Abstract:
A method for treating low barium frac water includes contacting a frac water stream with a radium selective complexing resin to produce a low radium stream, passing the low radium stream through a thermal brine concentrator to produce a concentrated brine; and passing the concentrated brine through a thermal crystallizer to yield road salt.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is a non-provisional of and claims priority from U.S. provisional application Ser. No. 61/405,806, filed 22 Oct. 2010, the entire disclosure of which is incorporated herein by reference. 
     
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT 
       [0002]    This invention was made with Government support under Subcontract 01822-36 to Research Partnership to Secure Energy for America (RPSEA), a contractor to the United States Department of Energy under prime contract DE-AC26-07NT42677. The Government has certain rights in the invention. 
     
    
     BACKGROUND 
       [0003]    The contribution to the US energy supply from unconventional gas sources is growing dramatically. Shale gas production in the US has increased from 0.3 TCF in 1996 to 1.1 TCF in 2006, accounting for 6% of the nation&#39;s supply. 
         [0004]    Water is used extensively in shale gas production. A typical well consumes 4-5 million gallons of water during the drilling and hydrofracturing processes. Typically this water is trucked in from remote locations. In addition, gas after the hydrofracturing process, much of this water is returned the surface as a brine solution termed “frac flowback water”, which is followed by “produced water”. Both flowback and produced water will be referred to as “frac” water. Because the frac water has very high salinity (50,000-200,000 ppm TDS), it cannot be disposed of in surface waters. Frac water is frequently disposed of in salt-water disposal wells, which are deep injection wells in salt formations. A significant problem with many of the shale gas plays, including the Marcellus Shale, is that there are few available deep well injection sites wells and environmental regulations prohibit discharge to rivers and other surface waters. In other shale gas plays, such as the Barnett Shale in Texas, water availability is limited and the use of large quantities of water for gas production generates much resistance from the public. Therefore, technology that enables cost-effective water reuse in shale gas production is essential for sustained development of this resource. 
         [0005]    In current water management models for shale gas operations using hydraulic fracturing, fresh water is injected to form cracks in the formation and deliver proppant to maintain permeability. In addition to proppant, a number of chemicals are added to the water to reduce friction, minimize corrosion and scale, prevent bacterial growth, and reduce drilling mud damage. About 20-50% of the water used to hydrofracture a well is returned as flowback, usually within a 2-3 weeks of injection. This water contains high amounts of dissolved solids (TDS ˜50,000-200,000 ppm for the Marcellus shales), in addition to many of the injected additives. It is stored in suitable containment tanks before being transported to appropriate disposal facilities. Historically, off-site disposal has been the more favorable wastewater treatment option. This is because the relatively small scale of water production and short time frame associated with drilling make capital investment in stationary local treatment options impractical. In recent years, there have been efforts to develop economically viable on-site treatment and recycling using mobile water treatment facilities. 
         [0006]    The process of drilling and preparing a natural gas well in a gas shale formation typically requires 4-5 million gallons of fresh water per well. The cost to treat and dispose of this water is a significant expense to the gas producers. Brine disposal usually entails shipping the wastewater to an old well for reinjection. Treatment of the water on or adjacent to the well site would eliminate the cost of shipping millions of gallons of wastewater to a treatment facility and/or disposal site, and obviate the need to truck in additional millions of gallons of fresh water. 
         [0007]    In the presence of sulfate ion, a solution of RaCl 2  and BaCl 2  coprecipitates as RaSO 4  and BaSO 4  even when the concentrations of Ra ++  and SO 4   =  are far below the solubility of RaSO 4  in water. Radium and barium coprecipitate to form a solid solution of RaSO 4 —BaSO 4 . Under ideal solid solution conditions, the calculated solubility of RaSO 4  in equilibrium with a solid solution of RaSO 4 —BaSO 4  is 8.2×10 −12  M, or 1.8×10 −6  ppm Ra. This solubility of Ra is equivalent to 1800 pCi/L of  226 Ra. The presence of NaCl enhances the coprecipitation of Ra with BaSO 4 . 
         [0008]    The sulfate treatment method generates a BaSO 4 /RaSO 4  sludge. This sludge may be combined with lime treatment sludge. The sludge stream must be dried, and then hauled to a landfill. The cost for sludge disposal as nonhazardous waste in a RCRA-D landfill is typically about $50/ton. However, to qualify for disposal as nonhazardous waste, the sludge must have an activity below a value of 5 to 50 pCi/gm (varies by state). The maximum activity for nonhazardous waste disposal in Pennsylvania is 25 pCi/gm. Sludge that exceeds this value needs to be disposed of as low-level radioactive waste (LLRW), which is discussed below. If the radium activity exceeds about 400 pCi/L, the sludge will need to be either blended with sufficient non-radioactive solid waste to meet the RCRA-D specification or treated as low-level radioactive waste (LLRW). The cost of LLRW disposal is too high for a sulfate precipitation process to be used for frac water from many, if not most, sites. 
         [0009]    Radium selective complexing (RSC) resins are a strong acid gelular cation exchange resins that have been completely exchanged with barium followed by sulfuric acid treatment to make finely dispersed, bound BaSO 4  microcrystallites. These bound BaSO 4  crystallites ion exchange with radium as shown below. 
         [0000]      RaCl 2(aq) +BaSO 4(resin) →RaSO 4(resin) +BaCl 2(aq)  
 
         [0010]    RSC resin is often utilized to remove radium from brine that is used to regenerate softening ion exchange resins in municipal water systems. For example, in a demonstration study (Mangelson, K. A. and Lauch, R. P., Removing and Disposing of Radium from Well Water, Journal of the American Water Works Association, 82 (6), 72-76 (1990)), hardness (Mg ++ , Ca ++ , Sr ++ , Ba ++ ) and radium were removed from drinking water using a conventional gelular sulfonic acid ion exchange resin (sodium form). The softening ion exchange resin was regenerated with NaCl brine (average 40,600 ppm TDS) to remove hardness and radium. The regeneration brine leaving the ion exchange resin contained an average of 1180 pCi/liter radium. Prior to disposal, this regeneration brine was treated with RSC resin. The RSC resin removed an average of 99.2% of the radium from the softener regeneration brine. After one year of operation, the resin loading was 3,000 pCi/cc resin. 
         [0011]    However, the results of some studies have indicated that RSC resins are not suitable for use with water containing the very high levels of total dissolved solids that are typically found in frac water. See, for example, Snoeyink, et al. (1987 Environmental Research Brief, Removal of Barium and Radium from Groundwater, February 1987), and references cited therein. 
         [0012]    Therefore, there remains a need for cost effective methods to treat frac waters before reusing or recycling. 
       BRIEF DESCRIPTION 
       [0013]    Briefly, in one aspect, the present invention relates to methods for treating low barium frac water, typically containing less than about 1000 ppm barium. The methods include contacting a frac water stream with a radium selective complexing resin to produce a low radium stream, passing the low radium stream through a thermal brine concentrator to produce a concentrated brine; and passing the concentrated brine through a thermal crystallizer. 
     
    
     
       DRAWINGS 
         [0014]      FIG. 1  shows a frac water pretreatment process for use in the methods of the present invention. 
           [0015]      FIG. 2  is a flow diagram of a thermal water and salt recovery process for the pretreated frac water. 
       
    
    
     DETAILED DESCRIPTION 
       [0016]      FIG. 1  shows a frac water pretreatment process for use in the methods of the present invention. In the context of the present invention, the term ‘low barium’ means that the frac water contains less than about 2,000 ppm barium; in some embodiments, less than about 1,000 ppm barium, and less than 100 ppm barium in still other embodiments. If higher levels of barium are present, capacity of the resin for radium may be reduced. 
         [0017]    In the first step, raw frac water that contains iron and manganese is treated with lime and air to oxidize Fe +2  and Mn +2  to Fe +3  and Mn +4 , respectively. In the second step, iron and manganese, as well as suspended solids, are precipitated in a clarifier. If iron or manganese is present, the oxidation and precipitation steps may be omitted if the RSC resin is not fouled in subsequent steps. Iron and manganese are well-known foulants for many types of ion exchange resins, and iron has been cited as a key foulant for RSC resins. 
         [0018]    The sludge from the lime treatment step is sent to a sludge thickener for dewatering. Sludge resulting from lime treatment typically does not contain a significant level of radioactivity. 
         [0019]    The clarified frac water stream may be filtered before it is passed through the RSC resin. Filtration may be omitted if desired or unnecessary. 
         [0020]    The frac water brine is then contacted with a RSC resin to remove radium. RSC resin is available from Dow Chemical Company as DOWEX™ RSC cation exchange resin. In the next step, the brine may be treated with sodium sulfate in a clarifier to coprecipitate BaSO 4  and any residual RaSO 4 . Because the bulk of the radium is removed from the frac water brine prior to sulfate treatment, the radium level in the sulfate sludge is typically acceptable for disposal in a RCRA-D landfill for non-hazardous waste. The sulfate sludge may be dewatered in a thickener and filter press. Water from the dewatering process may be recycled to the front of the process. The pretreated frac water brine may then be safely reused as NORM-free source water blendstock for hydrofracturing, or may be further purified as illustrated in  FIG. 2 . 
         [0021]      FIG. 2  shows a block flow diagram of a thermal water and salt recovery process for pretreated frac water according to methods of the present invention. 
         [0022]    In the first step, the pretreated frac water brine is passed through a thermal evaporator or an equivalent, such as a brine concentrator to preconcentrate the brine. Brine concentration technology is well established and one of skill in art would be able to configure and operate a system for use with frac water brine without difficulty. For example, vertical-tube, falling-film evaporators may be used in this step, such as the RCC® Brine Concentrator, available from GE Water &amp; Process Technologies. This is a type of falling film evaporator for treating waters saturated with scaling constituents such as calcium sulfate or silica. 
         [0023]    In the next step, the preconcentrated brine is passed through a salt crystallizer to recover distilled water and salable NaCl. Any crystallizer for use with concentrated brine may be used. RCC® Crystallizer systems from GE Water &amp; Process Technologies are particularly suitable, and mechanical vapor recompression (MVR) technology to recycle the steam vapor, minimizing energy consumption and costs. 
         [0024]    In a final, optional, step, the salt produced in the crystallizer may be washed to yield a material that may be sold for use as road salt. Even without a wash step, in some cases, the dry crystalline NaCl product may meet government standards for use as road salt, being free of toxic substances as determined by Toxicity Characteristic Leaching Procedure (TCLP) analysis and conforming to the ASTM D-635 standard for road salt. The wash water may be subjected to lime treatment to produce a sludge that may be dried prior to disposal as non-hazardous waste. 
       EXAMPLES 
     Screening Study of RSC Resin for Frac Water Treatment 
       [0025]    Composition of frac water samples is shown in Table 1. 
         [0000]    
       
         
               
             
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Frac Water Composition (mg/L except where noted) 
               
             
          
           
               
                   
                 E-1 
                 Spike-1 
                 Spike-2 
               
               
                   
                   
               
             
          
           
               
                   
                 TDS 
                 67,400 
                 67,400 
                 67,400 
               
               
                   
                 Na +   
                 19,200 
                 19,200 
                 19,200 
               
               
                   
                 Mg ++   
                 560 
                 560 
                 560 
               
               
                   
                 Ca ++   
                 5,360 
                 5,360 
                 5,360 
               
               
                   
                 Sr ++   
                 1,290 
                 1,290 
                 1,290 
               
               
                   
                 Ba ++   
                 32 
                 1032 
                 11,632 
               
               
                   
                 Fe ++   
                 55 
                 55 
                 55 
               
               
                   
                 Mn ++   
                 2 
                 2 
                 2 
               
               
                   
                 Cl −   
                 12,500 
                 12,500 
                 12,500 
               
               
                   
                 SO 4   =   
                 &lt;10 
                 &lt;10 
                 &lt;10 
               
               
                   
                   226 Ra pCi/liter 
                 4,596 
                 4,596 
                 4,596 
               
               
                   
                   
               
             
          
         
       
     
         [0026]    The sample “E-1” comprises frac water from a well in western Pennsylvania. This water was sampled on the 14th day after flowback water began to flow from a well that had been hydrofractured. Samples Spike-1 and Spike-2 are the same as E-1 except that Spike-1 was spiked with 1000 ppm Ba and Spike-2 was spiked with 11,600 ppm Ba (both as BaCl 2 ). All experiments were conducted at room temperature (22° C.). 
       Example 1 
       [0027]    Samples of 18 gm brine (E-1) were mixed with various amounts of DOWEX RSC resin to establish a radium adsorption isotherm. Brine and resin were added to centrifuge tubes and placed on a rotary laboratory mixer for 24 hours at 10 rpm. The samples were then decanted and measured for radioactivity by liquid scintillation counting. 
         [0028]    Radium has many short-lived daughter products (e.g. radon gas, polonium, lead, and bismuth). These daughter products are not ion exchanged onto RSC resin. When the daughter products decompose, they register along with radium in the liquid scintillation counter. Therefore, with RSC treatment, it is not possible to reduce the liquid scintillation count measurement down to the background level. Instead, we have found that the counts reach a plateau as the proportion of RSC resin to brine increases. We take the plateau count level as being indicative of substantially radium-free brine. We then estimate the total activity based on an assumed counting efficiency of 90% and a 2 mL volume of sample being counted. 
         [0000]    
       
         
           
             
               Activity 
                
               
                 ( 
                 
                   pCi 
                    
                   
                     / 
                   
                    
                   L 
                 
                 ) 
               
             
             = 
             
               
                 ( 
                 
                   
                     x 
                     - 
                     
                       blank 
                        
                       
                           
                       
                        
                       count 
                        
                       
                         / 
                       
                        
                       min 
                     
                   
                   
                     60 
                      
                     
                         
                     
                      
                     sec 
                      
                     
                       / 
                     
                      
                     min 
                   
                 
                 ) 
               
                
               
                 ( 
                 
                   
                     27 
                      
                     
                         
                     
                      
                     pCi 
                   
                   
                     decomp 
                      
                     
                       / 
                     
                      
                     sec 
                   
                 
                 ) 
               
                
               
                 ( 
                 
                   
                     decomp 
                      
                     
                       / 
                     
                      
                     sec 
                   
                   
                     0.9 
                      
                     
                         
                     
                      
                     count 
                      
                     
                       / 
                     
                      
                     sec 
                   
                 
                 ) 
               
                
               
                 ( 
                 
                   
                     1000 
                      
                     
                         
                     
                      
                     mL 
                      
                     
                       / 
                     
                      
                     L 
                   
                   
                     2 
                      
                     
                         
                     
                      
                     mL 
                   
                 
                 ) 
               
             
           
         
       
     
         [0000]    where x=counts per minute for a sample, as measured by liquid scintillation counting, LSC. 
         [0029]    The “Removable Activity in Solution” (RAS) is the difference between the measured activity and the lowest measured activity. For example 1, the lowest measured activity occurs for Sample E-1-5. The estimated concentration of radium on the resin is calculated as follows. 
         [0000]    
       
         
           
             
               Activity 
                
               
                   
               
                
               on 
                
               
                   
               
                
               
                 Resin 
                  
                 
                   ( 
                   
                     pCi 
                      
                     
                       / 
                     
                      
                     gm 
                      
                     
                         
                     
                      
                     resin 
                   
                   ) 
                 
               
             
             = 
             
               
                 ( 
                 
                   
                     
                       R 
                        
                       
                           
                       
                        
                       A 
                        
                       
                           
                       
                        
                       
                         S 
                          
                         
                           ( 
                           
                             no 
                              
                             
                                 
                             
                              
                             resin 
                           
                           ) 
                         
                       
                     
                     - 
                     
                       R 
                        
                       
                           
                       
                        
                       A 
                        
                       
                           
                       
                        
                       
                         S 
                          
                         
                           ( 
                           
                             with 
                              
                             
                                 
                             
                              
                             resin 
                           
                           ) 
                         
                       
                        
                       p 
                        
                       
                           
                       
                        
                       Ci 
                        
                       
                         / 
                       
                        
                       L 
                        
                       
                           
                       
                        
                       brine 
                     
                   
                   
                     gm 
                      
                     
                       
                           
                       
                        
                       
                           
                       
                     
                      
                     resin 
                   
                 
                 ) 
               
                
               
                 ( 
                 
                   
                     mL 
                      
                     
                         
                     
                      
                     brine 
                   
                   
                     1000 
                      
                     
                         
                     
                      
                     mL 
                      
                     
                         
                     
                      
                     brine 
                      
                     
                       / 
                     
                      
                     L 
                      
                     
                         
                     
                      
                     brine 
                   
                 
                 ) 
               
             
           
         
       
     
         [0030]    Based on this measurement approach, we estimated the resin isotherm as shown in Table 2. This shows that the resin has approximately 640 pCi/gm radium capacity for the brine composition E-1. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Liquid Scintillation Counting Results: Brine E-1 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Removable 
                   
               
               
                   
                   
                   
                   
                 Sample- 
                 Total 
                 Activity 
                 Conc on 
               
               
                   
                   
                   
                   
                 Blank 
                 Activity 
                 in solution 
                 Resin 
               
               
                   
                 Resin (g) 
                 Brine (g) 
                 Count/min 
                 Count/min 
                 (pCi/L) 
                 (pCi/L) 
                 (pCi/g) 
               
               
                   
                   
               
             
          
           
               
                 Blank 
                   
                   
                 32.4 
                 0 
                   
                   
                   
               
               
                 E-1-1 
                 0 
                 17.985 
                 65.07 
                 32.67 
                 8176 
                 4329 
               
               
                 E-1-2 
                 0.05 
                 18.071 
                 57.58 
                 25.18 
                 6301 
                 2455 
                 639 
               
               
                 E-1-3 
                 0.101 
                 18.06 
                 49.85 
                 17.45 
                 4367 
                 521 
                 643 
               
               
                 E-1-4 
                 0.151 
                 17.97 
                 49.67 
                 17.27 
                 4322 
                 475 
                 433 
               
               
                 E-1-5 
                 0.199 
                 19.073 
                 47.77 
                 15.37 
                 3846 
                 0 
                 391 
               
               
                 E-1-6 
                 0.301 
                 18.019 
                 48.92 
                 16.52 
                 4134 
                 288 
                 228 
               
               
                 E-1-7 
                 0.397 
                 18.123 
                 49.77 
                 17.37 
                 4347 
                 501 
                 165 
               
               
                 E-1-8 
                 0.601 
                 18.098 
                 48.37 
                 15.97 
                 3996 
                 150 
                 119 
               
               
                 E-1-9 
                 1.207 
                 18.258 
                 48.17 
                 15.77 
                 3946 
                 100 
                 60 
               
               
                 E-1-10 
                 0.203 
                 17.968 
                 49.18 
                 16.78 
                 4199 
                 353 
                 332 
               
               
                   
               
             
          
         
       
     
       Example 2 
       [0031]    E-1 brine was spiked with 1000 ppm Ba (as BaCl 2 ) and the isotherm was measured as shown in Table 3. 
         [0000]                                                                                        TABLE 3                   Liquid Scintillation Counting Results: Brine Spike-1                                    Removable                           Sample-   Total   Activity   Conc on                       Blank   Activity   in solution   Resin       Sample   Resin (g)   Brine (g)   Count/min   Count/min   (pCi/L)   (pCi/L)   (pCi/g)                    Blank           32.15   0                   Spike-1-1   0   18   50.38   18.23   9124   5277       Spike-1-2   0.091   18.2398   49.07   16.92   8468   4622   113       Spike-1-3   0.198   17.93   48.4   16.25   8133   4286   77       Spike-1-4   0.3973   17.89   46.75   14.6   7307   3460   71       Spike-1-5   0.6207   18.08   46.8   14.65   7332   3485   45       Spike-1-6   0.7874   17.989   45.12   12.97   6491   2645   52       Spike-1-7   0.2523   17.86   50.65   18.5   9259   5412   −8                    
This example shows that the resin capacity for radium decreased significantly to about 110 pCi/gm in the presence of about 1,000 ppm barium.
 
       Example 3 
       [0032]    E-1 brine was spiked with 11,600 ppm Ba (as BaCl 2 ) and the isotherm was measured as shown in Table 4. This example shows that the resin capacity for radium decreased even more significantly to about 70 pCi/L in the presence of 11,600 ppm barium. 
         [0000]    
       
         
               
             
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Liquid Scintillation Counting Results: Brine Spike-2 
               
             
          
           
               
                   
                   
                   
                   
                   
                   
                 Removable 
                   
               
               
                   
                   
                   
                   
                 Sample- 
                 Total 
                 Activity 
                 Conc on 
               
               
                   
                   
                   
                   
                 Blank 
                 Activity 
                 in solution 
                 Resin 
               
               
                 Sample 
                 Resin (g) 
                 Brine (g) 
                 Count/min 
                 Count/min 
                 (pCi/L) 
                 (pCi/L) 
                 (pCi/g) 
               
               
                   
               
             
          
           
               
                 Blank 
                   
                   
                 34.2 
                 0 
                   
                   
                   
               
               
                 Spike-2-1 
                 0 
                 18.158 
                 92.58 
                 41.4 
                 10372 
                 3414 
               
               
                 Spike-2-2 
                 0.103 
                 18.117 
                 88.52 
                 39.6 
                 9917 
                 2959 
                 69 
               
               
                 Spike-2-3 
                 0.196 
                 18.091 
                 86.88 
                 38.8 
                 9733 
                 2776 
                 51 
               
               
                 Spike-2-4 
                 0.395 
                 18.016 
                 87.9 
                 39.3 
                 9848 
                 2890 
                 21 
               
               
                 Spike-2-5 
                 0.601 
                 18.136 
                 82.75 
                 37.0 
                 9271 
                 2313 
                 29 
               
               
                 Spike-2-6 
                 0.789 
                 18.141 
                 77.48 
                 34.6 
                 8680 
                 1722 
                 34 
               
               
                 Spike-2-7 
                 0.202 
                 18.044 
                 87.87 
                 39.3 
                 9844 
                 2886 
                 41 
               
               
                   
               
             
          
         
       
     
       Example 4 
       [0033]    A laboratory column loaded with 8.36 gm dry DOWEX RSC resin was set up to continuously remove radium from frac water. The column was flushed with deionized water followed by hydrofracturing flowback water sample having a composition identical to that of the E-1 brine. 
         [0034]    The column was fed with the hydrofracturing flowback water sample at a rate of 0.6 mL/min. The column and feed were maintained at ambient temperature (25° C.). The column effluent was sampled approximately every 50 to 100 mL, and each sample was analyzed by liquid scintillation counting to determine the activity of radium and daughter products. The measure of column performance is the fraction of the feed activity remaining in the effluent, FFR, as shown in equation [1]. Complete removal of activity from the feed corresponds to a FFR value of 0; no removal of activity from the feed corresponds to a FFR value of 1. 
         [0000]    
       
         
           
             
               
                 
                   
                     F 
                      
                     
                         
                     
                      
                     F 
                      
                     
                         
                     
                      
                     R 
                   
                   = 
                   
                     ( 
                     
                       
                         
                           cpm 
                           effluent 
                         
                         - 
                         
                           cpm 
                           background 
                         
                       
                       
                         
                           cpm 
                           feed 
                         
                         - 
                         
                           cpm 
                           background 
                         
                       
                     
                     ) 
                   
                 
               
               
                 
                   [ 
                   1 
                   ] 
                 
               
             
           
         
       
     
         [0035]    The FFR for the first 36 effluent samples was 0.026±0.015, which is comparable to the noise level in the LSC measurement. Sample 36 was taken just as a total of 2.0 liters of feed brine had passed through the column. After the first 2.0 liters of feed, the FFR significantly increased, as shown in Table 5. 
         [0000]                                                TABLE 5                   Column Breakthrough Results                Cumulative flow through column, liters   Effluent FFR                            2.0   0.036           2.6   0.089           2.9   0.16           3.5   0.20                        
This example shows that the DOWEX RSC resin is effective for continuous removal of radium activity from hydrofracturing water with composition E-1.
 
         [0036]    While only certain features of the invention have been illustrated and described herein, many modifications and changes will occur to those skilled in the art. It is, therefore, to be understood that the appended claims are intended to cover all such modifications and changes as fall within the true spirit of the invention.