Reservoir simulation is used to predict the flow of fluids in an underground reservoir. The fluid flow may include oil, gas and water. Such reservoir forecasting is important in reservoir management and estimating the potential recovery from a reservoir.
Reservoir simulation is well known throughout the oil industry and in the scientific literature. A good primer on the principles behind reservoir simulation is K. Aziz and A. Settari, Petroleum Reservoir Simulation, Elsevier Applied Science Publishers, London (1979). Another description of how reservoir simulation is generally performed is described in U.S. Pat. No. 6,052,520 to Watts III et al. These references, are hereby incorporated by reference in their entireties.
The following are general steps taken in a conventional reservoir simulation. First, a reservoir is selected for which the rock and fluid properties are to be modeled and simulated. The reservoir is modeled and discretized into a plurality of cells. Nonlinear governing equations are constructed for each cell, generally in the form of finite difference equations, which are representative of properties of rocks and fluids in the reservoir. Examples of rock properties include porosity, capillary pressure, and relative permeability for each phase of fluid (oil, water, gas.) Examples of fluid properties include oil viscosity, oil formation factor (Bo), and pressure, temperature, and saturation in each of the cells. Nonlinear terms in these equations are linearized to arrive at a set of linear-equations for each timestep of the simulation. These linear equations can then be solved to estimate solutions for unknowns such as pressure and saturation in the cells. From these values of pressure and saturation other properties can be estimated including the overall production of oil, gas and water from the reservoir in a timestep. The aforementioned steps are repeated over many such timesteps to simulate fluid flow over time in the reservoir.
One of the key properties needed in reservoir simulation is the permeability of a rock to flow. Absolute permeability K is a measure of a rock's ability to transmit flow and can vary greatly throughout a reservoir and surrounding formations. When gas, oil and water move through porous rock, they do not move at equal velocities. Rather, the fluids compete with one another. Relative permeability, kr, is the ratio of the effective permeability, ke, when more than one fluid is present, to the absolute permeability K. Effective permeability ke is the measured permeability of a porous medium to one fluid when another is present. The relationship between relative permeability kr and saturation S depends on the reservoir rock and fluid and may vary between formations. Also, the relative permeability kr depends on the relative proportion of the fluids present, i.e. fluid saturations.
FIG. 1 illustrates a typical relative permeability krg versus saturation Sg curve for gas. Gas cannot flow at any appreciable rate until gas saturation reaches a minimum threshold value. Looking to FIG. 1, this threshold value is referred to as critical gas saturation Sgc0 and begins at a value of approximately 0.03 or about 3% saturation. At the other end of the curve is an endpoint relative permeability krgro0 which is the gas relative permeability value krg at which movement of residual oil remaining in the rock is minimal. As reservoir rock will always contain a minimal amount of residual oil, gas saturation cannot reach 100%. The total percentage of saturation must add up to 100%. In this case, there is a maximum 76% gas saturation Sg and 24% residual oil saturation Sorg. As seen in FIG. 1, the maximum relative permeability, krgro0, occurs at a saturation of approximately 0.76 with kr=0.40. These values of Sgc0 and krgro0 shall be referred to as endpoint baseline values for gas saturation Sg and relative permeability krg.
Ideally, relative permeability curves are developed through laboratory experiments on core samples taken from reservoirs for which reservoir simulation is to be performed. For example, displacement tests may be used to develop the relative permeability krg vs. saturation Sg curves. Such tests are well known. Particularly well known displacement test procedures are described in E. F. Johnson, D. P. Bossler, and V. O. Naumann, Calculations of Relative Permeability from Displacement Experiments, Trans. Am. Inst. Mining Engineers, Volume 216, 1959, pp. 370-378 and S. C. Jones and W. O. Roszelle, Graphical Techniques for Determining Relative Permeability from Displacement Experiments, Journal of Petroleum Engineering, Volume 30, pp. 807-817 (1978). These displacements experiments are usually conducted at slow depletion rates as it is commonly accepted that permeability curves are generally independent, of how fast gas flows through reservoir rock.
Alternatively, if core samples are not available, the relative permeability krg versus saturation Sk curves can be theoretically created. For example, the curves may be developed from comparable analogue reservoirs.
Once relative permeability krg versus saturation Sg curves have been obtained, then the relative permeabilities krg to be used in a reservoir simulation can simply be obtained from these curves assuming saturations Sg in the cells of the reservoir model are known. The saturations Sg are generally known either from initial conditions established at the beginning of a simulation, from the last timestep in the simulation or else from calculations within an iteration in a timestep.
The production of heavy oil is initially driven primarily by oil pressure. Heavy oil may be considered to include oil having an API gravity 20° or less. Significant quantities of gas are often entrained within the heavy oil while under high reservoir pressures. After sufficient production of heavy oil from a reservoir, the pressure in portions of the reservoir may drop below the bubble point pressure. At this pressure, gas readily comes out of solution from the heavy oil. Once sufficient gas has been released from the oil, the gas is believed to form a continuous phase and gas can flow through the reservoir and the rate of production of gas is significantly enhanced. As indicated above, the saturation Sg at which there is an initiation of gas flow is referred to as the critical gas saturation or Sgc. FIG. 11 shows a graph of cumulative gas produced from a core sample versus time in minutes. The breakpoint in the curve shown there represents Sgc.
Tests have shown that the amount of oil recovery from a heavy oil reservoir is dependent upon the rate of depletion of the reservoir. Often higher rates of depletion will lead to an overall enhanced oil recovery. As the mechanisms of heavy oil solution gas drive are not well understood, reservoir simulators typically utilize static gas relative permeability krg versus saturation Sg curves, such as the one seen in FIG. 1, which are independent of fluid flow or depletion rates. Once these curves are developed for respective types of rock which are to be modeled, the curves will remain the same (i.e., endpoints of Sgc0 and krgro0 remain fixed) throughout the reservoir simulation regardless of the rate of flow through the reservoir cells. Such assumptions that permeability curves are static for general reservoir simulation of hydrocarbon bearing subterranean formations containing non-heavy oil are generally satisfactory.
However, in the case of heavy oil, non-equilibrium solution gas drive (“Foamy Oil”) is a significant production mechanism affecting critical gas saturation Sgc and oil recovery. Currently, understanding of heavy oil solution gas drive at all scales (pore, core and field) is limited. Conventional reservoir simulators fail to accurately account for this solution gas drive in forecasting fluid flow in a reservoir. This is a significant shortcoming often resulting in forecasts which underestimate heavy oil production. The present invention overcomes this shortcoming by accounting for the effects of heavy oil solution gas drive.