How to Draw a Straight Line 1977

Reservoir Engineering and Secondary Recovery

M. Ibrahim Khan , M.R. Islam , in The Petroleum Engineering Handbook: Sustainable Operations, 2007

6.2.2.1 Pressure drawdown tests

Pressure drawdown tests can be defined as a series of bottom-hole pressure measurements completed during a period of flow at a constant producing rate. Many traditional analysis techniques are derived using the drawdown test as a basis. Generally, the well is closed in earlier to the flow test period of time because it is necessary to allow the pressure to become equal throughout the formation. Moreover, the well is shut-in until it reaches a constant reservoir pressure before testing. In a drawdown test, a well, now static, stable, and shut-in, is open to flow. It is completed by producing the well at a constant flow rate while continuously recording bottom-hole pressure. When a constant flow rate is attained, the pressure measuring equipment is lowered into the well. Figure 6-1 shows the production and pressure history during a drawdown test. It may take a few hours to several days, depending on the objectives of the test. Drawdown tests are normally recommended for new wells. If a well has been closed for some reason, a drawdown test may also be done. It is also recommended for a well where there are uncertainties in the pressure build-up interpretations. The main advantage of drawdown testing is the possibility for estimating reservoir volume. The shortcomings of this method are:

Figure 6-1. Idealized rate schedule and pressure response for drawdown testing.

Redrawn from Earlougher (1977). Copyright © 1977

1.

It is difficult to build the well flow at a constant rate, even after it has stabilized.

2.

The well condition may not initially be static or stable, especially if it was recently drilled or had been flowing previously.

3.

A single permeability value is obtained for the entire well.

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Pressure Drawdown Testing Techniques for Oil Wells

Amanat U. Chaudhry , in Oil Well Testing Handbook, 2004

4.1 Introduction

A pressure drawdown test is simply a series of bottom-hole pressure measurements made during a period of flow at constant production rate. Usually the well is closed prior to the flow test for a period of time sufficient to allow the pressure to stabilize throughout the formation, i.e., to reach static pressure. As discussed by Odeh and Nabor, ¹ transient flow condition prevails to a value of real time approximately equal to

Semi−steady-state conditions are established at a time value of

In this section, we will discuss drawdown tests in infinite-acting reservoirs and developed reservoirs including two-rate, variable, multiphase, multi-rate drawdown tests. An analysis technique applicable to pressure drawdown tests during each of these periods including other types of tests is presented in the following sections.

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Completion and output testing

Sadiq J. Zarrouk , Katie McLean , in Geothermal Well Test Analysis, 2019

6.8 Production pressure transient: drawdown/build-up

Drawdown tests are not commonly applied in geothermal wells. This is because most wells in two-phase systems have flashing taking place in the wellbore or the reservoir during drawdown, which complicates the well test analysis as discussed in Section 4.2. Most hot water and warm water wells do not self-discharge as discussed in Chapter 2, Geothermal Systems, therefore cannot be subject to a drawdown test. However, some hot water wells have a reservoir pressure higher than the hydrostatic head of water and do self-discharge. These wells are tested by flowing the wells for some time, then keeping them shut for about 8–10 times the flow test time to measure the pressure build-up.

In wells installed with a down-hole pump, using the down-hole pump for the drawdown (pumping test) can affect the build-up test since the pump tube will be full of fluid, while the annulus between the tube and casing will have a lower head (e.g. Fig. 3.13). This pressure differential can make the fluid flow from the tube back into the reservoir causing the pump to run in the opposite direction, which can be observed at the surface if a top drive pump is used. The effect will show up as a straight line during early build-up and is more prominent in low permeability wells, which take a longer time to recover (Fig. 6.30).

Figure 6.30. Drawdown/build-up of a well in a warm water system using the down-hole pump.

Data measured by authors.

This will also result in an extended (>1.5   log cycle) wellbore storage period, shown in the log-log pressure derivative plot of Fig. 6.31, which also shows that this well does not reach infinite-acting IARF behaviour even after 47   hours of pressure build-up as it has a low permeability of 1.2   mD. Additionally, the shape of the hump of pressure derivative is very steep (affected by fluid return from the pump) and will be difficult to match.

Figure 6.31. Log–log pressure derivative plot of build-up data from Figure 6.30 showing extended wellbore storage effect.

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Well Test Analysis: The Use of Advanced Interpretation Models

In Handbook of Petroleum Exploration and Production, 2002

Test procedure

Drawdown test : the flowing bottom hole pressure is used for analysis. Ideally, the well should be producing at constant rate but in practice, this is difficult to achieve and drawdown pressure data is erratic. The analysis of flowing periods (drawdown) is frequently difficult and inaccurate.

Build-up test: the increase of bottom hole pressure after shut-in is used for analysis. Before the build-up test, the well must have been flowing long enough to reach stabilized rate. During shut-in periods, the flow rate is accurately controlled (zero). It is for this reason build up tests should be performed.

Injection test / fall-off test: when fluid is injected into the reservoir, the bottom hole pressure increases and, after shut-in, it drops during the fall-off period. The properties of the injected fluid are in general different from that of the reservoir fluid, interpretation of injection and fall-off tests requires more attention to detail than for producers.

Interference test and pulse testing: the bottom hole pressure is monitored in a shut-in observation well some distance away from the producer. Interference tests are designed to evaluate communication between wells. With pulse tests, the active well is produced with a series of short flow / shut-in periods and the resulting pressure oscillations in the observation well are analyzed.

Gas well test: specific testing methods are used to evaluate the deliverability of gas wells (Absolute Open Flow Potential, AOFP) and the possibility of non-Darcy flow condition (rate dependent skin factor S′). The usual procedures are Back Pressure test (Flow after Flow), Isochronal and Modified Isochronal tests.

In Fig. 1.2, the typical test sequence of an exploration oil well is presented. Initially, the well is cleaned up by producing at different rates, until the fluid produced at surface corresponds to the reservoir fluid. The well is then shut-in to run the down hole pressure gauges, and reopened for the main flow. The flow rate is controlled by producing through a calibrated orifice on the choke manifold. Several choke diameters are frequently used, until stabilized flowing conditions are reached. After some flow time at a constant rate, the well is shut-in for the final build-up test.

Figure 1.2.

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Fractured Reservoirs

Tarek Ahmed , in Reservoir Engineering Handbook (Fifth Edition), 2019

Example 17-4

The drawdown test data for an infinite-conductivity fractured well are tabulated below:

t (hour)	pwf (psi)	Δp (psi)	$\sqrt{\mathbf{t}}\mathbf{hou}{\mathbf{r}}^{\mathbf{1}\mathbf{/}\mathbf{2}}$
0.0833	3,759.0	11.0	0.289
0.1670	3755.0	15.0	0.409
0.2500	3752.0	18.0	0.500
0.5000	3744.5	25.5	0.707
0.7500	3741.0	29.0	0.866
1.0000	3738.0	32.0	1.000
2.0000	3727.0	43.0	1.414
3.0000	3719.0	51.0	1.732
4.0000	3713.0	57.0	2.000
5.0000	3708.0	62.0	2.236
6.0000	3704.0	66.0	2.449
7.0000	3700.0	70.0	2.646
8.0000	3695.0	75.0	2.828
9.0000	3692.0	78.0	3.000
10.0000	3690.0	80.0	3.162
12.0000	3684.0	86.0	3.464
24.0000	3662.0	108.0	4.899
48.0000	3635.0	135.0	6.928
96.0000	3608.0	162.0	9.798
240.0000	3570.0	200.0	14.142

Additional reservoir parameters are:

$\begin{array}{c}\mathrm{h}=82\text{ft}\mathrm{\varphi }=0.12\\ {\mathrm{c}}_{\mathrm{t}}=21\times {10}^{-6}{\mathit{psi}}^{-1}\mathrm{\mu }=0.65\mathrm{cp}\\ {\mathrm{B}}_{\mathrm{o}}=1.26\mathrm{bbl}/\mathrm{STB}{\mathrm{r}}_{\mathrm{w}}=0.28\text{ft}\\ \mathrm{Q}=419\mathrm{STB}/\mathrm{day}{\mathrm{p}}_{\mathrm{i}}=3,770\mathrm{psi}\end{array}$

Estimate:

○

Permeability k

○

Fracture half-length x_f

○

Skin factor s

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Well Testing

John R. Fanchi , in Shared Earth Modeling, 2002

Reservoir Limits Test

The drawdown test provides information about the limits of a reservoir. The reservoir limits test requires that pressure drawdown be continued until pseudo-steady state (PSS) flow is achieved. The beginning of PSS flow is given by the stabilization time t_s :

(12.3.13) $t_s\approx 380\frac{\phi \mu c_{T}A}{K}$

where A is drainage area. Drainage area depends on drainage radius, which is uncertain. The drainage area for a radial system may be approximated as A = πr_e ² with r_e the drainage radius. The uncertainty in drainage radius will introduce uncertainty in the estimate of stabilization time. Consequently, the onset of PSS flow is only an approximation.

The pseudopressure equation for PSS flow has the straight line form

(12.3.14) $m\left(P_{wf}\right)=m^{\prime }t+m\left(P_{intercept}\right)$

when m(P_wf ) is plotted against t. The quantity m' is the slope of the line. It has the form

(12.3.15) $m^{\prime }=-2.356\frac{qT}{\phi \left(\mu c_T\right)HA}$

for a reservoir with thickness H and temperature T. The constant m(P _intercept) is the time independent intercept of the infinite-acting straight line. Given the slope m', we can estimate the drainage volume V_d [cu ft] as

(12.3.16) $V_d=\phi HA=-2.360\frac{qT}{m^{\prime }\left(\mu c_T\right)}$

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Well Testing

John R. Fanchi , in Integrated Reservoir Asset Management, 2010

8.3.5 The Reservoir Limits Test

The drawdown test provides information about the limits of a reservoir. The reservoir limits test requires that pressure drawdown be continued until pseudosteady state (PSS) flow is achieved. The beginning of PSS flow is given by the stabilization time t_s :

(8.3.14) $t_s\approx 380\frac{\mathrm{\varphi }\mu c_{T}A}{K}$

where stabilization time, t_s , is in hours and A is the drainage area in square feet. Drainage area depends on drainage radius, which is uncertain. The drainage area for a radial system may be approximated as A = πr_e ², with r_e the drainage radius. The uncertainty in drainage radius will introduce uncertainty in the estimate of stabilization time. Consequently, the onset of PSS flow is only an approximation.

The pseudopressure equation for PSS flow has the straight line form

(8.3.15) $m\left(P_{\mathit{wf}}\right)=m\prime t+m\left(P_{\text{intercept}}\right)$

when m(P_wf ) is plotted against t. The quantity m′ is the slope of the line. It has the form

(8.3.16) $m\prime =-2.356\frac{\mathit{qT}}{\varphi \left(\mu c_T\right)\mathit{HA}}$

for a reservoir with thickness H and temperature T. The constant m(P _intercept) is the time-independent intercept of the infinite-acting straight line. Given the slope m′, we can estimate the drainage volume V_d (cu ft) as

(8.3.17) $V_d=\varphi \mathit{HA}=-2.360\frac{\mathit{qT}}{m\prime \left(\mu c_T\right)}$

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Well Testing Analysis

Tarek Ahmed , Paul D. McKinney , in Advanced Reservoir Engineering, 2005

Example 1.37

The drawdown test data for an infinite conductivity fractured well is tabulated below:

t (hr)	p wf (psi)	Δp (psi)	$\sqrt{t}$ (hr1/2)
0.0833	3759.0	11.0	0.289
0.1670	3755.0	15.0	0.409
0.2500	3752.0	18.0	0.500
0.5000	3744.5	25.5	0.707
0.7500	3741.0	29.0	0.866
1.0000	3738.0	32.0	1.000
2.0000	3727.0	43.0	1.414
3.0000	3719.0	51.0	1.732
4.0000	3713.0	57.0	2.000
5.0000	3708.0	62.0	2.236
6.0000	3704.0	66.0	2.449
7.0000	3700.0	70.0	2.646
8.0000	3695.0	75.0	2.828
9.0000	3692.0	78.0	3.000
10.0000	3690.0	80.0	3.162
12.0000	3684.0	86.0	3.464
24.0000	3662.0	108.0	4.899
48.0000	3635.0	135.0	6.928
96.0000	3608.0	162.0	9.798
240.0000	3570.0	200.0	14.142

Additional reservoir parameters are:

h = 82 ft,

φ = 0.12

c _t = 21 × 10⁻⁶ psi⁻¹

μ = 0. 65 cp

B _o = 1.26bbl/STB,

r _w = 0. 28 ft

Q = 419 STB/day,

p _i = 3770 psi

Estimate:

•

permeability, k;

•

fracture half-length, x _f;

•

skin factor, s.

Solution

Step 1.

Plot:

•

Δp vs. t on a log-log scale, as shown in Figure 1.77;

Figure 1.77. Log-log plot, drawdown test data of Example 1.37.

(After Sabet, M. A. Well Test Analysis 1991, Gulf Publishing Company)

•

Δp vs. $\sqrt{t}$ on a Cartesian scale, as shown in Figure 1.78;

Figure 1.78. Linear plot, drawdown test data of Example 1.37.

(After Sabet, M. A. Well Test Analysis 1991, Gulf Publishing Company)

•

Δp vs. t on a semilog scale, as shown in Figure 1.79.

Figure 1.79. Semilog plot, drawdown test data from Example 1.37.

Step 2.

Draw a straight line through the early points representing logΔ(p) vs. log(t), as shown in Figure 1.77, and determine the slope of the line. Figure 1.77 shows a slope of ½(not 45° angle) indicating linear flow with no wellbore storage effects. This linear flow lasted for approximately 0.6 hours. That is:

$\begin{array}{l}{t}_{\text{elf}}=0.6\text{hours}\\ \Delta p_{\text{elf}}=30\text{psi}\end{array}$

and therefore the beginning of the infinite-acting pseudoradial flow can be approximated by the "double Δp rule" or "one log cycle rule," i.e., Equations 1.5.40 and 1.5.41, to give:

$\begin{array}{l}{t}_{\text{bsf}}\ge 10t_{\text{elf}}\ge 6\text{hours}\\ \Delta p_{\text{bsf}}\ge 2\Delta p_{\text{elf}}\ge 60\text{psi}\end{array}$

Step 3.

From the Cartesian scale plot of Δp $\sqrt{t}$ vs. draw a straight line through the early pressure data points representing the first 0.3 hours of the test (as shown in Figure 1.79) and determine the slope of the line, to give:

$m_{\text{vf}}=36\text{psi}/{\text{hr}}^{1/2}$

Step 4.

Determine the slope of the semilog straight line representing the unsteady-state radial flow in Figure 1.79, to give:

$m=94.1\text{psi}/\text{cycle}$

Step 5.

Calculate the permeability k from the slope:

$\begin{array}{l}k=\frac{162.6Q_{\text{o}}{B}_{\text{o}}{\mu }_{\text{o}}}{mh}=\frac{162.6\left(419\right)\left(1.26\right)\left(0.65\right)}{\left(94.1\right)\left(82\right)}\\ =7.23\text{md}\end{array}$

Step 6.

Estimate the length of the fracture half-length from Equation 1.5.37, to give:

$\begin{array}{l}{x}_{\text{f}}=\left[\frac{4.064QB}{m_{\text{vf}}h}\right]\sqrt{\frac{\mu }{k\varphi c_{\text{t}}}}\\ =\left[\frac{4.064\left(419\right)\left(1.26\right)}{\left(36\right)\left(82\right)}\right]\sqrt{\frac{0.65}{\left(7.23\right)\left(0.12\right)\left(12\times {10}^{-6}\right)}}\\ =137.3\text{ft}\end{array}$

Step 7.

From the semilog straight line of Figure 1.78, determine Δp at t = 10 hours, to give:

$\Delta p_{\text{at}\Delta t=10}=71.7\text{psi}$

Step 8.

Calculate Δp _1hr by applying Equation 1.5.39:

$\Delta p_{1\text{hr}}=\Delta p_{\text{at}\Delta t=10}-m=71.7-94.1=-22.4\text{psi}$

Step 9.

Solve for the "total" skin factor s, to give

$\begin{array}{l}s=1.151\left[\frac{\Delta p_{1\text{hr}}}{\left|\text{m}\right|}-log\left(\frac{k}{\varphi \mu c_{\text{t}}{r}_{\text{w}}^2}\right)+3.23\right]\\ =1.151\left[\frac{-22.4}{94.1}-log\left(\frac{7.23}{0.12\left(0.65\right)\left(21\times {10}^{-6}\right){\left(0.28\right)}^2}\right)+3.23\right]\\ =-5.5\end{array}$

with an apparent wellbore ratio of:

$r_{\text{w}}^{\backslash }=r_{\text{w}}{\text{e}}^{-s}=0.28{\text{e}}^{5.5}=68.5\text{ft}$

Notice that the "total" skin factor is a composite of effects that include:

$s=s_{\text{d}}+s_{\text{f}}+s_{\text{t}}+s_{\text{p}}+s_{\text{sw}}+s_{\text{r}}$

where:

s _d = skin due to formation and fracture damage

s _f = skin due to the fracture, large negative value s _f ^≪ 0

s _t = skin due to turbulence flow

s _p = skin due to perforations

s _w = skin due to slanted well

s _r = skin due to restricted flow

For fractured oil well systems, several of the skin components are negligible or cannot be applied, mainly s _t, s _p, s _sw, and s _r; therefore:

$s=s_{\text{d}}+s_{\text{f}}$

or:

$s_{\text{d}}=s-s_{\text{f}}$

Smith and Cobb (1979) suggested that the best approach to evaluate damage in a fractured well is to use the square root plot. In an ideal well without damage, the square root straight line will extrapolate to p _wf at Δt = 0, i.e, p _{wf at Δt=0}, however, when a well is damaged the intercept pressure p _int will be greater than p _{wf at Δt=0}, as illustrated in Figure 1.80. Note that the well shut-in pressure is described by Equation 1.5.35 as:

Figure 1.80. Effect of skin on the square root plot.

$p_{\text{ws}}=p_{\text{wf}\text{at}\Delta t=0}+m_{\text{vf}}\sqrt{t}$

Smith and Cobb pointed out that the total skin factor exclusive of s _f, i.e., s – s _f, can be determined from the square root plot by extrapolating the straight line to Δt = 0 and an intercept pressure p _int to give the pressure loss due to skin damage, (Δp _s)_d, as:

${\left(\Delta p_{\text{s}}\right)}_{\text{d}}=p_{int}-p_{\text{wf}\text{at}\Delta t=0}=\left[\frac{141.2QB\mu }{kh}\right]s_{\text{d}}$

Equation 1.5.35 indicates that if p _int = p _{wf at Δ=0}, then the skin due to fracture s _f is equal to the total skin.

It should be pointed out that the external boundary can distort the semilog straight line if the fracture half-length is greater than one-third of the drainage radius. The pressure behavior during this infinite-acting period is very dependent on the fracture length. For relatively short fractures, the flow is radial but becomes linear as the fracture length increases as it reaches the drainage radius. As noted by Russell and Truitt (1964), the slope obtained from the traditional well test analysis of a fractured well is erroneously too small and the calculated value of the slope progressively decreases with increasing fracture length. This dependency of the pressure response behavior on the fracture length is illustrated by the theoretical Horner buildup curves given by Russell and Truitt and shown in Figure 1.81. If the fracture penetration ratio x _f/x _e is defined as the ratio of the fracture half-length x _f to the half-length x _e of a closed square-drainage area, then Figure 1.82 shows the effects of fracture penetration on the slope of the buildup curve. For fractures of small penetration, the slope of the buildup curve is only slightly less than that for the unfractured "radial flow" case. However, the slope of the buildup curve becomes progressively smaller with increasing fracture penetrations. This will result in a calculated flow capacity kh which is too large, an erroneous average pressure, and a skin factor which is too small. Obviously a modified method for analyzing and interpreting the data must be employed to account for the effect of length of the fracture on the pressure response during the infinite-acting flow period. Most of the published correction techniques require the use of iterative procedures. The type curve matching approach and other specialized plotting techniques have been accepted by the oil industry as accurate and convenient approaches for analyzing pressure data from fractured wells, as briefly discussed below.

Figure 1.81. Vertically fractured reservoir, calculated pressure buildup curves.

(After Russell and Truitt, 1964)

An alternative and convenient approach to analyzing fractured well transient test data is type curve matching. The type curve matching approach is based on plotting the pressure difference Δp versus time on the same scale as the selected type curve and matching one of the type curves. Gringarten et al. (1974) presented the type curves shown in Figure 1.82 and 1.83 for infinite conductivity vertical fracture and uniform flux vertical fracture, respectively, in a square well drainage area. Both figures present log-log plots of the dimensionless pressure drop p _d (equivalently referred to as dimensionless wellbore pressure p _wd) versus dimensionless time t _{Dx f} . The fracture solutions show an initial period controlled by linear flow where the pressure is a function of the square root of time. In log-log coordinates, as indicated before, this flow period is characterized by a straight line with ½ slope. The infinite-acting pseudoradial flow occurs at a t _Dxf between 1 and 3. Finally, all solutions reach pseudosteady state.

Figure 1.82. Dimensionless pressure for vertically fractured well in the center of a closed square, no wellbore storage, infinite conductivity fracture.

(After Gringarten et al., 1974)

Figure 1.83. Dimensionless pressure for vertically fractured well in the center of a closed square, no wellbore storage, uniform-flux fracture.

(After Gringarten et al., 1974)

During the matching process a match point is chosen; the dimensionless parameters on the axis of the type curve are used to estimate the formation permeability and fracture length from:

[1.5.43] $k=\frac{141.2QB\mu }{h}{\left[\frac{p_{\text{D}}}{\Delta p}\right]}_{\text{MP}}$

[1.5.44] $x_{\text{f}}=\sqrt{\frac{0.0002637k}{\varphi \mu C_t}{\left(\frac{\Delta t}{t_{\text{D}{x}_{\text{f}}}}\right)}_{\text{MP}}}$

For large ratios of x _e/x _f, Gringarten and his co-authors suggested that the apparent wellbore radius r ^\ _w can be approximated from:

$r_{\text{w}}^{\backslash }\approx \frac{x_{\text{f}}}{2}=r_{\text{w}}{e}^{-s}$

Thus, the skin factor can be approximated from:

[1.5.45] $s=ln\left(\frac{2r_{\text{w}}}{x_{\text{f}}}\right)$

Earlougher (1977) points out that if all the test data falls on the ½-slope line on the log Δp vs. log(time) plot, i.e., the test is not long enough to reach the infinite-acting pseudoradial flow period, then the formation permeability k cannot be estimated by either type curve matching or semilog plot. This situation often occurs in tight gas wells. However, the last point on the ½ slope line, i.e., (Δp)_Last and (t)_Last, may be used to estimate an upper limit of the permeability and a minimum fracture length from:

[1.5.46] $k\le \frac{30.358QB\mu }{h{\left(\Delta p\right)}_{\text{last}}}$

[1.5.47] $x_{\text{f}}\ge \sqrt{\frac{0.1648k{\left(t\right)}_{\text{last}}}{\varphi \mu c_{\text{t}}}}$

The above two approximations are only valid for x _e/x _f >> 1 and for infinite conductivity fractures. For uniform-flux fracture, the constants 30.358 and 0.01648 become 107.312 and 0.001648.

To illustrate the use of the Gringarten type curves in analyzing well test data, the authors presented the following example:

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Fundamentals of Drawdown Test Analysis Methods

Amanat U. Chaudhry , in Gas Well Testing Handbook, 2003

5.12 Summary

A properly run drawdown test yields considerable information about the reservoir. However, the test may be hard to control because it is a flowing test. If a constant rate cannot be maintained, a multirate testing technique should be used. Those techniques also should be used if the well was not shut-in long enough to reach static reservoir pressure before the drawdown test. To ensure the best possible multiple-rate test, the engineer must have an idea of a well's flow characteristics. The rate change imposed must be large enough to give significant change in a pressure transient behavior of the well. Normally, rate is changed by a factor of two or three.

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Streamline Numerical Well Testing Interpretation Model Considering Components

In Streamline Numerical Well Test Interpretation, 2011

7.7.3 Testing curve analysis

For the pressure drawdown test before the miscible phase, because there are no changes in sub-surface fluid components, fluid viscosity, density and compressibility factor, the simulation testing curve shows the characteristics of a homogeneous reservoir.

For the pressure drawdown test after the miscible phase, because of the miscible phase between injection fluid and sub-surface fluid (the minimum miscible phase pressure in Pubei oilfield is 33 MPa), the components of sub-surface fluid change, as do the fluid viscosity, density and compressibility factor. As seen in the pressure derivative curve: compared with that before the miscible phase, derivation falls quickly after well bore storage effect; the main reason is due to viscosity variation of sub-surface fluid after miscible phase. The fluctuation of derivative curve is due to the instability of numerical solutions. The component distribution of sub-surface hydrocarbon at the time of well shut-in is shown in Figs 7.4 to 7.9.

Figure 7.4. Sub-surface distribution of the first component (C1, N2).

Figure 7.5. Sub-surface distribution of the second component (C₂, CO₂).

Figure 7.6. Sub-surface distribution of the third component (C3, C4).

Figure 7.7. Sub-surface distribution of the fourth component (C₅, C₆).

Figure 7.8. Sub-surface distribution of the fifth component (C7∼C16).

Figure 7.9. Sub-surface distribution of the sixth component (C₁₇₊).

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How to Draw a Straight Line 1977

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