Accurate modeling of gas through shale-gas reservoirs characterized by nano-meter pores where the effects of various non- Darcy flow regimes and the adsorbed-layer are important is presented and demonstrated by several examples. Quantification of gas transport may be accomplished using the transport equation that is valid for all flow regimes. This equation though needs further modification when transport is through a media where the gas is adsorbed onto the pore wall. In the presence of adsorption, there is a pore pressure dependent loss of porosity and cross-sectional area to free gas transport. The apparent gas permeability correction is accomplished for various flow regimes using the Knudsen number by consideration of the reduction of the cross-sectional area to free gas transport in the presence of adsorption. We show that transport in the adsorbed layer may contribute significantly in the total gas transport in these nanopores. An effective transport model is presented to account for the impact of adsorption through two mechanisms. First, we modify the transport equation to account for the pore-pressure dependent-reduction in the volume available to free gas transport; second, we model transport through the adsorbed layer using Fick's law of diffusion. The coupled model is then compare to conventional transport models over a wide range of reservoir properties and conditions. As pore-pressure is reduced, adsorbed phase gas desorbs into free gas and apparent permeability increases. The difference in the estimated apparent permeability with and without the consideration of the adsorption volume can be a factor of two or more at initial reservoir conditions. Diffusion on the surface of organic pores can be a substantial transport mechanism in shales depending on the pore connectivity, pore pressure, and pore size distribution in the organic pores. The interpretation of production data will be compromised without considering the effects of adsorption on apparent permeability. This work implies that permeability measurements for shale gas reservoirs must be done with methane at in-situ pore pressures. Because these corrections are pore-pressure not effective pressure dependent, effective pressure is not a valid parameter to use in quantifying the pressure dependence of these transport equations.
The effects of the parameters involved in shale gas reservoir simulation are investigated using an improved transport equation for description of gas flow in nano-Darcy permeability media. This approach takes into account the effects of molecular collisions at the pore wall and is valid in all flow regimes: Darcy, slip, transition, and free-molecular flow. The study generalizes a transport equation valid for all flow regimes for an ideal gas in a capillary tube and extends the formulation to quantify the effect of a distribution of pore sizes for different flow regimes. We first describe the adopted methodology to model ideal gas transport and then account for real gas behavior by modifying the conventional definition of the mean free-path. The relationship of this approach to the Klinkenberg correction for slip flow and other published formulations that are described as the sum of a Darcy term plus a diffusive transport term are examined. An application of the present approach and its implications are demonstrated by means of a numerical example involving a hydraulically-fractured shale gas reservoir producing at a constant rate. The bottomhole pressure predictions from the non-Darcy formulation indicate a substantial deviation from the bottomhole pressure predicted by assuming Darcy flow and consequently, can be expected to have serious implications for production forecasting and planning for well abandonment. In particular, for infinite acting flow regimes that are commonly observed for shale gas wells, our calculations indicate that flowing bottomhole pressures tend to be higher than those calculated using a transport formulation governed by Darcy's law, thereby describing the potential for significantly enhanced productive well life.
Effect of retardation in fluid displacement on transport inside capillary tubes during leak-off and clean-up for hydraulically stimulated reservoirs is investigated by modeling of the relevant phenomena. The effect of wall proximity during the transport in narrow capillaries is formulated. The importance of the critical properties alteration due to confinement is demonstrated by modification of the real gas deviation factor. The relaxation in fluid displacement observed in the fluid transport dynamics is coupled with the bundle of tubes representation of porous media for investigation of the relaxation effects on fluid saturation, capillary pressure, and relative permeability. An analytical formulation of the relaxation time corresponding to water removal during clean-up processes following hydraulic fracture stimulation is presented. The dynamics of advancement of the wetting and non-wetting fluids inside capillary tubes are illustrated by various applications.
Rigorous modeling of wax deposition in submarine oil pipelines undergoing a cooling process after shut-in is developed. Relevant mechanisms of wax deposition are described by accurate approaches. Fraction of wax precipitated under various conditions is estimated by an improved correlation and validated using experimental data. It is proven that consideration of a moving boundary between waxy gel and liquid oil is unnecessary and consideration of wax/oil mixtures as a continuously varying multiphase system is more effective. Introduction Wax appearance inside pipelines is an important phenomenon for transportation of hydrocarbon fluids where the temperature of the surroundings is below the phase-transition temperature. Particularly, submarine pipelines designed for flow of liquid hydrocarbons may experience precipitation of wax under shut-in conditions. Although such pipelines are usually properly insulated for preventing wax appearance and related problems, prolonged exposure to cooler environments may cause sufficient drop in temperature favorable for inducing wax separation from the liquid oil phase. After shut-in of a submerged pipeline, potential of complete wax separation is created by the cooler submarine environment. Wax and liquid oil usually form a highly viscous gel characterized by a solid-like structure. Thus, wax deposition may reduce the cross-sectional area of pipeline available for flow (choking) when the production operations are resumed or even worse if the deposited wax has effectively plugged the pipe. Obviously, coolest sections of pipes have the greatest risk of plugging. Several experimental studies have demonstrated that wax separation is mainly driven by thermodynamic interactions in systems containing hydrocarbons. Cooling due to heat loss in the liquid oil causes the separation of heaviest components (wax) in the form of a crystalline structure saturated with oil. Pressure drop at dynamic and static conditions has almost no effect on wax precipitation. Change in pressure induces little wax appearance because waxy crystals are incompressible and liquid hydrocarbons are slightly compressible. A large pressure differential is required to alter the specific volume, and thus change the mass fractions in both waxy crystals and the liquid hydrocarbon. However, the shear stress induced by flowing conditions plays a significant role in wax deposition. Shear stress causes erosion on the waxy layers deposited around the pipe wall. Therefore, the thickness of layered deposition reaches a plateau owing to equilibrium between growth and erosion under flowing conditions. Wax appearance causes a significant change in the nature of hydrocarbons. For instance, the behavior varies from Newtonian to non-Newtonian. For a cylindrical container or a cross-section of a pipe, the temperature does not remain constant in the radial direction after the wax separation has already taken place. Difference in physical properties between the various phases keeps the center warmer than the outer perimeter (wall). Consequently, waxy crystals are more abundant near the wall. Thus, particle aggregation in the form of layers (wax deposition) is observed first near the wall. Wax deposition progresses towards the center of the container as the fluid becomes cooler. Accurate prediction of the wax fraction is very important in modeling wax deposition inside pipelines. Comprehensive models considering thermodynamic interactions between the solid and liquid phases during wax deposition are still in development. Some compositional models have shown adequate prediction of wax appearance and the phase mass fractions (Zuo and Zhang, 2008, Coutinho, 2000). However, application of these models for simulation purposes requires a high computational effort. A more convenient approach is to develop an empirical correlation suitable for capturing the behavior of the wax mass fraction against temperature predicted by a compositional analysis or measured directly in experimental tests.
A homogenous model applicable for reservoir fluids flowing along a pipe with constant cross-sectional area is presented. This model is simplified for flowing fluids across a circular pipe at steady state. The differential conservation laws of mass, momentum, and energy are applied. By estimating the multiphase fluid properties, the differential laws of conservation are solved to compute the change in the pressure, temperature, and flowing velocity. The velocity is computed by knowing the fluid density. Because the flow might not be in equilibrium, the density of the multiphase fluid system is not calculated from any equation of state. Two approaches are presented to determine the density at non-equilibrium conditions. One is the differential conservation law of gas mass that can be solved by estimating the relaxation in time of gas separation, and the other is predicting the liquid holdup by estimating the slip ratio which is the ratio of the phase velocities. The later was used for the application. The presented homogeneous model combined with the proposed and novel liquid holdup model is applied to the study cases. The results of the application are employed to predict and characterize the nature of the relaxation time for hydrocarbon fluids. Introduction In general, hydrocarbon fluids present in reservoirs contain a large number of various substances. Each of these substances has different physical properties and behavior affecting in specific ways the properties of the fluid phases. Moreover, the interfaces or surface borders between the fluid phases have physical properties and behavior on their own. Consequently, large amounts of measurements have to be performed in order to determine the fluid properties by means of a detailed model. For that reason, theoretical models of fluid dynamics for reservoir fluids in producing wells have been proposed in various types and successes. Typically, the reservoir fluid consists of three distinct phases. These are the gas, oil, and water phases. Thus, the flow of the reservoir fluid in wells can be modeled as the flow of a multiphase-fluid system of several phases. By considering the well fluid as a single multiphase-fluid system containing gas, oil, and water phases, the flow in the production pipe can be described by the fundamental equations governing the flow of fluids in conduits. In the present modeling approach, it is assumed that the three fluid phases (gas, oil, and water) are homogeneous and uniformly distributed over a cross-sectional area. As the multi-phase fluid flows upward along the pipe from the bottom-hole to the wellhead, a spontaneous mass transfer is considered to occur across the gas and liquid (oil and water) interface. The mass transfer may be bidirectional. However, only the separation of the gas from the liquid phases (oil and water) is considered in this study. Because the pressure continuously decreases during the upward motion of the fluid, no gas-phase dissolution into the liquid phases may occur during flow. Within a particular cross-sectional area, the multiphase fluid has a distribution of the mass fraction for the various phases depending on the local state of properties. While moving upward, the multiphase fluid of various phases may undergo a change in mass fraction distribution along the well.
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