THE NEAR-WELLBORE PRESSURE CALCULATION MODEL INCORPORATING THERMOCHEMICAL EFFECT

Transcription

1 HERMAL CIENCE: Year 2018, Vol. 22, No. 1B, pp HE NEAR-WELLBORE PREURE CALCULAION MODEL INCORPORAING HERMOCHEMICAL EFFEC by Zhiqiang ANG, Qian LI *, and Hu YIN Petroleum and Natural Gas Engineering Institute, outhwest Petroleum University, Chengdu, China Introduction Original scientiic paper he potential dierence o hydraulic pressure, solute concentration and temperature between the drilling luid and the ormation luid can induce the low o solvent and cause changes in the pore pressure during drilling a tight ormation, which may result in wellbore instability. According to the continuity equation o luid, the pore pressure calculation model considering the eect o thermochemical coupling is established and the solution o the pore pressure in the Laplace domain is given. Using this model, the eects o the temperature, solute concentration and viscosity o drilling luid on the pore pressure around the wellbore are simulated. he results show that, when the wellbore pressure is higher than the ormation pressure and the solute concentration o the drilling luid is larger than that o the ormation luid, the near-wellbore pore pressure will decrease irst and then increase during drilling a tight ormation, and increasing the drilling luid temperature will decrease the pore pressure. Increasing the solute concentration o the drilling luid can inhibit the increase o the pore pressure. Key words: tight reservoir, pore pressure, solute concentration, temperature, coupling eect Except or rock mechanical properties, the near-wellbore pore pressure also will change with time during drilling a tight reservoir, resulting in a deterioration o wellbore instability. On the one hand, the tight reservoir has a certain permeability, which means that the hydraulic pressure will drive pore luid to move into or out o the ormation [1, 2]. On the other hand, the permeability o tight reservoir is extremely low and the solvent will low into or out o the ormation driven by chemical potential, as a similar eect o semipermeable membrane [3, 4]. In addition, the volume variation o ormation luid and rock caused by temperature change may also have some eect on the pore pressure around the wellbore. hereore, many scholars have analyzed the thermal eects [5-8] and chemical eects [3, 4, 9-12] on the variation o near-wellbore pore pressure. Lomba [13] established a pore pressure diusion equation by using the solute continuity equation and the relationship between the density and the pressure o ormation luid, ignoring the eect o temperature on pore pressure change. Combining the thermochemical constitutive equations o porelastic medium and equations or solute and thermal diusion, Araujo[14] and Araujo et al., [15] established a pore pressure calculation model incorporating thermochemical coupling eect. However, the eects o temperature on the variation o solute concentration and luid volume are neglected. Ghassemi et al. [16] and Zhou * Corresponding author, liqianswpu@126.com

2 624 HERMAL CIENCE: Year 2018, Vol. 22, No. 1B, pp and Ghassemi [17] established a ully coupled thermochemical model, but the model is too complex. In this paper, a new calculation model o near-wellbore pore pressure is established by assuming that the ormation luid is slightly compressible, and that the thermal diusion is aster than the solute diusion which is aster than the hydraulic diusion in tight reservoir. Using the model, the inluence o drilling luid perormance on the near-wellbore pore pressure is simulated. Pore pressure calculation model hermal diusion equation When a drilling luid contacts with the ormation, the heat diusion will occur between the drilling luid and the ormation rock. Kurashige [5] established a thermal diusion equation considering the heat diusion caused by the low o pore luid. But the eect o the low o pore luid on the heat diusion can be neglected because that the thermal diusion is much aster than the low o luid in a tight reservoir. hereore, the uniorm thermal diusion equation can be simpliied [6]: olute diusion equation t 2 = c Driven by hydraulic pressure, chemical potential, and thermal dierence the solvent o luid may low into or out o the ormation, resulting in a variation o the solute concentration near the wellbore. Considering that the permeability o tight reservoir is very low, the inluence o hydraulic pressure on the low o solvent can be neglected. Under the combined eect o chemical potential and thermal dierence, the variation o solute concentration can be determined by the diusivity equation [16]: Pore pressure calculation model C D 2 C D 2 = C+ t φ φ he low o ormation luid is driven by hydraulic pressure, chemical potential and thermal dierence, so the lux o ormation luid may be written [16]: k RρR J = P C + K (3) µ M C ( 1 C ) aking into account the slight compressibility o ormation luid, the relationship between density and pressure o ormation luid is [13]: ( ) ρ = ρ0exp cρ P P 0 (4) According to the continuity equation o luid, the luid density and lux have the ollowing relationship: ρ + ( ρ J ) = 0 (5) t ubstituting eq. (4) into eq. (5) yields: P 1 + J + J P = 0 t c ρ (1) (2) (6)

3 HERMAL CIENCE: Year 2018, Vol. 22, No. 1B, pp ubstituting eq. (3) into eq. (6): P 1 k k RρR + P+ C+ K + t cρ µ µ M C ( 1 C ) k k RρR + P+ C+ K P = 0 (7) µ µ M C ( 1 C ) Neglecting the third item [13, 18] in eq. (7) then substituting eqs. (1) and (2), the pore pressure incorporating thermochemical eects can be calculated by the equation: where P P 1 P C C C = + C C t r r r t t C olution in Laplace domain C C C (8) k 1 = (9) µ c ρ k 1 RρR = µ c M C ρ ( 1 C ) ( 1 C ) φ D k 1 RρR D 1 K = µ c M Dc c c ρ ρ Assuming that the wellbore pressure remains a constant during drilling a tight reservoir, the solution conditions or the pore pressure ield are: P( rw, t) = Pw P( r,0) = P0 (12) P(, t) = P0 I P (r, t) is the Laplace transorm o ΔP(r, t) = P(r, t) P 0, the Laplace conversion o eq. (8) can be written: 2 C 2 d P 1dP s sc sc P C 0 2 dr + r dr C + C + C = (13) where s is the Laplace transorm variable. he initial conditional and boundary conditions in eq. (12) ater Laplace conversion are expressed: 1 P ( rw, t) = ( Pw P0 ) s P ( r,0) = 0 (14) P (, t) = 0 Combining eqs. (1) and (2), the particular solution o eq. (13) in regard to the temperature and the solute concentration can be written [19]: C C * C c C C C D D C C D P = + C + (10) (15) c C C C D φc D φc D φc (11)

4 626 HERMAL CIENCE: Year 2018, Vol. 22, No. 1B, pp In eq. (15) the solutions o the temperature and the solute concentration in the Laplace domain are [15, 16, 19]: 1 K0 ( scr / ) ( rt, ) = ( w 0 ) (16) s K scr / 0 ( ( ) 0( / ) ( ) 0( / ) w 0 1 K φsdr w 0 1 K scr s K0( φsdr / φ s w) K0( scr / C D C D C ( rt, ) = Cw C0 + (17) c φ D c D hereore, the complete solution o eq. (13) can be determined by a combination o the particular solution eq. (15) and the solution o the homogeneous orm o eq. (13) aking into account the solution conditions o eq. (14), yields the solution o pore pressure in the Laplace domain: 1 K0 ( sc / r) w s 0 ( / 1 K0 ( sc / r) ( w 0 ) φ s 0 ( / 1 K0 ( scr / ) ( w 0 ) s 0 ( / ( ) 0 ( / ) w 0 1 K φsdr s 0 ( / C C D P ( rt, ) = Pw P0 ( C C0) D φc K sc r C C C c cc C D CD + c C c C D C + c φ D K sc r C C c cc CD D Example or analysis c C c C c D φ K scr C DC C D Cw C0 + φc c φ D K φsdr According to the model, the perormance o drilling luid will aect the pore pressure with time. Next, the inluence o temperature, solute concentration and viscosity on the pore pressure will be simulated by assuming that the solute o both drilling luid and ormation luid is NaCl. he relevant parameters are shown as in tab. 1. Because the drilling luid temperature is lower than the ormation temperature, the temperature near the wellbore will decrease with time ater drilling luid contacting with wellbore wall, as shown in ig. 1. he thermal diusion is quite ast, and it takes only 10 minutes or the temperature at 2r w to begin to decrease. he ormation water will low into the drilling luid driven by the chemical potential, so the solute concentration will gradually increase with time. Figure 2 indicates that solute diusion is relatively slow and the solute concentration at 2r w still keeps unchanged ater 20 hours. Figure 3 indicates that a drilling luid with high solute concentration will decrease the pore pressure and a high wellbore pressure will increase the pore pressure around the wellbore. Because solute diusion is aster than hydraulic diusion, the pore pressure decreases irst and then increases under the interaction o hydraulic pressure, chemical potential and thermal dierence. (18)

5 HERMAL CIENCE: Year 2018, Vol. 22, No. 1B, pp able 1. Parameters or analysis Parameters Value Unit Wellbore radius [m] Initial temperature o ormation 365 [K] emperature o drilling luid 315 [K] hermal diusivity [m 2 s 1 ] olute mass raction o ormation luid 0.05 olute mass raction o drilling luid 0.25 olute diusivity [m 2 s 1 ] Coeicient o thermal diusion [m 2 s 1 K 1 ] Porosity 0.08 Wellbore pressure 30 [MPa] Initial pore pressure 20 [MPa] Formation permeability [um 2 ] Viscosity o ormation luid 0.3 [mpa s] Relection coeicient 0.2 Density o ormation luid [kgm 3 ] hermal osmosis coeicient [m 2 s 1 K 1 ] Molar mass o solute [kgmol 1 ] Fluid compressibility [MPa 1 ] emperature [K] min 2 min 5 min min 20 min 310 r/ r w Figure 1. Variations o temperature proile with time olute concentration [MPa] h 2 h 5 h 10 h 20 h r/ r w Figure 2. Variations o solute concentration proile with time Pore pressure [MPa] h 2 h 5 h 10 h 20 h Pore pressure [MPa] = 315 K = 340 K = 365 K 15 r/ r w r/ r w Figure 3. Variations o pore pressure proile with time 15 t = 0.1 h t = 1 h t = 10 h Figure 4. Eects o temperature on pore pressure proile

6 628 HERMAL CIENCE: Year 2018, Vol. 22, No. 1B, pp Changing the drilling luid temperature and keeping the other parameters unchanged, the variations o pore pressure with the drilling time are shown as in ig. 4. Increasing the drilling luid temperature will decrease the near-wellbore pore pressure when the solute concentration o drilling luid is larger than that o ormation luid and the wellbore pressure is higher than ormation pressure. In a short time, the temperature has a non-negligible eect on the pore pressure near the wellbore wall. Figure 5 shows the variations o pore pressure with the solute concentration and temperature o drilling luid ater 1 hour. Both the temperature and the solute concentration o drilling luid will aect the pore pressure proile, but the temperature has a relatively slight inluence comparing to the solute concentration. When the solute concentration o drilling luid and ormation luid are equal (C w = 0.05), the near-wellbore pore pressure is mainly aected by hydraulic pressure. I the drilling luid temperature is 365 K and the solute mass raction o drilling luid is 0.05, the variation o pore pressure with the viscosity o ormation luid ater 1 hour is shown as in ig. 6. he pore pressure decreases with the viscosity o ormation luid. hereore, when the wellbore pressure is higher than the ormation pressure, a ormation luid with high viscosity is beneicial to a steady the pore pressure around the wellbore. Pore pressure [MPa] C w = 0.05 C w = 0.15 C w = 0.25 = 315 K = 340 K = 365 K r/ r w Figure 5. Eects o solute concentration on pore pressure proile ater 1 hour Pore pressure [MPa] mpa s 0.3 mpa s 0.4 mpa s 0.5 mpa s 0.6 mpa s 20 r/ r w Figure 6. Eects o viscosity on pore pressure proile ater 1 hour In summary, the change o pore pressure during drilling a tight reservoir is a process o thermochemical coupling interaction. Besides the wellbore pressure, both the solute concentration and the temperature o drilling luid will aect the near-wellbore pore pressure. When the wellbore pressure is higher than the ormation pressure, increasing the solute concentration o drilling luid is conductive to steady the pore pressure around the wellbore. When the solute concentration o drilling luid is larger than in the ormation and the wellbore pressure is higher than ormation pressure, the pore pressure around the wellbore will decrease irst and then increase. Conclusion According to the continuity equation o luid and diusion equations o thermal and solute, a thermochemical coupling model is established to calculate the pore pressure around the wellbore. Using this model, the eects o both the temperature and solute concentration o drilling luid and the viscosity o ormation luid on the pore pressure around the wellbore o tight reservoir are analyzed. he model and analysis results in this paper can help drilling engineers to optimize the perormance o drilling luid or reducing the wellbore instability caused by pore pressure change.

7 HERMAL CIENCE: Year 2018, Vol. 22, No. 1B, pp Acknowledgment his work is supported by China National cience and echnology Major Project (No.2016ZX ). Nomenclature C 0 solute mass raction o ormation luid, [ ] C w solute mass raction o drilling luid, [ ] C mean value o solute mass raction, [ ] c thermal diusivity, [m 2 s 1 ] c ρ luid compressibility, [MPa 1 ] D solute diusivity, [m 2 s 1 ] D coeicient o thermal diusion, [m 2 s 1 K 1 ] K thermal osmosis coeicient, [m 2 s 1 K 1 ] k permeability, [um 2 ] M molar mass o solute, [kgmol 1 ] P 0 initial pore pressure, [MPa] P w wellbore pressure, [MPa] R ideal gas constant, [m 3 Pa mol 1 K 1 ] R relection coeicient, [ ] r radial distance rom wellbore axis, [m] mean value o temperature, [K] w temperature o drilling luid, [K] 0 initial temperature o ormation, [K] t time, [s] Greeek symbols µ viscosity o ormation luid, [mpa s] ρ density o ormation luid, [kgm 3 ] ϕ porosity, [K] Reerences [1] Detournay, E., Cheng, A., Poroelastic Response o a Borehole in a Non-Hydrostatic tress Field, International Journal o Rock Mechanics and Mining ciences & Geomechanics Abstracts, 25 (1988), 3, pp [2] Yew, C. H., Liu, G., Pore Fluid and Wellbore tabilities, International Meeting on Petroleum Engineering, ociety o Petroleum Engineers, Beijing, China, 1992 [3] Mody, F. K., Hale, A. H., Borehole-tability Model to Couple the Mechanics and Chemistry o Drilling-Fluid/hale Interactions, Journal o Petroleum echnology, 45 (1993), 11, pp [4] Yu, M., et al., Chemical and hermal Eects on Wellbore tability o hale Formations, PE Annual echnical Conerence and Exhibition, ociety o Petroleum Engineers, New Orleans, La., UA, 2001 [5] Kurashige, M., A hermoelastic heory o Fluid-Filled Porous Materials, International Journal o olids and tructures, 25 (1989), 9, pp [6] Wang, Y., Papamichos, E., Conductive Heat Flow and hermally Induced Fluid Flow around a Well Bore in a Poroelastic Medium, Water Resources Research, 30 (1994), 12, pp [7] Chen, G., et al., A tudy o Wellbore tability in hales Including Poroelastic, Chemical, and hermal Eects, Journal o Petroleum cience and Engineering, 38 (2003), 3-4, pp [8] Chen, G., Ewy, R.., hermoporoelastic Eect on Wellbore tability, PE Journal, 10 (2005), 2, pp [9] Mody, F. K., Hale, A. H., Borehole-tability Model to Couple the Mechanics and Chemistry o Drilling-Fluid/hale Interactions, Journal o Petroleum echnology, 45 (1993), 11, pp [10] Chen, G., et al., A tudy o Wellbore tability in hales Including Poroelastic, Chemical, and hermal Eects. Journal o Petroleum cience and Engineering, 38 (2003), 3, pp [11] Yu, M., et al., Chemical-Mechanical Wellbore Instability Model or hales: Accounting or olute Diusion, Journal o Petroleum cience and Engineering, 38 (2003), 3-4, pp [12] Chen, G., et al., Analytic olutions with Ionic Flow or a Pressure ransmission est on hale, Journal o Petroleum cience and Engineering, 72 (2010), 1-2, pp [13] Lomba, R. F.., he Role o Osmotic Eects in Fluid Flow through hales, Journal o Petroleum cience and Engineering, 25 (2000), 1-2, pp [14] Araujo, E. M. P., A Coupled ermochemoporoelastic Model or Wellbore tability Analysis in hales (in Portuguese), Ph. D. thesis, Pontiícia Universidade Catoica do Rio de Janeiro, Rio de Janeiro, Brazil, 2005 [15] Araujo, E. M. P., et al., Incorporating hermochemoporoelastic Eects in Wellbore tability Design in hales, Proceedings, 41 st U.. ymposium on Rock Mechanics, American Rock Mechanics Association, Golden, Col., UA, 2006 [16] Ghassemi, A., et al., Inluence o Coupled Chemo-Poro-hermoelastic Processes on Pore Pressure and tress Distributions around a Wellbore in welling hale, Journal o Petroleum cience and Engineering, 67 (2009), 1-2, pp

8 630 HERMAL CIENCE: Year 2018, Vol. 22, No. 1B, pp [17] Zhou, X., Ghassemi, A., Finite Element Analysis o Coupled Chemo-Poro-hermo-Mechanical Eects around a Wellbore in welling hale, International Journal o Rock Mechanics and Mining ciences, 46 (2009), 4, pp [18] Yu, M., Chemical and hermal Eects on Wellbore tability o hale Formations, Ph. D. thesis, he University o exas at Austin, Austin, ex., UA, 2002 [19] ang, Z., et al., he Inluence o olute Concentration and emperature o Drilling Fluids on Wellbore Failure in ight Formation, Journal o Petroleum cience and Engineering, 160 (2018), Jan., pp Paper submitted: March 29, 2017 Paper revised: August 6, 2017 Paper accepted: August 6, ociety o hermal Engineers o erbia Published by the Vinča Institute o Nuclear ciences, Belgrade, erbia. his is an open access article distributed under the CC BY-NC-ND 4.0 terms and conditions