## 15 Mayıs 2008 Perşembe

### Incompressible Fluids

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

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

where Bg = gas formation volume factor, bbl/scf

Ahmed (2001)

### Pseudosteady-State Flow

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

Ahmed (2001)

### Steady-State Flow

Ahmed (2001)

### Flow Regimes

### Productivity Index

*Productivity Index*. Defined by the symbol J, the productivity index is the ratio of the total liquid flow rate to the pressure drawdown. For a water-free oil production, the productivity index is given by:

where

- Qo = oil flow rate, STB/day
- J = productivity index, STB/day/psi
- avg(Pr) = volumetric average drainage area pressure (static pressure)
- pwf = bottom-hole flowing pressure
- Deltap = drawdown, psi

The productivity index is generally measured during a production test on the well. The well is shut-in until the static reservoir pressure is reached. The well is then allowed to produce at a constant flow rate of Q and a stabilized bottom-hole flow pressure of pwf. Since a stabilized pressure at surface does not necessarily indicate a stabilized pwf, the bottom-hole flowing pressure should be recorded continuously from the time the well is to flow. The productivity index is then calculated from the above Equation.

It is important to note that the productivity index is a valid measure of the well productivity potential only if the well is flowing at pseudosteadystate conditions. Therefore, in order to accurately measure the productivity index of a well, it is essential that the well is allowed to flow at a constant flow rate for a sufficient amount of time to reach the pseudosteady-state as illustrated in the Figure. The figure indicates that during the transient flow period, the calculated values of the productivity index will vary depending upon the time at which the measurements of pwf are made.

Since most of the well life is spent in a flow regime that is approximating the pseudosteady-state, the productivity index is a valuable methodology for predicting the future performance of wells. Further, by monitoring the productivity index during the life of a well, it is possible to determine if the well has become damaged due to completion, workover, production, injection operations, or mechanical problems. If a measured J has an unexpected decline, one of the indicated problems should be investigated.

## 14 Mayıs 2008 Çarşamba

### Cricondentherm, Cricondenbar and Critical Point

- Cricondentherm (Tct)—The Cricondentherm is defined as the maximum temperature above which liquid cannot be formed regardless of pressure (point E at Pressure-Temperature Diagram). The corresponding pressure is termed the Cricondentherm pressure pct.
- Cricondenbar (pcb)—The Cricondenbar is the maximum pressure above which no gas can be formed regardless of temperature (point D at Pressure-Temperature Diagram). The corresponding temperature is called the Cricondenbar temperature Tcb.
- Critical point—The critical point for a multicomponent mixture is referred to as the state of pressure and temperature at which all intensive properties of the gas and liquid phases are equal (point C at Pressure-Temperature Diagram). At the critical point, the corresponding pressure and temperature are called the critical pressure pc and critical temperature Tc of the mixture.

### References

*Reservoir Engineering Handbook,*Second Edition, Gulf Professional Publishing, 2001

### Pressure-Temperature Diagram

*phase diagrams*. One such diagram is called the

*pressure-temperature diagram*.

Figure shows a typical pressure-temperature diagram of a multicomponent system with a specific overall composition.

These multicomponent pressure-temperature diagrams are essentially used to:

- Classify reservoirs
- Classify the naturally occurring hydrocarbon systems
- Describe the phase behavior of the reservoir fluid