WELL TESTING: INTRODUCTIONIn order to characterize the behaviour of oil and gas reservoirs, and to predict their future performance, it is essential to track the evolution of fluid pressures and production rates over time. Obtaining the latter is relatively straight forward, and fluid production tends to be metered with reasonable accuracy.

Reservoir pressures are determined by well testing.

During a well test, a transient pressure response is created by a temporary change in production rate. The well response is usually monitored during a relatively short period of time compared to the life of the reservoir, depending on the test objectives.

For well evaluation, tests are commonly conducted in less than 2 days.

In the case of reservoir limit testing, several months of pressure data may be needed!

Note: Pressures tend to be measured downhole, while production rates tend to be measured at surface.

WELL TESTING: INTRODUCTION (2)

Information obtained from well testingWell testing, often called pressure transient analysis (PTA), is a powerful tool for reservoir characterization. The following information can be extracted from well tests: Permeability The value obtained from a well test is much more useful than that from core analysis, because it represents the in-situ, effective permeability averaged over a large distance (tens or hundreds of metres). Skin (damage or stimulation) Most wells are either damaged or stimulated, and this has a direct effect on the deliverability of the well. The skin is a measure of the completion effectiveness of a well. A positive skin (typically +1 to +20) represents damage, while a negative skin (typically -1 to -6) represents improvement. Average reservoir pressure This parameter, which is either measured directly or extrapolated from well test data, is used in material balance calculations for determining hydrocarbons in-place. Deliverability potential The IPR (inflow performance relationship) or the AOF (absolute open flow) is used in forecasting a wells production. (Well productivity index (PI), flow rate per day per unit drawdown pressure) Reservoir description Reservoir shape, continuity, and heterogeneity can be determined from pressure transient tests Fluid samples The reservoir fluid composition and its PVT (pressure-volume-temperature) properties can have a significant effect on the economics and production operations.Well testing is also an integral part of good reservoir management and fulfills government regulations. (From: Mattar and Dean, 2008)

TYPES OF WELL TESTSDrawdown tests:The flowing bottomhole pressure (FBHP) is used for analysis. Ideally, the well should be producing at a constant rate... sometimes difficult to achieve.

Build-up test:The increase of BHP after shut-in is used for analysis. Before the build-up test, the well must have been flowing long enough to reach a stabilized rate. Flow rate is accurately controlled (i.e., 0)

Injection/Falloff test:Fluid is injected into reservoir. Pressure rise during injection, and falloff after shut-in, are analyzed. Properties of injected fluid are different from reservoir fluids... more difficult to interpret with confidence.

Interference test:BHP monitored in a shut-in observation well that is distant from the production well.

Deruyck et al., 1992

TYPES OF WELL TESTS (cont.)Gas well test:Analogous to oil wells, but some differences. E.G., Absolute Openhole Potential (AOFP) tests well is opened to patm (and/or a succession of relatively low back-pressures). Also, non-Darcy flow may occur, not to mention the fact that gas is highly compressible.WHEN THE TESTS ARE RUN:Production test:The well has been completed as a production well, commonly as a cased hole with a permanent completion (e.g., perforations). The well is monitored at surface, from the wellhead.

Drill stem test (DST):The well is completed temporarily with a downhole shut-in valve, and isolation is achieved using packers. The well may cased and perforated OR openhole. Usually conducted immediately after drilling using the drill stem, but more common to run the test on production tubing now.Test duration is usually relatively short compared to a production test.

Information obtained during the process of productionVella et al., 1992Testing a cased well: A test valve and pressure gauges downhole are combined with surface separation and flow measurement equipment to gather formation drawdown and buildup pressure and flow rate data. Samples of formation fluid are taken at surface for analysis.Reverse circulation valveDownhole test valvePackerPressure dataPressure recorderFm. being tested

Deruyck et al., 1992

In the following slides, we will study the pressure response during a conventional well test (constant production rate)

TRANSIENT FLOW (EARLY)prpiOuter flow boundaryFBHP response dominated by skin and reservoir permeability.No information about reservoir boundaries.FBHP or pwfre

TRUE STEADY STATE FLOW (E.G., Very Active Aquifer Support, Waterflooding)prpiOpen flow boundaryNot commonly achieved under natural conditions.final pwfre

SEMI (or PSEUDO) STEADY-STATE FLOW (LATE)prpiOuter flow boundaryFBHP response dominated by reservoir boundaries.pwf1t1t2pwf2re

DIFFUSION EQUATION FOR RADIAL FLOWThis equation is derived based on mass conservation and Darcys law.Top viewSide viewAssumptions:

HomogeneousIsotropicFully penetrating wellSingle-phase flowConstant viscositySmall & constant compressibility

e.g., undersaturated oil

TRANSIENT FLOW:APPROX. SOLUTION FOR INFINITE-ACTING RESERVOIRprpiFBHP response dominated by skin and reservoir permeability.Note the logarithmic dependence on time.FBHP or pwfre

MECHANICAL SKIN FACTOR: SConsider a well flowing at a given rate Q. With no near-well permeability impairment, the pressure profile would be as shown by the dashed line. However, in the case of a damaged well, the actual pressure required to achieve flow rate Q is shown by the solid line. The incremental pressure drop close to the well has been defined by ven Everdingen as:pQ

MECHANICAL SKIN FACTOR: SIF you know the radius and permeability of the damaged zone, you can solve for S as follows:Re-arranging gives:rwkekararepepwf

CONDITIONS RESULTING IN SKINPositive skin (impaired production)

Formation damagePartial well penetrationPerforationsNegative skin (stimulated production)

Hydraulic fracturesAcid fracturesAcid wash/squeezePRODUCTIVITY INDEX (PI)PI is a popular method of quantifying well performance. It includes the effect of skin. It is expresses in units of production rate per day per unit pressure drawdown... in metric field units: scm / day / kPa

SEMI (PSEUDO) STEADY-STATE FLOW SOLUTIONFBHP response dominated by reservoir boundaries (area A; shape factor CA).Note the linear dependence on time.prpipwft1repe

SHAPE FACTORS & SEMI STEADY-STATE FLOW (1)The semi steady-state inflow equation appears to be restrictive in that it only applies for a well producing from the centre of a circular-shaped drainage area.

Obviously, reservoirs will not be circular in general, nor will the producing well(s) be centered within them.

Further, when multiple wells are producing from a common reservoir, each well will assume its own ~fixed drainage area.

The so-called Dietz Shape Factors (CA) have been derived to enable the use of the semi steady-state inflow equation for a number of different geometries.

SHAPE FACTORS & SEMI STEADY-STATE FLOW (2)

Variables used in the preceding slides on well testing [SI units]:

r= radial distance [m]rw= wellbore radius [m]re= outer radius of the reservoir[m]p= fluid pressure [Pa]pwf= flowing bottomhole pressure [Pa]pi= initial reservoir pressure [Pa]pe= current reservoir pressure at the outer boundary [Pa]= porosity= Eulers number = 1.781= fluid viscosity [Pas]c= fluid compressibility, isothermal [Pa-1]k= (effective) permeability [m2]t= time [s]S= skin factorQ= fluid production rate [stcm/s]B= fluid formation volume factor [rcm/stcm]h= reservoir thickness [m]A= reservoir area (in plan view) [m2]CA= reservoir shape factor

EXAMPLE PRESSURE DRAWDOWN TEST (1)A well has been tested by producing at a constant rate of 240 scm/d for a period of 100 hours. It is suspected, from seismic and geological evidence, that the well is draining in isolated reservoir block which has approximately a 4:1 rectangular shape. The extended drawdown test has been run to confirm this, and to measure other properties of the reservoir. Following are the known reservoir properties, and the flowing bottomhole pressures that were measured during the test.

EXAMPLE PRESSURE DRAWDOWN TEST (2)Consider the early time flow data, for which we expect the transient inflow equation to hold true:We can re-work this equation like this:[Recall that ln(ab) = ln(a) + ln(b)]We see that a plot of pwf against ln(t) should have a slope of:no time-dependent terms... and an intercept of:

EXAMPLE PRESSURE DRAWDOWN TEST (3)A plot of pwf against ln(t) should have a slope of:From the regression line, we see that:

EXAMPLE PRESSURE DRAWDOWN TEST (4)The y-intercept of our regression tells us that:Which can be solved for S as follows:

EXAMPLE PRESSURE DRAWDOWN TEST (5)Consider the late time flow data, for which we expect the semi steady-state inflow equation to hold true:We can re-work this equation like this:We see that a plot of pwf against t should have a slope of:no time-dependent terms... and an intercept of:

EXAMPLE PRESSURE DRAWDOWN TEST (6)A plot of pwf against t should have a slope of:From the regression line, we see that:

EXAMPLE PRESSURE DRAWDOWN TEST (7)The y-intercept of our regression tells us that:Which can be solved for CA as follows:Error: These two terms should be multiplied by 2. See next slide for correct version.

EXAMPLE PRESSURE DRAWDOWN TEST (7)The y-intercept of our regression tells us that:Which can be solved for CA as follows:Corrected versionThese two terms have been corrected here.The final answer that was originally given was correct.

EXAMPLE PRESSURE DRAWDOWN TEST (8)Here is the closest matchfrom the table of Dietzshape factors.

EXAMPLE PRESSURE DRAWDOWN TEST (9)Reservoir shape:Here is what we have interpreted for this reservoir:

DIMENSIONLESS VARIABLESIts actually much more convenient to convert our well test data to dimensionless form, then perform type-curve matching to obtain our reservoir parameters.

PRESSURE DERIVATIVESMore advanced well test analyses often involve fitting to both the dimensionless pressure type-curves, as well as its derivative.

Deruyck et al., 1992

In the preceding slides, we saw how pressure data from a drawdown test in an oil well could be used to calculate k, S, A and CA. What about estimating initial reservoir pressure (pi)?

One way to estimate pi is using the bottomhole shut-in pressures (pws) recorded during a pressure build-up test.

The so-called Horner plot involves graphing:where t is the length of time that the well was flowed prior to the build-up test, and t is the time since shut-in.

If we could shut-in the well to infinite time, pws would reach pi.

Linear extrapolation of the data to ln[(t+t)/t] = 0 is equivalent to extrapolating the data to infinite shut-in time.ESTIMATING RESERVOIR PRESSURE:HORNER PLOT ANALYSIS

(DST Test)t t

APPENDIX A

Extra Stuff Regarding Well Testing

The hypothesis of slightly compressible fluids (i.e., small, constant compressibility) used for oil-well test analysis of not valid for gas systems.

Recall that gas compressibility is strongly dependent on pressure... in fact, so is gas viscosity.GAS WELL TESTING (1)

= 0.85; temperature = 200F).Gas compressibility

In 1966, Al-Hussaniy et al. demonstrated that the radial flow equation can be linearized approximately (i.e., rendered into a form that we can solve analytically) by replacing all pressure terms with the so-called gas pseudo-pressure, m(p).

The pseudo-pressure, also called the real gas potential, is defined as:GAS WELL TESTING (2)where:p=the pressure of interestp0=a reference pressure (chosen arbitrarily, usually a value less than the lowest pressure to be experience in the well test)=gas viscosityz=gas z-factor

The radial diffusion equation then becomes:GAS WELL TESTING (3)Remember the transient inflow equation for oil?Heres the analogous solution for gas inflow:

GAS WELL TESTING (4)Transient gas inflow equation:Note that the skin factor has been expanded to account for non-Darcy flow effects:Where D is called the non-Darcy flow coefficient.

With more time, we could go on to do an example calculation analogous to the one we did last lecture for an oil well.

Please note that the transformation between p and m(p) is not as stinky as it might seem.

Gas pseudo-pressure, as calculated in Table 8.1 (Gas gravity = 0.85; T = 200F)m(p), psi/cPp, psi

For an oil reservoir below the bubble point, we really shouldnt pretend that the total fluid compressibility (i.e., oil + gas + water) is small and constant.

There is also a multiphase pseudo-pressure, which linearizes the inflow equations and allows us to make use of the well test analysis techniques presented in the last lecture.

SOLUTION GAS DRIVE RESERVOIRSwhere:p=the pressure of interesto=oil viscosityBo=oil formation volume factor

CORRECTION FOR VARIABLE FLOW RATESThe mathematical basis for well test analysis assumes constant flow rate throughout the test. If rates have varied over time, once technique that allows you to use conventional interpretation is by calculating an equivalent flow time (te).

WORK-AROUNDS FOR TESTS OF NON-CONSTANT RATESee also Superposition Methods, in any textbook on well test analysis.

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GEOE 412April 2005*