REE191575 DOI: 10.

2118/191575-PA Date: 25-January-20 Stage: Page: 247 Total Pages: 14

Eagle Ford Huff ‘n’ Puff Gas-Injection Pilot:

Comparison of Reservoir-Simulation,
Material Balance, and Real Performance
of the Pilot Well
Daniel Orozco and Alfonso Fragoso, University of Calgary; Karthik Selvan*, Nexen Energy;
Graham Noble, CNOOC International; and Roberto Aguilera, University of Calgary

Summary
In this study we compare real data from an Eagle Ford Shale huff ‘n’ puff (H&P) gas-injection pilot with reservoir simulation and tank
material-balance calculations. The comparison is good and supports the conclusion that oil recovery from the Eagle Ford (and likely
other shales) can be increased significantly using H&P.
For H&P to work, the injected gas and the in-situ oil in the shale must be contained vertically and laterally following hydraulic frac-
turing. Containment is critical for the success of H&P. Containment implies that the injected gas flows into the hydraulic fractures, pen-
etrates the tight matrix, and does not escape or leak outside the target stimulated reservoir volume (SRV). Vertical and lateral
containment exists in the Eagle Ford as demonstrated previously (Ramirez and Aguilera 2016) with an upside-down distribution of
fluids: Natural gas is at the bottom of the structure, condensate in the middle, and oil at the top. Two different matching and forecasting
approaches are used in this study: reservoir simulation and tank-material-balance calculations.
The results show a good history match of primary recovery and secondary recovery by H&P in the pilot well. The history match is
good in the case of both reservoir simulation and tank material-balance calculations. Once a match is obtained, the simulation and mate-
rial balance are used to forecast secondary recovery over a period of 10 years with sustained H&P injection of dry gas. The results indi-
cate that dry-gas H&P can increase oil recovery from the Eagle Ford Shale significantly. Under favorable conditions, oil recovery can
be doubled and even tripled over time compared with the primary recovery. The addition of heavier ends to the H&P gas injection can
increase oil recovery even more, putting it on par with recoveries in conventional reservoirs. The benefit of H&P occurs in the case of
both immiscible and miscible gas injection. The H&P benefits can likely be also obtained in other shale reservoirs with upside-down
containment of dry gas, condensate, and oil.
The novelty of this work is the combined use of reservoir simulation and tank material-balance calculations to match the perfor-
mance of an H&P gas-injection pilot in the Eagle Ford Shale of Texas. We conclude that oil recoveries can be increased significantly
by H&P.

Introduction
After successful development of shale reservoirs through the combination of horizontal drilling and multistage hydraulic fracturing, the
petroleum industry has started to move on targeting the low oil recoveries from shales by implementing improved/enhanced-oil-
recovery (IOR/EOR) techniques. The methods under consideration include waterflooding (Hoffman and Evans 2016), H&P gas
injection (Gamadi et al. 2014a, 2014b; Fragoso 2016), surfactants for the reduction of interfacial tension (Rassenfoss 2017a), and
thermal stimulation by means of electromagnetic downhole heating (Egboga et al. 2017). Until now, most of the industry efforts for
EOR from shales have been devoted to H&P gas injection. Pilot wells indicate that this EOR technique has good potential for boosting
oil recovery in the Eagle Ford Shale of Texas. One of the main advantages of H&P gas injection over other IOR/EOR methods is that
gas-injection requirements generally can be met with gas production from neighboring wells. Gas from existing wells not being sold at
present because of current market conditions can be put to good use in H&P projects.
Fragoso et al. (2018a, 2018b) performed numerical simulation studies that indicated that H&P dry-gas injection in the oil container
of the Eagle Ford has the potential for adding 20% to the recovery of liquids. These results are obtained when there is containment of
the injected gas within the SRV. In this case, the injected gas flows into the hydraulic fractures, penetrates the tight matrix, and does not
escape or leak outside the target SRV. The proof of concept of gas containment is elaborated in numerical-simulation studies by
Ramirez and Aguilera (2016), which show vertical containment and inverted fluid distribution in the Eagle Ford Shale (oil at the top of
the structure, condensate in the middle, and gas in the deepest container), with contacts that have remained approximately the same
over geologic time. This is likely also the case for other world-class shales that might be potential candidates for H&P gas injection: for
example, the Duvernay Shale in Canada, the Niobrara Shale in the US, and the Vaca Muerta Shale in Argentina.
Orozco et al. (2018) introduced a semianalytical material-balance equation (MBE) to forecast the performance of shale oil reservoirs
under primary production and H&P gas injection. The MBE was tested with the real data of an H&P gas-injection pilot well in the
Eagle Ford. The key contribution of the new MBE was the mathematical formulation for the treatment of gas injection. The Newton-
Raphson iterative method was deployed for calculating the average reservoir pressure following injection. The approach considered a
dual-porosity system made up of matrix and fractures. The porosity of the matrix system comprises both the organic and the inorganic
matrix. The porosity of the fractured system includes natural and hydraulic fractures.
In this paper we present a comparison of the results of the 3D commercial reservoir simulator used by Fragoso et al. (2018a, 2018b),
the tank material balance of Orozco et al. (2018), and the real performance of a pilot well in the Eagle Ford Shale. The comparison dem-
onstrates the significant improvement in oil recoveries that can be attained by means of H&P gas injection in the Eagle Ford Shale.

* Now with Inpex Corporation

Copyright V
C 2020 Society of Petroleum Engineers

This paper (SPE 191575) was accepted for presentation at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, USA, 24–26 September 2018, and revised for publication.
Original manuscript received for review 18 July 2018. Revised manuscript received for review 18 March 2019. Paper peer approved 13 May 2019.

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Gas Injection in Shales

Successful oil production from shales has been achieved particularly in the United States and Canada because of advances in horizontal
drilling and multistage hydraulic fracturing. Tight oil production in the US has been growing almost continuously since 2008, and in
April 2018, it was more than 5.5106 STB/D (EIA 2018), and other countries such as Argentina and Mexico are starting to develop
these resources. The negative side is that high initial oil rates are followed by fast production decline, leading to very low oil recoveries
(5 to 10%). Gas injection has emerged as a potential solution to increase these low recoveries, and much effort in academia and industry
is currently focused on understanding how to properly implement this technique.
Continuous and H&P gas injection has been studied and tested in the field (Fragoso et al. 2015; Hoffman and Evans 2016; Fragoso
et al. 2018b). In the continuous injection, gas is injected through one or several injection wells in order to improve oil production from
one or several neighboring wells. Conversely, in the H&P method, the same well acts alternately as the producer and the injector. Each
cycle consists of an injection period, followed by a soaking time (optional), and then opening the well to production. Fragoso et al.
(2015, 2018b) have shown through numerical simulation that better results can be obtained by H&P gas injection. In fact, the term “gas
injection” in shale reservoirs generally refers to H&P gas injection.
Several factors and mechanisms are involved in the incremental recovery by H&P gas injection: reservoir pressurization, reduction
in oil viscosity, oil swelling, and vaporization and extraction of oil components by the injected gas and condensation of injected-gas
components into the oil, gravity segregation with counterflow, and containment of fluids (Fragoso et al. 2018a; Orozco et al. 2018). The
latter is particularly important. In reservoirs with vertical containment, the injected gas remains within the SRV, thus penetrating the
shale matrix more efficiently and consequently increasing oil recoveries.
Simulation studies (Wan et al. 2014; Fragoso et al. 2015, 2018b), laboratory work (Kovscek et al. 2008; Song and Yang 2013;
Gamadi et al. 2014a, 2014b; Li and Sheng 2017), and field pilot wells have shown that recoveries can be increased significantly by
H&P gas injection. Injection under miscible conditions has been found to provide better results than under immiscible conditions.
Therefore, rich natural gas and carbon dioxide (CO2) would be the most suitable fluids to be injected. However, gas availability and gas
cost can be important limiting factors.
During the last few years, several gas-injection pilots have been performed in shale reservoirs. In the US portion of the Bakken, con-
tinuous and H&P schemes have been tried in field pilots using CO2 and natural gas, with very poor results. On the contrary, positive
results have been obtained in the Canadian portion of the Bakken by means of an immiscible continuous gas injection using a toe-heel
scheme (Schmidt and Sekar 2014). In this approach, the toe-heel pattern was created with nine offsetting producers inside 1,280 acres.
The Canadian portion of the Bakken is shallower and has better reservoir properties than the US Bakken, which can help to explain
these opposite results. In addition, innovative techniques to control gas breakthrough have been reported in Canada (Hoffman and
Evans 2016). In the Eagle Ford, the development of gas-injection pilots started in 2013. Unlike in the Bakken, pilots in the Eagle Ford
have focused on H&P gas injection. Some of these pilots have been reported to be successful, and the number of pilot wells where H&P
is being performed has been increasing year after year.

Numerical Simulation
In this paper, real data from an H&P gas-injection pilot in the Eagle Ford shale are compared with the results from numerical simula-
tion and material-balance calculations. Oil-production history for the Eagle Ford pilot well is plotted in Fig. 1. The pilot well produced
for 29 months by primary means and then H&P gas injection was initiated. After five H&P cycles, the recovery has increased by a
factor of 1.74.
Average Daily Oil-Production Rate, qo (B/D)

600 180,000
Oil rate
Cumulative-Oil Production, Np (STB)

Cumulative-oil production 160,000

500
140,000

400 120,000

100,000
300
80,000

200 60,000

40,000
100
20,000

0 0
0 10 20 30 40 50 60
Time, t (months)

Fig. 1—Oil-production history for the Eagle Ford H&P pilot well (Orozco et al. 2018).

The numerical model is built in a compositional commercial simulator using a dual-permeability approach. Reservoir and fluid prop-
erties characteristic of the area where the well is located are used for building the model (Table 1). Relative permeability data published
by Honarpour et al. (2012) for fractures and calcite-rich shale matrix are used to build the relative permeability curves. Gas/oil capillary
pressures for the fractures are assumed to be zero. Matrix gas/oil capillary pressures were assigned following a methodology described
by Ramirez and Aguilera (2016). A horizontal well with multistage hydraulic fractures is drilled in the center of the grid. The injected
gas is methane (CH4), and it is assumed that the injected volume is evenly distributed throughout all the hydraulic fractures.
Production from shale reservoirs is possible as a result of the creation of hydraulic fractures that provide high-permeability channels
for fluid flow. Once the well goes on production, the reservoir pressure starts to decline and, conversely, the net stress increases. This in
turn tends to close the hydraulic fractures. This effect is taken into account during oil production in the numerical model by using the

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pressure-dependent porosity and permeability formulation shown in Eq. 1 developed by Piedrahita et al. (2018). Hysteresis effects are
considered during the injection segment of H&P cycles. This is the result of gas injection that reduces the effective stress on
the fractures,
 1=3
k ðlogpk Þa  ðlogDÞa
¼ ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð1Þ
ki ðlogEÞa  ðlogDÞa
where k is the permeability at a given net stress, ki is the permeability at the net stress corresponding to the reference pressure, pk is the
net stress, and D, E, and a are empirical parameters. The values of these parameters corresponding to the data for horizontal and vertical
samples published by Piedrahita et al. (2018) were used to build the main path of the stress-dependent-permeability curve (Table 2).
For further details on the development of this equation, please refer to the original paper by Piedrahita et al. (2018). Changes in permea-
bility as a function of net stress are included in Fig. 2.

Parameter Symbol Value Units

Initial reservoir pressure pi 6,000 psi
Reservoir temperature T 224 °F
Initial water saturation in matrix Swm 0.5 fraction
Initial water saturation in fractures Swf 0.10 fraction
−6
Water compressibility Cw 3.00×10 1/psia
−6
Matrix compressibility Cm 1.00×10 1/psia
−5
Natural-fracture compressibility Cf 1.00×10 1/psia
Reservoir depth d 8,000 ft
Initial total stress on fractures σt 8,000 psia
Matrix porosity φm 0.0597 fraction
Natural-fracture porosity φ2 0.00055 fraction
Matrix permeability km 0.001576 md
Natural-fracture permeability k2 0.3152 md
Natural-fracture spacing 10 ft
Reservoir thickness h 97.5 ft
Well drainage area A 73 acres
Length of the horizontal well L 6,240 ft
Skin factor S 0 –
Initial flow capacity of hydraulic fractures khf × w hf 50 md-ft
Hydraulic-fracture half-length xhf 150 ft
Hydraulic-fracture spacing 240 ft
Maximum gas-injection pressure Pinj 4,600 psi
Bottomhole flowing pressure Pwf 2,000 psi

Table 1—Reservoir and wellbore-geometry parameters.

Parameter Value
D 10,428.6
E 2,000
α 5.32

Table 2—Values of parameters in the Piedrahita et al. (2018)

correlation for estimating stress-dependent permeability.

The pressure/volume/temperature (PVT) properties of the reservoir fluid are summarized in Table 3.
Simulation results match the real data reasonably well, as shown in Figs. 3 and 4. The modified parameters during the history-
matching exercise were the original oil in place (OOIP) (size of the model), hydraulic-fracture half-length, hydraulic-fracture
flow capacity (conductivity), and gas-injection rate. We acknowledge that precise knowledge of the gas-injection rate in the contained
shale is very important and ideally would be a known variable. However, in this particular case, gas-injection rates are
unknown because publicly available data on gas-injection rates for H&P pilots in shales are rather scarce at present (especially on a
per-well basis). We also do not have access to a complete data set of instantaneous gas/oil ratio and bottomhole flowing pressure.
The tuned model is used to forecast the well performance during subsequent H&P cycles. The forecast is conducted using cycles of
100 days of injection and 100 days of production. Two forecast scenarios are considered. In the first one, the injected gas continues to
be CH4, which results in an oil recovery equal to 27.4% after 144 months of production (Figs. 5 and 6). This result is outstanding
because the oil recovery before the initiation of H&P injection is 7.3%. The recovery shown in Figs. 3 and 4 during the history-match
period is 12.6%.

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1.2
Main path
Hysteresis
1.0

0.8

khf /khfi
0.6

0.4

0.2

0.0
0 1,000 2,000 3,000 4,000 5,000 6,000 7,000
Net Stress (psi)

Fig. 2—Stress-dependent permeability.

Pressure Oil-Formation-Volume Gas/Oil Ratio Gas-Formation-Volume Gas Viscosity

(psi) Factor (RB/STB) (Solution) (scf/STB) Oil Viscosity (cp) Factor (cf/scf) (cp)
6,015 1.3866 671.38 0.8032 – –
5,515 1.3931 671.38 0.7678 – –
5,015 1.3999 671.38 0.7411 – –
4,515 1.4071 671.38 0.7109 – –
4,015 1.4149 671.38 0.6851 – –
3,515 1.4233 671.38 0.6630 – –
3,015 1.4328 671.38 0.6330 – –
2,404 1.4459 671.38 0.5978 – –
2,115 1.4063 596.53 0.5968 0.00800 0.01748
1,815 1.3723 521.17 0.5982 0.00930 0.01666
1,515 1.3372 448.88 0.6110 0.01120 0.01591
1,215 1.3038 376.74 0.6438 0.01410 0.01521
1,015 1.2823 330.85 0.6779 0.01710 0.01478
815 1.262 286.94 0.7286 0.02150 0.01437
615 1.2383 240.08 0.7702 0.02860 0.01391
415 1.2122 191.00 0.8489 0.04250 0.01340
215 1.1769 132.63 0.9262 0.08080 0.01260
15 1.0815 0.00 1.1750 1.28230 0.01094

Table 3—PVT properties of the reservoir fluid (Orozco et al. 2018).

600
Real data
500 Numerical simulation
Oil-Production Rate (B/D)

400

300

200

100

0
0 10 20 30 40 50
Time, t (months)

Fig. 3—History-matching results, Well Eagle Ford 1: real and simulated oil rates.

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200,000
Real data
180,000 Numerical simulation

Cumulative-Oil Production (STB)

160,000

140,000

120,000

100,000

80,000

60,000

40,000

20,000

0
0 10 20 30 40 50
Time, t (months)

Fig. 4—History-matching results, Well Eagle Ford 1: real and simulated cumulative-oil production.

600
Real data
500 Numerical simulation
Oil-Production Rate (B/D)

400

300

200

100

0
0 20 40 60 80 100 120 140
Time, t (months)

Fig. 5—Forecast oil-production rate. The injected gas is CH4 during the history match and during the forecast.

30
Real data
Numerical simulation
25

20
Oil Recovery (%)

15

10

0
0 20 40 60 80 100 120 140
Time, t (months)

Fig. 6—Forecast percent oil recovery. The injected gas is CH4 during the history match and during the forecast.

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In the second scenario, the injected fluid is changed to a richer gas with composition 70% C1 þ 20% C3 þ 10% C6 during the fore-
cast. This gas can achieve a higher degree of miscibility with the oil than pure CH4. The results are presented in Figs. 7 and 8. The use
of rich gas improves the performance of the H&P injection. In this case, the percent oil recovery is 34.7% after 144 months of produc-
tion (significantly larger than 27.4% by H&P CH4 injection). Oil recovery with the rich gas H&P is 4.8 times the recovery before
initiating the H&P injection. Fig. 9 presents a comparison of cumulative-oil production with H&P CH4 injection and H&P rich-gas
injection. After 12 years of production, using rich gas increases the cumulative-oil production by a factor of 1.27 compared with the
injection of pure CH4. The shapes of the curves suggest that the increment can be even higher in subsequent cycles. Swelling tests were
simulated for the reservoir-fluid/CH4 and reservoir-fluid/rich-gas systems. The swelling factor is defined as the ratio of the volume of
swollen fluid at saturation pressure to the volume of original fluid at saturation pressure (Computer Modelling Group 2017). Winprop
(Computer Modelling Group 2017) calculates the saturation pressure for a given reservoir-fluid composition, molar fraction (relative to
the mixture of reservoir fluid and injected fluid) and composition of injected fluid and temperature using the method developed by
Nghiem et al. (1985), and then the volume of saturated fluid is obtained from the equation of state. The results, presented in Fig. 10,
indicate that under the same conditions, a larger swelling effect is obtained when injecting rich gas compared with the injection of CH4.
Oil swelling can lead to the mobilization of trapped oil and more favorable relative permeabilities, thus providing incremental recov-
eries. This can explain the better performance of rich-gas injection.

600
Real data
Numerical simulation
500
Oil-Production Rate (B/D)

400

300

200

100

0
0 20 40 60 80 100 120 140
Time, t (months)

Fig. 7—Forecast oil-production rate. The injected gas is CH4 during the history match and rich gas (70% C1 1 20% C3 110% C6)
during the forecast.

35
Real data
30 Numerical simulation

25
Oil Recovery (%)

20

15

10

0
0 20 40 60 80 100 120 140
Time, t (months)

Fig. 8—Forecast percent oil recovery. The injected gas is CH4 during the history match and rich gas (70% C1 1 20% C3 110% C6)
during the forecast.

Material Balance
Orozco et al. (2018) presented a new semianalytical MBE that enabled the quick evaluation of H&P gas injection in shales. The novelty
of this MBE resides on its capability to easily determine the average reservoir pressure following injection. The formulation is simple
for mathematical handling, yet rigorous because it considers the effects of gas injection, including reservoir repressurization, progres-
sive increase in gas saturation, changes in relative permeabilities, and increases in the gas/oil ratio. The formulations for this MBE are
presented by Orozco et al. (2018), and only the treatment of H&P gas injection is reproduced here, with excerpts from that paper,
for completeness.

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600,000
Real data
Numerical simulation (rich gas injected during forecast)

Cumulative-Oil Production (STB)

500,000 Numerical simulation (CH4 injected during forecast)

400,000

300,000

200,000

100,000

0
0 20 40 60 80 100 120 140
Time, t (months)

Fig. 9—Comparison of cumulative-oil production by injecting pure CH4 vs. rich gas during the forecast period.

10,000 1.8
Saturation pressure, CH4
9,000 Saturation pressure, rich gas 1.7
8,000 Swelling factor, CH4
Saturation Pressure (psi)

Swelling factor, rich gas 1.6

7,000

Swelling Factor
1.5
6,000

5,000 1.4

4,000 1.3
3,000
1.2
2,000
1.1
1,000

0 1.0
0 0.1 0.2 0.3 0.4 0.5 0.6
Mole Fraction of Injected Fluid

Fig. 10—Results of swelling tests simulated with Winprop software.

Key assumptions of the implemented MBE are as follows:

1. The reservoir produces fluids under primary recovery during a certain period of time (e.g., 2 to 5 years).
2. The injected gas has a composition of 100% CH4.
3. The injected gas is contained within the target SRV—that is, it flows into the hydraulic fractures and penetrates the tight matrix
and, more importantly, it does not escape or leak outside of the SRV. This statement stems from the simulation work in Ramirez
and Aguilera (2016). They demonstrated that, over geologic time (1106 years), the fluids did not move out of their
respective containers.
4. Part of the gas volume injected during the huff period is produced during the puff period.
5. Gas injection may start when the average reservoir pressure is either greater than or slightly less than the bubblepoint. In the
second case, the first gas-injection cycle is able to restore the average reservoir pressure above the bubblepoint. Therefore, any
amount of free gas goes back in solution, and the injected gas remains free, creating a sort of secondary gas cap that grows
as injection goes on. Because the SRV is fixed, the gas saturation of the composite system of matrix and fractures
increases progressively.
6. As long as the H&P gas injection continues, the average reservoir pressure does not fall below the bubblepoint and, hence, the
reservoir oil remains undersaturated.
7. For the injection (or huff) period, the problem consists of determining the unknown average reservoir pressure resulting from
gas injection.
8. For the production (or puff) period, the problem consists of determining the fractional oil recovery, oil and gas rates, and
cumulative-oil and -gas production as a function of time.
For the injection (or huff) period, the MBE assumes an undersaturated reservoir, with the inclusion of a term that accounts for both
the cumulative-gas injection and production associated with the injected gas. Thus, the modified MBE (ignoring water production and
water influx) is

Nr BoI Coe ðpI  pÞ ¼ Np Bo  ðGinj  Ginj inj

p ÞBg ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð2Þ

where Nr and pI are the remaining oil in place and the average reservoir pressure before the start of each injection cycle, respectively;
p is the unknown average reservoir pressure following injection; BoI is the oil-formation-volume factor (FVF) at pI,; Ginj is the

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cumulative-gas injection in STB; Ginj inj

p is the cumulative-gas production (in STB) associated with the injected gas; and Bg is the FVF of
the injected gas.
Because the behavior of the FVF of both reservoir oil and injected gas is known in advance, Eq. 2 can be written as

Nr BoI Coe ðpI  pÞ ¼ Np f ðpÞ  ½ðGinj  Ginj

p ÞgðpÞ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð3Þ

where f( p) ¼ Bo is a linear function and g( p) ¼ Binj g is a power function. Eq. 3 is a nonlinear equation for p. The nonlinearity is
caused by the strong and highly nonlinear pressure dependence of the FVF of the injected gas (or of any real gas, in fact). Eq. 3 is rear-
ranged as
  " #
Np ðGinj  Ginj
p Þ
p  pI þ f ðpÞ  gðpÞ ¼ 0: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð4Þ
Nr BoI Coe Nr BoI Coe

We define the function F( p) with

  " #
Np ðGinj  Ginj
p Þ
FðpÞ ¼ p  pI þ f ðpÞ  gðpÞ: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð5Þ
Nr BoI Coe Nr BoI Coe

Thus, for each cycle, the problem of determining the average reservoir pressure resulting from gas injection is reduced to solving
the nonlinear equation

FðpÞ ¼ 0: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð6Þ

Given its quick-convergence feature, the iterative Newton-Raphson method is deployed (Chapra and Canale 2009) for the calcula-
tion. Eq. 6, written in the Newton-Raphson numerical form, becomes

Fðpk Þ
pkþ1 ¼ pk  ; . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ð7Þ
F0 ðpk Þ
where F0 ( pk) is the first derivative of function F( p) evaluated at the p value calculated in the kth iteration. A good initial guess p0 for
the unknown pressure might be simply pI. Notice that, as far as the calculation of p is concerned, Np, Nr, BoI, Coe, Ginj, and Ginj p are all
constants. Therefore, the first derivative F0 ( p) can be readily calculated. Newton-Raphson iterations are performed until a predeter-
mined tolerance level is reached (for example, 106).
Once the average reservoir pressure is determined with the Newton-Raphson iterative equation, material-balance calculations are
performed for each individual cycle to determine oil rates and recoveries as a function of time.
This paper introduces the following improvements to the MBE presented by Orozco et al. (2018):
1. Stress-sensitive reservoir properties using Eq. 1 developed by Piedrahita et al. (2016). The correlation was formulated using labo-
ratory data from tight-rock cores under different confining stresses.
2. Effect of hysteresis in the restoration of the hydraulic-fracture flow capacity. This is the result of gas injection that reduces the
effective stress on the fractures.
This section first presents history matching of the well-production history. When a fit of the production history (including five H&P
cycles) is attained, production forecasts at different gas-injection rates are generated for 7 years of sustained H&P gas injection. The
injection/production schedule consists of cycles of 100 days/100 days. For comparison purposes, the H&P gas injection for the MBE
base case corresponds to the base case of the numerical simulation discussed above. This is discussed in the next section, Material Bal-
ance vs. Numerical Simulation vs. Pilot Results Comparison.
The MBE uses exactly the same reservoir and fluid properties as the numerical-simulation model. Reservoir and wellbore-geometry
parameters are shown in Table 4. Table 5 displays the gas-injection rates used for fitting the oil rate with the material balance during
the five H&P cycles. This paper focuses on results, and to avoid unnecessary repetition of MBE formulations in the present manuscript,
the reader is referred to Orozco et al. (2018) for a detailed explanation of MBE calculations. Thus, only the pertinent results are dis-
cussed here. As in the case of the numerical-simulation study discussed in the preceding section, the modified parameters during the
material-balance history-matching exercise were OOIP, hydraulic-fracture half-length, hydraulic-fracture flow capacity (conductivity),
and gas-injection rate.
Figs. 11 and 12 show the MBE match of the well-production history. Figs. 13 through 15 correspond to the oil rate, cumulative oil,
and percent oil recovery under different gas-injection scenarios, respectively. Figs. 16 and 17 illustrate the effect of decreasing gas-
injection rates on oil-production rates and recoveries.
The first 28 months of oil recovery in Fig. 15 correspond to primary depletion in the pilot well. At this stage, the oil recovery is
approximately 7%. Between Months 28 and 58, there is H&P gas injection in the pilot well and the oil recovery increases to approxi-
mately 13%. The MBE indicates that primary recovery after 58 months would have been on the order of 7.8%. Thus, the incremental
recovery between Months 28 and 58 is 5.2%, which is equivalent to 67,340 STB. This results in a significant 67% increase in
oil recovery.
The forecast in Fig. 15 shows that at approximately 80 months, oil recovery by natural depletion becomes flat, and the primary
recovery after 144 months of production is on the order of 8%. On the other hand, sustained H&P gas injection at 0.86 MMscf/D yields
an oil recovery of 28% at 144 months, which corresponds to a very significant 250% increase, or an equivalent of 259,000 STB. If the
gas injection is reduced to 0.50 MMscf/D, or 0.30 MMscf/D, the increments in percent oil recovery with respect to natural depletion are
16.5% (206% increase, or 216,675 STB) and 14% (175% increase, or 181,300 STB), respectively. The performance in the last two
cases is not as good as in the first case, but the results are still compelling.
These numbers demonstrate that oil recoveries from shales can be significantly improved by means of H&P gas injection and high-
light the promising potential of this IOR technique for boosting oil recoveries in the Eagle Ford and, likely, in other shales around the
world with similar characteristics.
We also address the importance of maintaining a somewhat high gas-injection rate during the H&P process for achieving better
results. Fig. 16 depicts the behavior of the oil-production rate for the case in which the gas-injection rate is progressively decreased

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during the forecast period, with gas-injection rates of 0.5, 0.45, 0.40, 0.35, 0.30, 0.20, 0.15, and 0.10 MMscf/D from the sixth to the thir-
teenth cycle, correspondingly, and then with a constant gas-injection rate of 0.10 MMscf/D for each cycle thereafter. As observed,
decreasing gas-injection rates result in faster production declines, as opposed to the case in which the gas-injection rate remains at
0.86 MMscf/D during the forecasting period. Fig. 17 displays the corresponding comparison in terms of percent oil recovery.

Value
Numerical
Parameter Symbol Simulation MBE Units
Initial reservoir pressure pi 6,000 6,000 psi
Bubblepoint pressure pb 2,404 2,404 psi
OOIP N 1.295 1.295 MMSTB
Matrix OOIP Nm 1.274 1.274 MMSTB
Fractures OOIP Nf 0.021 0.021 MMSTB
Matrix water saturation Swm 0.50 0.50 fraction
Matrix oil saturation Som 0.50 0.50 fraction
Fractures water saturation Swf 0.10 0.10 fraction
Fractures oil saturation Sof 0.90 0.90 fraction
Reservoir depth d 8,000 8,000 ft
Initial total stress on fractures σt 8,000 8,000 psi
−6 −6 –1
Water compressibility Cw 3.00×10 3.00×10 psi
−5 −5 –1
Oil compressibility Co 1.00×10 1.00×10 psi
−6 −6 –1
Matrix compressibility Cm 1.00×10 1.00×10 psi
Residual oil saturation Sor 0.10* 0.10 fraction
Critical gas saturation Sgc 0.05* 0.00 fraction
0
Oil relative permeability at critical gas saturation kro 0.70* 0.70 –
0
Gas relative permeability at residual oil saturation krg 0.90* 0.90 –
Corey exponent for oil relative permeability no 1.50* 1.50 –
Corey exponent for gas relative permeability ng 1.20* 1.20 –
Matrix porosity φm 0.05970 0.05970 fraction
Natural-fractures porosity φ2 0.00055 0.00055 fraction
Reservoir temperature T 224 224 °F
Reservoir thickness h 97.50 97.50 ft
Well drainage area A 73.06 73.06 acres
Hydraulic-fracture half-length xhf 150 150 ft
Length of the horizontal well L 6,240 6,240 ft
Skin factor S 0 0 –
Permeability of natural fractures k2 0.3152 0.3152 md
Initial flow capacity of hydraulic fractures khfwhf 50 50 md-ft
Bottomhole flowing pressure pwf 2,000 2,000 psi
Number of hydraulic fracturing stages 26 26 –
Specific gravity of the injected gas (100% CH 4) SG 0.554 0.554 –
Gas-injection rate during forecast period qginj 0.860 0.860 MMscf/D
*Note: These values correspond to the endpoints and the exponents for generating gas/liquid relative permeabilities for the natural fractures with Corey’s equations
as used by Honarpour et al. (2012). The same relative permeabilities were used in the numerical simulator and the material balance.

Table 4—Reservoir and wellbore-geometry parameters used in the numerical simulation and material balance.

Gas-Injection Rate, qginj

H&P Cycle (MMscf/D)
1 1.50
2 0.30
3 0.80
4 0.40
5 0.68

Table 5—Material-balance history-matching gas-injection rates.

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600
Real data
500 Material balance

Oil-Production Rate (B/D)

400

300

200

100

0
0 10 20 30 40 50 60
Time, t (months)

Fig. 11—Material-balance history-matching results for the oil-production rate.

200,000

180,000 Real data

Cumulative-Oil Production (STB)

Material balance
160,000

140,000

120,000

100,000

80,000

60,000

40,000

20,000

0
0 10 20 30 40 50 60
Time, t (months)

Fig. 12—Material-balance history-matching results for the cumulative-oil production.

600
Real data
H&P gas-injection_material-balance_forecast-gas-injection rate = 0.86 MMscf/D
H&P gas-injection_material-balance_forecast-gas-injection rate = 0.50 MMscf/D
500 H&P gas-injection_material-balance_forecast-gas-injection rate = 0.30 MMscf/D
Oil-Production Rate (B/D)

400

300

200

100

0
0 20 40 60 80 100 120 140
Time, t (months)

Fig. 13—Oil-production-rate forecast for different gas-injection rates.

Material Balance vs. Numerical Simulation vs. Pilot Results Comparison

The MBE vs. numerical-simulation comparison is as rigorous as possible. However, it is not perfect, as a result of fundamental differen-
ces between the two approaches. One of the key differences is that the dual-porosity dual-permeability numerical simulator uses two
sets of relative permeability curves (one for the matrix blocks and one for the fracture blocks), whereas the tank MBE uses only one set.
In this study, the MBE calculations were run with the gas/liquid relative permeabilities of the fractured system. Other fundamental dif-
ferences between the two approaches include calculations of the average reservoir pressure and well productivity.

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600,000
Real data
Primary recovery_material balance

Cumulative-Oil Production (STB)

H&P gas-injection_material-balance_forecast-gas-injection rate = 0.86 MMscf/D
500,000 H&P gas-injection_material-balance_forecast-gas-injection rate = 0.50 MMscf/D
H&P gas-injection_material-balance_forecast-gas-injection rate = 0.30 MMscf/D

400,000

300,000

200,000

100,000

0
0 20 40 60 80 100 120 140
Time, t (months)

Fig. 14—Cumulative-oil-production forecast for different gas-injection rates.

45
Real data
40 Primary recovery_material balance
Oil-Recovery Factor, %OOIP (%)

Material-balance_forecast-gas-injection rate = 0.86 MMscf/D

35 Material-balance_forecast-gas-injection rate = 0.50 MMscf/D
Material-balance_forecast-gas-injection rate = 0.30 MMscf/D
30

25

20

15

10

0
0 20 40 60 80 100 120 140
Time, t (months)

Fig. 15—Percent-oil-recovery forecast for different gas-injection rates.

600
Real data
H&P gas-injection_material-balance_forecast-gas-injection rate = 0.86 MMscf/D
500 H&P gas-injection_material-balance_forecast with decreasing gas-injection rate
Oil-Production Rate (B/D)

400

300

200

100

0
0 20 40 60 80 100 120 140
Time, t (months)

Fig. 16—Effect of decreasing gas-injection rates on the oil-production rate.

Figs. 18 and 19 show real data from the pilot well and compare the numerical-simulation and MBE results of cumulative-oil produc-
tion and percent oil recovery, respectively. In both cases, the gas-injection rate starting in the sixth cycle at Month 58 is 0.86 MMscf/D.
Injection/production cycles are of 100 days/100 days. The comparison is reasonable. After 144 months (12 years), the simulator
predicts an oil recovery of 27.4%, while the MBE calculates 28.18%, a difference of only 0.78%. At earlier times, for example, after
100 months of production, the simulator gives an oil recovery of 23%, whereas the MBE calculates 21%.

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40
Real data
Primary recovery_material balance
35

Oil-Recovery Factor, %OOIP (%)

H&P gas-injection_material-balance_forecast-gas-injection rate = 0.86 MMscf/D
H&P gas-injection_material-balance_forecast with decreasing gas-injection rate

30

25

20

15

10

0
0 20 40 60 80 100 120 140
Time, t (months)

Fig. 17—Effect of decreasing gas-injection rates on the percent oil recovery.

400,000
Real data
350,000 Numerical simulation
Cumulative-Oil Production (STB)

Material balance
300,000

250,000

200,000

150,000

100,000

50,000

0
0 20 40 60 80 100 120 140
Time, t (months)

Fig. 18—Comparison of the numerical-simulation and MBE results for cumulative-oil production.

30
Real data
Numerical simulation
Oil-Recovery Factor, %OOIP (%)

25
Material balance

20

15

10

0
0 20 40 60 80 100 120 140
Time, t (months)

Fig. 19—Comparison of the numerical-simulation and MBE results for percent oil recovery.

Conclusions
1. A reasonable production history match of an H&P gas-injection pilot in the Eagle Ford Shale of Texas has been obtained using a
numerical reservoir simulator and with MBE calculations.
2. Numerical simulation and MBE results indicate that oil recoveries from the Eagle Ford Shale can be significantly improved by
means of dry-gas H&P gas injection.
3. Numerical-simulation results indicate that improvement in oil recoveries from shales can be even higher when rich gas is injected
during H&P.

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4. The validity of the MBE was tested against a commercial numerical reservoir simulator. The comparison is good but not perfect,
because of the fundamental differences in the nature of these two approaches.
5. The MBE provides quick estimates of performance and oil recovery by H&P gas injection.

Nomenclature
A ¼ well drainage area, acres
Bo ¼ oil FVF, RB/STB
BoI ¼ oil FVF at pI, RB/STB
Binj
g ¼ FVF of the injected gas, vol/vol
Cm ¼ matrix compressibility, psi1
Co ¼ oil compressibility, psi1
Coe ¼ effective oil compressibility, psi1
Cw ¼ water compressibility, psi1
d ¼ reservoir depth, ft
D ¼ empirical parameter in Eq. 1
E ¼ empirical parameter in Eq. 1
f ( p) ¼ linear function for expressing Bo as a function of p
F( p) ¼ function of pressure
F0 ( p) ¼ first derivative of function F
g( p) ¼ power function for expressing Binj g as a function of p
Ginj ¼ cumulative-gas injection, STB
Ginj
p ¼ cumulative-gas production from injected gas, STB
h ¼ reservoir thickness, ft
khf whf ¼ initial flow capacity of hydraulic fractures, md-ft
km ¼ matrix permeability, md
krg0 ¼ gas relative permeability at residual oil saturation
kro0 ¼ oil relative permeability at critical gas saturation
k2 ¼ permeability of natural fractures, md
L ¼ length of the horizontal well, ft
ng ¼ Corey exponent for gas relative permeability
no ¼ Corey exponent for oil relative permeability
N ¼ OOIP, STB
Nf ¼ fractures OOIP, STB
Nr ¼ remaining oil in place, STB
Nm ¼ matrix OOIP, STB
Np ¼ cumulative-oil production, STB
pb ¼ bubblepoint pressure, psi
pi ¼ initial reservoir pressure, psi
pI ¼ average reservoir pressure before the start of each H&P cycle, psi
pk ¼ net stress, psi
pwf ¼ bottomhole flowing pressure, psi
qginj ¼ gas-injection rate, MMscf/D
S ¼ skin factor
Sgc ¼ critical gas saturation, fraction
Sof ¼ fracture oil saturation, fraction
Som ¼ matrix oil saturation, fraction
Sor ¼ residual oil saturation, fraction
Swf ¼ fracture water saturation, fraction
Swm ¼ matrix water saturation, fraction
SG ¼ specific gravity of the injected gas
T ¼ reservoir temperature,  F
xhf ¼ hydraulic-fracture half-length, ft
a ¼ empirical parameter in Eq. 1
rt ¼ initial total stress on fractures, psi
/m ¼ matrix porosity, fraction
/2 ¼ natural-fracture porosity, fraction

Acknowledgments
The support of China National Offshore Oil Corporation (CNOOC) Petroleum North America ULC, Mitacs (through the Mitacs Accel-
erate Program), the Schulich School of Engineering at the University of Calgary, and Servipetrol Limited (Canada) is gratefully
acknowledged. We also thank the GFREE research team [GFREE refers to an integrated research program including Geoscience (G);
Formation Evaluation (F); Reservoir Drilling, Completion, and Stimulation (R); Reservoir Engineering (RE); and Economics and Exter-
nalities (EE)] at the University of Calgary for their continued help and support. We also acknowledge the donation of Computer Model-
ling Group simulation software to the University of Calgary. Special thanks to Gerame Galban for his assistance in using Winprop.

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Daniel Orozco is a PhD-degree candidate in petroleum engineering at the University of Calgary, where he is a member of the
GFREE research team on tight oil and unconventional gas. His current research interests include the numerical modeling of
hydraulic fracturing, material balance, and production forecasting of shale petroleum reservoirs. Orozco is a petroleum-
engineering graduate from Universidad Industrial de Santander in Bucaramanga, Colombia, and holds an MSc degree in petro-
leum engineering from the University of Calgary. He is a member of SPE.
Alfonso Fragoso is a PhD-degree candidate at the University of Calgary, where he is part of the GFREE research team on tight oil
and unconventional gas. His current research interests include numerical simulation, geomechanics, and IOR in shale reservoirs.
Fragoso holds a BSc degree from Universidad Industrial de Santander in Bucaramanga, Colombia, and an MSc degree from the
University of Calgary, both in petroleum engineering.
Karthik Selvan is a vice-president with Inpex in Houston. He holds a BE degree in chemical engineering from NUS, Singapore; an
MSc degree in petroleum engineering from Robert Gordon University, Scotland; and an MBA from the University of Calgary.
Graham Noble is an engineering advisor in unconventionals with CNOOC International and has been with the company for
more than 18 years. His current interests include improved-recovery methods and evaluations for unconventional reservoirs.
Noble holds a BAS degree from the University of Regina and is registered as a professional engineer in the province of
Alberta, Canada.
Roberto Aguilera is a professor of petroleum engineering and holds the CNOOC Chair in tight oil and unconventional gas in the
Schulich School of Engineering at the University of Calgary, and is a principal of Servipetrol Ltd. He is the creator and principal
investigator of the GFREE research program. He is a petroleum engineering graduate from the Universidad de America at
Bogota, Colombia, and holds ME and PhD degrees in petroleum engineering from the Colorado School of Mines. Aguilera is cur-
rently an executive editor for SPE Journal and is a member of the SPE Legion of Honor.

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