Water influx Carter-Tracy Model

 This method is an approximate solution to the diffusivity equation. It can be

combined conveniently with a suitable material balance equation to predict the

performance of water-drive reservoirs. 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. Mathemat￾ically, 

it is calculated as

Steps in Calculating Carter-Tracy’s Aquifer Model

Step 1: Calculate the total pressure drop at each time step

Step 2: Calculate the dimensionless time at each time step

Step 3: Calculate the dimensionless pressure and pressure derivative at each time

step

Step 4: Calculate the water influx at each time step (Table 4.8)

Table 4.8 Carter-Tracy aquifer model calculation

Example 4.5

Repeat Example 4.3 using the Carter Tracy’s aquifer model to calculate the cumu￾lative water influx at each time step.

Water Influx

Introduction

Water influx can also be referred to as water encroachment or aquifer influx. It can be

defined as an underground layer of water-bearing porous rock which flows out into

any available space in the reservoir rock. In this context, an aquifer is referred to as a

large pool of water body underlying a hydrocarbon accumulation in the reservoir

structure that is made up of more than one fluid arranged according to density

differences. Prior to hydrocarbon accumulation, the original system was occupied

or filled with water and during the drainage process; the migrated hydrocarbons from

the source rock displaced some of the water out of the pore space in the reservoir.

This means that majority of hydrocarbon pools discovered globally have an associ￾ated aquifer which could be a key source of energy (primary recovery) for the

hydrocarbon production once a well is drilled.

4.1.1 Classification of Aquifer Influx

Aquifer influx can be classified based on pressure maintenance, outer boundary

conditions, flow regime, flow geometry as shown in Fig. 4.1.

The classification of aquifer system as shown in Fig. 4.1, is key to understanding

and evaluation of hydrocarbon reservoirs performance. As hydrocarbon is produced

from the reservoir, the pressure of the reservoir declines (changes) and the aquifer

responds to offset the pressure decline due to fluids production, which is dependent

on the strength of the aquifer. Besides, if there is a strong support from the aquifer,

there will be a gradual decline in the reservoir pressure leading to a good hydrocar￾bon recovery. Also, there will be fairly steady gas-oil ratio during the life of the

reservoir with excessive water production in shallow wells.

Consequently, in evaluating the performance of hydrocarbon reservoirs, we need

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

Aquifer Models

There are several analytical aquifer models presented in the past to estimate the

amount of water encroaching into hydrocarbon reservoirs and some of these models

are briefly presented below. The aquifer analytical models make use of simplified

assumptions that do not consider the heterogeneous nature of the reservoir but a

relatively homogeneous reservoir which has deterred the ideal comparison that is

adopted in the analytical solutions. But when the equations are accurately

discretization, they are relatively easy to program in computer spreadsheets with

the exception of the Van Everdingen & Hurst, whose model does not demand much

computer power.

4.2.1 Pot Aquifer Model

This method is one the simplest model for estimating the amount of water

encroaching into hydrocarbon reservoirs. Mathematically, it is given as

Schilthuis Model

Schilthuis (1936) was the first to develop useful expressions for calculating water

influx in a hydrocarbon reservoir. His steady-state expression is given by:

Hurst Modified Steady-State Model

Analysis of water expansion into a hydrocarbon reservoir indicates that water influx

should often be an unsteady-state process. Hence, the Hurst modified steady-state

eq. (1958) should give better results. The equation is:

Van Everdingen & Hurst Model

Van Everdingen & Hurst method of calculating water influx 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. To abate the

intricacy of water influx calculations, Carter and Tracy (1960) proposed a direct

water influx calculation technique that does not require superposition. The primary

difference between Carter-Tracy and Van Everdingen & Hurst techniques is that the

former assumes constant water influx rates over each finite time interval. Hence, the

cumulative water influx at any time “tn” can be calculated directly from previous

values obtained at tn-1.

 

Condensate Reservoir Calculation

Condensate Reservoir Calculation

The example applies here for calculating condensate in place was written by Engr.

Ogbarode Napoleon Ogbon in his Lecture note on Natural Gas Engineering II.

3.5.1 Applications of Gas and Condensate Inplace Value

• Determination of economic value of gas and condensate in place to make a

decision on project economic viability

3.5.2 Major Points for Consideration

• As the gas-condensate reservoir fluid pressure drops below the dew point, liquid

hydrocarbon (condensate) will begin to drop.

• It is necessary to recombine the condensate with the gas in a proper ratio to

calculate the original volume of gas-in-place 

in the reservoir 

Data Required to Allow Estimates of the Gas-in-Place

Volume Are

• The geologic data

• The reservoir data

• The production data

• The geologic and reservoir data are used to provide plots of gas

compressibility, etc.

• This method uses standard charts and simple equations to calculate hydrocarbon￾in-place volumes in gas-condensate reservoirs.

3.5.4 Method Basic Requirements

• It is based on correlations established by Rzasa and Katz (2011) and provides a

means to calculate the gas-in-place volume in a gas-condensate reservoir Based

on

– The amount of produced gas

– The amount of produced associated condensate.

• Plots of correlations based on this method are readily available for use.

• However, it requires a clear understanding of the behaviour of oil and gas under

various reservoir and surface operating conditions including:

– Reservoir pressure and temperature, or depth to calculate the required

parameters,

– Compositions of oil and gas or their gravities and molecular weights,

– Gravities and production rates of separator condensate and gas,

– Rock porosity,

– Gas or interstitial water saturation

– Area-thickness, in the absence of which calculations are based on one acre of

reservoir volume.