Inflow Performance

Instructional ObjectivesCalculate the IPR for oil wellsCalculate the IPR for gas wells

Reservoir CapabilitiesDarcys LawLiquid flow in Laminar Flow through a permeable medium is described by Darcys Law

Reservoir Capabilitiess = Skin Factor (dimensionless)

Productivity IndexA common indicator of liquid reservoir behavior is PI or productivity index Referred to as J in SPE nomenclature

Productivity Index in Terms of Darcys Law

Calculating FlowrateUsing PI, we can calculate flowrate, q, quickly and easily from

Exercise 1Given reservoir parameters:k =30 mdh =40 fto =0.5 cpBo =1.2 RB/STBhole size = 8 inchess = 0

Exercise 1Calculate:J for re = 1,000 ftq for a drawdown ( ) of 750 psi q for a drawdown of 1,000 psiWith = 3,000 psia, calculate q for a complete drawdown (absolute open flow potential).

Multiphase FlowBubblepoint pressure (pb)Pressure at which first bubble of gas is released from reservoir oils

Multiphase FlowVogels BehaviorIPR Curve - Vogel plotted the data using the following dimensionless variables

and

Vogel Curve

Multiphase FlowMathematical model for Vogels curve

Multiphase FlowMathematical relationship between Vogel (qmax) and Darcy (AOF)

Finding Vogel qmax

Exercise 2Reservoir parameters: =2,350 psiak =140 mdh =35 fto=0.8 cpBo =1.25 rbbl/STBre =2,000 ftrw =0.411 ftpb =3,000 psias=2

Exercise 2Calculate JCalculate qmaxConstruct IPR curve

Multiphase FlowCombination Darcy/Vogel

Multiphase FlowHow to find qmax:

Gas ReservoirsPseudosteady StateThe behavior of gas flowing in laminar flow through a porous medium (Darcys Law)

Calculation of IPR Curve

Using the Real Gas Pseudopressure (pp (p))and

Exercise 3 Plot the IPR CurveGiven the following data and using the pressure squared relationship:

k= 100 mdh= 20 ftre= 1,500 ftrw= 0.33 fts= 0= 0.02 cpT= 610R= 0.9= 4,000 psigg= 0.65

IPR in Gas ReservoirsJones Gas IPRProblem - Darcys law valid for laminar flow onlyHigh permeability gas wells produce in turbulent flow near the wellbore

Definitions

Determination of h

Solving Jones EquationThe flow rate is:

Solving Jones EquationThe value of the AOF is then given by:

Solving Jones EquationSolve for the well flowing pressure:

Exercise 4Calculate the IPR curve for hp = 20 ft and hp = 10 ft with the data in notesCalculate the IPR using Darcys law onlyCompare the three IPR curves

Transient IPR CurvesAssumptionsDarcys and Jones laws assume that the average pressure is constant Drainage radius, re, is constant and that These assumptions are true in pseudo-steady state only, i.e. when all of the outer boundaries of the reservoir are reached.

Transient IPR CurvesThe time to reach pseudo-steady state (pss), tstab, can be calculated with the following equation

Exercise 5 Oil Well Stabilization TimeFind tstab with the following data f = 0.1o = 0.5 cpct = 2 X 10-5 psi-1 re = 1,500 ftFor the following values of k:0.1 md, 1.0 md, 10 md, and 100 md

Exercise 6 Gas Well Stabilization TimeFind tstab with the following data f = 0.1g = 0.02 cpct = 2 X 10-4 psi-1 re = 1,500 ftFor the following values of k:0.1 md, 1.0 md, 10 md, and 100 md

Transient Flow

Transient IPR CurvesTransient Flow Equationfor oil wells

for gas wells (low pressure only)

References

Inflow PerformanceInflow PerformanceCalculate the IPR for an oil well producing above or below the bubblepointCalculate the IPR for a gas well

Inflow PerformanceNomenclature:

q = flow rate (STB/day)k = reservoir permeability (md)h = height of the pay zone (ft) = average reservoir pressure (psi) = well flowing pressure at the sand face (psi)o = viscosity of the fluid (cp)Bo = formation volume factor (RB/STB)re = drainage radius (ft)rw = wellbore radius (ft)

The equation uses average reservoir pressure, p. The reservoir is circular with the well in the center. The outer boundary is closed (no flow).Inflow Performancewhere:k=Permeability of reservoir (md)ka =Permeability of damaged zone (md)ra =Radius of damaged zone (ft)rw=Wellbore radius (ft)

Inflow PerformanceWhile determining J from test data [q/ - pwf] is accurate, it can hide performance potential because it is measured downstream of the perforations. Thus, the effect of poor or plugged perforations is included in the productivity index of the well.While these data can be obtained from a test (and usually are) one can calculate them using Darcys Law.( - pwf) is usually called the drawdown.Inflow PerformanceThe equation above is a better indicator of reservoir performance because it describes the behavior upstream of the perforations.It assumes radial flow in a closed reservoir.Inflow PerformanceThe flow rate when we draw the well down completely (pwf = atmospheric pressure) is called the absolute open flow potential (AOF).Inflow PerformanceInflow PerformanceInflow PerformanceA well does not always produce only liquid. When pressure drops below the bubblepoint pressure, bubbles of gas start to form within the liquid. The pressure at which the first bubble of gas is released is called the bubblepoint pressure (pb). Moreover, as the quantity of gas increases, o increases, and the relative permeability to oil, kro, decreases.

Inflow PerformanceVogel1 simulated the performance of a large number of wells with a reservoir pressure below the bubblepoint pressure pb, and plotted pwf/p versus qo/qmax. qmax is defined as the theoretical maximum possible flow rate, at pwf = 0. The abbreviation IPR stands for Inflow Performance Relation. An IPR curve is a plot of flowing bottomhole pressure, pwf, vs production rate, q. Inflow PerformanceInflow PerformanceThis equation is valid for water cut below 50%.The pressure drop due to perforations/completion is already taken into account in the equation.Inflow PerformanceUse of this relationship allows us to make an Inflow Performance (IPR) curve that is valid upstream of the perforations, and that does not mask reservoir potential.Inflow PerformanceInflow PerformanceInflow Performance

Inflow PerformanceWhen is above pb, we can have both Darcy and Vogel behavior (depending on the value of the drawdown) for the IPR curve.

Inflow PerformanceInflow PerformanceThis equation is applicable for low-pressure gas reservoirs (< 2,000 psia). We can write a more general equation, valid at all pressures, in terms of the real gas pseudopressure, defined later.

Inflow PerformanceInflow PerformanceThis equation is valid for all pressure ranges.2The real gas pseudopressure,3 pp(p), accounts for gas viscosity and deviation factor changes with pressure.Inflow PerformanceNote that the average reservoir pressure, p, is high. however, we will use the pressure-squared IPR relation for simplicity. Most software programs allow the use of pseudo pressure, pp(p), for IPR calculations.Inflow PerformanceIn this equation, bq2 is the turbulent flow term, while aq is the laminar flow term. The more perforations present, the less turbulence will occur around the wellbore. It is then obvious that b must be somehow related to 1/hp, with hp being the perforated height. Note also that Jones IPR equation can use the real gas pseudo pressure2 for application at any reservoir pressure.Inflow Performancewhere: is calculated with the following formula: ,where k is the effective permeability to gas in md.

Inflow PerformanceNote that, as previously stated, b is strongly influenced by hp and that a comes directly from Darcys law. It should also be noted that, in case of deviated wells or steeply dipping beds, the perforated height, hp, could be greater than the pay zone height, h.

Inflow PerformanceInflow PerformanceInflow PerformanceInflow PerformanceData:k = 100 mdh = 20 ftre = 1,500 ftrw = 0.33 fts = 0 = 0.02 cpT = 610R= 0.9 = 4,000 psiag = 0.65

Inflow PerformanceInflow PerformanceNote that, in the formula to calculate time to pseudo-steady state, the drainage radius is squared. Thus, it is very important to have a good estimate of re when calculating time to pseudo-steady state.

Inflow PerformanceInflow PerformanceInflow PerformanceBefore pseudo-steady state is reached, the IPR curves will exhibit the characteristics shown in the figure until stabilized.Inflow PerformanceIf t < tstab, we have to use the transient flow equations, given above.

Inflow PerformanceReferences

1.Vogel, J.F.: Inflow Performance Relationships for Solution-Gas Drive Wells, JPT (Jan. 1968) 83-92.2.Lee, W.J. and Wattenbarger, R.A.: Gas Reservoir Engineering, SPE Textbook Series, Vol. 5, 1996.3.Al-Hussainy, R., Ramey, H.J. Jr., and Crawford, P.B.: The Flow of Real Gases Through Porous Media, JPT (May 1966) 624-636; Trans, AIME, 237.