Water influx

All hydrocarbon reservoirs are surrounded by water-bearing rocks called aquifers which they effect on reservoir performance. it's a key role for production evaluation and therefore it should be managed.

1. Water Influx Reservoir Management Sadeq Rajabi

2. Introduction Nearly all hydrocarbon reservoirs are surrounded by water-bearing rocks called aquifers . Aquifers may be substantially larger than the oil or gas reservoirs they adjoin as to appear infinite in size Aquifers may be so small in size as to be negligible in their effect on reservoir performance 2

3. As reservoir fluids are produced, a pressure differential develops between the surrounding aquifer and the reservoir. The aquifer reacts by encroaching across the original hydrocarbon-water contact. Many gas and oil reservoirs produced by a mechanism termed water drive . (natural water drive) water drive is dependent on the size of aquifer and the pressure drop from the aquifer to the reservoir. During production aquifer response comes in a form of water influx, commonly called water encroachment 3

4. Classification of AQUIFERS Degree of pressure maintenance Flow regimes Outer boundary conditions Flow geometries 4

5. Degree of Pressure Maintenance Active water drive : The term active water drive refers to the water encroachment mechanism in which the rate of water influx equals the reservoir total production rate. during any long period, the production rate and reservoir pressure remain reasonably constant Partial water drive: a relatively small. aquifer can guarantee only limited pressure maintenance Limited water drive: The term active water drive refers to the water encroachment mechanism in which the rate of water influx is less than the reservoir total production rate. 5

6. where We = cumulative water influx, bbl t = time, days Np = cumulative oil production, STB GOR = current gas-oil ratio, scf /STB Rs = current gas solubility, scf /STB Bg = gas formation volume factor, bbl / scf Wp = cumulative water production, STB dNp / dt = daily oil flow rate Qo , STB/day dWp / dt = daily water flow rate Qw , STB/day dWe / dt = daily water influx rate ew , bbl /day (GOR − Rs ) dNp / dt = daily free gas flow rate, scf /day 6

7. OUTER BOUNDARY CONDITIONS Infinite system indicates that the effect of the pressure changes at the oil/aquifer boundary can never be felt at the outer boundary. Finite system indicates that the aquifer outer limit is affected by the influx into the oil zone and that the pressure at this outer limit changes with time. 7

8. FLOW REGIMES & FLOW GEOMETRIES Steady-state Semisteady -state Unsteady-state Edge-water drive Bottom-water drive Linear-water drive 8

9. WATER INFLUX MODELS Pot aquifer Schilthuis ’ steady-state Hurst’s modified steady-state The van Everdingen -Hurst unsteady-state Edge-water drive Bottom-water drive The Carter-Tracy unsteady-state Fetkovich’s method unsteady-state Radial aquifer Linear aquifer 9

10. Small or pot aquifer Where We = cumulative water influx, bbl c w = aquifer water compressibility, psi−1 c f = aquifer rock compressibility, psi−1 W i = initial volume of water in the aquifer, bbl where r a = radius of the aquifer, ft r e = radius of the reservoir, ft h = thickness of the aquifer, ft φ = porosity of the aquifer Where f = fractional encroachment angle 10

11. Schilthuis ’ steady-state Where e w = rate of water influx, bbl /day k = permeability of the aquifer, md h = thickness of the aquifer, ft r a = radius of the aquifer, ft r e = radius of the reservoir t = time, days C = the water influx constant , bbl /day/psi 11

12. Hurst’s modified steady-state dimensionless radius 12

13. Dimensionless diffusivity equation for the following two reservoir-aquifer boundary conditions: • Constant terminal rate • Constant terminal pressure Constant terminal rate the rate of water influx = constant(for a given period) the pressure drop at the reservoir-aquifer boundary is calculated Constant terminal pressure a boundary pressure drop = constant (over some finite time period) water influx rate is determined 13 The van Everdingen -Hurst (VEH) model

14. 14 an edge-water drive a bottom-water drive

15. 15 Edge-Water Drive The authors expressed their mathematical relationship for calculating the water influx in a form of a dimensionless parameter that is called dimensionless water influx WeD. Dimensionless water influx as a function of the dimensionless time tD and dimensionless radius rD. Where t = time, days k = permeability of the aquifer, md φ = porosity of the aquifer μw = viscosity of water in the aquifer, cp ra = radius of the aquifer, ft re = radius of the reservoir, ft cw = compressibility of the water, psi−1 cf = compressibility of the aquifer formation, psi−1 ct = total compressibility coefficient, psi−

16. 16

17. 17 W e = cumulative water influx, bbl B = water influx constant, bbl /psi Δp = pressure drop at the boundary, psi W eD = dimensionless water influx

18. 18 Pressure Drop in Boundary principle of superposition where (We) Δ p1 = B Δ p1 ( W eD )t3 (We) Δ p2 = B Δ p2 ( W eD ) t3 − t1 (We) Δ p3 = B Δ p3 ( W eD ) t3 − t2

19. Bottom-Water Drive Coats (1962) W eD as a function of r D , t D , and z D where kv = vertical permeability kh = horizontal permeability Allard and Chen (1988) Where z D = dimensionless vertical distance h = aquifer thickness, ft 19

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21. The Carter-Tracy unsteady-state where B = the van Everdingen -Hurst water influx tD = the dimensionless time as defined by Equation 10-17 n = refers to the current time step n − 1 = refers to the previous time step Δ pn = total pressure drop, pi − pn , psi pD = dimensionless pressure p′D = dimensionless pressure derivative 21

22. The following approximation could also be used between tD > 100: 22

23. Fetkovich’s method where e w = water influx rate from aquifer, bbl /day J = productivity index for the aquifer, bbl /day/psi p a = average aquifer pressure, psi p r = inner aquifer boundary pressure, psi where Wi = initial volume of water in the aquifer, bbl ct = total aquifer compressibility, cw + cf , psi−1 pi = initial pressure of the aquifer, psi f = θ/360 23

24. Lee and Wattenbarger (1996) where w = width of the linear aquifer L = length of the linear aquifer rD = dimensionless radius, ra /re k = permeability of the aquifer, md t = time, days θ = encroachment angle h = thickness of the aquifer f = θ/360 24

25. References Advanced Reservoir Engineering by Paul McKinney, Tarek Ahmed Petrowiki 25

26. THANK YOU 26