Effect of pressure on early hydration

Transcription

1 Effect of pressure on early hydration Gary P. Funkhouser a, Sulapha Peethamparan b, Emily Weissinger c, Jie Zhang c, George Scherer c a Halliburton b Clarkson University c Princeton University 1

2 Effect of Pressure Oil well cementing Consistometer Effect of T & p on setting time Modeling Avrami equation Activation energy & Activation volume 2

3 Oil Well Cementing To secure casing and isolate multiple reservoirs, cement is injected into annulus between casing and formation Must exit casing before setting Compressive strength must reach ~3 MPa to stabilize casing before drilling resumes 3

4 Oil Well Cementing Geothermal gradient ~30 C/km Hydrostatic pressure ~10 MPa/km Cement in deep well may see T > 150 C, p > 50 MPa Need to predict setting time (limit of pumpability) integrated over T(t) and p(t) 4

5 Consistometer Rheology of well cement characterized using consistometer Rotation of blades in ~0.5 liter of paste Shear rate (150 RPM) is ~30 s -1 Limit of pumpability is ~70 Bc 20 Pa s 5

6 Temperature Shift Curves rise earlier & more steeply as T rises Effect of 4500 psi (~30 MPa) 5 F (~2.5 C) psi, 135 F atm 135 F atm 140 F Average Consistency, Bc atm 146 F Lehigh White 46% water bwoc 41 min to temperature Limit of pumpability Time, min 6

7 Pressure Shift Curves rise earlier and more steeply as p rises, so same qualitative effect from increase in T & P 160 atm 135 F psi, 135 F psi, 135 F Average Consistency, Bc psi, 135 F Lehigh White 46% water bwoc 41 min to temperature Limit of pumpability Time, min 7

8 Ramping p & T p and T independently ramped to final values if duration of ramp is significant fraction of pumping time, must integrate reaction rate 140 White Cement 60 Ave Consistency ( Bc ) T Ramp = 42 min 50 P (HP) min 20 C (Atm) 10 C (HP, t+6) P (Atm) Sample T ( C), Pressure (MPa) Ramp = 42 min Pumping time = 67 min so must integrate p Time ( min ) 8

9 Modeling the Reaction Assume that limit of pumpability corresponds to a fixed degree of hydration Model effect of T and p on rate of hydration Evaluate reaction at atmospheric pressure using chemical shrinkage Fit data with Avrami-Cahn-Thomas model (See poster by Jie Zhang) J.J. Thomas, J. Am. Ceram. Soc., 90 [10] (2007) 9

10 Measuring Chemical Shrinkage New method for quantifying volume change by measuring change in hydrostatic head Pressure sensor & Thermocouple Capillary tube Thermal jacket water cement 10

11 Measuring Chemical Shrinkage New method for quantifying volume change by measuring change in hydrostatic head Pressure sensor & Thermocouple Capillary tube Thermal jacket water cement 10

12 Measuring Chemical Shrinkage New method for quantifying volume change by measuring change in hydrostatic head Pressure sensor & Thermocouple Capillary tube Thermal jacket water cement 10

13 Reproducibility Three runs at 40 C 0 ClassH 40C w/c = 0.35 Volume Change ( ml / g ) Sample 1 (ml/g) Sample 2 (ml/g) Sample 3 (ml/g) Time ( s ) 11

14 Sensitivity Effect of temperature and retarder 0 Class H w/c = 0.35 Effect of Temperature and 0.1% HydroxyEthylCellulose Volume Change ( ml / g ) C 25 C 25 C + 0.1% HEC Time ( s ) 12

15 Modeling Shrinkage Use Avrami-Cahn model, as proposed by Jeff Thomas From Vicat and TGA, find that initial set occurs at ~4% DOH ( X) Much later than limit of pumpability At this early stage, at constant p and T, A-C-T model reduces to X π 3 O B I G 3 t 4 v B 13

16 Activated Process Chemical shrinkage data at various T indicate Arrhenius temperature dependence Assume nucleation and growth given by G = G 0 exp E + p V G G RT, I B = I 0 exp E + p V G G RT A-C-T model reduces (at constant p & T) to X = π 3 O B v I 0 G 3 0 exp 4( E + p V ) RT t 4 E = 3 E G + E I 4, V = 3 V G + V I 4 14

17 Pressure Dependence Assume that limit of pumpability corresponds to DOH where X = X P X P = π 3 O B v I 0 G 3 0 exp 4( E + p V ) RT t P 4 then, if T is constant, ( ) ( ) ln t p,t P 0 t P p 0,T 0 ( = p p 0 ) V RT 0 15

18 Pressure Dependence Class H cement, T = 27 C, 0.1 p (MPa) 135, no ramp ln [ t P (p) / t P (p 0 ) ] ( ) ( ) ln t p,t P 0 t P p 0,T 0 ( = p p 0 ) V RT 0 V -51 Å 3 /molecule ~1.7 times the volume of a molecule of water p ( MPa ) 16

19 Modeling Ramp Non-isothermal, non-isopiestic model: X( t) = 4π 3 t t G T ( t ), p ( t ) d t O B v I B T ( t ), p ( t ) d t 0 ( t )3 Must be integrated numerically over ramp T - T 0 T H - T 0 or p - p 0 p H - p t 17

20 Ramping p & T Class H cement Variable ramp times to reach p = 35 MPa, T = 330 K 40-minute ramp to p from 0.1 to 138 MPa, T = 330 K Integrate using: V -51 Å 3 /molecule (from pressure jump expts) and E/R = 4000 K (from chemical shrinkage expts) 18

21 Predicted Pumping Time Predictions accurate within a few minutes Error comparable to batch-to-batch variation t P Calculated ( min ) t P Measured ( min ) 19

22 T - p Equivalence Pressure change p needed to produce same change in pumping time as temperature change T is expected to be p = E V T T 1090MPa T T or, ~3.6 MPa/ C 20

23 Conclusions Chemical shrinkage kinetics fit by Avrami-Cahn model At p = 0.1 MPa, E 33 kj/mole Pressure affects rheology of paste in same way as temperature Activation volume V -51 Å 3 /molecule Assuming that viscosity corresponds to fixed DOH allows prediction of change in t P with p and T 21