Water Influx

Abstract

One of the forces responsible for the primary recovery of hydrocarbon, is the encroachment of a large pool of water body underlying the hydrocarbon accumulation in the reservoir structure. In the evaluation of hydrocarbon reservoir performance, it is paramount to accurately determine the amount of water encroaching into the reservoir whose value is dependent on the water viscosity, the permeability of the rock in the aquifer and the cross-sectional area between the water zone and the region where the hydrocarbon is accumulated. There are several analytical aquifer models presented in the past to estimate the amount of water encroaching into reservoirs, some of which can be applied to linear or radial aquifer, bottom aquifer and/or edge water, finite and/or infinite-acting. Van Everdingen & Hurst method requires the principle of superposition which is a tedious exercise, but it provides an exact solution to the radial diffusivity equation and can be applied at the early stage. The Carter-Tracy aquifer models can be applied to both finite and infinite-acting aquifers, it can be applied to both radial and linear aquifers and also applies to edge-water drive reservoirs only. Fetkovich model applies to both radial and linear aquifers, finite-acting aquifers, edge-water and bottom-water drive reservoirs. Thus, to understand the various aquifer models, several solved example questions and exercises are presented.

Exercises

• 1. What does it imply for a reservoir pressure profile to show a gradual decline?

• 2. Which of the aquifer model provides an exact solution to the radial diffusivity equation?

• 3. Which of the aquifer model provides an approximate solution to the radial diffusivity equation?

• 4. What is the primary difference between Carter-Tracy and Van Everdingen & Hurst Techniques?

• 5. State the aquifer models that can be applied to both finite and infinite-acting aquifers

• 6. Which of the aquifer models can be combined with material balance equation?

• 7. Why is Van Everdingen & Hurst aquifer model difficult to program in computer model?

• 8. State the aquifer model that can be applied to both radial and linear aquifers and also applies to edge-water drive reservoirs only.

• 9. Explain the concept of superposition as it applies to water influx model

• 10. Distinguish between van Everdingen-Hurst and Fetkovich model in terms of transient state flow

• 11. Which of the aquifer models calculates water influx less than the values predicted by other models?

• 12. A reservoir whose aquifer is strongly supported by edge water is best fitted with which aquifer model

• 13. Which of the aquifer model applies to finite-acting aquifers only?

• 14. State the aquifer model that assumes constant pressure at the original reservoir/aquifer boundary

Ex 4.1 :

Calculate the water influx at the end of 1, 2 & 5 years into a circular reservoir with an aquifer of infinite extent. Effective water permeability and compressibility are 100 mD and 1.0×10⁻⁶ psi⁻¹ respectively, reservoir viscosity is 0.84, the radius of the reservoir is 2100 ft, reservoir thickness is 27.5 ft with porosity of 22%. The initial and current reservoir pressure are 2700psig and 2380psig respectively.

Ex 4.2 :

Given the following reservoir and aquifer information with an infinite-acting aquifer:

$$ {r}_w=0.235 ft,\kern0.5em {r}_e=2200 ft,\kern0.5em {k}_w=120 mD,\kern0.5em h=40 ft,\kern0.5em {P}_i=4260 psi,\kern0.5em ,\kern0.5em {\mu}_w=0.65 cp,\kern0.5em \varnothing =0.25,\kern0.5em {c}_{tw}=1.07\times {10}^{-6},\kern0.5em \theta ={270}^{{}^{\circ}} $$

The pressure history is given as

Time (years)	Pressure (psi)
0	4260
1	4235
1.5	4203
2	4175
2.5	4115

Ex 4.3 :

Using the radial aquifer data provided below, determine the cumulative water influx at each time step, using Hurst van Everdingen and compare result with Fetkovich & Carter-Tracy models.

Time (yrs)	0	1	2	3	4	5
Pressure (psia)	2987	2962	2927	2882	2837	2793
WD(tD)	0	5.7126	9.0465	11.4326	13.1035	14.3835

Additional Data: K_w = 275 mD, μ_w = 0.94 cp, h = 56 ft, aquifer radius, r_a = 48,000 ft, reservior radius, r_o = 14,000 ft, porosity = 22%, encraochment angle of 1200, total compressibility = 7.50 x 10⁻⁶ psi⁻¹.

Ex 4.4 :

Calculate the cumulative water influx at each time given in the below of a finite reservoir sustended at encraochment angle of 120° with the following properties K_w = 78 mD, μ_w = 0.73 cp, h = 128 ft, aquifer radius, r_a = 30,000 ft, reservior radius, r_o = 6000 ft, porosity = 18%, total compressibility = 7.98 × 10⁻⁶ psi⁻¹.

Time (yrs)	0	1	2	3	4	5
Pressure (psia)	2850	2610	2400	2220	2070	1950