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Determination of flow efficiency and skin
To quantify formation damage and understand its impact on hydrocarbon production, one must have reasonable estimates of the flow efficiency or skin factor. Several methods have been proposed to evaluate these quantities for oil and gas wells. The most common methods are:
- Multirate tests
- Isochronal gas-well tests
- Transient well tests (pressure-buildup analysis)
Multirate tests
Multirate tests can be conducted on both oil and gas wells. In these tests, several stabilized flow rates, q_{i} , are achieved at corresponding stabilized flowing bottomhole pressures, p_{wf}. The simplest analysis considers two different stabilized rates and pressures. The IPR can be written as
Simplifying and solving for the flow efficiency, F, we obtain
where x ≠ 0.
The above equation clearly shows that it is possible to obtain flow efficiency rather simply with two stabilized bottomhole pressures and two stabilized flow rates. A similar analysis can be performed to obtain an expression for a linear IPR (x = 0).
Multirate tests in gas wells: inertial effects
For many gas wells and some oil wells, flow rates are sufficiently high that turbulent or inertial pressure drops near the wellbore can be significant. In such cases, the additional pressure drop measured by the skin can be confused with the pressure drop because of non-Darcy or inertial flow. It is very important to separate out the pressure drop caused by turbulent flow from that caused by physical skin because it has a significant impact on the stimulation recommendations made on the well. To analyze high-rate gas or oil wells, the following equation is needed. ^{[1]}
Darcy's law for high-rate gas wells can be written as
Here,
This equation can be rearranged to obtain
Here, Aq_{sc} represents a laminar pressure drop and Bq^{2}_{sc} represents an inertial or non-Darcy pressure drop (sometimes referred to as a turbulent pressure drop). Note that A contains the physical skin, S, and B is directly proportional to the non-Darcy coefficient, D. By plotting multirate test data as a plot of , we obtain A and B as an intercept and slope, respectively. It is then possible to compare the magnitude of the pressure drop caused by S with that caused by inertial effects, Dq_{sc}.
If S>Dq_{sc}, a stimulation treatment would be recommended. However, if Dq_{sc} > S, the well may need to be reperforated or fractured to increase the inflow area and to reduce inertial effects.
Isochronal test in gas wells
In gas wells in which it takes a long time to achieve stabilized rates, wells are shut in and produced for a fixed time interval (Δt) at several different rates. These isochronal tests are then interpreted by the following "deliverability" relation,
where the exponent n lies between 0.5 and 1. An exponent closer to 0.5 indicates that non-Darcy effects are important; an exponent close to 1 indicates that they are not. ^{[2]}
It should be noted that the "deliverability" equation is a variation of the equation derived in the previous section.
Pressure-buildup analysis
The most common method for determining skin is a pressure-buildup test. ^{[2]}^{[3]} In this test, a well that has been producing for a time, t_{p}, is shut in for time Δt. The pressure buildup is recorded as a function of time. By constructing a Horner plot^{[2]}^{[3]} like the one shown in Fig. 1, we can compute the skin and the product of the permeability and formation thickness, kh, of the reservoir (in field units).
and
Here, m is the slope of the straight-line portion of the Horner plot, and p_{ws,1hr} is the extrapolated shut-in pressure at a shut-in time of 1 hour.
It is also possible to obtain the average reservoir pressure with the Matthew, Brons, and Hazelbrook method from the pressure-buildup data. ^{[4]} Knowing both the average reservoir pressure and skin, we can calculate the flow efficiency of the well. This method provides a direct and quantitative measure of the extent of formation damage in a well.
Methods following the same principle have been developed for deviated and horizontal wells. Equations for analysis are more complex and are not discussed in this page. The same methods can also be used to analyze data from gas wells and from wells on artificial lift.
The short discussion presented above shows how near-wellbore formation damage can be quantified by measurements made on oil and gas wells. Such measurements are essential for determining the extent and magnitude of the formation damage and its impact on hydrocarbon production. However, these measures do not provide us with any clues on the reasons for the formation damage.
Nomenclature
Aq_{sc} | = | laminar pressure drop |
B | = | proportional to the non-Darcy coefficient, D |
Bq^{2}_{sc} | = | inertial or non-Darcy pressure drop |
c | = | compressibility |
Dq_{sc} | = | inertial effects |
F | = | well flow efficiency |
k | = | overall permeability, md |
k_{I} | = | initial permeability, md |
k_{h} | = | permeability and formation thickness |
m | = | slope |
n | = | exponent |
p | = | pressure |
p_{b} | = | bubblepoint pressure |
p_{R} | = | average reservoir pressure |
p_{wf} | = | flowing bottomhole pressure |
p_{ws,1hr} | = | extrapolated shut-in pressure at a shut-in time of 1 hour |
ΔP_{skin} | = | additional pressure drop caused by formation damage |
q | = | flow rate |
q_{i} | = | flow rates |
q_{sc} | = | volumetric flow rate, surface conditions |
r_{e} | = | external boundary radius |
r_{w} | = | well radius |
S | = | skin factor |
T | = | temperature |
t | = | time |
Δt | = | fixed time interval |
z | = | real gas compressibility factor |
μ | = | viscosity |
μ_{g} | = | gas viscosity |
References
- ↑ Jones, L.G., Blount, E.M., and Glaze, O.H. 1976. Use of Short Term Multiple Rate Flow Tests To Predict Performance of Wells Having Turbulence. Presented at the SPE Annual Fall Technical Conference and Exhibition, New Orleans, Louisiana, 3-6 October 1976. SPE-6133-MS. http://dx.doi.org/10.2118/6133-MS
- ↑ ^{2.0} ^{2.1} ^{2.2} ^{2.3} Matthews, C.S. and Russell, D.G. 1967. Pressure Buildup and Flow Tests in Wells, 1. Richardson, Texas: Monograph Series, SPE.
- ↑ ^{3.0} ^{3.1} Horner, D.R. 1951. Pressure build-up in wells. Proc., 1951. . Proc., Third World Petroleum Congress, The Hague, Sec. II, 503–523.
- ↑ Matthews, C.S., Brons, F., and Hazelbrook, P. 1954. A Method for Determination of Average Pressure in a Bounded Reservoir. Trans., AIME, 201, 182–191.
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