This study demonstrates the application of an alternative numerical-simulation approach to effectively describe the flow field in a two-scale carbonate-matrix-acidizing model. The modified model accurately captures the dissolution regimes that occur during carbonate-matrix acidizing. Sensitivity tests were performed on the model to compare the output with experimental observations and previous two-scale models in the literature. A nonlinear reaction-kinetics model for alternative acidizing fluids is also introduced.
In this work, the fluid-field flow is described by the Navier-Stokes momentum approach instead of Darcy’s law or the Darcy-Brinkman approach used in previous two-scale models. The present model is implemented by means of a commercial computational-fluid- dynamics (CFD) package to solve the momentum, mass-conservation, and species-transport equations in Darcy scale. The software is combined with functions and routines written in the C programming language to solve the porosity-evolution equation, update the pore-scale parameters at every timestep in the simulation, and couple the Darcy and pore scales.
The output from the model simulations is consistent with experimental observations, and the results from the sensitivity tests performed are in agreement with previously developed two-scale models with the Darcy approach. The simulations at very-high injection rates with this model require less computational time than models developed with the Darcy approach. The results from this model show that the optimal injection rate obtained in laboratory coreflood experiments cannot be directly translated for field applications because of the effect of flow geometry and medium dimensions on the wormholing process. The influence of the reaction order on the optimal injection rate and pore volumes (PVs) of acid required to reach breakthrough is also demonstrated by simulations run to test the applicability of the model for acids with nonlinear kinetics in reaction with calcite.
The new model is computationally less expensive than previous models with the Darcy-Brinkman approach, and simulations at very-high injection rates with this model require less computational time than Darcy-based models. Furthermore, the possibility of extending the two-scale model for acid/calcite reactions with more-complex chemistry is shown by means of the introduction of nonlinear kinetics in the reaction equation.
Zhang, Zhao (Heriot-Watt University) | Geiger, Sebastian (Heriot-Watt University) | Rood, Margaret (Imperial College London) | Jacquemyn, Carl (Imperial College London) | Jackson, Matthew (Imperial College London) | Hampson, Gary (Imperial College London) | De Carvalho, Felipe Moura (University of Calgary) | Silva, Clarissa Coda Marques Machado (University of Calgary) | Silva, Julio Daniel Machado (University of Calgary) | Sousa, Mario Costa (University of Calgary)
Flow diagnostics is a common way to rank and cluster ensembles of reservoir models depending on their approximate dynamic behavior before beginning full-physics reservoir simulation. Traditionally, they have been performed on corner-point grids inherent to geocellular models. The rapid-reservoir-modeling (RRM) concept aims at fast and intuitive prototyping of geologically realistic reservoir models. In RRM, complex reservoir heterogeneities are modeled as discrete volumes bounded by surfaces that are sketched in real time. The resulting reservoir models are discretized by use of fully unstructured tetrahedral meshes where the grid conforms to the reservoir geometry, hence preserving the original geological structures that have been modeled.
This paper presents a computationally efficient work flow for flow diagnostics on fully unstructured grids. The control-volume finite-element method (CVFEM) is used to solve the elliptic pressure equation. The flux field is a multipoint flux approximation (MPFA). A new tracing algorithm is developed on a reduced monotone acyclic graph for the hyperbolic transport equations of time of flight (TOF) and tracer distributions. An optimal reordering technique is used to deal with each control volume locally such that the hyperbolic equations can be computed in an efficient node-by-node manner. This reordering algorithm scales linearly with the number of unknowns.
The results of these computations allow us to estimate swept-reservoir volumes, injector/producer pairs, well-allocation factors, flow capacity, storage capacity, and dynamic Lorenz coefficients, which all help approximate the dynamic reservoir behavior. The total central-processing-unit (CPU) time, including grid generation and flow diagnostics, is typically a few seconds for meshes with O (100,000) unknowns. Such fast calculations provide, for the first time, real-time feedback in the dynamic reservoir behavior while models are prototyped.
Widely distributed organic-rich shales are being considered as one of the important carbon-storage targets, owing to three differentiators compared with conventional reservoirs and saline aquifers: (1) trapping of a significant amount of carbon dioxide (CO2) permanently; (2) kerogen-rich shale’s higher affinity of CO2; and (3) existing well and pipeline infrastructure, especially that in the vicinity of existing power or chemical plants. The incapability to model capillarity with the consideration of imperative pore-size-distribution (PSD) characteristics by use of commercial software may lead to inaccurate modeling of CO2 injection in organic shale. We develop a novel approach to examine how PSD would alter phase and flow behavior under nanopore confinements. We incorporate adsorption behavior with a local density-optimization algorithm designed for multicomponent interactions to adsorption sites for a full spectrum of reservoir pressures of interests. This feature elevates the limitation of the Langmuir isotherm model, allowing us to understand the storage and sieving capabilities for a CO2/N2 flue-gas system with remaining reservoir fluids. Taking PSD data of Bakken shale, we perform a core-scale simulation study of CO2/N2 flue-gas injection and reveal the differences between CO2 injection/storage in organic shales and conventional rocks on the basis of numerical modeling.
Various types of ultrahigh-molar-mass polyacrylamides (HPAMs) and their copolymers and terpolymers used not only in enhanced oil recovery (EOR) but also in drilling, fracturing, water treatment, and tailing applications require an accurate description of polymer molar mass (Mw) and hydrodynamic size for their optimal design. The range of Mw for various types of available HPAMs is between 4 and 30 million g/mol and is typically determined by use of intrinsic-viscosity measurement.
Molecular-weight distribution (MWD) cannot be determined because neither standard with low polydispersity index (PDI) nor gel-permeation-chromatography (GPC) or size-exclusion-chromatography (SEC) techniques exist today for such ultrahigh-molar-mass polymers. Moreover, the solution environment in underground reservoirs, characterized by high temperatures, pH values, and the presence of monovalent and divalent ions, may often lead to changes in polymer-macromolecular conformation. Current techniques, SEC, ultraviolet-visible measurements, and liquid chromatography, are not capable of accurately investigating these complex macromolecular structures for various reasons. In this paper, the asymmetrical-flow field-flow fractionation (AF4) system was used to fractionate four different ultrahigh-molecular-weight HPAM samples, varying in molar mass and commercially used for oilfield applications, in various carrier pH values ranging from 12 to 3 (pH values of 12, 7.4, and 3). The system uses field-flow fractionation (FFF), a family of analytical techniques developed specifically for separating and characterizing macromolecules, colloids, and particles. The theoretical separation range for AF4 is between 103 to 1012 g/mol. Other advantages over conventional GPC/SEC include minimum shear degradation, mild operating conditions, and no sample loss caused by adsorption. The flow system was equipped with a multiangle-light-scattering (MALS) and refractive-index (RI) detectors to measure molar mass and radius of gyration (Rg).
The results show that the observed molecular weight of the polymer aggregate increased substantially as the pH value of the carrier solution decreased from 12 to 3, especially for higher-molar-mass polymers. The sample Rg showed the opposite trend, decreasing as the pH of the carrier solution changed from basic to acidic. For ultrahigh molecular HPAM at high pH, a narrower molar mass and radius distribution was observed with disaggregated molar mass and increased branching or swelling (therefore larger hydrodynamic radius). Use of this direct separation and measurement technique can improve understanding of polymer-macromolecular structure and corresponding changes in the reservoir brines.
The decrease of permeability and porosity with increasing net stress in consolidated and unconsolidated porous media is a well-known phenomenon to petroleum and geomechanics engineers. Conversely, permeability and porosity are observed to increase when net stress decreases; however, they typically follow a different path; this discrepancy is known as hysteresis. The trend of permeability and porosity hysteresis is a signature of porous media that depends on several chemical, physical, and mechanical properties. Understanding permeability and porosity hysteresis plays a significant role in production strategies of hydrocarbon reservoirs. The hysteresis effect on production strategies can be even more important in very-low-permeability reservoirs such as tight sandstone, tight carbonate, and shale/mudstone formations. The reason is that the stress change associated with permeability and porosity hysteresis can affect adsorption/desorption and diffusion-transport mechanisms that are among the main driving mechanisms in low- or ultralow-permeability reservoirs.
In this study, matrix permeability and porosity hysteresis of nano-, micro-, and millidarcy core samples are measured for a wide range of net stresses (500 to 4,500 psia). The matrix includes nano- and micrometer-sized cracks (fractures) that are open or mineral-filled (sealed) cracks. The nano- and microdarcy core samples are from the Niobrara, Bakken, Three Forks, and Eagle Ford formations. The millidarcy core samples are from Middle East carbonate, Indiana Limestone, and Torrey Buff Sandstone formations. Bakken, Three Forks, and Middle East carbonate core samples are from oil-producing reservoirs, whereas others are from outcrop. The major experimental observations of this study are that (a) the stress dependency and hysteresis of permeability and porosity were observed to be larger for nanodarcy cores compared with those of microdarcy and millidarcy core samples; (b) stress dependency and hysteresis of porosity are smaller than those of permeability; (c) pore shape, pore size and their distributions, and mineralogy affect the stress dependency and hysteresis of both permeability and porosity; and (d) increase in permeability with increasing temperature and permeability hysteresis through temperature loading and unloading were observed in organic-rich core sample from Eagle Ford.
Jin, Luchao (University of Oklahoma) | Li, Zhitao (Ultimate EOR Services) | Jamili, Ahmad (University of Oklahoma) | Kadhum, Mohannad (University of Oklahoma) | Lu, Jun (University of Tulsa) | Shiau, Bor-Jier (University of Oklahoma) | Harwell, Jeffrey H. (University of Oklahoma) | Delshad, Mojdeh (University of Tulsa and University of Texas at Austin)
Microemulsion phase behavior is crucial to surfactant flooding performance and design. In previous studies, analytical/numerical solutions for surfactant flooding were developed dependent on the classical theory of multicomponent/multiphase displacement and empirical microemulsion phase-behavior models. These phase-behavior models were derived from empirical correlations for component-partition coefficients or from the Hand-rule model (Hand 1930), which empirically represents the ternary-phase diagram. These models may lack accuracy or predictive abilities, which may lead to improper formulation design or unreliable recovery predictions.
To provide a more-insightful understanding of the mechanisms of surfactant flooding, we introduced a novel microemulsion phase-behavior equation of state (EOS) dependent on the hydrophilic/lipophilic-difference (HLD) equation and the net-average curvature (NAC) model, which is called HLD-NAC EOS hereafter. An analytical model for surfactant flooding was developed dependent on coherence theory and this novel HLD-NAC EOS for two-phase three-component displacement. Composition routes, component profile along the core, and oil recovery can be determined from the analytical solution.
The analytical solution was validated against numerical simulation as well as experimental study. This HLD-NAC EOS based analytical solution enables a systematic study of the effects of phase-behavior-dependent variables on surfactant-flooding performance. The effects of solution gas and pressure on microemulsion phase behavior were investigated. It was found that an increase of solution gas and pressure would lead to enlarged microemulsion bank and narrowed oil bank. For a surfactant formulation designed at standard conditions, the analytical solution was able to quantitatively predict its performance under reservoir conditions.
Preformed particle gels (PPGs) have been successfully applied as a plugging agent to solve the conformance problem in fractured reservoirs. They are injected to plug fractures and then divert displacing fluid into poorly swept zones/areas. However, PPG-propagation and -plugging mechanisms through open void-space conduits (VSCs) have not been studied thoroughly. This paper investigated various situations involving heterogeneous conduits and their geometrical effect on PPG injectivity. Five-foot tubes were used to mimic VSCs. Three models were designed to gain understanding on how conduit geometry and PPG properties affect gel transportation, including a single conduit with a uniform internal diameter (ID); a single conduit with a nonuniform ID along its length; and two parallel conduits with different ID ratios with respect to each other. Results obtained from single-conduit models with uniform and nonuniform diameters showed PPGinjection pressure increased significantly as the conduit became more heterogeneous. Particle gels accumulated at the choke point within each conduit and caused injection pressure to increase accordingly. When two parallel conduits are available for flow, the relative distance of PPG penetration into the conduits depends strongly on the ratio of the conduit diameters and the gel strength. In addition, the ratio of gel-particle-size diameter to conduit diameter contributes significantly to the gel-transport selection. This paper demonstrates important impact elements of gel propagation for different heterogeneous-conduit situations.
Carbon dioxide (CO2) sequestration in coal seams combines CO2 storage with enhancing methane (CH4) recovery. The efficiency of CO2 sequestration depends on the coal-formation properties and the operating conditions. This study investigated the effects of the sodium chloride (NaCl) salinity of coal-seam water, injection flow rate, injected-gas composition, and CO2 state (formation pressure) on CO2 sequestration in coal formations. Coreflood tests were conducted on nine coal cores to simulate the injection of CO2 into coal formations. The change in the effective water/coal permeability after CO2 injection was measured. A commercial simulator was used to match the pressure drop across the core from the experimental study by adjusting the relative permeability curves. Moreover, permeability dynamic measurements were conducted to estimate the absolute permeability reduction caused by coal swelling.
The effective water permeability in the tested coal decreased during CO2 injection because of its adsorption onto the coal surface, coupled with a reduction in the relative water permeability. As salt concentration increased, the change in the pressure drop across the core increased, but this effect decreased as the formation pressure increased. Higher formation pressure and lower nitrogen (N2) concentrations led to further permeability reduction as a result of the higher CO2 adsorption onto the coal surface. Furthermore, as the injection flow rate increased, the contact time of CO2 at the coal surface decreased. Hence, the CO2 adsorption to the coal matrix decreased, and thus the difference in the effective water permeability slightly decreased. CO2 injectivity in fully water-saturated formations increased initially as the gas relative permeability increased, then the injectivity decreased as a result of matrix swelling and absolute permeability reduction. Moreover, the water salinity in coal formations decreased the overall gas relative permeability and increased the water relative permeability. Similar behavior occurred in the presence of N2. It is derived from these observations that the injection of CO2 into highly volatile bituminous coal seams for CO2 sequestration purpose is more efficient as the salt concentration increases, especially at high injection pressures.
Fluid flow in unpropped and natural fractures is critical in many geophysical processes and engineering applications. The flow conductivity in these fractures depends on their closure under stress, which is a complicated mechanical process that is challenging to model. The challenges come from the deformation interaction and the close coupling among the fracture geometry, pressure, and deformation, making the closure computationally expensive to describe. Hence, most of the previous models either use a small grid system or disregard deformation interaction or plastic deformation.
In this study, a numerical model is developed to simulate the stress-driven closure and the conductivity for fractures with rough surfaces. The model integrates elastoplastic deformation and deformation interaction, and can handle contact between heterogeneous surfaces. Computation is optimized and accelerated by use of an algorithm that combines the conjugate-gradient (CG) method and the fast-Fourier-transform (FFT) technique. Computation time is significantly reduced compared with traditional methods. For example, a speedup of five orders of magnitude is obtained for a grid size of 512 × 512. The model is validated against analytical problems and experiments, for both elastic-only and elastoplastic scenarios.
It is shown that interaction between asperities and plastic deformation cannot be ignored when modeling fracture closure. By applying our model, roughness and yield stress are found to have a larger effect on fracture closure and compliance than Young’s modulus. Plastic deformation is a dominant contributor to closure and can make up more than 70% of the total closure in some shales. The plastic deformation also significantly alters the relationship between fracture stiffness and conductivity. Surfaces with reduced correlation length produce greater conductivity because of their larger apertures, despite more fracture closure. They have a similar fraction of area in contact as compared with surfaces with longer fracture length, but the pattern of area in contact is more scattered. Contact between heterogeneous surfaces with more soft minerals leads to increased plastic deformation and fracture closure, and results in lower fracture conductivity. Fracture compliance appears not to be as sensitive to the distribution pattern of hard and soft minerals. Our model compares well with experimental data for fracture closure, and can be applied to unpropped or natural fractures. These results are obtained for a wide range of conditions: surface profile following Gaussian distribution with correlation length of 50 µm and roughness of 4 to 50 µm, yield stress of 100 to 1500 MPa, and Young’s modulus of 20 to 60 GPa. The results may be different for situations outside this range of parameters.
Xiao, Cong (China University of Petroleum, Beijing) | Tian, Leng (China University of Petroleum, Beijing) | Zhang, Yayun (China University of Petroleum, Beijing) | Hou, Tengfei (China University of Petroleum, Beijing) | Yang, Yaokun (China University of Petroleum, Beijing) | Deng, Ya (China National Petroleum Corporation) | Wang, Yanchen (Shengli Oilfield Service Corporation) | Chen, Sheng (China National Petroleum Corporation)
The detection of interacting behavior between the hydraulic fracture (HF) and the natural fracture (NF) is of significance to accurately and efficiently characterize an underground complex-fracture system induced by hydraulic-fracturing technology. This work develops a semianalytical pressure-transient model in the Laplace domain to detect interacting behavior between HF and NF depending on pressure-transient characteristics. Our results have shown that no matter what the flow state (compressible or incompressible flow) within a hydraulically induced fracture system, we can easily detect interacting behavior between HF and NF depending on whether the “dip” shape occurs at the formation radial-flow regime. Referring to sensitivity analysis, distance between NF and well, horizontal distance between NF and HF, and NF length are the three most sensitive factors to detect fracture-interacting behavior. Depending on interference analysis, although the pressure-transient characteristics of a pseudosteady-state dual-porosity model can interfere with our proposed methodology, the difference between our model and a pseudosteady-state dual-porosity system lies in whether the value of the horizontal line of dimensionless pressure derivative is equal to 0.5 at the formation radial-flow regime. Our work obtains some innovative insights into detecting fracture-interacting behavior, and the valuable results can provide significant guidance for refracturing operations and fracture detection in an underground fracture system.