Reservoir Performance Prediction

Abstract

Reservoir performance prediction is a key aspect of the oil and gas field development planning and reserves estimation which depicts the behaviour of the reservoir in the future; its success is dependent on accurate description of the reservoir rock properties, fluid properties, rock-fluid properties and flow performance. It therefore implies that engineers must have sound knowledge of the reservoir characteristics and production operations optimization and more importantly, to develop a mathematical model that will adequately depict the physical processes occurring in the reservoir such that the outcome of any action can be predicted within reasonable engineering tolerance of errors. Several Authors such as Muskat, Tarner’s, Tracy’s and Schilthuis developed a method of reservoir performance prediction based on material balance equation (MBE) by combining the appropriate MBE with the instantaneous GOR. These techniques are iterative and the calculations are repeated at a series of assumed reservoir pressure drops. These calculations are usually based on stock-tank barrel of oil-in-place at bubble point pressure and above the bubble point pressure, the cumulative oil produced is calculated directly from he material balance equations. In this chapter, the various mathematical models and algorithms for each technique are explicitly presented and validated with case studies. Also, at the end of the chapter, several exercises and references are given to further help strengthen readers understanding of the subject matter.

Exercises

Ex 11.1 :

Given the data below of a volumetric oil reservoir

Bubble point pressure, P b	1700 psia
STOIIP, N	77.89 MMstb
Connate water saturation, S wc	25%
Water influx, W e	0
Water injection, W inj	0
Reservoir temperature	2000 F

Fluid properties
P (psi)	Bo (bb//STB)	Rs (scf/STB)	Bg (cuft/SCF)	μo (cp)	μg (cp)
1700	1.265	962	0.00741	1.19	0.0294
1500	1.241	873	0.00842	1.22	0.0270
1300	1.214	784	0.00983	1.25	0.0251
1099	1.191	689	0.01179	1.3	0.0235
900	1.161	595	0.01471	1.35	0.0232
700	1.147	495	0.011931	1.5	0.0230
501	1.117	392	0.02779	1.8	0.0226
300	1.093	282	0.04828	2.28	0.0223
100	1.058	150	0.15272	3.22	0.0209

kg/ko Curve versus liquid saturation

Using the Tarner method and adopting the following criteria for the maximum allowable error:

$$ \left| Error\right|=\left|\frac{\ {\left({G}_p\right)}_{GOR,\kern0.5em 2870}-{\left({G}_p\right)}_{MBE,\kern0.5em 2870}}{\ {\left({G}_p\right)}_{GOR,\kern0.5em 2870}}\right|\times 100\%\le 1\% $$

Calculate the following:

• The oil cumulative production for (P = 1500, 1300, 1099)

• The instantaneous gas-oil production ratio

• The gas cumulative production

Ex 11.2 :

Repeat Ex 11.1 using Muskat method

Ex 11.3 :

Given the following data of Level GT oil reservoir in Ugbomro:

Bubble point pressure, P b	2650 psia
STOIIP, N	12.89 MMstb
Connate water saturation, S wc	23%
Water influx, W e	0
Water injection, W inj	0
Reservoir temperature	2000 F

Pressure (psia)	Bo (rb/STB	Bg (rb/STB)	Rs (scf/STB)	Uo (cp)	Uo (cp
2650	1.3814	0.000895	680	0.956	0.018
2180	1.3791	0.000947	574	1.236	0.0165
1825	1.3572	0.000988	528	1.492	0.0152

The relative permeability ratio is calculated as

$$ \frac{k_{rg}}{k_{ro}}=0.000128{e}^{17.257{S}_g} $$

Predict the performance (oil and gas production) of the reservoir at 2180 psia and 1825 psia

Ex 11.4 :

The following data are obtained from a depletion drive reservoir:

P.psia	2600	2400	2100	1800	1500	1200	1000	700	400
Rsi, SCF/STB	1340	1340	1340	1280	1150	985	860	662	465
ΒO, bbl/STB	1.45	1.46	1.480	1.468	1.440	1.339	1.360	1.287	1.202
Βg, B/SCF × 10−3	…	…	1.283	1.518	1.853	2.365	2.885	4.250	7.680
μO/μg	…	…	34.1	38.3	42.4	48.8	53.6	62.5	79.0

Additional Data:

Initial reservoir pressure, P i	2925 psia
Bubble point pressure, P b	2100 psia
STOIIP, N	100 MMstb
Connate water saturation, S wc	15%
Initial oil formation volume factor, β oi	1.429 bbl/stb

Kg/Ko	26	12.5	3.3	0.8	0.19	0.022	0.01
So,%	30	40	50	60	70	80	84

Predict the reservoir performance, using Tarner method, effective from the time when the pressure is 2400 psia up to the time when the pressure becomes 400 psia. The productivity index was determined as 0.5 bbl/day/psi when the reservoir pressure was 2400 psia. Assume P_wf = 200 psia and J₂ = J₁ (β_O1/ β_O2) to plot P, Np, Gp, Rp & qo Vs. time.

Ex 11.5 :

Given the following data for a depletion drive reservoir, calculate the cumulative oil and gas production and the average GOR when the pressure reaches 700 psi using Tarner method.

Oil viscosity, μ o	1.987 cp
Gas viscosity, μ g	0.01426 cp
STOIIP, N	90.45 MMstb
Connate water saturation, S wc	20.5%

P, psi	ΒO, bbl/STB	Rs SCF/STB	Βg, bbl/SCF	Np, MMSTB	Gp, MMSCF	Ri. SCF/STB
1125	1.1236	230	--------	0.0	0.0	------
900	-------	--------	--------	6.76	--------	-------
800	1.0965	150	--------	9.41	4708	850
700	1.0925	132	0.003748	?	?	?

Kg/Ko	0.018	0.02	0.025	0.028	0.033	0.038	0.044	0.050
Sg,%	10	10.5	11	11.5	12	12.5	13	13.5

Ex 11.6 :

The following data are obtained from a gas cap drive reservoir:

P.psia	1710	1400	1200	1000	800	600	400	200
Rsi, SCF/STB	462	399	359	316	272	225	176	122
ΒO, bbl/STB	1.205	1.18	1.164	1.148	1.131	1.115	1.097	1.075
Βg, bbl/SCF	0.00129	0.00164	0.00197	0.00245	0.00316	0.00436	0.0068	0.0143
μO/μg	…	113.5	122	137.5	163	197	239	284

Additional Data:

Initial reservoir pressure, P i	1710 psia
Current point pressure, P	1400 psia
STOIIP, N	40 MMstb
Gas initially in place, G	790*N
Cumulative oil produced, N p @1400 psia	0.176*N stb
Solution GOR, R s	8490 scf/stb
Gas cap size, m	4.0
Connate water saturation, S wc	15%
Reservoir, β oi	1.429 bbl/stb

Kg/Ko	0.9	0.4	0.18	0.075	0.034	0.02	0.01	0.0028
SL,%	70	75	80	85	90	92.5	95	97.5

• (a) Predict the reservoir performance, using Tarner method, effective from the time when the pressure is 1400 psia up to the time when the pressure becomes 200 psia.

• (b) Plot the predicted reservoir performance (Np Vs. P. & GOR)

Ex 11.7 :

Given the following data for a saturated depletion drive reservoir. Calculate the cumulative oil and gas production and the average GOR, when the pressure reaches 2100 psi using Schilthuis method. μ_O / μ_g = 41.645 at 2100 psi, Initial reservoir pressure = 2500 psi, and connate water saturation = 0.20.

P, psi	ΒO, bbl/STB	Rs SCF/STB	Βg × 10−3, bbl/SCF	Np/N	Gp/N	Ri. SCF/STB
2500	1.498	721	1.048	0.0	0.0	721
2300	1.463	669	1.155	0.0168	11.67	669
2100	1.429	617	1.280	?	?	?

Kg/Ko	27.0	7.5	0.3	0.55	0.2	0.05	0.01	0.001
SL,%	30	40	50	60	70	80	90	93

Ex 11.8 :

Given the following data for a depletion drive reservoir, calculate the cumulative oil and gas production and the average GOR when the pressure reaches 1200 psi using Schilthuis method. N = 10.025 MM STB, Sw = 0.22. μ_o / μ_g = 108.96 at 1200 psi. Pi = 3013 psi, Pb =2496 psi.

P, psi	ΒO, bbl/STB	Rs SCF/STB	Βg bbl/SCF	Np/N	Gp/N	Ri. SCF/STB
3013	1.315	650	--------	0.0	0.0	650
2496	1.325	650	-------	-------	--------	650
1302	1.233	450	---------	1.179	1.123	2080
1200	1.224	431	0.001807	?	?	?

Kg/Ko	0.71	0.255	0.095	0.03	0.01
SL,%	70	75	80	85	89

Ex 11.9 :

Given the following data for a saturated depletion drive reservoir. Calculate the cumulative oil and gas production and the average GOR, when the pressure reaches 1900 psi using Schilthuis method. μ_O / μ_g = 41. 645 at 1900 psi, Initial reservoir pressure = 2500 psi, and connate water saturation = 0.20.

P, psi	ΒO, bbl/STB	Rs SCF/STB	Βg × 10−3, bbl/SCF	Np/N	Gp/N	Ri. SCF/STB
2500	1.498	721	1.048	0.0	0.0	721
2300	1.463	669	1.155	0.0168	11.67	669
2100	1.429	617	1.280	0.0427	28.87	658
1900	1.395	565	1.440	?	?	?

Kg/Ko	0.012	0.018	0.02	0.025	0.033	0.044	0.057	0.074
Sg,%	9	10	10.5	11	12	13	14	15