Reservoir Engineering - Effects of Transient Conditions in Gas Reservoirs

A simple disturbance in a gas reservoir travels with a finite velocity which is nearly independent of the amplitude of the disturbance. As a result very complex transients may be set up which seriously affect observation at a well. The time of transient is much longer than commonly supposed. INTRODUCTION A change in pressure at a gas well is not propagated through the reservoir instantaneously but with a definite fin- ite velocity. Knowledge of the period ! of this transient is of value because: 1. Observations of pressure and flow-rate during the transient may affect interpretation of back-pressure tests. 2. Interference effects between wells may be used to determine continuity of formation. 3. Additional information concerning the physical characteris- tics may possibly be deduced from the behavior of a well during the transient. MATHEMATICAL DEVELOPMENT It will be assumed that the well is initially closed in and that the pressure is constant throlughout the reservoir. As the initial disturbance passes outward from the well it is further assumed that a logarithmic pressure distribution is established between the most distant point reached and the well, so that: <l> = ((/)r-<t>w) I ------------ + (/) . (1) Manuscript received at office of the Branch September 15. 1948. Paper presented at Branch Fall Meeting, Dallas. Texas. Oct. 4-6, 1948. r. = distance to any point between r and rw r = radius of drainge iw= radius of well (/) = potential (P for incompressible fluids, P2 for perfect gases) Up to the time the effect reaches the point r the production from the well will be: W= (Pr-P,,,) . (2) i b W = volume produced t = sand thickness F = fractional porosity Pr = reservoir pressure Pm = average pressure between r and rw Pb = atmospheric Pressure All pressures will subsequently be stated in atmospheres and the constant Pb will be omitted. This will be produced at a rate: dw t k (Pr³-PW2) do d 0 - . (3) log — Pw = pressure at the well k = permeability 0 = time = viscosity