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SPE Society of Petroleum Engineers SPE 16233 Study on the Effect of Pore Blocking Mechanisms on Formation Damage by A.K. Wojtanowicz, Louisiana State U.; Z. Krilov, INA Naftaplin; and J.P. Langlinais, Louisiana State U. SPE Members Copyright 1987, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Production Operations Symposium held in Oklahoma City, Oklahoma, March 8-10, 1987. This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Write Publications Manager, SPE, P.O. Box 833836, Richardson, TX 75083-3836. Telex, 730989 SPEDAL. ABSTRACT The process of formation permeability damage due to solids movement and capture was quantitatively modeled by using principles of deep bed filtration and chemi- cal reactions kinetics. The developed theory des- cribes the pore blocking mechanism caused by particles from completion fluids (foreign particles invasion) as well as the mechanism of release and capture of rock fines (in-situ mobilization). For practical applications, this theory was used in the context of pattern recognition, ie, to examine the experimental data on rock permeability change vs time from the laboratory flow experiments. Thus, a straight line section of data plotted in a certain system of coordinates indicates the type of formation damage occurring. The verification study was performed in two series of laboratory experiments. In the first, a drilling mud, consisting of a contaminated completion fluid, was pumped through the simulated synthetic rock. In the second, four typical, solids-free completion brines were pumped through actual samples of water sensitive, unconsolidated sandstones taken from Adriatic Sea gas fields. The experiments revealed the applicability of the theory and the method of diagnostic plots to describe and analyze formation permeability damage. INTRODUCTION The last two decades have seen significant progress made in understanding the mechanisms of formation damage. In summary: - all sandstones are water sensitive to some degree - permeability damage is associated with particles movement and clay swelling effects - there is a strong correlation between fluid salinity and permeability impairment Traditionally, permeability damage has been classi- fied as chemical or mechanical, the latter being bro- ken into two categories: foreign particles invasion and in-situ mobilization of formation fines. Most conventional studies on mechanical permeability damage allowed for qualitative statements regarding a bridging mechanism and a cake invasion zone [1], critical size of the damaging particles [2], qualita- tive relationships between permeability vs time and suspended solids [3], and non-harmful size of mobile solids [4]. Recent developments include x-ray analysis of formation fines [5] showing that mobile particles are not only clay minerals, but fine particles are present in all formations in sufficient quantities to cause formation damage. The mechanism of water sensi- tivity of sandstones containing clay has been quanti- tatively analyzed [7] revealing an existence of a critical salt concentration below which the permea- bility varies with salt concentration as well as the dynamic effects of the rate of salinity change on permeability reduction. A fully quantitative description of permeability damage due to solids movement was attempted previously [6], by developing a phenomenological model of the rock where a system of plugging and non-plugging pathways is postulated. In this research, an intui- tive guess is made on rock permeability as a function of the mobile solids concentration. A mathematical predictive model was developed previously [8], to describe water sensitivity in Berea sandstone. This model, based on an exponential model of clay release and capture, was used to find correlations between the release/capture coefficients as well as the effects of temperature and flowrate. A sophisticated statistical model of the interactions between particles size dis- tribution and formation pore size distribution was recently presented [9]. This model was used for simu- lation studies only without experimental verification. The approach applied in this work was to derive a mathematical theory concerning all types of mechanisms of permeability damage and then analyze experimental data on permeability damage. A similar analysis was attempted for foreign particle capture alone [10]. The concept used here is based on a systems analysis 449

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  • SPE Society of Petroleum Engineers

    SPE 16233

    Study on the Effect of Pore Blocking Mechanisms on Formation Damage by A.K. Wojtanowicz, Louisiana State U.; Z. Krilov, INA Naftaplin; and J.P. Langlinais, Louisiana State U. SPE Members

    Copyright 1987, Society of Petroleum Engineers

    This paper was prepared for presentation at the SPE Production Operations Symposium held in Oklahoma City, Oklahoma, March 8-10, 1987.

    This paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the author(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Write Publications Manager, SPE, P.O. Box 833836, Richardson, TX 75083-3836. Telex, 730989 SPEDAL.

    ABSTRACT

    The process of formation permeability damage due to solids movement and capture was quantitatively modeled by using principles of deep bed filtration and chemi-cal reactions kinetics. The developed theory des-cribes the pore blocking mechanism caused by particles from completion fluids (foreign particles invasion) as well as the mechanism of release and capture of rock fines (in-situ mobilization).

    For practical applications, this theory was used in the context of pattern recognition, ie, to examine the experimental data on rock permeability change vs time from the laboratory flow experiments. Thus, a straight line section of data plotted in a certain system of coordinates indicates the type of formation damage occurring.

    The verification study was performed in two series of laboratory experiments. In the first, a drilling mud, consisting of a contaminated completion fluid, was pumped through the simulated synthetic rock. In the second, four typical, solids-free completion brines were pumped through actual samples of water sensitive, unconsolidated sandstones taken from Adriatic Sea gas fields.

    The experiments revealed the applicability of the theory and the method of diagnostic plots to describe and analyze formation permeability damage.

    INTRODUCTION

    The last two decades have seen significant progress made in understanding the mechanisms of formation damage. In summary:

    - all sandstones are water sensitive to some degree - permeability damage is associated with

    particles movement and clay swelling effects - there is a strong correlation between fluid

    salinity and permeability impairment

    Traditionally, permeability damage has been classi-fied as chemical or mechanical, the latter being bro-ken into two categories: foreign particles invasion and in-situ mobilization of formation fines. Most conventional studies on mechanical permeability damage allowed for qualitative statements regarding a bridging mechanism and a cake invasion zone [1], critical size of the damaging particles [2], qualita-tive relationships between permeability vs time and suspended solids [3], and non-harmful size of mobile solids [4]. Recent developments include x-ray analysis of formation fines [5] showing that mobile particles are not only clay minerals, but fine particles are present in all formations in sufficient quantities to cause formation damage. The mechanism of water sensi-tivity of sandstones containing clay has been quanti-tatively analyzed [7] revealing an existence of a critical salt concentration below which the permea-bility varies with salt concentration as well as the dynamic effects of the rate of salinity change on permeability reduction.

    A fully quantitative description of permeability damage due to solids movement was attempted previously [6], by developing a phenomenological model of the rock where a system of plugging and non-plugging pathways is postulated. In this research, an intui-tive guess is made on rock permeability as a function of the mobile solids concentration. A mathematical predictive model was developed previously [8], to describe water sensitivity in Berea sandstone. This model, based on an exponential model of clay release and capture, was used to find correlations between the release/capture coefficients as well as the effects of temperature and flowrate. A sophisticated statistical model of the interactions between particles size dis-tribution and formation pore size distribution was recently presented [9]. This model was used for simu-lation studies only without experimental verification.

    The approach applied in this work was to derive a mathematical theory concerning all types of mechanisms of permeability damage and then analyze experimental data on permeability damage. A similar analysis was attempted for foreign particle capture alone [10]. The concept used here is based on a systems analysis

    449

  • of complex phenomena in which the empirical record of permeability response vs flowing time is used to infer quantitative values of factors involved in the fluid-rock interaction. This concept is similar to that used in transient well testing or well logging.

    There are basically two sources of particles migra-ting into the reservoir rock: foreign particles from completion fluids and particles generated inside the formation rock. The latter might be caused by incom-patibility of a completion fluid with the formation rock or with formation waters. Foreign clay particles are generated outside the formation as a result of completion fluid contamination with drilling mud [16] and the foreign iron colloids are produced due to corrosion and ozidation of steel casing, pumps, drill string and surface equipment [11]. Foreign particles concentration in the completion fluid invading a formation is approximately constant and their migra-tion in the rock has been often modeled as a constant rate filtation process. Formation fines can be mobilized as a result of chemical (precipation) or physical-chemical (electrokinetic forces, Zeta poten-tial on ionic strength) reactions. In any case, the phenomenological model of solids release should re-flect a decrease with time in the amount of available rock solids. Such a model can be based on the first-order decay process [8] or on the general form of the first-order chemical kinetics equation [12]. There-fore it can be assumed that the concentration of the mobilized rock particles exponentially decreases with time during the constant-rate filtration process.

    The mechanics of particle transport across the streamlines include sedimentation, adsorption, diffusion and hydrodynamics [10]. Ultimate capture of particles that have come into direct contact with a grain surface is determined by friction, fluid pressure, gravity, electrokinetic interactions, mole-cular forces and surface tension [13], [14]. Three basic mechanisms of blocking formation pores were analyzed with regard to foreign particles migration [10]: gradual pore blocking, single pore blocking [screening], and cake forming [straining]. In the case of rock particles mobilization, all three mechanisms can be effectively modeled with that of pore seepage.

    The generalized, modulation model of the porous medium is presented in fig. 1. The fundamental assumption is that the pressure drop occurs at the pore throats; thus the recorded permeability of a core is controlled by the throat area rather than the pore area. Tortuosity here might include effects of pore throat length and curvilinearity of the flowpaths. The pore areas are a source of in-situ mobilized particles, and also the location of solids capture.

    Mathematical analysis of complex statistical interactions between populations of particles and populations of pores, as attempted in [9], is here replaced with the simple systems analysis approach to the pattern recognition problem. In the core flow test, a known signal (flow volume and rate) is applied to an unknown system (the rock) and the response of that system (permeability change) is measured during the test. Usually, the response implies various con-current mechanisms of solids-rock interactions which precludes any sound analysis. At certain times, how-ever, only one single mechanism of permeability damage is dominant, thus providing data for effective analysis. The theory presented below provides a practical tool for identification of the prevailing mechanism of permeability impairment in the linear flow systems (laboratory flow tests). The general assumptions are as follows:

    SPE 1 6 2 3 3 constant rate filtation low solids concentration, so volume reduction due to particles capture can be ignored linear geometry of flow homogeneous formation cake incompressibility laminar flow regular pore geometry

    The last assumption was thoroughly discussed in [10], together with resulting geometrical simplifications.

    ANALYSIS OF FOREIGN SOLIDS INVASION AND CAPTURE

    Practical aspects of foreign solids invasion into a formation are associated with completion fluid clean-liness. Traditionally, it was suggested that there is a "critical" size of solids below which there is no permeability impairment. Recent research, howeve:, shows that completion fluid fines an order of magn1-tude smaller than a given pore size can cause con-siderable damage [15],[6]. Analysis of pore blocking mechanisms based on a deep bed filtration theory [10] indicated that the differential pressure response to foreign solids loading during flow tests will be mani-fested in one of three functional relationships with time: linear, hyperbolic,or quadratic.

    1. Gradual Pore Blocking

    This mechanism is associated with a continuous capture of fines at the rock walls due to retention forces. It was reported as a "surface-type depos-ition" [6], for which the rate of capture is directly proportional to the solids concentration in the flow-stream. A similar function was offered by another investigator [8] by considering particles deposition on spherical collectors.

    Using a first-order particles capturing model the permeability response to the gradual blocking is

    K= r- (1) and the relative permeability function is

    JK/Ki = 1 - C4t (2)

    which defines a straight-line diagnostic plot of ~ vs t.

    2. Single Pore Blocking (Screening)

    The single pore blocking occurs when single particles of size close to the pore size (critical size) instantly blocks an individual pore, thus elim-inating it from the flow system. The permeability response to this mechanism is

    K t (3)

    and the relative permeability function is

    (4)

    450

  • SPE 1 6 2 33 thus indicating a diagnostic straight-line plot (klki) vs time.

    3. Cake Forming (Straining)

    of assuming the initial mass of mobile solids at the throats is negligible when compared to the mobile solids on the pore walls. In this case, the ultimate, equilibrium permeability reached after long flowing time will be equal to the initial permeability. The permeability response is

    The straining mechanism is associated with building up a filtration cake at or close to the formation face. Though it can basically be initiated by particles greater than pore size, high solids concen-traton was also reported to cause cake building by solids smaller than pore size [17] [14]: The permea-bility response to straining is

    K (5)

    and the relative permeability function is

    (6)

    indicating straight line of the (kilk) vs time plot.

    ANALYSIS OF FORMATION SOLIDS MOBILIZATION AND CAPTURE -- ------ ---

    Clean, incompatible completion fluids release formation fines at the pore areas and deposit them in the throat areas. This happens in practically all granular rocks which contain some concentration of mobile fines [5]. As it is shown in fig. 2, there is some potentially mobile mass of solids on the pore surface, M~i and on the throat surface, Mti This may be e1ther diagenetic clay minerals such as kaolinite and illite, or non-clay minerals such as quartz, as well as amorphous materials [5]. Mobile solids can also be generated as precipitates from chemical reaction between completion fluid and forma-tion waters. Assuming an exponential behavior for the solids mobilization, which stems from its analogy to the decay equation and chemical reaction kinetics, then the pore throat blocking mechanisms can be mathe-matically modeled similarly to that used for the foreign particles invasion.

    1. Concurrent Gradual Blocking and Sweeping.

    When the size of mobilized particles is signifi-cantly smaller than the pore throat size, a simul-taneous deposition and sweepage occurs. The instant-aneous size of the pore throat results from a dynamic balance between rate of release and rate of capture. The permeability response to this mechanism is

    and the relative permeability change is

    JKIKi = 1 + C7 - (Cat + C7) exp(-frt)

    (7)

    (8)

    It can be proven that function (8) has a distinctive minimum indicating a transition from the initial stage when gradual capture prevails to the final stage when pore sweepage plays a dominant role.

    Though no simple diagnostic plot can be made for function (8), a simplified model can be derived by

    451

    and the minimum permeability is reached at time

    The diagnostic straight-line plot is ln( (1 - ./KIKi) It) vs time.

    2. Gradual Pore Blocking

    (9)

    (10)

    The gradual pore blocking mechanism can also be analyzed separately in the case when following stages are more complex than that presented above. Hence, the permeability response is

    jKIKi = 1 - Cg 1 - exp(-frt) (11) and the diagnostic straight-line plot is ln((C- 1 +,fiflifi)l C) vs time, while constant Cis calculated as

    c (12) yl + y2 - 2Y3

    where

    and the function Y(t) is defined as

    Y(t) = 1 - JKIKi (13)

    3. Single Pore Blocking

    This mechanism occurs when the mobilized particles resulting from formation interaction with a completion fluid are within the range of the pore throat size and the elimination of pore channels takes place. The permeability response is

    KIKi = 1 - C10 [ 1 - exp(-frt) ] (14)

    and the diagnostic straight line plot is ln ((C -1 + KIKi) I C) vs time. The constant, C, is defined by eq. (12) and Y(t) is

    Y(t) 1 - KIKi (15)

    4. Cake Forming (Plugging)

    When the size of mobilized particles in the pore areas is significantly greater than the pore throat size, they accumulate in the form of permeable cake (plug). A constant-rate filtration takes place with a steady increase of the plug thickness. The rock permeability response to plugging is

    KIKi = 1 + ell [ 1 - exp(-frt) ] (16)

    and the diagnostic straight-line plot is ln((l + C - KIKi) I C) vs time. Here, function Y(t)

  • is defined as

    Y(t) = (K/Ki) - 1 (17)

    and constant Cas eq. (12).

    5. Pore Sweeping

    The mechanism of pore sweeping is associated with permeability recovery due to the release of solids from the pore throats. This mechanism may occur at the late stage of flow as a result of breaking a solids bridge at the pore throat or when rock solids supplied from the pore areas is small. The permea-bility resonse is

    JK/Ki = 1 + C12 [ 1 - exp(-frt) ] (18)

    and the diagnostic straight-line plot is ln((1 + C - JK/Ki) / C) vs time, with constant C defined by equation(12) and function Y(t) defined as

    Y(t)

    EXPERIMENTAL DESIGN

    Verification of the mathematical models of permea-bility damage was performed as part of an experimental project directed toward identifying new completion fluids for use in the unconsolidated gas bearing sands of the Adriatic Sea area [17].

    The laboratory setup for injecting completion fluid through the hand-made compacted cores is shown in fig. 2. A similar setup was used for measuring absolute permeability using Nitrogen gas. Before each flow test, the core was vacuum-saturated with the comple-tion fluid and was then transferred to the Hassler cell. Confining pressures of 7 atm were applied to prevent bypassing. A volume of 1000 ml of completion fluid was then pumped through the core sample by a metered pump at the rate of 10 ml/min. The elapsed time and pressure differential were recorded at inter-vals during the test. Influent and effluent samples were characterized by measuring pH, particle size distribution (laser beam analyzer, range 0.7 - 300 microns), total suspended solids, capillary suction time and turbidity. All experiments were performed at room temperature. Exit pressure of the cell was main-tained at atmospheric.

    Two series of experiments were performed; foreign solids invasion tests and rock solids mobilization tests. Synthetic rock, hand packed cores, and Sodium Chloride brine completion fluid comtaminated with drilling mud were used for the foreign solids invasion experiments. A detailed description of these tests was presented in a previous work [10]. The synthetic rock samples were made of quartz grains and glass beads to simulate the grain distribution of the ori-ginal rock. The comparison of reservoir rock and synthetic rock properties is shown in Table I. At similar grain size distributions, the permeability of the synthetic rock was significantly higher than that for the actual rock. The effect of various levels of total mass contamination and the effect of solids size on permeability damage were evaluated as well in these experiments.

    The rock solids mobilization tests were performed by flowing solids-free completion fluids through actual rock samples. Completion fluids used in these

    452

    SPE 1 6 2 3 3 tests are shown in Table II. The mineral composition of the Adriatic rock samples is presented in Table III. The formation rock is known for its water sensi-tivity and high suseptability to permeability damage [ 16].

    The interpretation method used in the experiments was based on processing the experimental records of relative permeability change with flowing time. The computer aided diagnostic plots were made in which the straight line segments were sought using linear regression analysis. The linearity of a diagnostic plot over certain time periods was considered an indi-cation of a pore blocking mechanism prevailing at that time.

    FOREIGN SOLIDS INVASION EXPERIMENTS

    In this case, experiments were conducted by flowing completion fluids with various levels of mud comtam-ination through the synthetic rock cores. The permea-bility recorded is shown in fig. 3. The plots show some fundamental qualitative change in permeability damage associated with contamination change from 1% to 2% . The diagnostic plots presented in fig. 4 and 5 indicate gradual pore blocking followed by single pore blocking damage for mud contaminations of 0.2%, 0.5%, and 1.0% In the case of 2% and 3% mud contamin-ation, the cake forming mechanism occurred, shown in fig. 6.

    Another experiment performed was with a completion fluid with a mud contamination of 3% where the fluid was filtered through various size filters prior to flow through the cores. Properties of prefiltered completion fluids are presented in Table IV. Relative premeabilities recorded in these experiments is shown in fig. 7. The diagnostic plots (fig. 8) indicated gradual pore blocking and single pore blocking mech-anisms. Pore blocking time (duration of a gradual pore blocking phase) was clearly dependent on solid sizes and concentrations.

    Solids capture phenomena were further analyzed in view of their relationship to passing particle size. The median size of passing particles versus flowing time was superimposed on the dignostic plots (fig. 9). A rapid, linear decrease in particle size is associated with a gradual pore blocking. An onset of the screening phase is indicated by the sharp stabili-zation of particle size which precisely coincides with the diagnostic plot behavior. Screening and straining are represented by the constant size of passing parti-cles, though their diagnostic plots are different.

    An effort was made to relate pore blocking time to solids concentration and solids size. Data from all experiments were used to make the pore blocking time plots presented in fig. 10. The strong effect of particle concentration on pore blocking time is evi-dent. Much less significant is the effect of particle size. All the blocking time curves indicate asymp-totic behavior. For suspended solids concentrations approaching the value of about 350 mg/1 the onset of particle screening occurs after a very long time. It can also be noticed that for the particle sizes below 22 microns, the pore blocking time is the same as that for unfiltered completion fluids (solids size up to 125 microns). It makes sense if we consider the fact that the pore size of the rock samples is within the range of 16.6 - 22 microns. Apparently, particles larger than the pore size do not contribute to gradual pore blocking.

  • The above observations can be summarized from a practical viewpoint by considering the rate of reser-voir permeability damage (skin effect) and the depth of particles invasion (the radius of the damage zone). Cake filtration and straining mechanisms of particle capture is associated with a sharp, hyperbolic-type permeability reduction, the shallow invasion of parti-cles into formation rock, and with the small size of particles passing through the damaged zone into the original formation. In actual field operations, this type of particle capture is detrimental due to the difficulty of cake removal. Particle retention by screening is associated with the steep, linear reduc-tion in permeability, the deep invasion of solids into the rock, and the small size of passing particles. It may produce permanent permeability damage with no remedial options. The gradual blocking mechanism is always present to some extent since a solids-free completion fluid is virtually impossible. This mech-anism is indicated by slow, parabolic-type permea-bility reduction, deep particles invasion and a steady decrease in the size of passing solids. The duration of this stage is dependent upon the size and concen-tration of completion fluid particles and it can be tolerated within practically acceptable limits.

    IN-SITU MOBILIZED PARTICLES EXPERIMENTS

    The permeability change recorded in the flow tests with four completion fluids and the actual rock samples are shown in fig. 11 and 13. The superiority of the low pH completion fluids is qualitatively evi-dent. The graphical analysis based on diagnostic plots (fig 12) shows that the calcium chloride brine interaction with the formation rock instantaneously triggered the pore plugging mechanism of formation damage. The sodium chloride brine record, on the other hand, shows nearly linear permeability change with flowing time. This can be explained by a single pore blocking mechanism described by equations (3) and (15) . For early times, exponential reduction of solids released from the rock might by overshadowed by other effects, thus indicating a constant-concentra-tion response.

    The diagnostic plots for the low-pH completion fluids in fig. 14 and 15 indicate gradual pore blocking followed by pore sweeping. In addition, the diagnostic plot for combined effects of gradual blockage and sweepage revealed straight line response at two flowrates of 3 cc/min and 10 cc/min. The latter might be associated with the effect of flowrate on the release coefficient. The five fold increase of the release coefficient in response to the three fold increase of the flowrate shows that the effect might be stronger than linear [8]. Additional verification of the model was made by comparing values of the release coefficient recorded and calculated from equa-tion (10). The calculated value was approximately 0.006 /min , which roughly corresponds to the experi-mental values of 0.004 and 0.005 /min.

    The properties of effluents from the flow tests, containing in-situ mobilized rock solids, are shown in Table V and fig. 17. An interesting observation was that the total amount of mobilized rock solids was the same for various completion fluids and various degrees of permeability damage. Moreover, the particle size distribution in combined effluents were also similar. However, the various mechanisms of solids capture were clearly indicated by analyzing the size of moving solids with respect to flowing time as shown in fig. 18. Here, the permeability improvement resulting from the pore sweepage favorably correlated with the in-crease of passing particles.

    453

    SP'E 1 6 2 3 3 CONCLUSIONS

    The permeability damage of an oil or gas reservoir is a time dependent function, controlled by mobile solids supply and capture mechanisms.

    1. The theory of particle movement and capture and the method of diagnostic plots proved applicable for analyzing empirical data on permeability damage. The resolution of the relative permea-bility data, however, is not as good as that for the raw measurement of pressure differential [10]. Thus, a continuous record of pressure differential should be analyzed in further appli-cations.

    2. For the formation damage caused by foreign parti-cles invasion, there are two limits controlling damage: total solids concentration to avoid cake filtration (here at 2000 mg/1), and the assymp-totic limit of solids concentration below which the gradual pore blocking time is long enough to finish a well completion before the single pore blocking occurs.

    3.

    4.

    For the formation damage caused by mobile rock particles, it seemed the amount of s.olids avail-able for mobilization is the same for a parti-cular formation and not dependent on the type of completion fluid used. The mechanism by which particles were mobilized and captured, however, varied with the type of completion fluid. Thus, the completion fluid compatibility with a forma-tion can be quantified by values of the release and capture coefficients. The size of the mobilized solids can be indirectly inferred from the type of formation damage.

    Further developments in this work may include velocity and temperature effects as well as con-version of the linear model into a radial geo-metry, utilizing a constant pressure filtration rather than a constant rate of flow as used in these experiments.

    NOMENCLATURE

    area of single pore, sq em area of cake, sq em area of flow, sq em rock area, sq em process constants cake-to-filter ratio, dimensionless pore size (diameter of the inscribed circle), em critical size of particles, em equivalent diameter, em permeability, cp average length of the flowpath, em average length of the pore throats, em actual length of the rock, em mass of mobile solids on the rock surface, gm number of flowpaths, dimensionless perimeter of a single pore, em pore volume, cc flow rate, cc/min cake resistance to filtration, 1/cm rock resistance to filtration, 1/cm

  • S0 specific surface T tortuosity, dimensionless Ts solids concentration in the flow stream,

    gm/cc oC= average flow resistance, cm/gm

    AP = differential pressure, atm = porosity, dimensionless

    JU= viscosity, cp f = mobile solids density, gm/cc subscripts

    c = capture i initial value (time 0) p pore r release t throat 1 onset of pore sweeping

    AKNOWLEDGEMENT

    The authors wish to thank Baker Sand Control for their cooperation and use of their laboratory facili-ties for some of the experiments conducted. Also, appreciation is extended to Mr. Mark Kristoff of Baker Sand Control for his efforts.

    1.

    2.

    3.

    4.

    5.

    6.

    7.

    8.

    REFERENCES

    Glenn, E. E. and Slusser, M. L.' "Factors Affecting Well Productivity. II. Drilling Fluid Particle Invasion into Porous Media," Petroleum Transactions, AIME, Vol 210, (1957). Abrams, A., "Mud Design to Minimize Rock Impairment Due to Particle Invasion," Jour Pet Tech, (May, 1977), pp 586-92. Tuttle, R. N. and Bankman, Nondamaging and Acid Degradable Completion Fluids," Jour Pet Tech,

    Y. H., "New Drilling and (Nov, 1974),

    pp 1221-26. .

    Meyer, R. L., and Vargas, R. H., "Process of Selecting Completion and Workover Fluids Requires Series of Tradeoffs," Oil and Gas Jour, (Jan 30, 1984). Muecke, T. W., "Formation Fines and Factors controlling Their Movement in Porous Media," Jour Pet Tech, (Feb, 1979), pp 144-50.

    Gruesbeck, C., and Collins, R. E., "Entrainment and Deposition of Fine Particles in Porous Media," Soc Pet Eng Jour, (Dec, 1982), pp 847-56. Khilar, K. C., Fogler, H. S. and Ahluwalia, Y. S., "Sandstone Water Sensivity: Existance of a Critical Rate of Salinity Decrease for Particles Capture," Chern Eng Science, Vol 38, No. 5, (1983), pp 789-800. Khilar, K. C. and Fogler, H. Sensitivity of Sandstones," Soc Pet (Feb, 1983), pp 55-64.

    s.' Eng

    "Water Jour,

    SPE 1 6 2 33

    9. Sharma, M. M. and Yartsos, Y. C., "Permeability Impairment due to Fines Migration in Sandstones," SPE paper 14819, presented at the seventh SPE Symposium on Formation Damage Control, Lafayette, LA, (Feb, 1986).

    10. Wojtanowicz, A. K., Krilov, Z., and Langlinais, J. P., "Oilwell Completion Fluid Solids Interaction with an Unconsolidated Oil Reservoir," paper presented at the seventeenth Annual Meeting of the Fine Particle Society, San Francisco, CA, (Aug, 1986).

    11. Patte, J. M., and Dibble, W. E., Jr., "Formation Damage due to Colloid Plugging," SPE paper 11801, presented at the International Symposium on Oilfield and Geothermal Chemistry, Denver, CO, (June, 1983).

    12. Smith, J. M., Chemical Engineering Kinetics, McGraw-Hill Inc, 1970.

    13. Ives, K. J., "Deep Bed Filtration," Solid Liquid Separation by L. Svarovsky, Butterworths, London, (1981).

    14. Selmeezi, Y. G., "Capture Mechanism in Deep Bed Filtration," Indurstrial Water Eng, (June/July, 1971).

    15.

    16.

    Hashemi, "Proper Oil and

    Krilov,

    R., Ershagi, I., and Ammerer, N., Filtration Minimizes Formation Damage,"

    Gas Jour, (Aug 13, 1984).

    Z., "A Compatibility Study on Completion Fluids with Unconsolidated Adriatic Sea Gas Bearing Formations--An Experimental Approach," MS Thesis, Louisiana State University, Baton Rouge, LA, (1986).

    17. Cheremisinoff, N. P., and Azbel, D. S., Liquid Filtration, Ann Arbor Science, Woburn, Mass., (1983).

    18. Tiller, F. M., "Deposition of Fine Particles in Porous Beds," University of Houston, Texas, short course, (Nov. 1984), not published.

    APPENDIX ~

    MATHEMATICAL MODEL OF PERMEABILITY DAMAGE

    The physical basis for following equations:

    this analysis includes the

    Darcy Law equation: p..QLr

    p ---

    Hagen-Poiseuille equation: Q}"'L

    p 32

    Filtration equation: .AP Ac

    Q

    (A1)

    (A2)

    (A3)

    454

  • Solids release equation: dM

    dt

    Solids capture equation (d D): dM

    dt

    and the material balance equation

    dM (dM) (dM _) --:;- = -;Jc - -;;Jr

    (A4)

    (AS)

    (A6)

    The equivalent diameter in eq. (A2) media flow geometry [18] is:

    for a porous

    de= 4(/so) (1/(1 -~)) (A7) It was discussed and proved in [10] that for the regular pore geometry the following holds:

    de = D P = C1D A = c2n2 (A8)

    Thus eq. 2 becomes

    p 32 Q c2 N_f-t L

    (A9) Af2

    Comparison of eqs. (Al) and (A2) gives

    Af2 K (AlO)

    32 c2 N Ar T

    Note that for the linear flow through the core at a constant flowrate, eq. (AlO) can be written as

    (All)

    Invasion and Capture of Foreign Particles

    Eq. (A6) becomes

    dM (Al2)

    dt

    and solids concentration in the flowstream is constant, Ts constant. Three mechanisms of permeability damage (pore blocking) can be considered; gradual pore blocking, single pore blocking (screening), and cake forming (straining).

    1. Gradual Pore Blocking

    Flow area is dAf c: )c dt Le

    or, considering eq (AS) dAf Fe Ts

    dt

    Integration of eq (Al4) within the limits and Af(t) gives

    t p L

    (Al3)

    (Al4)

    Afi(t=O)

    (AlS)

    SPE 1 6 2 3 3 or, considering eq (All)

    (Al6)

    Eq. (Al6) is identical to eqs. (1) and (2). Note that the physical meaning of the capture coef-ficient, fc, is analogous to the cake-to-filter ratio, used in filtration t~eory. Their relationship is

    (PV) Ts CFR (Al7)

    Q e 2. Single Pore Blocking

    The concentration of particles of critical size, d, is fd and these particles cause an instantaneous blockage of individual pores. Thus, the flow area equation is

    (Al8) dt

    and after integration and substitution from eq. (All), we obtain

    t cs t 7fc3 2 d3 ~

    (Al9)

    which is identical to eqs. (3) and (4).

    3. Cake Forming (straining)

    For a constant rate of flow and constant solids concentration eq. (A3) becomes

    (A20)

    or, considering eq. (Al)

    K (A21) Rm ( 1 + o( Ar T s Q t)

    Eq. (A21) is identical to eqs. (S) and (6).

    Mobilization and Capture of Rock Particles

    Mobilization of formation fines takes place in the pore area and their capture in the pore throats (fig. 1). There are four mechanisms of solids transport in the pore throat that affects formation permeability: gradual blockage, single blockage, cake forming and sweepage.

    1. Mobilization equation Eq. (A4) controls solids mobilization as

    dMP

    dt

    and after integration within limits Mpi(t=O), we obtain

    Mpi exp(-fr t )

    (A22)

    (A23)

    455

  • Thus solids concentration in the flowstream is

    (-1)

    Q Q exp(-fr t)

    2. Concurrent Pore Blockage and Sweepage

    (A24)

    The material balance eq. (A6) written for the pore throat area becomes

    (A25) dt Q

    and its solution is

    Mt = (Mti + (fc fr Mpi t)/Q) exp(-fr t) (A26)

    The relationship between the mass of solids retained at the throat and the area of flow is

    Mt = f Lt (Afi + (Mti/ fLt) - Af) (A27) Substituting (A27) and (All) into (A26) yields

    C3 f Lt JN (fKj_ - JK) (A28) (Mti + (fc fr Mpi t)/Q ) exp(-frt) - Mti

    Eq. (A28) is identical to eqs. (7) and (8). The flowing time at which formation permeability reaches its minimum is

    (A29)

    For the case when Mti Mpi eq (A28) simplifies to

    VK =JKi- exp(-fr t) fc fr Mpi t C3 ~ Lt JN'

    (A30) Q

    which is identical to the eq. (9) and eq. (A29) becomes equal to eq. (10).

    3. Gradual Pore Blocking

    The flow area equation is derived from eqs. (A25) and (A27) as

    exp(-fr t) (A31) dt

    and its solution, combined with eq. (All) is

    .JK = JKi- (A32) Eq. (A32) is equivalent to eq. (11).

    4. Single Pore Blocking

    Substituting Ts from eq. (A24) into eq. (AlB) gives

    dAf exp(-fr t) (A33)

    dt

    SP'E 1 6 2 3 3 This solution to eq. (A33) combined with eq. (All) gives

    6 fd A2 Mpi

    1(c32 d3 ~ [ 1 - exp(-fr t)]

    which is identical to eq. (14).

    4. Pore Cake Forming

    (A34)

    Filtration resistance of the solids cake formed at the pore throat increases in time as

    (A35)

    Integrating eq. (A35) and substituting into eq. (A3) gives

    p QJ-"Rm

    [ 1 - exp(-fr t)] + -----Ac

    or, considering eq. (A2), we obtain

    1/K Ar Rm

    [ 1 - exp(-fr t)] + ---Ac Lr

    which is identical to eq. (16).

    5. Pore Sweeping

    (A36)

    (A37)

    Since the pore sweeping begins at a certain time t1 0, the initial mass of solids at the pore throa~ is

    Mt = Mt(tl) = Mtl . Using eq. (A23), the mass of solids swept from the throat is

    6 M = Mtl [ 1 - exp(-fr t)] (A38)

    and the corresponding flow area increase is

    - exp(-fr t)] (A39)

    Substituting for Af from eq. (All) gives

    Mtl jK -[Ki = CJ JN fLt

    1 - exp(-fr t)] (A40)

    Eq. (A40) is identical to eq. (18).

    456

  • PROPERTY

    Average Pore Size (micron)

    Permeability (millidarcy)

    Median Grain Size (micron)

    TABLE I

    CUMULATIVE EFFLUENTS WITH IN-SITU MOBILIZED ROCK PARTICLES

    METHOD ACTUAL ROCK*

    Grimshair ~ Olivier Rule 18.2

    Nitrogen 527

    Klinkenberg 372

    ASTM Sieve 93 Test

    *Average of 10 samples

    TABLE III ---

    MINERAL COMPOSITION OF THE RESERVOIR ROCK SAMPLES

    Mineral Concentration % wt/wt

    quartz 56-68

    Fled spar 11-23

    Calcite 5-8

    Dolomite 4-11

    Illite/Mica 3-7

    Chlorite 3-5

    SYNTHETIC ROCK*

    16.5

    25.1

    884

    672

    107

    FLUID

    Calcium Chloride

    Sodium Chloride

    Ammonium Nitrate

    Ammonium Nitrate + 20% Methanol

    TSS (ppm) 1-:-o

    0.0

    0.2

    0.3

    SPE 1 6 2 33

    TABLE II

    COMPLETION FLUIDS TESTED

    CST SALT CONC. DENSITY VISCOSITY (sec) (g/1) (ppg) (cp) ----g:-J 190 -----g:s- 1.5

    8.9 215 9.5 1.9

    9.8 260 9.5 1.7

    10.0 320 9.5 1.9

    *Filtered through 0.4 micron filter

    TABLE IV ---

    SODIUM CHLORIDE BRINE CONTAMINATED WITH DRILLING MUD

    Conta- TSS CST Turbi- Visco-mination dity sity (vol %) (ppm) (sec) (NTU) (cp)

    0.0 0 -----s:9 --0- -----y:-g

    0.2 405 19.1 90 1.9

    0.5 976 36.3 165 2.0

    1.0 1990 113.7 270 2.1

    2.0 3843 310.7 385 2.5

    3.0 5790 769.9 690 3.0

    TABLE V

    CUMULATIVE EFFLUENTS WITH IN-SITU MOBILIZED ROCK PARTICLES

    Total Particle size suspended CST (microns)

    FLUID solids -------------

    (ppm) (sec) D50 MV

    NaCl 470 9.7 39.08 41.49

    cac12 494 10.2 35.90 39.38

    NH4N03 429 10.1 26.89 37.01

    NH4N03 506 10.4 40.42 42.88 + MeOH

    457

    Turbi dity

    (NTU)

    10.8

    15.8

    10.9

    8.8

    pH

    8.6

    8.1

    3.2

    3.1

  • SPE 1 6 2 3 3

    Fig. 1-Hypothetical model of a porous rock.

    I. CONTAINER WITH DISTILLED WATER 2. LIQUID METERED PUMP {0- 10 m/min.) 3. FLUID ACCUMULATOR WITH PISTON {1000 m ; 270otm) 4. PRESSURE TRANSDUCER {0-6 otm) 5. INLET FOR CONFINING PRESSURE SET

    {NITROGEN; 7 otm) 6. HAND PACKED CORE IN LEAD SLEEVE {PV = 18.3 m.f) 7. RUBBER SLEEVE 8. ANNULUS 9. SAMPLE BOTTLE {60 m.t')

    Fig. 2-Laboratory setup with Hassler cell for flow tests.

    >- -t: :::.::: 0.8 _. .......

    -:::.::: IIl ..... 0.6

  • 1.0

    ..:z

    ...... 0.6 ~

    i 0 6.0 0 0 6. 0 0 6.

    6.

    0 TSS = 405 mg/ ( No Single Pore Blockage l

    D. TSS = 976 mg/, 2 (SLOPE= -1.273 x 10- l!min) TSS = 1990 mg/

    (SLOPE= -1.337 x 10- 2 1/min)

    50 TIME(Min)

    0 0 0

    100

    SP'E 1 6 2 3 3

    35~--------------------------------~~-.

    30

    10

    TSS= 3843 mg/ (SLOPE= 0.389 ltmin INTERCEPT= -5.36 l

    o TSS = 5790 mg/ (SLOPE=0.13961fmin INTERCEPT= -3.09)

    50 TIME(Min)

    D

    D

    100

    Fig. 5-Diagnostic plot: foreign particles invasion, gradual pore blockage. Fig. 6-Diagnostic plot: foreign particles invasion, cake forming.

    IJ) IJ) Q)

    c: ::::>

    ~ ......

    ~ ..

    >-!::: .....1 CD I-

  • .25

    .20

    ~15 .10

    .05

    0

    en 6 t:. c:

    e u

    ::!: 5

    LIJ !::::! U) z =-CD LIJ ...... _ a:: D < IOp.m --0

    D a.. 30

    25 40 50 60 70 80 90 100

    Tl ME (Min) Fig. 9-Relation between pore blocking mechanism and size of passing foreign

    particles. 20~------~------~-------L------~--------

    460

    500 1000 1500 2000 TOTAL SUSPENDED SOLIDS (mg/L)

    Fig. 10-Effect of size and concentration of completion fluid particles on gradual pore blockage duration.

  • 1.4 Ill 0 Ill Q)

    c: 1.2 ::::>

    ..:.:: 1.0

    ' ..:.::

    >- 0.8 1-.....J CD 0.6 0.2 i=

    ..iZ 10 ' ..:.::

    ~ 8 :J CD 1- 2

  • SPE 1 6 2 3 3

    1.0.------------------------. 0.5.-----------------------~

    o NH4N03 (fr=3.2S.xlo- 3 1/min) t:. NH4N03+MeOH (fr=4.3xlo- 3 1/minl

    ~ + I

    u

    c: ~

    25 50 75 100 125 TIME (Min)

    u

    0.0

    -0.5

    - 1.0

    -1.5 o NH4N03(fr =3.46xlo- 2 1/min) t:. NH4N03+ MeOH ( fr = 3.51 x 10-2 1/min)

    Q = IOcc/min

    -2.0 ~----L-----~----~----~ 150 175 200 225 250

    TIME (Min)

    Fig. 14-Diagnostic plot for the ammonium nitrate/alcohol-based completion fluids: gradual pore blocking.

    Fig. 15-Diagnostic plot for the ammonium nitrate/alcohol-based completion fluids: pore sweeping.

    -6.0~~-----------------=------------. Q=IOcc/min I

    -6.5

    -7.0

    -7.5

    .,. ...

    \ \ \ \ \ .... ~ ,.......... , ..........

    \ ........... , -..... \ -.....

    o NH4N03 fr1 = 3.76xlo-

    3 ltmin fr2 = 20.6 x 10-

    3 1/min

    t:. NH4N03tMeOH fr1 = 5.35 x lo-

    3 1/min fr2= 30.0 x I0-

    3 11m in

    I .. Q=3cc/min

    \

    100 150 TIME (Min)

    \ \

    200

    \ \

    250

    Fig. 16-Verification of the combined effects of gradual pore blockage and pore sweeping.

    462

  • 25

    20

    ~ 0 15

    >-(.) z LLJ ::> 0 10 LLJ a:: IJ.

    5

    6---

    o----D---

    ---

    ....... 100 (/) c::

    e 90 u ~

    80 (/) LLJ 70 ..J (.)

    ~ 60 a::