Introduction reservoir engineering 5 ( Unsteady or Transient-State Flow )

 The state of fluid flow is termed unsteady-state flow, if the rate of change of pressure

with respect to time at any position in the reservoir is not zero or constant. It is also

called transient state whose behavior occurs when the boundary effect of the

reservoir has not been felt and at this point, the reservoir is said to be infinite￾acting. It can simply be defined as the flow regime where the distance/radius of

pressure wave propagation from the wellbore has not reached any of the reservoir

boundaries as shown in the figure below. Thus, at a short period of flow, the reservoir

behaves as if it has no boundary, this will continue until the pressure transient gets to

the boundary of the reservoir. Therefore, after the reservoir boundary has been

contacted, the flow will either buildup to steady state or pseudo-steady state flow.

Pseudo-Steady with the Effect of Skin (Tables 1.4, 1.5

and 1.6a, b)

The pressure drop due to skin at the well is

Values of exponential integral,
Ei(
y)

PD vs tD – Infinite

radial system, constant rate at

inner boundary

PD vs tD – Finite radial system with closed exterior, constant rate at inner boundary

reD

¼ 4.5 reD

¼ 5.0 reD

¼ 6.0 reD

¼ 7.0 reD

¼ 8.0 r

Pseudo-Steady or Semi-State Flow

A reservoir attains pseudo-steady state (PSS), if the rate of change of pressure

decline with time is constant. The pressure throughout the reservoir decreases at

the same constant rate, this scenario cannot occur during build-up or falloff tests. In

this state of flow, the boundary has been felt and static pressure at the boundary is

declining uniformly throughout the reservoir. Mathematically, this definition states

that the rate of change of pressure with respect to time at every position in the

reservoir is constant, or a state where the mass rate of production is equal to the rate

of mass depletion. This state can also be referred to as semi-steady state (SSS) or

quasi-steady state.