compressibility

The term "geopressure," introduced in the late 1950s by Charles Stuart of Shell Oil Co., refers to reservoir fluid pressure that significantly exceeds hydrostatic pressure (which is 0.4 to 0.5 psi/ft of depth), possibly approaching overburden pressure (approximately 1.0 psi/ft). Geopressured accumulations have been observed in many areas of the world. In regressive tertiary basins (the geologic setting for most geopressured accumulations), such pressures in sand/shale sequences generally are attributed to undercompaction of thick sequences of marine shales. Reservoirs in this depositional sequence tend to be geologically complex and exhibit producing mechanisms that are not well understood. Both of these factors cause considerable uncertainty in reserves estimates at all stages of development/production and reservoir maturity.

Compressibility is the volume change of a material when pressure is applied. When water is produced, the pressure changes from reservoir pressure, affecting the volume of produced water. Understanding the compressibility of formation water is also important to the understanding of volumes of oil, gas, and water in the reservoir rock. The compressibility of formation water at pressures above the bubblepoint is defined as the change in water volume per unit water volume per psi change in pressure. Water compressibility also depends on the salinity.

In cold heavy oil production with sand (CHOPS) production, the two limiting physical mechanisms for sand are compact growth of the remolded zone as a cylindrical (or spherical or ellipsoidal) body or extension of an anastomosing piping channel system comprising a network of tubes ("wormholes"). These lead to different geometries in situ, although the impact on well productivity may not be quantifiable through measurements. Figure 1 shows a compact zone growth hypothesis for CHOPS. In compact growth, the ratio of the area of the fully yielded zone to the volume enclosed approaches a minimum because a cylindrical or elliptical shape is spatially more compact than a channel network. Discrete zonal boundaries do not really exist: a gradual phase-transition zone develops, although it may be treated mathematically as a thin front, just as in a melting alloy. The complex and diffuse boundary shape is approximated by a geometrically regular shape and a distinct liquefaction front. A circular 2D assumption is simplest for analysis because the radius of the zone and, hence, the pressure gradient can be scaled directly to sand-production volume with no additional assumptions.

The isothermal compressibility is also the reciprocal of the bulk modulus of elasticity. Gas usually is the most compressible medium in the reservoir; however, care should be taken so that it is not confused with the gas deviation factor, z, which is sometimes called the compressibility factor. For gases at low pressures, the second term is small, and the isothermal compressibility can be approximated by cg 1/p. Eq. 4 is not particularly convenient for determining the gas compressibility (See Real gases),because z is not actually expressed as a function of p but of pr. Mattar et al.[2] also developed an analytical expression for calculating the pseudoreduced compressibility; that expression is Then taking the derivative of Eq. 8, the following is obtained: Parameters A1 through A11 are defined after the Dranchuk and Abou-Kassem[3] equation (See Eq. 13 in Real gases).

The following topic describes the compressibility of produced water. The compressibility of formation water at pressures above the bubblepoint is defined as the change in water volume per unit water volume per psi change in pressure. Water compressibility also depends on the salinity. In contrast to the literature, laboratory measurements by Osif[1] show that the effect of gas in solution on compressibility of water with NaCl concentrations up to 200 g/cm3 is essentially negligible. At GWRs of 35 scf/bbl, there is probably no effect, but certainly no more than a 5% increase in the compressibility of brine.

Hydrocarbons occur in a variety of conditions, in different phases, and with widely varying properties, This page will cover the important geophysical properties of pore fluids. Pore fluids are fluids that occupy pore spaces in a soil or rock. Figure 1 shows schematically the relation among the different mixtures. In contrast, if we restrict the temperatures and pressures to those typical of reservoirs, we could again move in this phase "space" by changing compositions. Velocities and densities will be high (close to water) for heavy "black" oils to the left of the figure and decrease dramatically as we move right toward lighter compounds.

This page provides a number of examples that illustrate the mathematical calculations behind the different fundamental gas properties. The density is calculated from Eq. 3 in Gas formation volume factor and density: The formation volume factor is calculated from Eq. 2 in Gas formation volume factor and density: The viscosity is determined using the charts of Carr et al.[1] in Figs.

Characterizing geothermal reservoirs draws on techniques common to petroleum reservoirs. Key differences create special challenges to gaining a good understanding of geothermal reservoirs. This article covers appropriate approaches and caveats for well testing, drawdown/buildup analyses and decline curve analysis for characterizing geothermal reservoirs. Geothermal well testing is similar in many respects to transient pressure testing of oil/gas wells, with some significant differences. Many geothermal wells induce boiling in the near-well reservoir, giving rise to temperature transients as well as pressure transients. Substantial phase change may also take place in the well, further complicating analysis. Pressure tools must be kept in a high-temperature environment for long periods of time, and production intervals are frequently very small portions of overall well depth.

Nevertheless, a decade of efforts has achieved substantial progress toward the correct physical simulation of CHOPS. Adequate simulation models are now available,[1] and progress continues. This section discusses the major physical processes in an attempt to identify first-order controls on CHOPS. Sand liquefaction accompanies all CHOPS processes. In this solid-to-fluid phase transition, porosity plays the same role as temperature in the melting of a solid.

This page introduces how fluid flow in porous media can be translated into a mathematical statement and how mathematical analysis can be used to answer transient-flow problems. This broad area is common to many other disciplines, such as heat conduction in solids and groundwater hydrology. The objective is to introduce the fundamentals of transient analysis, present examples, and guide the interested reader to relevant references. Most physical phenomena in the domain of transient fluid flow in porous media can be described generally by partial differential equations (PDEs). With appropriate boundary conditions and sometimes with simplifying assumptions, the PDE leads to an initial boundary value problem (IBVP) that is solved to find a mathematical statement of the resulting flow in the porous medium.