6.3.1
Average Reservoir Pressure
The material balance equation describes the whole reservoir in terms of average reservoir pressure, initial volumes of oil, gas and water in-place and cumulative oil, water and gas production volumes. In order to use the material balance equation it is necessary to determine average reservoir pressure for the time (cumulative oil, water and gas production) when the material balance equation is to be applied. Direct measurement of average reservoir pressure would require that all the wells are shut-in and that the bottom-hole pressure is measured at a time after shut-in which is sufficiently long for all the pressure gradients in the reservoir to equalize. This may take months to years (depending on reservoir permeability) and result in considerable loss in revenue because of lost production. The direct measurement approach is therefore impractical.
Pressure data obtained from a pressure buildup test can be used to estimate the average pressure in the volume or area drained by the tested well. These tests require short test times (hours to days) and allow reservoir pressure to be mapped over the field. The mapped pressures may be averaged to give the average reservoir pressure as,
p =
P
pjVpj
P
Vpj (6.6)
where pj and Vpj are the drainage area pressure and pore volume drained by well
j.
6.3.2
Knowns and Unknowns
When solving the material balance equation the parameters may be classified into the following groups of knowns and unknowns.
knowns unknowns Np N Gp G Wp We Swc p (Bo, Bg, Rs) cw cf Bw
The PVT properties (Bo, Bg, Rs) may be considered to be known if the aver-
age reservoir pressure is known and representative fluid samples have obtained and analysed. This reduces the number of unknowns to five but we have only one equation. This is the central problem with the use of the material balance equation.
Before considering specific examples of the application of the material balance equation, lets consider some of the parameters in the material balance equation. Knowns
Np - this is usually known because oil is the primary production target which is
sold to generate revenue.
Gp, Wp - cumulative gas and water production be unknown for older oil and gas
fields because they had little or no value at the time of production. When these are unknown it is not possible to perform material balance calculations for the reservoir.
Swc - is usually considered to be accurately known from petrophysical evaluation.
cw, Bw - these are known, or may be estimated, from laboratory tests on forma-
tion brine. Unknowns
N, G - volumetric estimates of the original oil and gas-cap volumes in-place are always known from the field appraisal stage. These are disregarded as soon as production-pressure data becomes available and an attempt is made to estimate in-place volumes from material balance calculations. This is because volumetric estimates include all the mapped hydrocarbon volume, whereas material balance calculation provides the effective volume or the volume which contributes to ac- tual production. This will usually be smaller than the volumetric estimate due to compartmentilization of the reservoir by faults or low permeability zones. We - this is probably the greatest unknown in reservoir development - whether
there has been any water influx or not. One of the most important uses of material balance calculations is to estimate water influx.
p - although we usually consider reservoir pressure to be known, problems with the interpretation of pressure buildup test data may introduce serious errors and there may be considerable uncertainty in estimates of average reservoir pressure. cf - pore volume or formation compressibility is usually considered to be small
and constant. In some cases it may be large and variable. When it is large, compaction may form a major part of the reservoir drive energy and usually leads
to considerable subsidence at the surface. This may be of little consequence on land in remote areas but may cause serious problems for operations offshore.
Problem 6.1Calculating water influx from material balance for history matching aquifer performance
The first step in characterizing or history matching an aquifer is to calculate water influx from available production and pressure data. You will be performing this history match in the reservoir engineering course which follows from the present course. After the aquifer has been characterized, the resultant aquifer model is attached to a numerical reservoir simulation model which is used to predict future reservoir performance.
The reservoir for this exercise is a small offshore oil field which has been on-stream for only 700 days. The field was shut-in for a 250 day period for upgrading of the gathering system and production facilities. There was a strong and clear aquifer response to the shut-in (use Mathcad to plot the field pressure as a function of time to see the response).
The field production history is given in the table below. PRODUCTION HISTORY Time P Np Gp Wp (day) (psia) (MMSTB) (BSCF) (MMSTB) 0 4217 0.00000 0.00000 0.00000 50 3915 0.34270 0.17821 0.00000 100 3725 0.63405 0.32970 0.00121 150 3570 1.06898 0.55587 0.02636 200 3450 1.36788 0.71130 0.07041 250 3390 1.64397 0.85487 0.12218 300 3365 1.91465 0.99562 0.17304 350 3600 1.91465 0.99562 0.17304 400 3740 1.91465 0.99562 0.17304 450 3850 1.91465 0.99562 0.17304 500 3900 1.91465 0.99562 0.17304 550 3920 1.91465 0.99562 0.17304 600 3720 2.11402 1.09929 0.20368 650 3650 2.24921 1.16959 0.25094 700 3640 2.33133 1.21229 0.31690
The initial oil in-place is estimated (volumetrically) to be 33.2 MMSTB. Reservoir system properties were estimated to be:
cf = 5×10−6psi−1
cw = 3×10−6psi−1
Swc = 0.248
PVT data for the reservoir oil is given in the following table. PVT DATA P Bo Rs Bg Bw (psia) (RB/STB) (SCF/STB) (RB/SCF) (RB/STB) 3365 1.2511 510 - 1.0 3465 1.2497 510 - 1.0 3565 1.2483 510 - 1.0 3665 1.2469 510 - 1.0 3765 1.2455 510 - 1.0 3865 1.2441 510 - 1.0 3965 1.2427 510 - 1.0 4065 1.2413 510 - 1.0 4165 1.2399 510 - 1.0 4265 1.2385 510 - 1.0
Reservoir temperature is 210oF and the gas gravity is 0.69.
Determine the cumulative water influx for each of the 50 day time periods in the production history table.
Solution hint
You need to calculate a cumulative water influx volume for each 50 day period (a total of 14 calculations). Each calculation is identical to the calculations performed in Examples 6-1 to 6-6. You can simply use [MBE.mcd] to do the calculation for each period. Alternatively, you could modify [MBE.mcd] to read- in the production data and do the 14 calculations in one pass or prepare your owm spreadsheet using whatever software you are most comfortable with. [Answer: We at 700 days is 2.778 MMRB]