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This report presents well test analysis and interpretation of production vertical well. Performed test is pressure build-up test which was done after 100000 hours of production. Well worked with the rate 581 bbl/day and then was stopped for the period of 69.1 hours. Thus, we have 85 points of measurements. Figure 1 presented pressure and rate change behavior. Input date, which were used in calculation present in table 1.
According to geological data, it is possible to consider that the well is drilled into the fluvial type reservoir. Hence, the parallel faults model for the boundary conditions was chosen.
This region reflects influence on flow behavior of wellbore storage, fluid within the well and damage region near wellbore. From figure 2 we can see that wellbore storage dominated part of Early Time Region, but in this case unit slope is not good recognize. This slope be seen from the Type Curve graph (Figure 3) that this region occurs much earlier in time. This is means that well bore storage coefficient calculated from the log-log plot is not accurate, but using type curve matching, this coefficient can be determine more exactly. Next diagnostic characteristic which might be possible to observe is 'hump'. The height of 'hump' shows influence of the damage near wellbore area - skin factor value. Skin factor in the case of pressure build-up analysis is caused by afterflow. From figure 3 we can see that first point doesn't match theoretical curve well, it can be explained as some disturbance during measurement.
2.1.2. Middle time region (MTR)
The Middle Time Region is corresponds to the infinite-acting homogeneous reservoir and characterized by radial flow. This region is also identified on the Figure 2. The pressure disturbance has not already reached boundaries. The fingerprint of this flow pattern is the so-called plateau on the derivative plot - the flat part, which can be recognized on the figure 2. Radial flow may be identified there and this flow is continued until the pressure profile reaches outer boundary of constant pressure or no flow boundaries such as faults. In our case from the log-log plot it is possible to determine radial flow. Also using special analysis we can estimate values of skin factor and permeability.
2.1.3. Late time region (LTR)
The Late Time Region corresponds to the linear flow regime and starts when pressure disturbance achieves boundaries. Type Curve Matching (figure 3) confirmed our supposition about the linear flow regime in the fluvial type of reservoir. Curve corresponding to the linear flow model, and accordingly can be described by the parallel faults model, best fits our data.
2.1.4. Type curve matching
The type curves are help to identify the appropriate model and determinate the primary reservoir parameters. In Pan System software we comparing different derivative curves in log-log plot with data and chose similar curves for determination reservoir parameters. Type curves also may be used to estimate the influence of boundaries. Figure 3 shows type curve matching analysis.
The results of calculation parameters from log-log plot and after type curve matching are represented in Table 2.
2.2. Specialized Analysis
2.2.1. Radial Flow Analysis
Infinite-acting or transient flow regime is known as the period in which the propagating pressure disturbance has not yet encountered any boundaries. Using diagnostic log-log plot Middle Time Region was defined. During an infinite-acting period pressure is described by next equation:
In this regime, pressure behavior is described by the expression where there is logarithmic dependence on time. The bottom-hole pressure will consequently build-up to the initial reservoir pressure.
Equation (2) describes a straight line with the slope m and intercept P*=Pi:
The intercept P* corresponds to ln((tp+Δt)/Δt) equal to zero or (tp+Δt)/Δt=1 which implies Δt>>tp. Analysis show that in our case from Horner plot: for a build-up test is true. Also reservoir average permeability can be determined as:
Reservoir kh product can be determined from the slop of the build-up test. Skin factor can be calculated from equation:
where m - measured slope of the build-up Horner plot.
Parameters obtained in this log presented in table 3 (figure 4).
2.2.2. Linear Flow Analysis
The Linear Flow Plot allows along with permeability and skin factor obtain information about geometry of the reservoir, notably interval to the boundaries and width of the channel. Logarithmic derivative of the pressure is a linear function of time with the slope of 0.5. Figure 5 illustrated the linear region. Radial flow analysis results are correspond The values of reservoir permeability and skin factor. Initial pressure Pint, the pressure at equivalent time equal zero, and the mechanical skin factor, help to calculated Flow convergence skin factor. Width of reservoir body and distance to nearest boundary can be calculated using obtained parameters. Table 4 illustrated results of calculation.
Intercept of the approximating line with the vertical line and presents computed initial pressure in the reservoir determined extrapolated pressure:
Analysis of data shown that well is placed between two parallel faults.
2.3. Simulation / History Matching
Auto match process is used for parameter optimization by non-linear regression to obtain the parameter set that best matches the plotted test data. Commencing from the initial starting values it is searching optimum parameters within predetermined boundaries. Figures 6 - 9 illustrated different plots with approximating curves. Table 5 represented results of auto match.
Wellbore storage coefficient (bbl/psi)
Results obtained by the auto matching process are quite differs from the results obtained from the conventional calculations. The reasons of that are: very high level of noise and small amount of points, MTR lasts less then one logarithmic cycle, The MTR is poorly expressed.
3. WELL TEST INTERPRETATION
Well test interpretation examines as an opportunity to determine reservoir parameters by comparing model with given input data. In build up test we considered radial homogeneous model of the reservoir with wellbore storage and boundary model of parallel faults. Then these models were confirmed by auto match process. Consequently it is possible to say that model describes this reservoir sufficiently accurate. Radial homogeneous flow model correspond comparatively uniform structure of the reservoir without layering. Presence of positive skin factor tell about some damage zone around the well. According supposed model of two parallel boundaries we can assume that reservoir has elongate form. It is possible to draw a conclusion that reservoir compose of channel sandstones of braided river about 301 ft width and well penetrates them at the distance of 158 ft from the nearest boundary. The received conclusions allows is simulation of fluid flow, reservoir modelling, determination of reservoir parameters such as type and number of boundaries, size, shape of reservoir, k*h, permeability and skin factor, in field management and others. Buy using these data many models may be constructed and they can describe the reservoir adequately enough. It is necessary to take into account that all models are wrong. But if we want obtain sufficiently adequate model we must use additional information, such as seismic, petrophysics, logging and geology, and correct our date.
4. SUMMARY AND CONCLUSIONS
In this tutorial initial date interpreted using the model of radial homogeneous flow and two parallel boundaries. Table 6 illustrated obtained results.
Type curve plot
Radial flow plot
Linear flow plot
Wellbore storage coefficient, bbl/psi
Width of channel (L1+L2), ft
The following results are sufficiently; good representation of the reservoir properties. But these result were obtained by the analysis of the data with relatively small amount of points and high level of noise, and proceed from this using these results must be very carefully.