Pressure data filtering and horizontal well test analysis case study
Authors: Osman Magdy S. , Stewart G. 
Published: December 2007

Abstract
Two innovative approaches were used to filter pressure data. The analysis started by reviewing field geology. Core data were used to obtain average values for horizontal and vertical permeabilities. Production logging data were analyzed to get the effective well length for Well (1) and Well (2).
Well test analysis proceeded at this stage. A numerical model was also constructed to confirm the results of the analysis. Some aspects of representing horizontal well in numerical reservoir simulator were discussed.

Data Filtering
The total number of the data points during build up period for well (1), and well (2) are in the range of 15000, and 19000 points respectively, equally spaced in time. Typical well test interpretation packages normally use a limited number of points per flow period to conduct the analysis. The way these points are chosen is normally very basic. For example, one point is chosen every nth number of data points, or a certain number of points is chosen per log cycle. To illustrate the drawback of this method, an example is given here. A point was chosen every 50 points and a log-log plot of this data is shown in Figure 1. It is obvious that any useful analysis is impossible on this set of data at its current state. Normally well interpretation software will allow the user to apply some sort of smoothing to the pressure data. This is a subjective procedure dependent on the user. There is always a risk of over smoothing and smearing the pressure data trend or under smoothing and masking the pressure data trend.

Butterworth Digital Filter Method
Using digital filtering technique can provide us with robust and objective method of getting rid of noise. If we consider a signal p(t) contaminated by a noise signal n(t). Then the total measured signal m(t) is given by:
(1)
If we plot the spectral power density of the measured signal m(t) we cannotice that the power spectrum of the signal is sticking up on a continuous noise spectrum, (Ref. 1).
Ideally we want to apply an ideal low pass filter to the data to get rid of most of the noise signal. Unfortunately the implementation of an ideal filter is impossible, but there are practical approximations to it (Ref. 2). One of these approximations is the Butterworth filter. A typical response of a Butterworth filter is shown in Figure 2. This methodology is applied in our case. A plot of the power spectral density of the pressure of well (1) is shown in Figure 3. A digital Butterworth filter with a frequency cutoff of 0.07 was chosen after inspecting the spectral power density plot. The digital filtering was carried out in the frequency domain, and then was transformed back to the time domain. A plot of the power spectral density of well (1) after filtering is shown in Figure 4. The first data points in the data set will be spoiled due to transient response of the filter, this is not important, since the first data points are dominated by well bore storage. The spoiled data points were then replaced by the original data points for the 1st 300 points. A plot of the pressure derivative after using this method is also shown in Figure 5. Now we can see clearly the trend of the pressure derivative. The same method was applied to the pressure data of well (2).

Most Representative Pressure Point (MRPP) Method
Another method for eliminating noisy points was developed. P. 375