase flow through fractured vuggy porous media. Multiple levels of fractures can be not only modeled as different superimposed continua but also embodied as discrete fracture network based on their geometrical characteristics. We develop a systematic coupling using Multiscale Finite Element Method (MsFEM) as a framework for coarsening and refinement. MsFEM is used to capture subgrid scale heterogeneities and interactions through multiscale basis functions calculated based on the triple-continuum background. Unstructured mesh is applied to model discrete fractures in arbitrary. This paper presents a significant advancement in terms of elevating the limitations of the triple-continuum models in handling complex fractures and extending the model reduction capability of MsFEM. Several numerical examples are carried out to demonstrate the capability of the proposed coupling method.
Geological sequestration of CO2 is one of the most promising technologies to mitigate the greenhouse effect by decreasing the anthropogenic CO2 emissions into the atmosphere. Deep saline reservoirs are a suitable target for CO2 storage because very often they can be found relatively close to today's large CO2 releasing sources. To investigate the chemical and physical impacts of a CO2-rich brine solution injection to a quartz rich sandstone, we flooded a Berea Sandstone core sample with CO2-saturated synthetic brine at the elevated temperature (60°C) and pressure (20MPa). After flooding, the porosity and permeability of the core were measured and compared to the pre-flooding values. We found that the porosity had increased by 1.8% while the permeability decreased by 5.1%. The decrease in permeability may be attributed to the movement of particles in the pore space of the sample (fines migration) and/or sample's physical compaction under net effective stress. Effluent brine samples were also collected during the core-flood experiment to be analysed for their chemical composition. We found that, on average, the concentration of Ca2+, Mg2+ and Fe2+ in the effluent samples to increase by approximately 100mg/l, 80mg/l and 95mg/l, respectively, with traces of other metals. It is believed that the Ca2+, Mg2+ and Fe2+ were liberated from the dissolution of the carbonate cement in the sample. As revealed by the differential pressure evolution of the experiment, for the quartz-rich sandstone reservoirs, where fines migration is not significant and reactive minerals are scarce, the injectivity may not be affected during the fluid injection process.
Steady-state two-phase relative permeability upscaling in synthetic and X-ray computerized tomography (CT) coal cores is performed with a three-dimensional (3D) reservoir simulator using an automated control procedure to drive a series of steady-state fractional flows. A clear understanding of relative permeability in coal is important for coalbed methane reservoir management from pore scale to sales point, as it is valuable for helping forecast production. Automation control enables greater continuity between physical corefloods and the numerical upscaling of the same coreflood procedure. Absolute permeability is computed for primitive synthetic core types using the reservoir simulator and is compared to an analytical formulation to validate the use of the simulator solution for core scale property determination.
Relative permeability was computed for synthetic cores considering several scenarios: fracture geometry/abundance (parallel vs. intersecting), rock-type matrix distribution (homogeneous vs. heterogeneous), ratios of matrix-to-fracture permeability (high vs. low), and injection rate conditions [capillary limit (CL) vs. viscous limit (VL)]. Additionally, injection rate conditions were evaluated in the upscaled relative permeability of an X-ray CT segmented composite coal core. Analysis of the upscaled relative permeability curves in the composite and synthetic cores illustrated the impact of each scenario on upscaling relative permeability and suggests that selected characteristics of unconventional cores can potentially be used to delineate parameter dependence in a manner similar to rock type volume fraction and ordering in conventional cores. The consistency of the developed upscaled results with previous studies confirms the applicability of automated process control in core scale multiphase upscaling using a commercial reservoir simulator at varied injection rates and upscaling conditions.