## Sample Calculation

During the drilling of a relatively uniform 2000-foot shale section, an API 200 continuous screen cloth was mounted on a linear shale shaker. An 11.2-ppg, freshwater, gel/lignosulfonate drilling fluid was circulated at 750 gpm while drilling. A typical set of samples will be described here.
Large pieces of shale were removed from the shaker screen and excess drilling fluid washed from the surface with distilled water. The shale pieces were ground and dried in an oven at 250F overnight. The shale was placed in a 173.91-cc pycnometer and weighed. Water was added to the pycnometer and pressurized to about 350 psi. The increase in weight of the pycnometer indicated the volume of water added to fill the pycnometer. (Room and water temperature was 68F, so the density of water was about 1.0 g/cc.) Subtracting this volume of water from the known volume of the pycnometer calculates the volume of shale sample. Once the volume of the shale sample and the weight were known, the density could be calculated. The shale drilled in this well had a density of 2.47 g/cc.
After movement of solids across the shale shaker screen appeared to be relatively uniform for more than 10 minutes, all the shaker discard was collected in a bucket. In 16.21 seconds, 3720.7 g of discard was captured. The discard rate was 13,772 g/min. The discard had a density of 1.774 g/cc or 14.8 ppg.
Calculation Procedure
A sample of the discard was placed in the pycnometer and weighed:
pycnometer+ sample weight = 869.68 g.
Since the pycnometer weighed 660.61 g dry and empty, the sample weight was 209.07 g.
The pycnometer with shaker discard sample was filled with distilled water, pressurized, and weighed:
pycnometer + sample +water =948.32 g.
The weight of water added was 948.32 g – 869.68 g=78.64 g. Volume of70°F. water added=78.64 g/0.998 g/cc.
Since the pycnometer volume was 173.91 cc, the sample volume was
173:91 cc -78:80 cc = 95:11 cc
The density of the sample was 209.07 g/95.11 cc=2.2 g/cc.
The objective of the shale shaker is to remove drilled solids, preferably without excessive quantities of drilling fluid. The fraction of the discard stream that is water, barite, and low-gravity solids can be determined by the preceding equations. These calculations indicate that the discard stream had 5.06 %vol barite, 38.38 %vol low-gravity solids, and 56.56 %vol water.
Calculation Procedure to Determine Low-Gravity Solids Discarded
The discard from the screen weighs 14.8 ppg and contains 43.44 %vol solids. We use the equation presented previously: To determine the quantity of drilled solids discarded by the shale shaker, a sample of the discarded material was placed in a metal dish and dried in an oven overnight. The weight percentage of (wt%) dry solids was 68.11 and had a density of 2.78 g/cc.
The rate of dry solids discarded (RDSD) is calculated from the product of the wet discharge flow rate and the weight fraction of dry solids in the discharge (with the appropriate unit conversion factors): Experimental and Calculation Procedure
A sample of discard was placed in a 40.10-g crucible and weighed:
crucible + sample weight = 114.94 g.
The wet sample weight was 74.84 g. Since the wet discard density was 1.77 g/cc, the wet sample had a volume of 74.84 g/1.77 g/cc=42.19 g/cc.
After heating overnight at 250°F, the crucible and sample weight were 91.08 g. The dry solids weight in the sample was 91.08 g- 40.10 g=50.98 g.
The wt% dry solids in the discard was the weight of dry solids divided by the wet-sample weight times 100, or
[50.98 g/74.84 g]× 100=68.12 wt%.
The volume of the dry sample was calculated by subtracting the volume of water lost from the volume of the wet sample:
The 42.19-cc wet sample lost 114.94 cc-91.08 cc=23.86 cc of water.
The volume of the dry sample was 42.19 cc-23.86 cc=18.33 cc.
The density of the dry solids was the weight of dry solids divided by the volume of dry solids, or 50.98 g/18.33 cc=2.78 g/cc.
Calculation of Barite Discarded by Shale Shaker
Assuming that all of the drilled and other low-gravity solids in the drilling fluid have a dried density of 2.47 g/cc and the barite has a density of 4.2 g/cc, the wt% barite in the dry sample may be calculated from the mass-balance equation:
Density of Dry Solids =Weight of Solids/Volume of Solids
or
Density of Dry Solids=[Weight of Barite+ Weight of Low Gravity Solids]/[Volume of Barite + Volume of Low Gravity Solids]
To determine the terms on the right side of the equation:
1. The volume of barite is the density (4.2 g/cc) divided by the weight of barite.
2. The volume of low-gravity solids is the total volume of dry solids minus the volume of barite.
3. The volume of low-gravity solids in 1 cc of solids equals 1 cc minus the volume of barite in 1 cc of solids.
Volume of low gravity solids in 1 cc of solids=1cc-[Wb/4.2 g/cc]
Weight of Low Gravity Solids in 1 cc of dry solids={1cc-[Wb/4.2 g/cc]}×(2.47 g/cc)
Density of Solids (D)={WB+ 2:47 g/cc[1 -WB/4.2 g/cc]×1 cc}/[Wb/4.2 g/cc]+{1-[Wb/4.2 g/cc]}
This equation may be reduced to the expression:
D = 0:4119WB + 2.47
or
Weight percent barite=D-2.47/0.4119
The discard density is 2.78 g/cc, so the wt% barite is 27.07. The weight of dry discard from the shaker screen is 1239 lb/hr. The quantity of barite discarded is (0.2707)(1239 lb/hr), or 377 lb/hr. The low-gravity-solids discard rate is 1239 lb/hr-377 lb/hr, or 862 lb/hr.
Calculation of Solids Discarded as Whole Drilling Fluid
A water-base drilling fluid contains 13% volume of solids in the liquid phase of the shale shaker discard, which could be associated with the whole drilling fluid.
The wt% dry solids discarded from the shaker screen is calculated to be 68.12; so 31.89% of the discard must be liquid. Assume that this liquid is composed of drilling fluid with the solids distribution of the drilling fluid in the pits. The liquid discard rate is (13,772 g/min)(0.3189), or 4391.9 g/min. This liquid should contain 13% volume of solids.
Since the drilling fluid contains 13% volume of solids, a 100 cc sample contains 87 cc of liquid. In this 100 cc sample, the water fraction wouldweigh 87 g. With an 11.2-ppg (1.343 g/cc) density drilling fluid, the 100 cc sample should weigh 134.3 g. Since the liquid weighs 87 g, the solids must weigh 47.3 g. Or, stated another way, the drilling fluid contains 47.3 g of solids for every 87 g of water. The total liquid discard rate is 4391.9 g/min. The solids discarded by the screen that are associated with the drilling fluid would be:
[47:3 g solids/87 g water][4391:9g/min]=2387.8g/min; or 315:6 lb/hr.
The wt% barite in the drilling fluid is 77.4 and the wt% low-gravity solids in the drilling fluid is 22.4. From the solids discarded from the screen associated with the whole drilling fluid, 244 lb/hr are barite and 71.2 lb/hr are low-gravity solids.
Previously, the dry solids discarded by the shaker screen were calculated to be 377 lb/hr barite and 861 lb/hr low-gravity solids. Subtracting the solids associated with the drilling fluid from the solids removed by the screen indicates the discarded solids in excess of those associated with the drilling fluid:
Barite:
377 lb/hr – 244 lb/hr = 133 lb/hr
Low-gravity solids:
861.0 lb/hr – 71.2 lb/hr = 789.8 lb/hr
This indicates that the API 200 screen is removing 133 lb/hr of barite and almost 800 lb/hr of drilled solids in addition to the quantity contained in the associated drilling fluid.
Note that the technique of using the concentration of barite in the discard does not allow an accurate measurement of the quantity of drilling fluid in the shaker discard. Some measurements even indicate that less barite is in the discard than is in the whole drilling fluid. Shaker screens can pass much of the small-size barite and remove it from the liquid before it is discarded by the shaker screen.