Asphaltene Near-Wellbore Formation Damage Modeling

1. Asphaltene Near-WellboreFormation Damage ModelingByKosta J. Leontaritis, Ph.D.AsphWax, Inc.E-mail: kosta@asphwax.comWeb: www.asphwax.com

2. Asphaltene Near-WellboreFormation Damage Modeling • Asphaltene-Induced Formation Damage • Asphaltene Particle-Size Distribution (psd) • Hydraulic Radius • Permeability Impairment • Porosity Loss • Skin Factor • Asphaltene Deposit Erosion • Solution Algorithm • FDModel Application

3. Formation Damage Mathematically, formation damage is a reduction in the flowing phase mobility, l:

4. Formation Damage For the oil phase, the hydrocarbon effective mobility, lo, is:

5. Asphaltene-Induced Formation Damage Mechanisms • Absolute permeability impairment (k) • Wettability Changes (kro) • Viscosity (mo) increase due to: • Emulsion formation • Asphaltene particle increase near the borehole

6. Asphaltene-Induced Formation Damage Mechanisms From the previous three mechanisms of asphaltene-induced formation damage the first one appears to be the dominant mechanism, although occasionally the second and third mechanisms do seem to play a role under certain circumstances. If there is no water production, which is the most likely case, then no emulsion of water-in-oil is expected. Hence, any viscosity increase measured in the laboratory would have to be attributed to asphaltene particle concentration increase as the reservoir fluid approaches the wellbore. Past experiments have shown that asphaltene flocculation in-of-itself does not result in a significant viscosity increase. Also, from experience, reservoirs that have asphaltene problems seem to be mixed-wet to oil-wet even before production commences. It evident then that the major cause of asphaltene-induced formation damage in asphaltenic reservoirs is the first mechanism.

7. Physical Blockage of Pore Throats Caused by In-Situ Asphaltene Deposition

8. Reservoir characterization Reservoir characterization is an enormous subject that consumes a lot of manpower energy in the oil industry. Some of the parameters that characterize a reservoir are: • k, permeability • f, porosity • RQI, Reservoir Quality Index (mean hydraulic radius) • Fluid Saturations • Wettability • Electrical Properties (Formation Factor and Resistivity Index)

9. Formation Mean Hydraulic Radius Pore throat radii of a formation depend on many reservoir parameters and they certainly vary from one formation to another. However, some general statements about the distribution of hydraulic radii of formations can be made: • Largest distribution is 0.001 to 100 micron • Usual distribution is 0.01 to 10 micron • Occasional distribution is 0.1 to 1 micron

10. Flocculated Asphaltene Micelles Forming an Asphaltene Particle 12 Å 45 Å

11. Obvious question: How can so small flocculated asphaltene particles plug pore throats of much larger size?

12. Physical Blockage of 100 m Pore Throat Caused by In-Situ Flocculation of Much Smaller Asphaltene Particles 100 m

13. Physical Blockage Caused byIn-Situ Asphaltene Deposition-Sandstone

14. Asphaltenes Adsorbed on the RockCause Wettability Changes

15. Wettability Change Caused byIn-Situ Asphaltene Deposition-Carbonate

16. Asphaltene-Induced Formation DamageNear Production Wells • High draw-down • Miscible-gas breakthrough • Contact of oil with incompatible fluids during drilling, completion, stimulation, fracturing, and gravel packing operations • Drop in reservoir pressure below onset of asphaltene pressure

17. 1st Mechanism Well Producing with Asphaltene-Induced Formation Damage 2nd Mechanism

18. Well Producing withAsphaltene-Induced Formation Damage

19. Well Producing withAsphaltene-Induced Formation Damage The previous slide shows an aerial view of a producing well suffering from asphaltene-induced formation damage. The well is on flow control from the choke. As Pw drops, when asphaltene deposition starts, the choke opens so that the lower Pw can push all of the oil flow, q, through the tubing. Pe and PAF remain constant. However, when the choke is completely open both re and rAF begin to decrease due to the production rate decrease caused by the ever-increasing asphaltene-induced formation damage. When rAF becomes equal to rw no additional formation damage is incurred. This is referred to as "true steady state condition". The production rate at this state, however, may not be economical.

20. Asphaltene Near-WellboreFormation Damage Modeling • Asphaltene-Induced Formation Damage • Asphaltene Particle-Size Distribution (psd) • Hydraulic Radius • Permeability Impairment • Porosity Loss • Skin Factor • Asphaltene Deposit Erosion • Solution Algorithm • FDModel Application

21. Asphaltene Deposition Envelope

22. Asphaltene psd at P=2975 psia & T=122 °F

23. Asphaltene Particle Size and Sedimentation

24. Asphaltene Near-WellboreFormation Damage Modeling • Asphaltene-Induced Formation Damage • Asphaltene Particle-Size Distribution (psd) • Hydraulic Radius • Permeability Impairment • Porosity Loss • Skin Factor • Asphaltene Deposit Erosion • Solution Algorithm • FDModel Application

25. 1st Mechanism Well Producing with Asphaltene-Induced Formation Damage 2nd Mechanism

26. Hydraulic Radius – Single Channel The hydraulic radius of a single flow channel is given by: • Where: • S = x-sectional area of flow channel • LP = wetted perimeter of flow channel • L = length of flow channel

27. Hydraulic Radius – Core Plug The hydraulic radius of a core plug is given by: • Where: • f = core plug porosity (= void volume/total volume) • SP = surface area of one core plug grain or particle • VP = volume of one core plug grain or particle

28. Hydraulic Radius By further mathematical manipulation, the hydraulic radius of a core plug is given by: • Where: • f = core plug porosity (= void volume/total volume) • dg = average grain diameter. There are proprietary correlations for sandstones and carbonates that allow one to calculate dg from k and f.

29. Mean Hydraulic Pore-Throat Radius A simple, quick and dirty way to estimate the Mean Hydraulic Pore-Throat Radius is via the following equation:

30. Retained Asphaltene Particle Diameter, dAP The simplest rule-of-thump from filtration theory is that a filter retains particles with diameters 1/3 of the nominal rating of the filter. In this case, the filtration rule-of-thump means that: • Where: • dAP is the diameter of the average size asphaltene particle retained by the formation

31. Physical Blockage of 100 m Pore Throat Caused by In-Situ Flocculation of Much Smaller Asphaltene Particles 100 mm

32. Retained Asphaltene Particle Diameter, dAP In the more general case, however, a more appropriate definition for dAP is: • Where: • a is a constant that accounts for the variation of the size of the asphaltene particle filtered by the formation. a varies from 0 to 1. • dH is the average hydraulic diameter of the producing horizon

33. Asphaltene Near-WellboreFormation Damage Modeling • Asphaltene-Induced Formation Damage • Asphaltene Particle-Size Distribution (psd) • Hydraulic Radius • Permeability Impairment • Porosity Loss • Skin Factor • Asphaltene Deposit Erosion • Solution Algorithm • FDModel Application

34. Darcy's equation for steady state radial flow is: • Where: • m is viscosity, centipoise • q is reservoir barrels per day • k is permeability, Darcy • P is pressure, psia • r is distance from center of wellbore, feet

35. The Darcy equation applies to each radial segment Dr at location r

36. Initial Area Available to Flow Ainitial(r) At time equal to zero, i.e., before any asphaltene plugging, the total area available to flow at a distance r from the center of the wellbore is: • Where: • h is the net thickness of the formation or the net pay zone • f is the initial average effective porosity of the formation

37. Net Area Available to Flow Anet(r,t) The net area available to flow at location r, after asphaltene plugging for time t, is obtained as follows: • Where: • AAP(r,t) is the total area plugged by asphaltene particles at location r at time t. The calculation of AAP(r,t) is described next.

38. Total Area Plugged AAP(r,t) The total area plugged by asphaltene particles at location r at time t is AAP(r,t): • Where: • DAAP(r,j) , is the incremental area plugged by asphaltene particles at location r within time interval j • Nis the number of time intervals

39. Calculation of Incremental Area Plugged DAAP(r,j) Very Effective Pore-Throat Plugging by Least Number of Asphaltene Particles Pore-Throat Asphaltene Particle

40. Calculation of Incremental Area Plugged DAAP(r,j) The incremental area plugged by asphaltene particles at location r within time interval j, DAAP(r,j), is: • Where: • IMAT, is the number of incremental moles of asphaltene particles being trapped at location r within time interval j • MVA, is the molar volume of asphaltene particles at location r at time interval j • CSAAP, is the cross-sectional area of the average size asphaltene particle retained by the formation at location r at time interval j • VAP, is the volume of the average size asphaltene particle retained by the formation at location r at time interval j

41. Calculation of Incremental Area Plugged DAAP(r,j) The equation giving the incremental area plugged by asphaltene particles at location r within time interval j, DAAP(r,j), is: • Where: • DAPtrap(r,t), is the number of incremental moles of asphaltene particles being trapped at location r within time interval j • uA(r,j) is the molar volume of asphaltene particles at location r at time interval j • dAP, the diameter of the average size asphaltene particle retained by the formation

42. Calculation of Incremental Area Plugged DAAP(r,j) After rearrangement and substitution, the equation giving the incremental area plugged by asphaltene particles at location r within time interval j, DAAP(r,j), is: • Where: • DAPtrap(r,t), is the number of incremental moles of asphaltene particles being trapped at location r within time interval j • uA(r,j) is the molar volume of asphaltene particles at location r at time interval j • dAP, the diameter of the average size asphaltene particle retained by the formation

43. Total Area Plugged AAP(r,t) Substitute into the equation giving the total area plugged by asphaltene particles at location r and time t,AAP(r,t), to get:

44. Total Area Plugged AAP(r,t) Hence, to calculate the total area plugged by asphaltene particles at location r at time t, AAP(r,t), we need the following: • dAP, the diameter of the average size asphaltene particle retained by the formation • uA(r,j), the molar volume of average size asphaltene particles at location r at time increment j • DAPtrap(r,j), is the number of incremental moles of asphaltene particles being trapped at location r within time interval j

45. Average Diameter of Asphaltene Particles Retained Remember that dAP is the diameter of the average size asphaltene particle retained by the formation and is given by:

46. Molar Volume of Asphaltene Particles Retained uA(r,j), the molar volume of asphaltene particles at location r at time interval j, is calculated by the phase behavior model. In this case, it is calculated by the TC Model, AsphWax’s asphaltene phase behavior simulator.

47. Incremental Moles of Asphaltene Particles Retained DAPtrap(r,j), the incremental moles of asphaltene particles retained, is obtained as follows: • At the pressure and temperature prevailing at location r at time t, the asphaltene phase behavior model (TCModel) calculates the moles of asphaltene particles per mole of reservoir fluid, s, and their psd, f(x), where x is the asphaltene particle diameter. • f(x) is then integrated from x = dAP to x =¥ to obtain the moles of asphaltene particles being trapped, ftrap, per mole of reservoir fluid at location r within time interval Dt. • The total number of moles of reservoir fluid, MRF, flowing at location r is obtained by flowing the well at flowrate q for some specified production time interval Dt.

48. Incremental Moles of Asphaltene Particles Retained Hence, from a material balance, the number of incremental moles of asphaltene particles being trapped at location r within time increment j, DAPtrap(r,j), is:

49. Total Area Plugged AAP(r,t) Substitute into the previous equation to get the total area plugged by asphaltene particles at location r at time t, AAP(r,t), as: • Where: • gis a constant whose value is greater or equal to 1. it is related to a by the relation g=1/a. Recall that a varies from 0 to 1. g (or a) indicates the "efficiency" of plugging of the asphaltene particles. It may be used as a tuning parameter, if well history-matching data are available.

50. "Degree of Damage", DOD It is convenient to introduce the "Degree of Damage", DOD, at each location r at time t. DOD may be defined as: