Patent Publication Number: US-6902001-B2

Title: Cementing compositions and application of such compositions for cementing oil wells or the like

Description:
The present invention relates to techniques for drilling oil, gas, water, or geothermal wells or the like. More precisely, the invention relates to cementing compositions which are particularly suitable for cementing zones which are subjected to extreme dynamic stresses. 
     In general, a well which is over a few hundred meters deep is cased and the annular space between the subterranean formation and the casing is cemented over all or part of its depth. Cementing essentially prevents the exchange of fluid between the different layers of formation traversed by the hole and controls the ingress of fluid into the well, and in particular limits the ingress of water. In production zones, the casing—and the cement and the formation—is perforated over a height of several centimeters. 
     The cement placed in the annular space of an oil well is subjected to a number of stresses throughout the lifetime of the well. The pressure inside a casing can increase or decrease because the fluid which fills it can change or because a supplemental pressure is applied to the well, for example when the drilling fluid is replaced by a completion fluid, or during a stimulation operation. A change in temperature also creates stress in the cement, at least during the transition period preceding temperature equilibration between the steel and the cement. In the majority of the above cases, the stress event is sufficiently slow for it to be treated as a static event. 
     However, the cement is subject to other stresses which are dynamic in nature, either because they are produced over a very short period or because they are either periodic or repetitive in nature. Perforations create an over-pressure of several hundred bars inside a well which is dissipated in the form of a shock wave. Further, perforations create a shock when the projectile penetrates the cement and that shock subjects the zone surrounding the hole to large forces over a depth of several meters. 
     A further event, which is now routine in oil well operations and which creates dynamic stresses in the cement, is the opening of a window in a casing which is already cemented to create a multi-branch lateral well. Milling the steel over a depth of several meters followed by drilling a lateral well subjects the cement to shocks and vibrations which frequently damage it irreparably. 
     The present invention aims to provide novel formulations, in particular for cementing regions of oil wells or the like which are subjected to extreme dynamic stresses. 
     In an article presented at the SPE (Society of Petroleum Engineers) annual technical conference and exhibition of 1997, Marc Thiercelin et al. (SPE 38598, 5-8 Oct. 1997)—and French patent application FR-A-97 11821 of 23 rd  Sep. 1997, demonstrated that the risk of rupture of a cement sleeve depends on the thermoelastic properties of the casing, the cement and the formation surrounding the well. A detailed analysis of the mechanisms leading to rupture of the cement sleeve has shown that the risk of rupture of a cement sleeve following an increase in pressure and/or temperature in the well is directly linked to the tensile strength of the cement and is attenuated when the ratio between the tensile strength R T  of the cement and its Young&#39;s modulus E is increased. 
     Young&#39;s modulus is known to characterize the flexibility of a material. To increase the R T /E ratio, it is advantageous to select materials with a low Young&#39;s modulus, in other words to select very flexible materials. 
     One known means for increasing the flexibility of a hardened cement is to reduce the density of the slurry by extending it with water. However, that leads to a degradation in the stability of the slurry, in particular with separation of the solid and liquid phases. Such phenomena can, of course, be controlled in part by adding materials such as sodium silicate, but the permeability of the hardened cement is nevertheless very high, which means that it cannot fulfill its primary function of isolating zones to prevent fluid migration, or at least it cannot guarantee its long-term isolation. Further, lightened cements have lower strength, in particular lower shock resistance, which constitutes a clear handicap for cements intended for use in zones which are subjected to extreme mechanical stresses such as perforation zones. 
     In the building field, incorporating particles of rubber into a concrete is known to result in better resilience, durability and elasticity (see, for example, A. B. Sinouci, Rubber-Tire Particles as Concrete Aggregate, Journal of Materials in Civil Engineering, 5, 4, 478-497 (1993)]. Concretes which include rubber particles in their formulation can be used, for example, in highway construction to absorb shocks, in anti-noise walls as a sound insulator and also in constructing buildings to absorb seismic waves during earthquakes. In such applications, the mechanical properties in particular are improved. 
     In the field of oil well cementing, it is also known [Well Cementing 1990, E. B. Nelson, Schlumberger Educational Services] that adding ground rubber particles (grain size in the range 4-20 mesh) can improve the impact strength and bending strength. Such an improvement in mechanical properties has also been indicated in Russian patents SU-1384724 and SU-1323699. More recently, U.S. Pat. No. 5,779,787 has proposed the use of particles derived from recycled automobile tires with grain size in the range 10/20 or 20/30 mesh, to improve the mechanical properties of hardened cements, in particular to improve their elasticity and ductility. 
     The present invention aims to provide oil well cements reinforced with flexible particles, of low compressibility, with low density and with an average size not exceeding 500 μm. 
     The term “flexible particles” means particles made of a material having a Young&#39;s modulus of less than 5000 MPa, preferably less than 3000 MPa, more preferably less than 2000 MPa. The elasticity of the materials selected for these flexible particles is thus at least tour times greater than that of cement and more than thirteen times that of the silica usually used as an additive in oil well cements. 
     The flexible particles added to the cementing compositions of the invention are also remarkable because of their low compressibility and are characterized by a Poisson ratio of over 0.3. 
     In order to lighten the slurry, it is also important for the density the flexible particles to be less than 1.5 g/cm 3 , preferably less than 1.2 g/cm 3 , more preferably less than 1 g/cm 3 . Preferably, this low density is intrinsic in the choice of the constituent materials and not by dint of high porosity or hollow particles. Preferably again, materials of low porosity are used. 
     Further, the particles must be insoluble in an aqueous medium which may be saline, and must be capable of resisting a hot basic medium, since the pH of a cementing slurry is generally close to 13 and the temperature in a well is routinely over 100° C. 
     Regarding particle size, essentially isotropic particles are preferred. Spherical or near spherical particles may be synthesized directly, but usually the particles are obtained by grinding, in particular cryo-grinding. The average particle size is generally in the range 80 μm to 500 μm, preferably in the range 100 μm to 400 μm. Particles which are too fine, or on the other hand too coarse, are difficult to incorporate into the mixture or result in pasty slurries which are unsuitable for use in an oil well. 
     Particular examples of materials which satisfy the various criteria cited above are thermoplastics (polyamide, polypropylene, polyethylene, . . . ) or other polymers such as styrene divinylbenzene or styrene butadiene (SBR). Recycled products are generally not preferred because of the variability in supply sources and in physico-chemical properties. 
     In addition to the flexible particles of the invention, the cementing compositions of the invention comprise a hydraulic binder, in general based on Portland cement and water. Depending on the specifications regarding the conditions for use, the cementing compositions can also be optimized by adding additives common to the majority of cementing compositions, such as suspension agents, dispersing agents, anti-foaming agents, expansion agents (for example magnesium oxide), fine particles, fluid loss control agents, gas migration control agents, retarders or setting accelerators. Thus the systems are either bimodal in type, the solid fraction of the slurry being constituted by a mixture of cement and flexible particles, or they can comprise three (trimodal) or more types of solid constituents, the solid mixture comprising fine micronic particles and possibly submicronic particles in addition to the cement and flexible particles. 
     The volume of flexible particles represents between 5% and 40% of the total volume of the cementing slurry, preferably between 10% and 35%, and preferably again, between 15% and 30% of the total slurry volume. 
     The formulations of the invention are preferably based on Portland cements in classes A, B, C, G and H as defined in Section 10 of the American Petroleum Institute&#39;s (API) standards. Classes G and H Portland cements are particularly preferred but other cements which are known in this art can also be used to advantage. For low-temperature applications, aluminous cements and Portland/plaster mixtures (deepwater wells, for example) or cement/silica mixtures (for wells where the temperature exceeds 120° C., for example) can be used. 
     The water used to constitute the slurry is preferably water with a low mineral content such as tap water. Other types of water, such as seawater, can possibly be used but this is generally not preferable. 
     These particles with low density with respect to the cement can reduce the density of the slurry and result in lower permeability and better impact resistance. It also affects the flexibility of the system, since adding flexible particles produces cements with a lower Young&#39;s modulus. 
     The compositions comprising flexible particles of the invention have remarkable mechanical properties which render them particularly suitable for cementing in areas of an oil well which are subjected to extreme stresses, such as perforation zones, junctions for branches of a lateral well or plug formation. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention is illustrated below in the following examples, along with the enclosed drawings that show: 
         FIG. 1  plots the rupture modulus vs. the concentration of flexible particles (in % vol.) for different types of particles; 
         FIG. 2  plots the Young/s modulus vs. the concentration of flexible particles (in % vol.) for different types of particles; 
         FIG. 3  plots the bending Young&#39;s modulus vs. the concentration of flexible particles (in % vol.) for different types of particles; 
         FIG. 4  plots compressive strength vs. the concentration of flexible particles (in % vol.) for different types of particles; 
         FIG. 5  plots the compression Young&#39;s modulus vs. the concentration of flexible particles (in % vol.) for different types of particles; 
         FIG. 6  plots the tensile strength of the cement vs. the bending Young&#39;s modulus of the cement, showing the requirements for three rock types (hard, medium and weak rock); 
         FIG. 7  plots the rupture modulus in bending (in MPa) vs. the effective porosity (in %), defined as the sum of the porosity of the hardened cement and the volume percentage of the flexible particles; 
         FIG. 8  plots the Young&#39;s modulus in bending (in MPa) vs. the effective porosity (in %). 
     
    
    
     EXAMPLE 1 
     Formulations for Cement Slurries with Styrene Divinylbenzene Particles 
     In this example, particles of styrene divinylbenzene (STDVB) with grain size in the range 45-100 mesh (355 μm-150 μm) were tested. 
     The cement slurries were composed of Portland Dyckerhoff North class G cement, styrene divinylbenzene particles, water, a dispersing agent and a retarder. The formulations and properties of the cement slurry are given in Tables 1 to 3; they were all optimized to the same temperature (76.7° C.—170° F.); two cement slurry densities ρ were selected (1.677 g/cm 3 —14 ppg and 1.431 g/cm 3 —12 ppg). The dispersing agent was a polynaphthalene sulfonate; the retarder was a lignosulfonate. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Formulations for cement slurries with STDVB particles 
               
            
           
           
               
               
               
               
               
               
            
               
                 Slurry 
                 STDVB 
                 Dispersing 
                 Retarder 
                 ρ 
                 Porosity of 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 n° 
                 % bwoc 
                 % vol 
                 agent gps 
                 gps 
                 g/cm 3   
                 slurry φ 
               
               
                   
               
               
                 A1 
                 27.8 
                 24.8 
                 0.012 
                 0.06 
                 1.666 
                 45% 
               
               
                 A2 
                 50.9 
                 30.0 
                 0.014 
                 / 
                 1.450 
                 50% 
               
               
                   
               
            
           
         
       
         
         
           
             bwoc is the abbreviation for “by weight of cement”; 
             % vol corresponds to the volume of flexible particles in the slurry (aqueous and solid phases); 
             gps is the abbreviation for “gallons per sack”, namely 3.78541 liters per sack of 42.637 kilograms (kg) of cement, in other words, 1 gps=0.0888 liters (l) of additive per kg of Portland cement. 
           
         
       
    
     The rheology of the cement slurry and the free water were measured using the procedure recommended in API 10 (American Petroleum Institute). At laboratory temperature, the rheology was measured immediately after mixing and after 20 minutes of conditioning to temperature. The results are shown in Table 2. The rheology of a slurry is characterized by its plastic viscosity PV (in cP or mPa.s), the conversion factor being equal to 1) and the yield point or Ty (in lbf/100 ft 2 , conversion to Pascals being obtained by multiplying by 0.478803), assuming the slurry to be a Bingham fluid. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Rheology and free water for systems with STDVB particles 
               
            
           
           
               
               
               
               
            
               
                   
                 Rheology after 
                   
                   
               
               
                   
                 mixing at labora- 
               
               
                   
                 tory temperature 
                 Rheology after conditioning 
                 Free water 
               
            
           
           
               
               
               
               
               
            
               
                 Formula- 
                 PV 
                 Ty (lbf/ 
                 at 76.6° C. 
                 after 2 
               
            
           
           
               
               
               
               
               
               
            
               
                 tion 
                 (mPa.s) 
                 100 ft 2 ) 
                 PV (mPa.s) 
                 Ty (lbf/100 ft 2 ) 
                 hours (ml) 
               
               
                   
               
               
                 A1 
                 35.4 
                 30 
                 66.4 
                  7.2 
                 2 
               
               
                 A2 
                 24.5 
                 4.1 
                 40.7 
                 20.3 
                 0 
               
               
                   
               
            
           
         
       
     
     The development of the compressive strength during setting of the cement was evaluated by UCA (Ultrasonic Cement Analyzer) measurements. These measurements enabled the setting time required to produce a given strength (0.34 MPa—50 psi and 3.4 MPa=500 psi) and the compressive strength Rt obtained after a given time (72 hours) at a pressure of 3000 psi (20.7 MPa) to be determined. 
     
       
         
           
               
             
               
                 TABLE 3 
               
             
            
               
                   
               
               
                 UCA and setting time at T = 76.6° C. for systems 
               
               
                 with STDVB particles 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Time to 0.34 
                 Time to 3.4 
                   
                 Setting 
               
               
                   
                 MPa at 
                 MPa at 
                 Compressive strength 
                 time 
               
               
                 N° 
                 T (min) 
                 T (min) 
                 after 72 hours (psi) 
                 (min) 
               
               
                   
               
               
                 A1 
                 970 
                 1088 
                 3000 
                 270 
               
               
                 A2 
                 171 
                  383 
                 1167 
                 210 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 2 
     Formulations for Cement Slurries with Polyamide Particles 
     The cement slurries were principally composed of Portland Dyckerhoff North class G cement, polyamide particles, water, a dispersing agent, a retarder and an anti-foaming agent. 
     A number of polyamides were tested: Nylon 6, Nylon 12 and a polyamide 11, the principal characteristics of which are shown in Table 4. 
     
       
         
           
               
             
               
                 TABLE 4 
               
             
            
               
                   
               
               
                 Characteristics of test polyamides 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                 Average 
                   
               
               
                   
                   
                 Product 
                   
                 grain 
                 ρ 
               
               
                 Source 
                 Supplier 
                 name 
                 Polyamide 
                 size (μm) 
                 (g/cm 3 ) 
               
               
                   
               
               
                 1 
                 Goodfellow 
                 AM306015 
                 Nylon 6  
                 350 
                 1.13 
               
               
                 2 
                 Goodfellow 
                 AM306010 
                 Nylon 6  
                 15-20 
                 1.13 
               
               
                 3 
                 Elf Atochem 
                 Rilsan 
                 11 
                 100 
                 1.0  
               
               
                 4 
                 Huls 
                 Vestosint 1111 
                 Nylon 12 
                 100 
                 1.06 
               
               
                   
               
            
           
         
       
     
     The formulations and properties of the cement slurry are shown in Tables 5 to 9. They were all formulated at the same temperature (76.7° C.—170° F.), the same slurry density (14 ppg), and different grain sizes were studied. The dispersing agent used was a polynaphthalene sulfonate; the retarder was a lignosulfonate. The fine particles used for test B2 was filtered fly ash, a detailed description of which is given in French patent FR-A-96 1176. The magnesium oxide added for test B5 acted as an expansion agent. 
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 Cement slurry with polyamide particles - list of formulations 
               
            
           
           
               
               
               
            
               
                   
                   
                 Polyamide 
               
               
                 N 
                 Description of solid fraction 
                 source 
               
               
                   
               
               
                 B1 
                 Bimodal mixture: cement + polyamide 
                 1 
               
               
                 B2 
                 Trimodal mixture: cement + polyamide + fine particles 
                 1 
               
               
                 B3 
                 Trimodal mixture: cement + nylon 350 μm + 
                 1 and 2 
               
               
                   
                 nylon 15-20 μm 
               
               
                 B4 
                 Bimodal mixture: cement + polyamide 
                 3 
               
               
                 B5 
                 Bimodal mixture: cement + polyamide + 
                 1 
               
               
                   
                 magnesium oxide 
               
               
                 B6 
                 Bimodal mixture: cement + polyamide 
                 4 
               
               
                   
               
            
           
         
       
     
     It should be noted that it was not possible to prepare a slurry with source 2 alone as the slurry was too viscous even with a low concentration of reinforcing particles. 
     
       
         
           
               
             
               
                 TABLE 6 
               
             
            
               
                   
               
               
                 Formulations for cement slurries with polyamide particles 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Polyamides 
                 Fine 
                 Dispersing 
                 Retarder 
                 Anti-foaming 
                 ρ 
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 % bwoc 
                 % vol 
                 % bvob 
                 agent gps 
                 gps 
                 agent gps 
                 g/cm 3   
                 φ 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 B1 
                 29.4 
                 24.8 
                 / 
                 / 
                 0.097 
                 / 
                 1.67 
                 45% 
               
               
                 B2 
                 22.8 
                 19.3 
                 10 
                 0.026 
                 0.051 
                 0.037 
                 1.75 
                 45% 
               
               
                 B3 
                 22.8 
                 24.8 
                 10 
                 0.018 
                 0.073 
                 / 
                 1.67 
                 45% 
               
               
                 B4 
                 17.8 
                 16.8 
                 / 
                 / 
                 0.066 
                 0.033 
                 1.67 
                 52% 
               
               
                 B6 
                 18.1 
                 16.7 
                 / 
                 / 
                 0.067 
                 0.033 
                 1.67 
                 52% 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                 Formulation for cement slurry with polyamide particles and an expansion agent 
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                   
                 Polyamides 
                 Expansion agent 
                 Dispersing 
                 Retarder 
                 Anti-foaming 
                 Extension 
                 ρ 
                   
               
               
                   
                 % bwoc 
                 % bwoc 
                 agent gps 
                 gps 
                 agent gps 
                 agent gps 
                 g/cm 3   
                 φ 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 B5 
                 24.9 
                 5 
                 0.059 
                 0.176 
                 0.035 
                 0.106 
                 1.77 
                 45% 
               
               
                   
                 (22.6% vol) 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8 
               
             
            
               
                   
               
               
                 Rheology and free water for systems with 
               
               
                 polyamide particles 
               
            
           
           
               
               
               
               
            
               
                   
                 Rheology after 
                   
                   
               
               
                   
                 mixing at labora- 
               
               
                   
                 tory temperature 
                 Rheology after conditioning 
                 Free water 
               
            
           
           
               
               
               
               
               
            
               
                 Formula- 
                 PV 
                 Ty (lbf/ 
                 at 76.6° C. 
                 after 2 
               
            
           
           
               
               
               
               
               
               
            
               
                 tion 
                 (mPa.s) 
                 100 ft 2 ) 
                 PV (mPa.s) 
                 Ty (lbf/100 ft 2 ) 
                 hours (ml) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 B1 
                 156.2 
                 1.0 
                 118.9 
                 17.0 
                 1.5 
               
               
                 B2 
                 203.9 
                 26.6 
                 215.4 
                 35.4 
                 2.0 
               
               
                 B3 
                 475.8 
                 13.6 
                 294.6 
                 26.5 
                 0 
               
               
                 B4 
                 47.7 
                 4.4 
                 34.4 
                 30.2 
                 3.0 
               
               
                 B5 
                 230.5 
                 1.0 
                 48.9 
                 26.4 
                 0.5 
               
               
                 B6 
                 48.6 
                 4.6 
                 44.1 
                 24.3 
                 3 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 9 
               
             
            
               
                   
               
               
                 UCA and setting time at 76.7° C. (170° F.) for 
               
               
                 systems with polyamide particles 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Time to 0.34 
                 Time to 3.4 
                   
                 Setting 
               
               
                 Formula- 
                 MPa at 
                 MPa at 
                 Compressive strength 
                 time 
               
               
                 tion 
                 T (min) 
                 T (min) 
                 after 72 hours (psi) 
                 (min) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 B1 
                 1695 
                 1916 
                 1500 
                 348 
               
               
                 B2 
                 525 
                 585 
                 2377 
                 221 
               
               
                 B3 
                 580 
                 699 
                 1703 
                 170 
               
               
                 B4 
                 708 
                 827 
                 1829 
                 205 
               
               
                 B5 
                 661 
                 738 
                 2167 
                 263 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 3 
     Formulations for Cement Slurries with Polypropylene Particles 
     The cement slurries were composed of Portland Dyckerhoff North Class G cement, polypropylene particles, water, a dispersing agent, a retarder and an anti-foaming agent. The polypropylene used in this Example was produced by ICO Polymer under the trade name ICORENE 9013P. Its density was 0.905 g/cm 3 . Its initial grain size specification was such that at most 5% of particles had a size of more than 800 μm, 30% had a size of more than 500 μm and less than 5% of the particles had a size of less than 200 μm. For these tests, the particles were also sieved at 300 μm. The polypropylene from Solvay, trade name ELTEX P HV001PF, was also tested but it was found to be difficult to mix and optimize, in particular for our bimodal systems. This can be explained by its very broad grain size specifications since they wore in the range 30 μm-1500 μm; this effect was reinforced by the low density of the polypropylene. 
     The formulations and properties of the cement slurry are shown in Tables 10 to 12; they were all optimized at the same temperature (76.7° C.—170° F.), and a single cement slurry density was selected (14 ppg). The dispersing agent used was a polynaphthalene sulfonate; the retarder was a lignosulfonate. Formulation 1 was constituted by a bimodal mixture (cement+polypropylene particles); formulation 2 was a trimodal mixture (cement+polypropylene particles+fine particles). 
     
       
         
           
               
             
               
                 TABLE 10 
               
             
            
               
                   
               
               
                 Formulations for cement slurries with polypropylene particles 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Polypropylene 
                 Fine 
                 Dispersing 
                 Retarder 
                 Anti-foaming 
                 ρ 
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 N° 
                 % bwoc 
                 % vol 
                 % bvob 
                 agent gps 
                 gps 
                 agent gps 
                 g/cm 3   
                 φ 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 C1 
                 19.4 
                 19.4 
                 0 
                 0.022 
                 0.045 
                 0.030 
                 1.67 
                 45% 
               
               
                 C2 
                 23.9 
                 23.9 
                 10 
                 0.059 
                 0.046 
                 0.039 
                 1.65 
                 42% 
               
               
                   
               
            
           
         
       
         
         
           
             % bvob is the abbreviation for “by weight of blend”, and is the proportion of fine particles in the mixture of solid cement particles, flexible particles, fines. 
           
         
       
    
     
       
         
           
               
             
               
                 TABLE 11 
               
             
            
               
                   
               
               
                 Rheology and free water for systems with polypropylene particles 
               
            
           
           
               
               
               
               
            
               
                   
                 Rheology after 
                   
                   
               
               
                   
                 mixing at labora- 
               
               
                   
                 tory temperature 
                 Rheology after conditioning 
                 Free water 
               
            
           
           
               
               
               
               
               
            
               
                 Formula- 
                 PV 
                 Ty (lbf/ 
                 at 76.6° C. 
                 after 2 
               
            
           
           
               
               
               
               
               
               
            
               
                 tion 
                 (mPa.s) 
                 100 ft 2 ) 
                 PV (mPa.s) 
                 Ty (lbf/100 ft 2 ) 
                 hrs (ml) 
               
               
                   
               
               
                 C1 
                 175 
                 6.1 
                 228 
                 13.1 
                 1.5 
               
               
                 C2 
                 387 
                 1.9 
                 332 
                 18.8 
                 0.1 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 12 
               
             
            
               
                   
               
               
                 UCA and setting time at 76.7° C. (170° F.) for 
               
               
                 systems with polypropylene particles 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Time to 0.34 
                 Time to 3.4 
                   
                 Setting 
               
               
                 Formula- 
                 MPa at 
                 MPa at 
                 Compressive strength 
                 time 
               
               
                 tion 
                 T (min) 
                 T (min) 
                 after 72 hours (psi) 
                 (min) 
               
               
                   
               
               
                 C1 
                 580 
                 665 
                 1911 
                 173 
               
               
                 C2 
                 863 
                 973 
                 2089 
                 369 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 4 
     Formulations for Cement Slurries with SBR Particles 
     The cement slurries were composed of Portland Dyckerhoff North Class G cement, SBR particles, water, a dispersing agent and a retarder. The formulations for and properties of the cement slurries are shown in Tables 13 to 15; they were all optimized at the same temperature (76.7° C.—170° F.), and a single cement slurry density (14 ppg) was selected. The dispersing agent used was a polynaphthalene sulfonate; the retarder was a lignosulfonate. Two different grain sizes were tested: 500 μm for formulation N1 and 200 μm for formulation N2. 
     
       
         
           
               
             
               
                 TABLE 13 
               
             
            
               
                   
               
               
                 Formulations for cement slurries with SBR particles 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 SBR 
                 Dispersing agent 
                 Retarder 
                 ρ 
                 Porosity of 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 % bwoc 
                 % vol 
                 gps 
                 gps 
                 g/cm 3   
                 slurry φ 
               
               
                   
               
               
                 D1 
                 30.6 
                 24.8 
                 0.037 
                 0.025 
                 1.69 
                 45 
               
               
                 D2 
                 20.5 
                 16.8 
                 0.017 
                 0.023 
                 1.70 
                 52 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 14 
               
             
            
               
                   
               
               
                 Rheology and free water for systems with SBR particles 
               
            
           
           
               
               
               
               
            
               
                   
                 Rheology after 
                   
                   
               
               
                   
                 mixing at labora- 
               
               
                   
                 tory temperature 
                 Rheology after conditioning 
                 Free water 
               
            
           
           
               
               
               
               
               
            
               
                 Formula- 
                 PV 
                 Ty (lbf/ 
                 at 76.6° C. 
                 after 2 
               
            
           
           
               
               
               
               
               
               
            
               
                 tion 
                 (mPa.s) 
                 100 ft 2 ) 
                 PV (mPa.s) 
                 Ty (lbf/100 ft 2 ) 
                 hrs (ml) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 1 
                 156.7 
                 5.0 
                 185.5 
                 17.1 
                 0 
               
               
                 2 
                 69.4 
                 1.8 
                 84.3 
                 29.5 
                 1.5 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 15 
               
             
            
               
                   
               
               
                 UCA and setting time at 76.7° C. (170° F.) for 
               
               
                 systems with SBR particles 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Time to 0.34 
                 Time to 3.4 
                   
                 Setting 
               
               
                 Formula- 
                 MPa at 
                 MPa at 
                 Compressive strength 
                 time 
               
               
                 tion 
                 T (min) 
                 T (min) 
                 after 72 hours (psi) 
                 (min) 
               
               
                   
               
               
                 1 
                 373 
                 478 
                 1535 
                 130 
               
               
                 2 
                 291 
                 492 
                 1209 
                 200 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 5 
     Optimized Formulations with Polyethylene Particles 
     The cement slurries were composed of Portland Dyckerhoff North Class G cement, polyethylene particles, water, a dispersing agent, a retarder and an anti-foaming agent. The formulations for and properties of the cement slurries are shown in Tables 16 to 18; they were all optimized at the same temperature (76.7° C.—170° F.), and a single density for the cement slurry (14 ppg) was selected. The dispersing agent used was a polynaphthalene sulfonate. 
     Formulation 1 contained ground high density polyethylene powder sold by BP Chemicals under the trade name RIGIDEX HD 3840-2WA. Its density was 0.94 g/cm 3  and its grain size was less than 500 μm. Formulation 2 also contained polyethylene powder with a density of 0.96 g/cm 3  and a grain size of less than 500 μm, but this was a recycled product. 
     
       
         
           
               
             
               
                 TABLE 16 
               
             
            
               
                   
               
               
                 Formulations for cement slurries with polyethylene particles 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                 Anti- 
                 Dispersing 
                   
                   
                 Porosity 
               
               
                   
                 Polyethylene 
                 foaming 
                 agent 
                   
                 ρ 
                 of 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 % bwoc 
                 % vol 
                 agent 
                 (gps) 
                 Retarder 
                 g/cm 3   
                 slurry 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 E1 
                 24.4 
                 24.7 
                 0.035 
                 / 
                 0.094 
                 1.63 
                 45% 
               
               
                 E2 
                 25.0 
                 24.7 
                 0.038 
                 0.035 
                 0.047 
                 1.64 
                 45% 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 17 
               
             
            
               
                   
               
               
                 Rheology and free water for systems with polyethylene particles 
               
            
           
           
               
               
               
               
            
               
                   
                 Rheology after 
                   
                   
               
               
                   
                 mixing at labora- 
               
               
                   
                 tory temperature 
                 Rheology after conditioning 
                 Free water 
               
            
           
           
               
               
               
               
               
            
               
                 Formula- 
                 PV 
                 Ty (lbf/ 
                 at 76.6° C. 
                 after 2 
               
            
           
           
               
               
               
               
               
               
            
               
                 tion 
                 (mPa.s) 
                 100 ft 2 ) 
                 PV (mPa.s) 
                 Ty (lbf/100 ft 2 ) 
                 hours (ml) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 E1 
                 84.4 
                 3.7 
                 147.8 
                 46.6 
                 3 
               
               
                 E2 
                 82.9 
                 5.1 
                 54.7 
                 7.5 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 18 
               
             
            
               
                   
               
               
                 UCA and setting time at 76.7° C. (170° F.) for 
               
               
                 systems with polyethylene particles 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Time to 0.34 
                 Time to 3.4 
                   
                 Setting 
               
               
                 Formula- 
                 MPa at 
                 MPa at 
                 Compressive strength 
                 time 
               
               
                 tion 
                 T (min) 
                 T (min) 
                 after 72 hours (psi) 
                 (min) 
               
               
                   
               
               
                 E1 
                 784 
                 871 
                 2315 
                 187 
               
               
                 E2 
                 291 
                 492 
                 1209 
                 200 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 6 
     Mechanical Properties—Bending and Compression 
     Bending and compression mechanical properties were measured for cement slurries which contained flexible particles. The exact formulations are given in Examples 1 to 6. 
     The influence of flexible particles on the mechanical properties of a set cement was studied using systems placed under high pressure and temperature in high pressure and high temperature chambers for several days to simulate the conditions encountered in an oil well. 
     The bending tests were carried out on 3 cm×3 cm×12 cm prisms obtained from cement slurries placed at 76.7° C. (170° F.) and 20.7 MPa (3000 psi) for several days. The compression tests were carried out on cubes with 5 cm (2 inch) sides obtained after several days at 76.7° C. (170° F.) and at 20.7 MPa (3000 psi). 
     For comparison purposes, systems with no flexible particles with the formulations given in Tables 19 and 20 were included:
         a NET “system” with a density of 1.89 g/cm (15.8 ppg) with 0.03 gps of anti-foaming agent (S1) as the sole additive;   a 1.67 g/cm 3  (14 ppg) system extended with bentonite (S2);   a 1.44 g/cm 3  system (12 ppg) extended with sodium silicate (S3).       

     
       
         
           
               
             
               
                 TABLE 19 
               
             
            
               
                   
               
               
                 Formulations for cement slurries without 
               
               
                 flexible particles 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Extender 
                 Retarder 
                 Anti-foaming 
                 ρ 
                 Porosity of 
               
               
                 N° 
                 % bwoc 
                 gps 
                 agent gps 
                 (g/cm 3 ) 
                 slurry % 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 S1 
                 0 
                 / 
                 0.03 
                 1.89 
                 58 
               
               
                 S2 
                 4 
                 0.08 
                 0.03 
                 1.68 
                 68 
               
               
                 S3 
                 1.7 
                 / 
                 0.03 
                 1.44 
                 79 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 20 
               
             
            
               
                   
               
               
                 Rheology and free water for systems without 
               
               
                 flexible particles 
               
            
           
           
               
               
               
               
            
               
                   
                 Rheology after 
                   
                   
               
               
                   
                 mixing at 
                 Rheology after condi- 
               
               
                   
                 laboratory temperature 
                 tioning at 76.6° C. 
                 Free water 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 PV 
                 Ty (lbf/ 
                 PV 
                 Ty (lbf/ 
                 after 2 
               
               
                 Formulation 
                 (mPa.s) 
                 100 ft 2 ) 
                 (mPa.s) 
                 100 ft 2 ) 
                 hours (ml) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 S1 
                 30.8 
                 23.3 
                 / 
                 / 
                 3.5 
               
               
                 S2 
                 12.7 
                 3.5 
                 11.2 
                 26.7 
                 3 
               
               
                 S3 
                 9.2 
                 9.9 
                  8.5 
                  8.5 
                 0 
               
               
                   
               
            
           
         
       
     
     The results are shown in Tables 21 and 22. Table 21 concerns the bending strength (rupture modulus Mr and bending Young&#39;s modulus Ef). It also shows the number of days of cure under pressure and temperature. Table 22 shows the compressive strengths (compressive strength Cs and compression Young&#39;s modulus Ec). 
     The bending strength was easier to measure than the tensile strength. It was empirically estimated that the bending strength was twice as high as the tensile strength. 
     The bending and compression tests were used to calculate the quantity of energy released at rupture (obtained by integrating the stress-strain curve for a displacement in the range 0 to the maximum displacement of the load (corresponding to rupture). 
     Each property is represented as a function of the concentration of flexible particles expressed as the % by volume (FIGS.  1 - 6 ). 
     The results obtained for the flexible particles show that, for equal densities, adding particles simultaneously resulted in:
         a reduction in the rupture modulus (FIG.  1 );   a reduction in the bending Young&#39;s modulus (FIG.  2 ), but this tendency was not as clear for polyamide particles or for STDVB particles; the same was true for the compression Young&#39;s modulus (FIG.  5 );   a reduction in the bending energy for STDVB (FIG.  3 );   a reduction in the compressive strength for SBR particles, the contrary for polyamides regardless of the mixture or grain size. For polypropylene, different effects were observed: in the bimodal system, the compressive strength decreased slightly while in the trimodal system, the compressive strength increased; STDVB increased the compressive strength for 25% by volume (FIG.  4 ).       

     
       
         
           
               
             
               
                 TABLE 21 
               
             
            
               
                   
               
               
                 Bending results with flexible particles 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 Formula- 
                 Number 
                 Mr 
                 Ef 
                 Mr/Ef 
                 Energy 
               
               
                 Particles 
                 tion 
                 of days 
                 (MPa) 
                 (MPa) 
                 (×1000) 
                 (J) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
            
               
                 None 
                 S1 
                 5 
                 8.47 
                 5021.6 
                 1.69 
                 0.0706 
               
               
                 None 
                 S2 
                 5 
                 6.69 
                 3758.8 
                 1.81 
                 0.0437 
               
               
                 None 
                 S3 
                 3 
                 1.19 
                 504.2 
                 2.37 
                 0.0101 
               
               
                 STDVB 
                 A1 
                 3 
                 5.04 
                 3595.0 
                 1.44 
                 0.0285 
               
               
                 STDVB 
                 A2 
                 5 
                 2.20 
                 1338.6 
                 1.68 
                 0.0142 
               
               
                 Polyamide 
                 B1 
                 5 
                 5.60 
                 2580.0 
                 2.18 
                 0.0490 
               
               
                 Polyamide 
                 B2 
                 4 
                 5.57 
                 3377.5 
                 1.65 
                 0.0386 
               
               
                 Polyamide 
                 B3 
                 3 
                 6.13 
                 3852.4 
                 1.59 
                 0.0397 
               
               
                 Polyamide 
                 B4 
                 5 
                 5.67 
                 2813.4 
                 2.04 
                 0.0450 
               
               
                 Polyamide 
                 B5 
                 4 
                 4.75 
                 3320.9 
                 1.43 
                 0.0288 
               
               
                 Poly- 
                 C1 
                 5 
                 4.53 
                 2941.2 
                 1.55 
                 0.0296 
               
               
                 propylene 
               
               
                 Poly- 
                 C2 
                 5 
                 5.25 
                 3019.6 
                 1.75 
                 0.0389 
               
               
                 propylene 
               
               
                 SBR 
                 D1 
                 3 
                 3.41 
                 1674.6 
                 2.10 
                 0.0285 
               
               
                 SBR 
                 D2 
                 3 
                 4.12 
                 2085.8 
                 2.00 
                 0.0326 
               
               
                 Polyethylene 
                 E1 
                 4 
                 4.21 
                 2066.5 
                 2.07 
                 0.0343 
               
               
                 Polyethylene 
                 E2 
                 3 
                 4.22 
                 2481.8 
                 1.74 
                 0.0305 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 22 
               
             
            
               
                   
               
               
                 Compression results with flexible particles 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                 CS/Ec 
                 Energy 
               
               
                 Particles 
                 Formulation 
                 CS (MPa) 
                 Ec (MPa) 
                 (×1000) 
                 (J) 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 None 
                 S1 
                 36.6 
                 6257.3 
                 5.85 
                 16.22 
               
               
                 None 
                 S2 
                 22.9 
                 3341.8 
                 6.88 
                 12.97 
               
               
                 None 
                 S3 
                 3.2 
                 519.6 
                 6.24 
                 1.88 
               
               
                 STDVB 
                 A1 
                 33.5 
                 4880.7 
                 6.88 
                 18.84 
               
               
                 STDVB 
                 A2 
                 13.3 
                 2093.3 
                 6.39 
                 6.23 
               
               
                 Polyamide 
                 B1 
                 27.9 
                 3898.7 
                 7.15 
                 23.83 
               
               
                 Polyamide 
                 B2 
                 27.9 
                 4391.6 
                 6.37 
                 18.32 
               
               
                 Polyamide 
                 B3 
                 30.7 
                 4117.7 
                 7.46 
                 24.55 
               
               
                 Polyamide 
                 B4 
                 32.5 
                 4295.7 
                 7.59 
                 22.01 
               
               
                 Polyamide 
                 B5 
                 26.4 
                 4080.1 
                 6.49 
                 19.61 
               
               
                 Polypropylene 
                 C1 
                 21.6 
                 3977.2 
                 5.49 
                 14.28 
               
               
                 Polypropylene 
                 C2 
                 26.3 
                 3904.2 
                 6.77 
                 18.49 
               
               
                 SBR 
                 D1 
                 10.11 
                 1614.59 
                 6.38 
                 5.50 
               
               
                 SBR 
                 D2 
                 14.52 
                 2659.14 
                 5.50 
                 7.19 
               
               
                 Polyethylene 
                 E1 
                 22.89 
                 2863.17 
                 8.01 
                 20.65 
               
               
                 Polyethylene 
                 E2 
                 20.30 
                 2688.19 
                 7.58 
                 19.53 
               
               
                   
               
            
           
         
       
     
     To compare these different systems, a flexibility criterion (MT) was defined: a cement was considered to be better if the ratio between its bending rupture modulus and its bending Young&#39;s modulus was higher. 
     This flexibility criterion can, for example, be seen in  FIG. 6  where the tensile strength of the cement is shown as a function of the bending Young&#39;s modulus of the cement.  FIG. 6  was obtained for the following casing geometry: external diameter 21.6 cm (8½″), internal diameter 17.8 cm (7″), grade 52 kg/m (35 lb/ft). The pressure increase in the well was assumed to be 34.5 MPa (5000 psi). 
     In this Figure, the minimum condition required is traced for three rock types (hard rock, medium rock and weak rock). Each-curve obtained defines the minimum condition required to obtain good cement strength for the geometry and the pressure increase selected for this example. For a given rock, a cement was said to be satisfactory if these characteristics (tensile strength and bending Young&#39;s modulus) placed it above the-curve. 
     It appears that the different formulations satisfied the flexibility criterion. However, these tendencies are directly linked to a reduction in density resulting from an increase in the concentration of flexible particles and thus in the porosity of the system. Thus porosity measurements were carried out and will be developed in the following example. 
     EXAMPLE 7 
     Porosity Measurements 
     The porosity of different cement samples obtained after several days of curing at 76.7° C. (170° F.) and at 20.7 MPa (3000 psi) was measured for the different formulations. 
     The following principle was applied in measuring the porosity measurement. Cylinders ½ inch in diameter and 1 cm long were cored from the cement sample which had been hardened at temperature and pressure. They were dried for two weeks in a freeze drier and during that time the weight loss was studied as a function of time. When the sample was dry (corresponding to a time-stable weight), the real volume or framework volume Vs was measured using a helium pycnometer; the mean volume Vb was obtained from the external dimensions of the cylinder. The difference in the two volumes (Vb−Vs) gave the void volume and thus the porosity Φ of the material which was accessible to the helium. 
     The porosity Φ of the slurry was the % by volume of water and liquid additives in the formulation. For each formulation, a volume percentage of flexible particles was calculated, and the effective porosity Φ was defined as the sum of the porosity of the hardened cement and the volume percentage of the flexible particles. 
     The results are shown in Table 23. It can be seen that the bending Young&#39;s modulus decreased almost linearly as a function of the effective porosity with a saturation threshold after 70% porosity (FIG.  7 ). The same applies to the bending rupture modulus (FIG.  8 ). 
     In conclusion, it appears that flexible particles can reduce the slurry density and thus act on the flexibility of the system to a minor extent. Primarily, flexible particles do not improve the above mechanical properties of cements. 
     
       
         
           
               
             
               
                 TABLE 23 
               
             
            
               
                   
               
               
                 Porosity results 
               
            
           
           
               
               
               
               
               
               
            
               
                 Flexible 
                   
                 Φ slurry 
                 Φ material 
                 Particle 
                 Φ effective 
               
               
                 particles 
                 N° 
                 (1) % 
                 (2) % 
                 volume (3) % 
                 (2) + (3) % 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 None 
                 S1 
                 60 
                 36.9 
                 0 
                 36.9 
               
               
                 None 
                 S2 
                 68 
                 45.7 
                 0 
                 45.7 
               
               
                 None 
                 S3 
                 79 
                 65.5 
                 0 
                 65.5 
               
               
                 STDVB 
                 A1 
                 45 
                 23.6 
                 24.8 
                 48.4 
               
               
                 STDVB 
                 A2 
                 50 
                 36.6 
                 30.0 
                 66.6 
               
               
                 Polyamide 
                 B1 
                 45 
                 28.3 
                 24.8 
                 53.1 
               
               
                 Polyamide 
                 B2 
                 45 
                 29.6 
                 19.3 
                 48.9 
               
               
                 Polyamide 
                 B5 
                 45 
                 27.7 
                 22.6 
                 50.30 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 8 
     Measurement of Poisson Ratio 
     The Poisson ratio was measured for different formulations with flexible particles to evaluate the compressibility of these systems. The compositions of the different formulations were given in the preceding examples. 
     When a cement sample is subjected to a normal compressive force, while remaining within the elastic region of the material, the longitudinal fibers of the sample are shortened the amount of which depends on the Young&#39;s modulus of the material (and on the stress applied and on the geometry of the sample). Simultaneously, the transverse dimension of the sample is elongated. The ratio of the transverse deformation (relative to the transverse dimension) to the longitudinal deformation (longitudinal relative variation) is a dimensionless coefficient known as the Poisson ratio. 
     In our tests, the loading rate was 1 kN/min and the samples were cylindrical, with a diameter of 30 mm and a length of 60 mm. The longitudinal deformation was measured using LVDT type displacement gauges; the transverse deformation was measured using a strain gauge. 
     The samples were placed in a chamber filled with water for several days at 76.7° C. (170° F.) and at 3000 psi. These were the same aging conditions as those used to prepare the samples for the bending tests, for example. After curing, the samples were kept permanently submerged and were simply drained before carrying out the mechanical tests which were then carried out on the moist samples. 
     The results are shown in Table 24 and demonstrate that adding flexible particles does indeed lead to an increase in the Poisson ratio of the hardened cement, and because of this, to a reduction in the compressibility of the hardened cement. Because of this lower compressibility, a cement reinforced with flexible particles can more readily distribute lateral forces or can more readily distribute forces in response to a compressive stress, which is very favorable to good zone isolation. 
     
       
         
           
               
             
               
                 TABLE 24 
               
             
            
               
                   
               
               
                 Poisson ratio results 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Particles 
                 N° 
                 ρ (g/cm 3 ) 
                 ν 
               
               
                   
                   
               
               
                   
                 none 
                 S1 
                 1.89 
                 0.15 
               
               
                   
                 none 
                 S2 
                 1.67 
                 0.17 
               
               
                   
                 STDVB 
                 A1 
                 1.67 
                 0.21 
               
               
                   
                 Polyamide 
                 B1 
                 1.67 
                 0.20 
               
               
                   
                 Polyamide 
                 B2 
                 1.67 
                 0.22 
               
               
                   
                 Polyamide 
                 B3 
                 1.67 
                 0.21 
               
               
                   
                 Polyamide 
                 B5 
                 1.67 
                 0.19 
               
               
                   
                 Polypropylene 
                 C2 
                 1.67 
                 0.22 
               
               
                   
                   
               
            
           
         
       
     
     EXAMPLE 9 
     Permeability Measurements 
     Cement samples were generated under pressure (20.7 MPa—3000 psi) and temperature (76.7° C.) under the same conditions as those used for the bending or compression tests, and for the same time. The hardened material obtained was cored into the following dimensions: 51.4 mm in diameter and 25 mm in length. 
     The moist sample was placed in a Hassler type cell which could apply a confinement pressure of 10 to 100 bars to the sample A small constant flow of water (in the range 0.005 ml/min to 1 ml/min) was sent through the sample by means of a chromatography pump. The differential pressure either side of the sample was measured and recorded. The value recorded was that corresponding to equilibrium. 
     The permeability K in milliDarcy was calculated using Darcy&#39;s law: 
       K   =     14700   ⁢           ⁢       Q   ⁢           ⁢   μ   ⁢           ⁢   L       A   ⁢           ⁢   P             
 
where Q is the flow rate expressed in ml/s, μ is the viscosity of water in cP, L is the length of the sample in cm, A is the surface area of the sample in cm 2  and P is the differential pressure in psi.
 
     The results for the different formulations are shown in Table 25 and demonstrate that, at a constant density, adding flexible particles reduces the permeability of the cement. 
     
       
         
           
               
             
               
                 TABLE 25 
               
             
            
               
                   
               
               
                 Permeability results 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                   
                 Flexible 
                   
               
               
                   
                   
                 ρ 
                 particles 
                 Permeability to 
               
               
                 Particle 
                   
                 g/cm 3   
                 % bwoc 
                 water, mD 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 None 
                 S1 
                 1.89 
                 0 
                 0.001 
               
               
                 None 
                 S2 
                 1.67 
                 0 
                 0.008 
               
               
                 None 
                 S3 
                 1.44 
                 0 
                 0.138 
               
               
                 STDVB 
                 A2 
                 1.44 
                 50.9 
                 0.031 
               
               
                 Polyamide 
                 C1 
                 1.67 
                 29.4 
                 0.001 
               
               
                   
               
            
           
         
       
     
     EXAMPLE 10 
     Impact Tests 
     Impact tests were carried out on cement samples. These tests consisted of allowing a projectile to fall onto disks of set cement from a height of 1 meter. The disks were circular with a diameter of 70 mm and a thickness of 10 mm. The dynamic load was measured and recorded as a function of time. 
     The cement containing no flexible particles behaved as a fragile material and the energy absorbed by the sample was estimated to be less than 10 joules. The energy absorbed by cements formulated with flexible particles was considerably improved, as shown in Table 26. 
     
       
         
           
               
             
               
                 TABLE 26 
               
             
            
               
                   
               
               
                 Results of impact with flexible particles 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 ρ 
                 Flexible particles 
                   
               
               
                 Particle 
                   
                 g/cm 3   
                 % bwoc 
                 Energy (J) 
               
               
                   
               
            
           
           
               
               
               
               
               
            
               
                 None 
                 S1 
                 1.89 
                 0 
                 7.4 
               
               
                 None 
                 S3 
                 1.44 
                 0 
                 4.0 
               
               
                 STDVB 
                 A1 
                 1.67 
                 27.8 
                 23.4 
               
               
                   
               
            
           
         
       
     
     This good shock behavior is particularly important when cementing multi-branch lateral wells. 
     EXAMPLE 11 
     Expansion Measurements 
     Linear expansion of cement slurries during setting at a temperature simulating the well conditions was measured in an annular expansion mold. This mold was constituted by two concentric rings, respectively with a diameter of 51 mm and 89 mm, placed between two flat disks 22 mm apart. The external ring had longitudinal slits and included two scales located either side of the slit enabling the distance to be measured during expansion of the cement. The cement slurry to be studied was poured into the mold, and the mold was then placed in a water bath thermostatted at 76.7° C. (170° F.). The slurry remained in contact with the water throughout the test. 
     The expansion results are shown in Table 27 and demonstrate that a slurry containing flexible particles has expansion properties. 
     
       
         
           
               
             
               
                 TABLE 27 
               
             
            
               
                   
               
               
                 Expansion results 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                 Linear 
                 Linear 
                 Linear 
               
               
                   
                   
                   
                 expansion, 
                 expansion, 
                 expansion, 
               
               
                 Flexible 
                   
                 Particle 
                 % after 
                 % after 
                 % after 
               
               
                 particle 
                   
                 % bwoc 
                 1 day 
                 2 days 
                 7 days 
               
               
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 None 
                 S2 
                 0 
                 ≦0 
                 ≦0 
                 ≦0 
               
               
                 Polyamide 
                 B1 
                 29.4 
                 0.02 
                 / 
                 0.16 
               
               
                 Polyamide 
                 B5 
                 24.9 
                 0.11 
                 0.13 
                 0.3 
               
               
                 ST DVB 
                 A1 
                 27.8 
                 0.01 
                 0.08 
                 0.09 
               
               
                   
               
            
           
         
       
     
     The expansion behavior is of particular interest for preventing the cement from separating from the casing and to prevent it from separating from the formation. This behavior is more significant when a cement is flexible and thus is confined by the rock.