part 2 basics wta sept 2013 semester

Well Test Analysis 1

MOnur Sept. 2013


MOnur Sept. 2013


Indirect measurement means that a property (e.g. Permeability) p p y ( g y)could not be directly measured.

MOnur Sept. 2013

To model the dual-packer and observation probe pressures, we p p p ,need to solve the diffisuivity equation, which is derived from the principle of mass conservation in the porous media with the appropriate initial and boundary conditions. If we have a homogeneous/anisotropic media, then we can solve this diffusivity equation describing flow in a 3D r-theta-z system by analytical means to have closed form solution On the otheranalytical means to have closed form solution. On the other hand, if we consider a heterogeneous/anistorpic media where formation properties may exhibit spatial variation then, we solve this equation by finite difference techniques, as we cannot solve this problem analyticall. Numerical techniques are also useful to study multiphase flow effects on IPTT, though I will not consider such effects. Here, I concentrate on the single phase flow of a slightly compressible fluid in both homogeneous and heterogeneous formations.

MOnur Sept. 20135


MOnur Sept. 2013


Obtained by combiningy g Continuity equation Equation of state for slightly compressible liquids Flow equation - Darcys law

MOnur Sept. 2013


The continuity equation is a restatement of the conservation of matter. y qThat is, the rate of accumulation of fluid within a volume element is given by the rate at which the fluid flows into the volume minus the rate at which the fluid flows out of the volume.

NomenclatureA = Cross-sectional area open to flow, ft2

m = Rate of accumulation of mass within the volume, lbm/secv = Fluid velocity, ft/sec = Density of fluid, lbm/ft3

MOnur Sept. 2013


This equation describes the change in density with pressure for a q g y pliquid with small and constant compressibility.

Nomenclaturec = Compressibility, psi-1

P ip = Pressure, psi = Density of fluid, lbm/ft3

MOnur Sept. 2013


NomenclatureA = Cross sectional area open to flow, cm2

k = Permeability, darciesL = Length of flow path, cmp = Pressure, atmp = Pressure difference between upstream and

downstream sides, atmq = Flow rate, cm3/secux = Flow velocity, cm/secx = Spatial coordinate, cmx Spatial coordinate, cm = Viscosity, cp

MOnur Sept. 2013


The diffusivity equation is obtained by combiningy q y g- The continuity equation- The equation of state for a slightly compressible liquid- Darcys law

Other transient flow equations may be obtained by combiningOther transient flow equations may be obtained by combining different equations of state and different flow equations

- Gas flow equation- Multiphase flow equation

MOnur Sept. 2013


MOnur Sept. 2013


The formation volume factor is the volume of fluid at reservoir conditions necessary to produce a unit volume of fluid at surface conditions.

Symbol Bo, Bg, Bw Units res bbl/STB, res bbl/ Mscf Source Lab measurements, correlations Range and typical values

Oil 1 2 res bbl/STB, Black oil 2 4 res bbl/STB, Volatile oil

Water 1 1.1 res bbl/STB

Gas 0.5 res bbl/Mscf, at 9000 psi 5 res bbl/Mscf at 680 psi

MOnur Sept. 2013

5 res bbl/Mscf, at 680 psi 30 res bbl/Mscf, at 115 psi


The solution gas causes a considerable increase in the gvolume of the oil. Note the decrease in oil volume with increasing pressure above the bubble point; this is due to the compressibility of the oil when all the available gas is in solution.

MOnur Sept. 2013


The volume of gas at reservoir conditions of pressure and g ptemperature that produces 1 cubic foot of gas at standard conditions.

Unitsft3/scf or ft3/Mscf used in gas reservoir engineeringbbl/scf or ft3/Mscf use in oil reservoir engineeringbbl/scf or ft /Mscf use in oil reservoir engineering

MOnur Sept. 2013


Viscosity is a measure of resistance to flow. Specifically, it is y p y,the ratio of the shear stress to the resulting rate of strain within a fluid.

Symbolso, g, w

Units cp

Source Lab measurements, correlations

Range and typical values- 0 25 10 000 cp Black oil- 0.25 10,000 cp, Black oil- 0.5 1.0 cp, Water- 0.012 0.035 cp, Gas

MOnur Sept. 2013


MOnur Sept. 2013


Compressibility is the fractional change in volume due to a unit p y gchange in pressure.

Symbol co, cg, cw Units psi-1, microsips (1 microsip = 1x10-6 psi-1) Source Lab measurements, correlationsTypical ValuesTypical Values Oil

15x10-6 psi-1, undersaturated oil 180x10-6 psi-1, saturated oil

Water 4x10-6 psi-1

Gas 1/p, Ideal gas 60x10-6 psi-1, at 9000 psi

1 5 10 3 i 1 t 680 i

MOnur Sept. 2013

1.5x10-3 psi-1, at 680 psi 9x10-3 psi-1, at 115 psi


MOnur Sept. 2013


Porosity is the ratio of volume of pore space to bulk volume of y p prock.

Symbol - Units

Equations - fractionEquations fraction Reports - % (or fraction)

Source Logs, cores

R T i l V l Range or Typical Value 30%, unconsolidated well-sorted sandstone 20%, clean, well-sorted consolidated sandstone 8%, low permeability reservoir rock

0 5% natural fracture porosity

MOnur Sept. 2013

0.5%, natural fracture porosity


Permeability is the measure of capacity of rock to transmit y p yfluid.

Symbol k

UnitsUnits Darcy or millidarcy (md or mD)

Source Well tests, core analysis

R Range 0.001 md - 10,000 md

MOnur Sept. 2013


Pore volume compressibility is the fractional change in porosity p y g p ydue to unit change in pressure.

Symbol cf

Units psi-1, microsips

Source Lab measurement, correlation, guessSource Lab measurement, correlation, guess

Range or Typical Value 4x10-6 psi-1, well-consolidated sandstone 30x10-6 psi-1, unconsolidated sandstone 4 to 50 x 10-6 psi-1 consolidated limestones 4 to 50 x 10 psi consolidated limestones

MOnur Sept. 2013


The net pay thickness is the total thickness of all productive p y players in communication with the well.

Net pay includes any rock that has sufficient vertical permeability to allow fluid to move to a layer from which it may be produced.

Thickness is measured perpendicular to bed boundaries.

Symbol h

Units ft

Source logs Source logs

Range or Typical Value

May be as small as 5 ft or even less

May be as large as 1,000 ft or more

MOnur Sept. 2013


MOnur Sept. 2013


Saturation is the fraction of pore volume occupied by a p p yparticular fluid.

Symbol So, Sw, Sg

Units fraction or %

Source logs Source logs

Range or Typical Value 15 to 25% connate water saturation in well-sorted,

coarse sandstones 40 to 60% connate water saturation in poorly sorted 40 to 60% connate water saturation in poorly sorted,

fine-grained, shaly, low-permeability reservoir rock

MOnur Sept. 2013


Wellbore radius is the size of wellbore.

Symbol rw

Unitsfeet feet

Source Bit diameter/2 Caliper log

Range or Typical Value 2 to 8 in.

MOnur Sept. 2013


The total compressibility is the sum of pore compressibility and p y p p ysaturation weighted fluid compressibilities.

Symbol ct

Units psi-1, microsips

Source Calculated

Range or Typical Value See exercises See exercises

MOnur Sept. 2013


Exercise 1W ll T t A l iWell Test Analysis

Define Variables Used In Well Testing

Define, give the units for, and name a common source for each of the following variables used in well testing Complete as much ofthe following variables used in well testing. Complete as much of this exercise as possible before referring to the notes.

1. Porosity

2. Water saturation

3. Total compressibility

4. Oil compressibility

5. Formation volume factor

6. Viscosity

7. Wellbore radius

8. Net pay thickness

9. Permeability

MOnur Sept. 2013



Calculate Compressibility for Undersaturated Oil Reservoir

Calculate total compressibility for the following situation. Assume solution gas/oil ratios do not include stock tank vent gas.Undersaturated oil reservoir (above the bubblepoint)

Sw = 17%, TDS = 18 wt %, oil gravity = 27API,Rso = 530 scf/STB, gas gravity = 0.85, Tf = 185F,p = 3500 psi, cf = 3.610-6 psi-1Tsep = 75F, psep = 115 psia

From fluid properties correlations,

pb = 2803 psi

co = 1.158 x 10-5 psi-1

cw = 2.277 x 10-6 psi-1

MOnur Sept. 2013



Calculate Compressibility for Saturated Oil Reservoir

Calculate total compressibility for the following situation. Assume solution gas/oil ratios do not include stock tank vent gas.

Saturated oil reservoir (below the original bubblepoint)

Sw = 17%, Sg = 5%, TDS = 18 wt %, oil gravity = 27API,Rso = 530 scf/STB, gas gravity = 0.85, Tf = 185F,p = 2000 psi, cf = 3.610-6 psi-1Tsep = 75F, psep = 115 psia

From fluid properties correlations,

pb = 2803 psi

c = 1 429 x 10-4 psi-1co = 1.429 x 10 psi

cg = 5.251 x 10-4 psi-1

cw = 4.995 x 10-6 psi-1

MOnur Sept. 2013



Calculate Compressibility for Low-Pressure, High-Permeability Gas Reservoir

Calculate total compressibility for the following situation. Assume a dry gas.Low-pressure, high-permeability gas reservoir

Sw = 20%, gas gravity = 0.74, Tf = 125F, p = 125 psi,cf = 3.610-6 psi-1, cw = 4 x 10-6 psi [Tf is outside range of

correlations]

F fl id ti l tiFrom fluid properties correlations,

cg = 8.144 x 10-3 psi-1

cw = 4x10-6 psi-1w p

MOnur Sept. 2013



Calculate Compressibility for High-Pressure, Low-Permeability

Gas Reservoir

Calculate total compressibility for the following situation. Assume a dry gas.

High pressure, low permeability gas reservoir

Sw = 35%, TDS = 22 wt %, gas gravity = 0.67, Tf = 270F,p = 5,000 psi, cf = 2010-6 psi-1

From fluid properties correlationsFrom fluid properties correlations,

cg = 1.447 x 10-4 psi-1

cw = 3.512 x10-6 psi-1

MOnur Sept. 2013

part 2 basics wta sept 2013 semester

Documents