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 crosssectional 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 infiniteacting. 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 CarterTracy aquifer models can be applied to both finite and infiniteacting aquifers, it can be applied to both radial and linear aquifers and also applies to edgewater drive reservoirs only. Fetkovich model applies to both radial and linear aquifers, finiteacting aquifers, edgewater and bottomwater drive reservoirs. Thus, to understand the various aquifer models, several solved example questions and exercises are presented.
Keywords
 Aquifer
 CarterTracy
 Van Everdingen & Hurst
 Fetkovich
 Reservoir
 Diffusivity equation
 Edge water
 Bottom water
 Radial aquifer
 Linear aquifer
 Finite aquifer
 Infinite aquifer
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References
Carter RD, Tracy GW (1960) An improved method for calculating water influx. Trans AIME 219:415–417
Fetkovitch MJ (1971) A simplified approach to water influx calculationsfinite aquifer systems. J Pet Technol 23:814–828
Schilthuis RJ (1936) Active oil and reservoir energy. Trans AIME 118:37
Van Everdingen, A. F (1953) The skill effect and its influence on the production capacity of a well. Trans. AIME, 198: 171–176
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Exercises
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 CarterTracy and Van Everdingen & Hurst Techniques?

5.
State the aquifer models that can be applied to both finite and infiniteacting 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 edgewater drive reservoirs only.

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

10.
Distinguish between van EverdingenHurst 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 finiteacting 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 infiniteacting aquifer:
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 & CarterTracy models.
Time (yrs)  0  1  2  3  4  5 

Pressure (psia)  2987  2962  2927  2882  2837  2793 
W_{D(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 
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Okotie, S., Ikporo, B. (2019). Water Influx. In: Reservoir Engineering. Springer, Cham. https://doi.org/10.1007/9783030023935_4
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DOI: https://doi.org/10.1007/9783030023935_4
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