Field studies have shown that, if an inclined fracture has a significant inclination angle from the vertical direction or the fracture has a poor growth along the inclined direction, this fracture probably cannot fully penetrate the formation, resulting in a partially penetrating inclined fracture (PPIF) in these formations. It is necessary for the petroleum industry to conduct a pressure-transient analysis on such fractures to properly understand the major mechanisms governing the oil production from them. In this work, we develop a semianalytical model to characterize the pressure-transient behavior of a finite-conductivity PPIF. We discretize the fracture into small panels, and each of these panels is treated as a plane source. The fluid flow in the fracture system is numerically characterized with a finite-difference method, whereas the fluid flow in the matrix system is analytically characterized on the basis of the Green’s-function method. As such, a semianalytical model for characterizing the transient-flow behavior of a PPIF can be readily constructed by coupling the transient flow in the fracture and that in the matrix. With the aid of the proposed model, we conduct a detailed study on the transient-flow behavior of the PPIFs. Our calculation results show that a PPIF with a finite conductivity in a bounded reservoir can exhibit the following flow regimes: wellbore afterflow, fracture radial flow, bilinear flow, inclined-formation linear flow, vertical elliptical flow, vertical pseudoradial flow, inclined pseudoradial flow, horizontal-formation linear flow, horizontal elliptical flow, horizontal pseudoradial flow, and boundary-dominated flow. A negative-slope period can appear on the pressure-derivative curve, which is attributed to a converging flow near the wellbore. Even with a small dimensionless fracture conductivity, a PPIF can exhibit a horizontal-formation linear flow. In addition to PPIFs, the proposed model also can be used to simulate the pressure-transient behavior of fully penetrating vertical fractures (FPVFs), partially penetrating vertical fractures (PPVFs), fully penetrating inclined fractures (FPIFs), and horizontal fractures (HFs).
There are currently two types of relative permeability models that are used to model gas production from hydrate-bearing sediments: fully empirical parameter-fitting models [such as the University of Tokyo model (Masuda et al. 1997) and the Brooks and Corey model (Brooks and Corey 1964)] and partially empirical models [such as the Kozeny and Carman model (Wyllie and Gardner 1958) and capillary-tube-based models that assume only a single phase]. This study proposes an analytical model to estimate relative permeability of gas and water in a hydrate-bearing porous medium without curve fitting or use of any empirical parameters. The model is derived by conserving the momentum balance with the steady-state form of the Navier-Stokes equation for gas/water flow in a hydrate-bearing porous medium. The model is validated against a number of laboratory studies and is shown to perform better than most empirical models over a full range of experimental data. The proposed model is an analytical function of rock properties (average pore size and shape, porosity, irreducible water saturation, and saturation of hydrate), fluid properties (gas/water saturations and viscosities), and the hydrate-growth pattern [pore filling (PF), wall coating (WC), and a combination of PF and WC]. The benefits of the proposed model include sensitivity analysis of relevant physical parameters on relative permeability and estimation of rock parameters (such as porosity, pore size, and residual water saturation) using inverse modeling. The model can also be used to estimate two-phase permeability in a permeable medium without hydrates.
The proposed model was used to analyze the effects of pore shapes, the hydrate-growth pattern, variable gas saturation, and wettability on relative permeability. The sensitivity results produced by the proposed model were verified using observations from other studies that investigated similar problems using either experiments or computationally expensive pore-scale simulations.
Mancilla-Polanco, Adel (University of Calgary) | Johnston, Kim (University of Calgary) | Richardson, William D. L. (University of Calgary) | Schoeggl, Florian F. (University of Calgary) | Zhang, Y. George (University of Calgary) | Yarranton, Harvey W. (University of Calgary) | Taylor, Shawn D. (Schlumberger-Doll Research)
The phase behavior of heavy-oil/propane mixtures was mapped from temperatures ranging from 20 to 180°C and pressures up to 10 MPa. Both vapor/liquid (VL1) and liquid/liquid (L1L2) regions were observed. Saturation pressures (VL1 boundary) were measured in a Jefri 100-cm3 pressure/volume/temperature (PVT) -cell and blind-cell apparatus. The propane content at which a light propane-rich phase and a heavy bitumen-rich (or pitch) phase formed (L1/L1L2 boundary) was visually determined with a high-pressure microscope (HPM) while titrating propane into the bitumen. High-pressure and high-temperature yield data were measured using a blind-cell apparatus. Here, yield is defined as the mass of the indicated component(s) in the pitch phase divided by the mass of bitumen in the feed. A procedure was developed and used to measure propane-rich-phase and pitch-phase compositions in a PVT cell.
Pressure/temperature and pressure/composition phase diagrams were constructed from the saturation-pressure and pitch-phase-onset data. High-pressure micrographs demonstrated that, at lower temperatures and propane contents, the pitch phase appeared as glassy particles, whereas at higher propane contents and temperatures, it appeared as a liquid phase. Ternary diagrams were also constructed to present phase-composition data. The ability of a volume-translated Peng-Robinson cubic equation of state (CEOS) (Peng and Robinson 1976) to match the experimental measurements was explored. Two sets of binary-interaction parameters were tested: temperature-dependent binary-interaction parameters (SvdW) and composition-dependent binary-interaction parameters (CDvdW). Models derived from both types of binary-interaction parameters matched the saturation pressures and the L1L2 boundaries at one pressure but could not match the pressure dependency of the L1L2 boundary or the measured L1L2 phase compositions. The SvdW model could not match the yield data, whereas the CDvdW model matched yields at temperatures up to 90°C.
Abeeb A. Awotunde, King Fahd University of Petroleum and Minerals Summary This paper evaluates the effectiveness of six dimension-reduction approaches. The approaches considered are the constant-control (Const) approach, the piecewise-constant (PWC) approach, the trigonometric approach, the Bessel-function (Bess) approach, the polynomial approach, and the data-decomposition approach. The approaches differ in their mode of operation, but they all reduce the number of parameters required in well-control optimization problems. Results show that the PWC approach performs better than other approaches on many problems, but yields widely fluctuating well controls over the field-development time frame. The trigonometric approach performed well on all the problems and yields controls that vary smoothly over time. Introduction Field-development optimization has continued to attract interest among researchers and end users of the technology.
Fredriksen, Sunniva B. (University of Bergen) | Alcorn, Zachary P. (University of Bergen) | Frøland, Anders (University of Bergen) | Viken, Anita (University of Bergen) | Rognmo, Arthur U. (University of Bergen) | Seland, John G. (University of Bergen) | Ersland, Geir (University of Bergen) | Fernø, Martin A. (University of Bergen) | Graue, Arne (University of Bergen)
An integrated enhanced-oil-recovery (EOR) (IEOR) approach is used in fractured oil-wet carbonate core plugs where surfactant prefloods reduce interfacial tension (IFT), alter wettability, and establish conditions for capillary continuity to improve tertiary carbon dioxide (CO2) foam injections. Surfactant prefloods can alter the wettability of oil-wet fractures toward neutral/weakly-water-wet conditions that in turn reduce the capillary threshold pressure for foam generation in matrix and create capillary contact between matrix blocks. The capillary connectivity can transmit differential pressure across fractures and increase both mobility control and viscous displacement during CO2-foam injections. Outcrop core plugs were aged to reflect conditions of an ongoing CO2-foam injection field pilot in west Texas. Surfactants were screened for their ability to change the wetting state from oil-wet using the Darcy-scale Amott-Harvey index. A cationic surfactant was the most effective in shifting wettability from an Amott-Harvey index of –0.56 to 0.09. Second waterfloods after surfactant treatments and before tertiary CO2-foam injections recovered an additional 4 to 11% of original oil in place (OIP) (OOIP), verifying the favorable effects of a surfactant preflood to mobilize oil. Tertiary CO2-foam injections revealed the significance of a critical oil-saturation value below which CO2 and surfactant solution were able to enter the oil-wet matrix and generate foam for EOR. The results reveal that a surfactant preflood can reverse the wettability of oil-wet fracture surfaces, lower IFT, and lower capillary threshold pressure to reduce oil saturation to less than a critical value to generate stable CO2 foam.
Controlled laboratory experiments and some field studies have shown that the onset of sand production in gas wells differs from that in oil wells. Results from a general 3D sand-production numerical model are presented to explain the differences in the onset of sanding and sand-production volume for different fluids and under different flow and in-situ stress conditions. The sand-production model accounts for multiphase-fluid flow and is fully coupled with an elasto-plastic geomechanical model. The sanding criterion considers both mechanical failure and sand erosion by fluid flow. Non-Darcy flow is implemented to account for the high flow rates. The drag forces on the sand grains are computed on the basis of the in-situ Reynolds number. Both the intact rock strength and the residual rock strength depend on water saturation. Water evaporation (drying) resulting from gas flow is modeled using phase equilibrium calculations.
The onset of sand production is compared for different fluid types (oil and gas). Model results are shown to be consistent with experimental observations reported in the literature. For example, the onset of sanding is observed at higher compressive stresses for gas wells as compared with oil wells. The primary mechanism for this is for the first time shown to be sand strengthening induced by evaporation of water. This effect is not observed in oil wells. The sand-production rate when non-Darcy effects are considered is lower than for Darcy flow. The reason for this is the lower fluid velocity (for the same drawdown) and, consequently, smaller drag forces on the failed sand grains. The effect of water breakthrough and water cut on sand production is studied from both mechanical and erosion perspectives. The model is shown to be capable of accurately predicting the onset of sanding and sand production induced by multiphase- and compressible-fluid flows, helping us to predict sanding issues in both oil and gas wells.
Enhanced oil recovery (EOR) by solvent injection offers significant potential to increase recovery from shale oil reservoirs, which is typically between 3 and 7% original oil in place (OOIP). The rather sparse literature on this topic typically models these tight reservoirs on the basis of conventional-reservoir processes and mechanisms, such as by convective transport using Darcy’s law, even though there is little physical justification for this treatment. The literature also downplays the importance of the soaking period in huff ’n’ puff.
In this paper, we propose, for the first time, a more physically realistic recovery mechanism based on solely diffusion-dominated transport. We develop a diffusion-dominated proxy model assuming first-contact miscibility (FCM) to provide rapid estimates of oil recovery for both primary production and the solvent huff ’n’ soak ’n’ puff (HSP) process in ultratight oil reservoirs. Simplified proxy models are developed to represent the major features of the fracture network.
The key results show that diffusion-transport considered solely can reproduce the primary-production period within the Eagle Ford Shale and can model the HSP process well, without the need to use Darcy’s law. The minimum miscibility pressure (MMP) concept is not important for ultratight shales where diffusion dominates because MMP is based on advection-dominated conditions. The mechanism for recovery is based solely on density and concentration gradients. Primary production is modeled as a self-diffusion process, whereas the HSP process is modeled as a counter-diffusion process. Incremental recoveries by HSP are several times greater than primary-production recoveries, showing significant promise in increasing oil recoveries. We calculate ultimate recoveries for both primary production and for the HSP process, and show that methane injection is preferred over carbon dioxide injection. We also show that the proxy model, to be accurate, must match the total matrix-contact area and the ratio of effective area to total contact area with time. These two parameters should be maximized for best recovery.
Hydrocarbon-reservoir-performance forecasting is an integral component of the resource-development chain and is typically accomplished using reservoir modeling, by means of either numerical or analytical methods. Although complex numerical models provide rigorous means of capturing and predicting reservoir behavior, reservoir engineers also rely on simpler analytical models to analyze well performance and estimate reserves when uncertainties exist. Arps (1945) empirically demonstrated that certain reservoirs might decline according to simple, exponential, hyperbolic, or harmonic relationships; such behavior, however, does not extend to more-complex scenarios, such as multiphase-reservoir depletion. Because of this limitation, an important research area for many years has been to transform the equations governing flow through porous media in such a way as to express complex reservoir performance in terms of closed analytical forms. In this work, we demonstrate that rigorous compositional analysis can be coupled with analytical well-performance estimations for reservoirs with complex fluid systems, and that the molar decline of individual hydrocarbon-fluid fractions can be expressed in terms of rescaled exponential equations for well-performance analysis. This work demonstrates that, by the introduction of a new partial-pseudopressure variable, it is possible to predict the decline behavior of individual fluid constituents of a variety of gas/condensate-reservoir systems characterized by widely varying richness and complex multiphase-flow scenarios. A new four-region-flow model is proposed and validated to implement gas/condensate-deliverability calculations at late times during variable-bottomhole-pressure (BHP) production. Five case studies are presented to support each of the model capabilities stated previously and to validate the use of liquid-analog rescaled exponentials for the prediction of production-decline behavior for each of the hydrocarbon species.
An accurate description of the microemulsion-phase behavior is critical for many industrial applications, including surfactant flooding in enhanced oil recovery (EOR). Recent phase-behavior models have assumed constant-shaped micelles, typically spherical, using netaverage curvature (NAC), which is not consistent with scattering and microscopy experiments that suggest changes in shapes of the continuous and discontinuous domains. On the basis of the strong evidence of varying micellar shape, principal micellar curves were used recently to model interfacial tensions (IFTs). Huh’s scaling equation (Huh 1979) also was coupled to this IFT model to generate phase-behavior estimates, but without accounting for the micellar shape.
In this paper, we present a novel microemulsion-phase-behavior equation of state (EoS) that accounts for changing micellar curvatures under the assumption of a general-prolate spheroidal geometry, instead of through Huh’s equation. This new EoS improves phase-behavior-modeling capabilities and eliminates the use of NAC in favor of a more-physical definition of characteristic length. Our new EoS can be used to fit and predict microemulsion-phase behavior irrespective of IFT-data availability. For the cases considered, the new EoS agrees well with experimental data for scans in both salinity and composition. The model also predicts phase-behavior data for a wide range of temperature and pressure, and it is validated against dynamic scattering experiments to show the physical significance of the approach.
Previous experimental observations have shown the formation of distinct failure patterns and cavity shapes under different stress and flow conditions. With isotropic stress, spiral failure patterns with localized shear bands are likely to form. On the other hand, under anisotropic stress, V-shaped cavities, dog-ear cavities, or slit-mode cavities are usually observed. However, the mechanisms for the development of these sanding cavities have not been fully articulated. In addition, to accurately predict the onset of sanding and to predict the sand-production rate, it is crucial to capture the physics of the formation of these cavities during sand production.
This paper presents a fully coupled poro-elasto-plastic, 3D sand-production model for sand-production prediction around openhole and perforated wellbores in a weakly consolidated formation. Sanding criteria are based on a combination of shear failure, tensile failure, and compressive failure from the Mohr-Coulomb theory and strain-hardening/softening. After the failure criteria are met, an algorithm for the entrainment of the sand based on the calculation of hydrodynamic forces is implemented to predict sand erosion and transport. Dynamic mesh refinement has been implemented to effectively capture the strain-localization regions.
The model has been validated with multiple analytical solutions. In addition, it is applied to compare with previous sand-production experiments that have explored the different cavity shapes formed under different conditions. The model is capable of not only explaining the mechanisms responsible for each type of cavity shape but also predicting the cavity shape that will be formed under a specific set of conditions. Parametric studies for these cases provide an additional insight into the important role that the post-yield, poro-elastoplastic properties of the sand play in controlling the sanding mechanisms and cavity development. This allows us to predict, much more accurately, the onset of sanding and the sanding rate.