PSS Models

Introduction

Pseudo-steady state (PSS) occurs when there is boundary-dominated flow and the transient period ends. The boundary-dominated flow is a flow regime that starts when the drainage radius of the well reaches the reservoir boundaries. It can also be called Semi-steady state (SSS).

Other descriptions include:

• A flow regime where the pressure at any point in the reservoir declines at the same constant rate over time (I.e., the entire reservoir depletes uniformly).

Mathematically, the above definition can be expressed as:

Where C is a constant.

PSS differs from Steady-State Flow, where the pressure at any point in the reservoir remains constant, and does not change with time. Mathematically, this condition is expressed as:

The very first efforts to analyse well performance were an attempt to quantify deliverability potential, not to estimate properties. The primary well deliverability equation (for gas) was in the form of:

Where:

q = Rate

P_r = Reservoir pressure

P_wf = Flowing pressure

n = 1 for laminar flow

n = 0.5 for turbulent flow.

PSS and Drainage Area

PSS may also occur in located regions of the greater reservoir if the drainage area of a subject well is stabilized.

In the figure below, T1 represents an earlier time than T2 (and each colour represents a different well). As time progresses, drainage area of the RED well increases but will eventually stabilize due to offset production. In cases where two DIFFERENT coloured streamlines run parallel, an apparent no-flow boundary has developed.

In PSS, if one were to perform an FMB and Rate Transient Analysis (RTA) on a particular well, the estimated drainage volume would represent effectively the area of the colored streamline.

See Also:

References:

• Streamline Simulation, Marco R. Thiele StreamSim Technologies, Inc. International Forum on Reservoir Simulation September 3rd-7th, 2001, Schloss Fuschl, Austria