Afterflows and Buildup Interpretation on Pumping Wells
Authors: Brownscombe E.R. 
Published: December 2007

Summary
Afterflow measurement identifies downhole problems as indicated by the presence of (1) a long fluid column, (2) U-tubing of liquid from the tubing to the annulus, (3) gas coning, and (4) stratification, as evidenced by highpressure gas stringers or high-pressure liquid stringers.

Introduction
Pumping wells are generally older wells with declining production. They are prime candidates for estimation of skin damage, fracture length, reservoir pressure, effective permeability, and other diagnostic information provided by pressure buildup curves. However, the necessity of removing the rods and pumps to place the conventional pressure bomb and then temporarily replacing the rods and pumps to restabilize the well and get the flowing bottomhole pressure, which is essential to well damage estimates, has meant that buildup curves practically never were run on pumping wells.We have been getting buildup curves on pumping wells by determining the liquid level in the annulus acoustically, measuring the surface annulus pressure, and calculating the sandface pressure. This permits following the liquid level and bottomhole pressure before shut-in to check pump operation or well stabilization and then following the buildup from the moment of shut-in. This also gives direct measures of the well storage factor and the afterflows of gas and liquid during buildup.

Calculation of Bottomhole Pressure, Afterflows, and Well Storage
A schematic of a typical well configuration is shown in Fig. 1. There is no packer. The gas and liquid entering the well separate in the annulus, the gas rising up through the fluid column to be produced out of the wing valve and the liquid being pumped out through the tubing.Our well sounder has a three-way valve that maintains a pressure above the annulus pressure in an expansion chamber. Upon signal from a preprogrammed self-contained monitor, a pulse of nitrogen from the expansion chamber enters, the annulus, starting a counter. The returning echo from the fluid stops the counter. The speed of the counter is adjusted by a dial calibrated in acoustic velocity. When setting up, we measure the liquid depth with a collar counting device and adjust the counter speed to give feet depth to liquid directly. Under favorable conditions, our reproducibility is about 1 ft. The setting on the acoustic velocity dial gives the acoustic velocity of the gas in the annulus. Knowing the acoustic velocity, we calculate the specific gravity of the gas in the annulus and its Z factor. Knowing the surface pressure, the annulus area, the depth to liquid, and the Z factor at each point along the curve, we can calculate the gas column weight to get the average pressure in the gas and the standard cubic feet of gas in the annulus at each point. The increase in this gas between successive points directly gives the Mcf/D flowing into the gas space during each time intervalthe gas afterflow.The sandface pressure is calculated starting with the measured surface pressure. The weight of the gas column is calculated by integration knowing the gas gravity, temperature, and average Z factor. This gives the pressure at the top of the fluid column.The weight of the fluid column is calculated stepwise. starting at the top, a depth interval is taken such that the pressure at the bottom of the interval will be 1.2 times the pressure at the top of the interval. The average pressure is 1.1 times the pressure at the top of the interval, the annulus area is known, and the rate of gas flow is the previously measured gas afterflow. From these three data, published correlations give the fraction of liquid in the interval.
JPT
P. 397^