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It is known, that the Well Test consists of only a few principal types of tests, there are Drawdown Test, Buildup Test, Injection Test, Falloff Test, Interference Test, Drill Stem Test. In the tutorial the Buildup Test has been considered. It is a basic transient well-testing method, which has been used in the petroleum industry.
The main purpose of performing a Buildup test is to determine the wellbore damage (skin) and the reservoir permeability. However, during the course of a Buildup, it is possible to identify reservoir boundaries. If all the reservoir's boundaries are contacted during the Buildup, the size of the reservoir can also be determined. This technique demands the well work at a constant rate as long as enough to establish a stabilized pressure distribution before shut-in. The pressure is measured at once before the shut-in and recorded as a function of time during the shut-in period. An ideal pressure build-up test is presented on Fig. 1:
Fig. 1. Schematic Buildup Test
(tp , Î”t - production time and running shut-in time respectively)
The given Buildup test might be presented on Fig. 2 and has been characterised by following parameters: q=581 STB/D, tp=100000 hours, Î”t=69.1 hours. Regarding on geology, the test was made in a production well drilled in a fluvial reservoir. Other initial data presented in following table:
rw (wellbore radius), ft
h (formation thickness), ft
Bo (oil formation volume factor), RB/STB
Î¼o (oil viscosity), cp
Ct (total compressibility), psi^-1
Table 1. Initial data
The main purposes of this tutorial: understanding theoretical principles of Well Test, pressure data analysis, marking out flow regimes and reservoir parameters calculating.
2. Well Test Analysis
2.1 Diagnostic Analysis
Diagnostic Analysis is based on Diagnostic Plot - log-log plot of drawdown and its logarithmic derivative vs. time. By the Diagnostic Analysis three flow regimes are usually remarkable: Early Time Region - wellbore storage dominated flow, Middle Time Region - infinite acting flow, and Late Time Region - steady-state (or pseudo steady-state) flow regime at late times.
Early time region
Wellbore storage and wellbore damage are the principal factors that influence on this region. Wellbore storage - is mainly effected by fluid expansion (compressibility) or changing fluid level in the well. Wellbore damage - reservoir fluid flow pressure changing through damaged zone near the well (due to drilling and completion operations). ETR is the flow regime identified as s line with a unit slope on a bi-logarithmic pressure vs. time plot. In a hydraulically fractured well ETR presented as a ½ or ¼ slope and associated with a linear flow. It might be noted that at the region value of skin can be estimated by the analyzing of derivative hump. In this tutorial at Early Time Region unit slope is not observable (Fig.3), therefore value of wellbore storage coefficient cannot be determined.
Middle time region
This region reflects the infinite-acting flow regime at a middle time period, when ETR is done (wellbore storage effect is stopped) and pressure profile does not achieve boundaries or impermeable faults. MTR is a region identified as a line with a zero slope (derivative plateau - DP) on the diagnostic plot (Fig. 3). During this period can be observed few different types of flow, but in most times it assumed to be radial or pseudoradial. On a semilog plot the regime may be marked out as a straight line with a constant slope. The further description of radial flow is exhibited in the section below.
Late time region
The region might be identified by a changing a trend line (going up or down) with a different slope on a diagnostic plot. LTR get on when pressure profile reached a boundary (unit slope line). Different reservoir geometry (and so fluid flow characteristics) may leads to different fingerprints. Given test represents a half slope straight line and indicates linear flow regime (Fig. 3).
Type curve method of matching was developed by Ramey. This method applies for reservoir model selection and estimating some reservoir parameters. The procedure of type matching in PanSystem program is sufficiently simple. There are two types of curves: first one represents tD/Dc vs. PD (dimensionless ratio vs. dimentionless pressure), second - dimensionless logarithmic derivative. Each type curve has an individual value of CDe2S (Fig. 4). After the matching radial flow homogeneous reservoir with parallel boundaries was chosen. Selected specified curve gives permeability, skin and wellbore storage coefficient.
2.2. Specialised Analysis
Radial flow analysis
Infinite acting radial flow , which occurs due to Buildup Test might be specified by formula obtained from case of superposition:
where (tp+dt)/dt - is a Horner time. On a semi-log Horner's plot radial flow detected as a straight line. By the slope of this line average permeability may be found from formula:
Skin factor might be estimated by equation:
where P* - pressure taken from Horner plot (intersection between y-axis and infinite acting flow straight line).
Estimated results presented in Table 2.
k (permeability), md
k*h (permeability*thickness), md.ft
P* (extrapolated pressure), psia
Rinv (radius of investigation), ft
FE (flow efficiency)
dPS (skin effect), psia
S (skin factor)
Table 2. Estimated results from Radial Flow analysis
Linear flow analysis
Infinite acting radial flow will be done when pressure drop achieve the boundary. It might be changed to hemi-radial and later to linear flow. After carefully analyzing of diagnostic plot it might be seen half slope line and second horizontal line - it is a obvious sign of a parallel impermeable boundaries. Linear flow analyse is based on pressure vs. square root of time plot. It may be used to estimate geometry parameters, such a distance to the nearest boundary D and width of channel W (scheme below):
Due to linear flow relation pressure vs. square root of time lies on straight line, by this slope can be determined width of channel (Fig. 6). Results of linear flow analysis presented in table below:
W (reservoir width), ft
Sconv (flow convergence skin factor)
P* (computed initial pressure), psi
Table 3. Estimated results from Linear Flow analysis
2.3. Simulation / History Matching
Auto matching process based on numerical algorithms for parameters optimization by non-linear regression. Parameters divided from the matching depends on first point for iteration and range.
Quick matching - is a manual type of matching, when apply selected model parameters for best fit with given data. It can be seen, that results of matching satisfied the tolerance. The derived results data are shown on plots (Fig. 7, 8, 9).
3 Well Test Interpretation
Reservoir parameters can be obtained by several different methods: by seismic, core analysis, well logging, petrophysics analysis and etc. By the Well Test interpretations
The Well Test gives the opportunity to not only for defining such reservoir parameters as the average permeability, the skin factor, PVT properties more accurately, but also to identification the geometry of reservoir. Consequently the input data for reservoir simulation operations becomes more accurate. It is patient, that source of data have great influence on result. Misinterpretation of the model can leads to wrong parameters. The problem might be excluded by comparing with additional information received from other disciplines, for example geology, core analysis, seismic and petrophysics. For that reason interconnecting of whole available information must take into account at well test design and analysis.
4 Summary and Conclusions
In the given test it was defined the radial homogeneous model of the reservoir, with the wellbore storage effect and parallel faults boundary. Positive skin factor indicates presence of the damage zone near the well.
Taking everything into consideration it can be concluded, that the well is situated into "channel" about 305 ft width and the distance to the nearest boundary is about 148 ft. Obtained results are presented in the following table:
Type curve analysis
Permeability (md), k
Wellbore storage coefficient (bbl/psi), Cs
Skin factor, S
Distance to boundary (ft), D
Width of canal (ft), L