Reservoir rocks are fine- to medium-grained sublitharenite in the stratigraphic unit of the Lower Tuscaloosa formation in the Late Cretaceous, Cenomanian, deposited in the fluvial meander belt environment. The productive facies are point bars. Rock total porosity is 21% to 27% with 13% to 15% primary, 3% to 4% secondary dissolution, and 5% to 8% microporosity. Core porosity ranges 10% to 35% with an average value of 24%. The core permeability measured with air ranges from 0.1 to 100 md with an average value of 10 md. The initial water saturation is between 40% and 75%, averaging at 55%. The reservoir is composed of Q and Q2 sandstone members at an average depth of 10,770 ft (3283 m) in an area of 6 × 3 mi2 (9.7 × 4.8 km2).
The productive area is 6200 acres (2510 ha.) The hydrocarbon column height is 100 ft (30.5 m) with oil-water at 10,390 ft (3167 m) subsea. The gross sandstone thickness ranges from 15 to 85 ft (4.6–25.9 m), averaging at 40 ft (12.2 m). The average net sandstone thickness is 30 ft (9.1 m). The original reservoir pressure is 4840 psi (3.3 × 104 kPa) at 10,340 feet (3152 m) subsea. The oil has an API gravity of 39° with a GOR (gas/oil ratio) of 555:1 scf/stb and formation volume factor of 1.32. Oil viscosity is up to 5 cp (5.0 × 10−3 Pa·s) at 200 °F (93 °C).
TMS needs to use multifractured horizontal wells to become rejuvenated into a key exploration target for the industry as a leading oil field. Production rate and cumulative production data in May 2018 were gathered from 80 TMS wells in Louisiana and Mississippi. The majority of TMS wells were characterized by transient production behaviors.
Selection of wells for analysis in this study was based on the bubble map of the initial well productivity shown in Figure 4. Wells were selected from the Louisiana side of TMS with analyzable production decline curves. Only wells with initial oil production rates between 300 and 1200 stb/d were selected so wells with severe formation damage could be excluded. Wells with abnormal water cuts and gas-oil ratios were also excluded.
Figure 4. Bubble map of the initial well productivity of Tuscaloosa Marine Shale (TMS) wells.
Figure 5 shows the statistical results of slopes of 44 TMS wells that were used to identify RLF. It should be mentioned that 11 TMS wells were not analyzed owing to their abrupt changes in production rate over time. We saw that the slopes of 15 wells were in the range of −0.52 and −0.48. Based on the log–log plot of data from 44 oil wells in the TMS trend, a slope of −0.5 was observed for some wells but not all wells. The correlation coefficient between the initial production rate and the slope was −0.076, which meant that there was no linear correlation.
Figure 5. Statistical results of slopes used to identify reservoir linear flow (RLF).
Figure 6 shows the log–log diagnostic plot of production rate data from Well #1. This well was drilled and completed with a horizontal length of 9102 ft and a 29-stage fracturing operation. Four perforation clusters were made in each stage, giving an average cluster spacing of 69 ft. Time data up to five months showed a −0.51 slope (very close to −0.5), indicating RLF. Late time production rate data versus material balance time followed a linear trend line with a slope of −0.78. A plot of the same production data versus actual production time formed a linear trend line with a slope of −1.03, indicating typical behavior for the boundary-dominated flow.
Figure 6. Plot of production rate data for Well #1.
Figure 7 shows the log–log diagnostic plot of production rate data from Well #2. This well was 11,300 ft deep with an effective lateral length of 4791 ft. Time data up to five months showed a −0.51 slope (very close to −0.5), indicating RLF. RLF ended at a production rate of about 226 stb/d. Late time production rate data versus material balance time followed a linear trend line with a slope of −0.76. A plot of the same production data versus actual time formed a linear trend line with a slope of −1.03, indicating typical behavior for BDF.
Figure 7. Plot of production rate data for Well #2.
Figure 8 demonstrates the log–log diagnostic plot of production rate data for Well #3. This well was drilled and completed with a 6099 ft lateral length and a 24-stage fracturing operation. Time data up to four months showed a −0.50 slope, indicating RLF. Late time production rate data versus material balance time followed a linear trend line with a slope of −0.72. A plot of the same production data versus actual production time formed a linear trend line with a slope of −1.00. The pseudosteady production rate was about 126 stb/d at the beginning of the BDF.
Figure 8. Plot of production rate data for Well #3.
Table 1 presents a summary of the estimated reservoir and well completion/fracture data for these three wells. It was assumed that fractures were created from all perf clusters for simplicity. The fracture height used in this analysis was discounted from the pay zone thickness to the net pay. It should be mentioned that typical values were taken from the area for all wells because there was a lack of fracture job data.
The formation pressure gradient and the bottom hole pressure gradient were assumed to be 0.52 and 0.35 psia/ft, respectively. Matrix permeability was estimated using the following equation [33,34]:
where tehs is the time at the end of the half slope in days.
Table 1. Reservoir and well completion data.
The average fracture spacing can be estimated using the following equations [33,34]:
where η is the diffusivity in md∙psia∙cp−1, m is the slope of the inverse of production rate versus (t)1/2 in day1/2∙stb−1, and ct is the total compressibility in psi−1.
Figure 9 illustrates the calculated well productivity curve generated using the data as input to Equation (7). It showed that the model-predicted well production rate at the beginning of BDF was 121 stb/d (at Sf =69 ft), which was 0.83% higher than the observed value of 120 stb/d. The production rate at the beginning of BDF of Well #1 for Sf = 15 ft was 89% higher than that for Sf = 69 ft. This was explained by Wattenbarger’s solution for the initial production rate . It demonstrated that well production rate in the RLF period was proportional to the total fracture surface area.
For a given horizontal wellbore length, the total fracture surface is dependent on the number of hydraulic fractures. Therefore, decreasing fracture spacing can increase production rate if the fracture half-length is held constant. Similarly, this indicated that the model-calculated well production rate at the beginning of BDF of Well #2 was 94 stb/d (at Sf = 63 ft), which was 2.08% lower than the observed value of 96 stb/d. When the fracture spacing was reduced to 15 ft, the production rate at the beginning of BDF should be 71% higher than that the original one, assuming no other complex factors were missing in the model development.
Of course, the decrease in perf cluster spacing may have less than ideal impacts on well productivity as a result of other complex factors that were not considered in the model development.
Figure 9. Model-calculated productivity for TMS wells.
Figure 10 demonstrates the diagnostic plot of production rate data for Well #4. Early production data showed a trend with a slope of −0.57, which was between −0.5 and −1, not indicating RLF. This could be due to the existence of natural fractures or the interference of hydraulic fractures. Figure 11 and Figure 12 present the diagnostic plot of production rate data for Well #5 and Well #6, respectively. Early production data showed trends with slope values of −0.58 and −0.62, respectively, not indicating RLF. This could be due to the existence of natural fractures or the interference of hydraulic fractures.
The bubble map in Figure 4 was compared with geological maps for natural fracture/shale quality identification. A further examination of locations of Wells #4, #5, and #6 confirmed that these wells were drilled in an area where multiple natural fractures were found. It was generally believed that not all the hydraulic fractures were equal in length, owing to heterogeneity within the reservoir or stress shadow. Ambrose et al.  indicated fracture interference had a great effect on the performance of a well. They demonstrated that fracture interference tended to increase the cumulative production. However, the higher the heterogeneity, the less the recovery factor. It was therefore not recommended to reduce fracture spacing for these wells or wells in the areas.
Figure 10. Plot of production rate data for Well #4.
Figure 11. Plot of production rate data for Well #5.
Figure 12. Plot of production rate data for Well #6.
In summary, the performances of multifracture horizontal wells (MFHW) in shale oil fields in different regions of the world are mixed. This is believed partially because of the lack of optimization of well completion parameters, especially fracture spacing. Optimization of such spacing is generally recognized as one of the most important steps in enabling economic horizontal wells and requires a lot of attention. A data-driven workflow approach is presented in this study for optimizing fracture spacing of MFHW in shale oil reservoirs. Fracture spacing should be as short as possible unless “interference” occurs, and this “interference” can be found from the pressure transient analysis. If the interference does not happen in initial stages, well productivity can be improved by shortening the fracture spacing. The following conclusions were drawn from this study.
1- This workflow procedure has the advantage of using an analytical well productivity model driven by real production data, making it a practical approach to optimize MFHW in shale oil reservoirs.
2- This workflow procedure employs a closed-form analytical solution and provides a transparent approach to the identification of important fracturing parameters affecting well productivity.
3- This workflow procedure uses transient pressure or production data to identify fracture interference. This offers a reliable and cost-effective means for assessing well production potential in terms of optimizing fracture spacing in the MFHW.
4- Results of a field case study indicated that three wells were drilled and completed with fracture spacing values that were short enough to effectively drain the stimulated reservoir volume (SRV), while the other three wells were drilled and completed with fracture spacings that could be shortened to significantly improve well productivity.
Data curation, X.Y.; Investigation, B.G.; Methodology, B.G.; Project administration, B.G.; Resources, X.Y.; Validation, X.Y.; Writing—original draft, X.Y.; Writing—review & editing, B.G.
This research was supported by the U.S. DOE project (Project No. DE-FE0031575).
Conflicts of Interest
The authors declare no conflict of Interest.
- Rafiee, M.; Soliman, M.Y.; Pirayesh, E. Hydraulic fracturing design and optimization: A modification to zipper frac. In Proceedings of the SPE Easter Regional Meeting, San Antonio, TX, USA, 8–10 October 2012.
- Ren, J.; Guo, P. A general analytical method for transient flow rate with the stress-sensitive effect. J. Hydrol. 2018, 565, 262–275.
- Xue, L.; Chen, X.; Wang, L. Pressure transient analysis for fluid flow through horizontal fractures in shallow organic compound reservoir of hydrogen and carbon. Int. J. Hydrogen Energy 2019, 44, 5245–5253.
- Bajwa, A.I.; Blunt, M.J. Early-time 1D analysis of shale-oil and-gas flow. SPE J. 2016, 21, 1254–1262.
- Abbasi, M.; Madani, M.; Sharifi, M.; Kazemi, A. Fluid flow in fractured reservoirs: Exact analytical solution for transient dual porosity model with variable rock matrix block size. J. Pet. Sci. Eng. 2018, 164, 571–583.
- Sesetty, V.; Ghassemi, A. A numerical study of sequential and simultaneous hydraulic fracturing in single and multi-lateral horizontal wells. J. Pet. Sci. Eng. 2015, 132, 65–76.
- Li, J.; Xiao, W.; Hao, G.; Dong, S.; Hua, W.; Li, X. Comparison of different hydraulic fracturing scenarios in horizontal wells using XFEM based on the cohesive zone method. Energies 2019, 12, 1232.
- Du, X.; Nydal, O.J. Flow models and numerical schemes for single/two-phase transient flow in one dimension. Appl. Math. Model. 2017, 42, 145–160.
- Yu, W.; Xu, Y.; Weijermars, R.; Wu, K.; Sepehrnoori, K. Impact of well interference on shale oil production performance: A numerical model for analyzing pressure response of fracture hits with complex cemeteries. In Proceedings of the SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, TX, USA, 24–26 January 2017.
- He, Y.; Cheng, S.; Rui, Z.; Qin, J.; Fu, L.; Shi, J.; Wang, Y.; Li, D.; Patil, S.; Yu, H.; Lu, J. An improved rate-transient analysis model of multi-fractured horizontal wells with non-uniform hydraulic fracture properties. Energies 2018, 11, 393.
- Sun, H.; Zhou, D.; Chawathé, A.; Du, M. Quantifying shale oil production mechanisms by integrating a Delaware basin well data from fracturing to production. In Proceedings of the Unconventional Resources Technology Conference, San Antonio, TX, USA, 1–3 August 2016.
- Orangi, A.; Nagarajan, N.R.; Honarpour, M.M.; Rosenzweig, J.J. Unconventional shale oil and gas-condensate reservoir production, impact of rock, fluid, and hydraulic fractures. In Proceedings of the SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, TX, USA, 24–26 January 2011.
- Guo, B.; Yu, X.; Khoshgahdam, M. A simple analytical model for predicting productivity of multifractured horizontal wells. SPE Reserv. Eval. Eng. 2009, 12, 879–885.
- Zhang, C.; Wang, P.; Guo, B.; Song, G. Analytical modeling of productivity of multi-fractured shale gas wells under pseudo-steady flow conditions. Energy Sci. Eng. 2018, 6, 819–827.
- Li, G.; Guo, B.; Li, J.; Wang, M. A mathematical model for predicting long-term productivity of modern multifractured shale gas/oil wells. SPE Drill. Complet. 2019, 34.
- Guo, B.; Liu, X.; Tan, X. Petroleum Production Engineering, 2nd ed.; Elsevier: Cambridge, MA, USA, 2017; pp. 432–489. ISBN 978-0-12-809374-0.
- Potapenko, D.I.; Williams, R.D.; Desroches, J.; Enkababian, P.; Theuveny, B.; Willberg, D.M.; Conort, G. Securing long-term well productivity of horizontal wells through optimization of postfracturing operations. In Proceedings of the SPE Annual Technical Conference and Exhibition, San Antonio, TX, USA, 9–11 October 2017.
- Feng, F.; Wang, X.; Guo, B.; Ai, C. Mathematical model of fracture complexity indicator in multistage hydraulic fracturing. J. Nat. Gas Sci. Eng. 2017, 38, 39–49.
- Zhang, Q.; Wang, X.; Wang, D.; Zeng, J.; Zeng, F.; Zhang, L. Pressure transient analysis for vertical fractured wells with fishbone fracture patterns. J. Nat. Gas Sci. Eng. 2018, 52, 187–201.
- Li, D.; Zha, W.; Liu, S.; Wang, L.; Lu, D. Pressure transient analysis of low permeability reservoir with pseudo threshold pressure gradient. J. Pet. Sci. Eng. 2016, 147, 308–316.
- Wu, Z.; Cui, C.; Lv, G.; Bing, S.; Cao, G. A multi-linear transient pressure model for multistage fractured horizontal well in tight oil reservoirs with considering threshold pressure gradient and stress sensitivity. J. Pet. Sci. Eng. 2019, 172, 839–854.
- Fekete, F.A.S.T. Well Test User Manual; Fekete Associates, Inc.: Calgary, AB, Canada, 2003.
- E-Production Services, Inc. PanSystem User Manual; E-Production Services, Inc.: Edinburgh, UK, 2004.
- Shan, L.; Guo, B.; Weng, D.; Liu, Z.; Chu, H. Posteriori assessment of fracture propagation in refractured vertical oil wells by pressure transient analysis. J. Pet. Sci. Eng. 2018, 168, 8–16.
- Pang, W.; Wu, Q.; He, Y. Production analysis of one shale gas reservoir in China. In Proceedings of the SPE Annual Technical Conference and Exhibition, Houston, TX, USA, 28–30 September 2015.
- He, Y.; Cheng, S.; Li, S.; Huang, Y.; Qin, J.; Hu, L.; Yu, H. A semianalytical methodology to diagnose the locations of underperforming hydraulic fractures through pressure-transient analysis in tight gas reservoir. SPE J. 2017, 22, 924–939.
- Cinco, L.H.; Samaniego, V.F. Transient Pressure Analysis for Fractured Wells. J. Pet. Technol. 1981, 33, 1749–1766.
- Gringarten, A.C.; Ramey, H.J.; Raghavan, R. Applied pressure analysis for fractured wells. J. Pet. Technol. 1975, 27, 887–892.
- Cinco, L.H.; Samaniego, V.; Dominguez, A. Transient pressure behavior for a well with a finite-conductivity vertical fracture. Soc. Pet. Eng. J. 1978, 18, 253–264.
- Uzun, I.; Kurtoglu, B.; Kazemi, H. Multiphase rate-transient analysis in unconventional reservoirs: Theory and application. SPE Reserv. Eval. Eng. 2016, 19, 553–566.
- Yang, C.; Sharma, V.K.; Datta-Gupta, A.; King, M.J. Novel approach for production transient analysis of shale reservoirs using the drainage volume derivative. J. Pet. Sci. Eng. 2017, 159, 8–24.
- Marsden, J.; Kostyleva, I.; Fassihi, M.R.; Gringarten, A.C. A conceptual shale gas model validated by pressure and rate data from the Haynesville shale. In Proceedings of the SPE Annual Technical Conference and Exhibition, San Antonio, TX, USA, 9–11 October 2017.
- Ambrose, R.J.; Clarkson, C.R.; Youngblood, J.E.; Adams, R.; Nguyen, P.D.; Nobakht, M.; Biseda, B. Life-cycle decline curve estimation for tight/shale reservoirs. In Proceedings of the SPE Hydraulic Fracturing Technology Conference, The Woodlands, TX, USA, 24–26 January 2011.
- Wattenbarger, R.A.; El-Banbi, A.H.; Villegas, M.E.; Maggard, J.B. Production analysis of linear flow into fractured tight gas wells. In Proceedings of the SPE Rocky Mountain Regional/Low-Permeability Reservoirs Symposium, Denver, CO, USA, 5–8 April 1998.
© 2019 by the authors. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).