Compressibility of Natural Gases

For a liquid phase, the compressibility is small and usually assumed to be constant. For a gas phase, the compressibility is neither small nor constant.

By definition, the isothermal gas compressibility is the change in volume per unit volume for a unit change in pressure or, in equation form:

where cg = isothermal gas compressibility, 1/psi

Incompressible Fluids

An incompressible fluid is defined as the fluid whose volume (or density) does not change with pressure, i.e.:

Incompressible fluids do not exist; this behavior, however, may be assumed in some cases to simplify the derivation and the final form of many flow equations.

Ahmed (2001)

Isothermal Compressibility Coefficient of Crude Oil

Isothermal compressibility coefficients are required in solving many reservoir engineering problems, including transient fluid flow problems, and they are also required in the determination of the physical properties of the undersaturated crude oil.

By definition, the isothermal compressibility of a substance is defined mathematically by the following expressions:

• In terms of fluid volume:

• In terms of fluid density:

where V and ρ are the volume and density of the fluid, respectively.

For a crude oil system, the isothermal compressibility coefficient of the oil phase co is defined for pressures above the bubble-point by one of the following equivalent expressions:

where

• co = isothermal compressibility, 1/psi
• ρo = oil density lb/ft^3
• Bo = oil formation volume factor, bbl/STB

At pressures below the bubble-point pressure, the oil compressibility is defined as:

where Bg = gas formation volume factor, bbl/scf

Ahmed (2001)

Pseudosteady-State Flow

When the pressure at different locations in the reservoir is declining linearly as a function of time, i.e., at a constant declining rate, the flowing condition is characterized as the pseudosteady-state flow. Mathematically, this definition states that the rate of change of pressure with respect
to time at every position is constant, orIt should be pointed out that the pseudosteady-state flow is commonly referred to as semisteady-state flow and quasisteady-state flow.

Ahmed (2001)

Unsteady-State (Transient) Flow

The unsteady-state flow (frequently called transient flow) is defined as the fluid flowing condition at which the rate of change of pressure with respect to time at any position in the reservoir is not zero or constant. This definition suggests that the pressure derivative with respect to time is essentially a function of both position i and time t, thus
Ahmed (2001)

Steady-State Flow

The flow regime is identified as a steady-state flow if the pressure at every location in the reservoir remains constant, i.e., does not change with time. Mathematically, this condition is expressed as:The above equation states that the rate of change of pressure p with respect to time t at any location i is zero. In reservoirs, the steady-state flow condition can only occur when the reservoir is completely recharged and supported by strong aquifer or pressure maintenance operations.

Ahmed (2001)

Flow Regimes

There are basically three types of flow regimes that must be recognized in order to describe the fluid flow behavior and reservoir pressure distribution as a function of time. There are three flow regimes:

• Steady-state flow


• Unsteady-state flow


• Pseudosteady-state flow

Ahmed (2001)