Shale swelling during drilling is attributed to osmotic pressure, where low-salinity water enters the shale pores to cause swelling. Low-salinity water injected into high-salinity Bakken formation could similarly enter the matrix pores to displace oil by counter-current flow observed in core experiments. As a result, we believe, low-salinity water can potentially enhance oil recovery from oil-wet Bakken formation.In this paper, we report experimental and numerical modeling studies we conducted to evaluate the potential of lowsalinity waterflooding in Bakken. For laboratory experiments, we used horizontal core plugs drilled parallel to the bedding plane.The mathematical included osmotic pressure, gravity and capillary effects. In the mathematical model, the osmotic pressure mass transfer equations were calibrated by matching time-dependent salinities in a published laboratory osmotic pressure experiment. We also modeled oil recovery for a Bakken core using our osmotic pressure mass transport model. The results indicate that osmotic pressure promotes counter-current flow of oil from both the water-wet and oil-wet segments of the core.

No abstract

No abstract

a b s t r a c tSome shale gas and oil wells undergo month-long shut-in times after multi-stage hydraulic fracturing well stimulation. Field data indicate that in some wells, such shut-in episodes surprisingly increase the gas and oil flow rate. In this paper, we report a numerical simulation study that supports such observations and provides a potentially viable underlying imbibition and drainage mechanism. In the simulation, the shale reservoir is represented by a triple-porosity fracture-matrix model, where the fracture forms a continuum of interconnected network created during the well stimulation while the organic and inorganic matrices are embedded in the fracture continuum. The effect of matrix wettability, capillary pressure, relative permeability, and osmotic pressure, that is, chemical potential characteristics are included in the model.The simulation results indicate that the early lower flow rates are the result of obstructed fracture network due to high water saturation. This means that the injected fracturing fluid fills such fractures and blocks early gas or oil flow. Allowing time for the gravity drainage and imbibition of injected fluid in the fracture-matrix network is the key to improving the hydrocarbon flow rate during the shut-in period.

Recent laboratory studies and analyses (Lai et al. Presented at the 2009 RockyMountain Petroleum Technology Conference, 14-16 April, Denver, CO, 2009) have shown that the Barree and Conway model is able to describe the entire range of relationships between flow rate and potential gradient from low-to high-flow rates through porous media. A Buckley and Leverett type analytical solution is derived for non-Darcy displacement of immiscible fluids in porous media, in which non-Darcy flow is described using the Barree and Conway model. The comparison between Forchheimer and Barree and Conway non-Darcy models is discussed. We also present a general mathematical and numerical model for incorporating the Barree and Conway model in a general reservoir simulator to simulate multiphase nonDarcy flow in porous media. As an application example, we use the analytical solution to verify the numerical solution for and to obtain some insight into one-dimensional non-Darcy displacement of two immiscible fluids with the Barree and Conway model. The results show how non-Darcy displacement is controlled not only by relative permeability, but also by non-Darcy coefficients, characteristic length, and injection rates. Overall, this study provides an analysis approach for modeling multiphase non-Darcy flow in reservoirs according to the Barree and Conway model. List of SymbolsA Cross-section area of flow, m 2 A i j Common interface area between the connected blocks or nodes i and j, m 2 C β non-Darcy constant, m 0.25 D Depth from a datum, m D i Distance from the center of block i to the common interface of blocks i and j f β Fractional flow of phase β, fraction flow β mass flux of fluid β, kg/s g Gravitational acceleration constant, m/s 2 k d Darcy permeability, m 2 k min Minimum permeability at high rate, m 2 k mr Minimum permeability ratio, relative to Darcy permeability, fraction k rβ Relative permeability to fluid β, fraction N Total number of nodes/elements/gridblocks of the grid P β Pressure of fluid β, Pa P cgo Gas-oil capillary pressure, Pa P cgw Gas-water capillary pressure, Pa P cow Oil-water capillary pressure, Pa ∇ P Pressure gradient, Pa/m q Injection rate, m 3 /sec q β Mass sink/source per unit volume for the fluid β, kg/m 3 Q Fluid volumetric flow rate, m 3 /s Q βi Mass sink/source term at element i, for the fluid β, kg/m 3 R i Residue term of mass balance at element i, kg S β Saturation of fluid β, fraction S β Average saturation of fluid β, fraction t Time step size, s V i Volume of block i, m 3 v β Velocity of fluid β, m/s x sw Location of the specific saturation, m Greeks α Angle from horizontal plane, Degree β Non-Darcy coefficient, 1/m ρ β Fluid density of fluid β, kg/m 3 μ β Viscosity of fluid β, Pa s τ Characteristic length, 1/m φ Effective porosity of the medium, fraction ∇ Flow potential gradient, Pa/m