## How to determine cut points curves

1. If a flow meter is unavailable, determine the flow rate to the solids control equipment. To calculate the flow rate, one must know the fluid pump’s gallons per stroke, strokes per minute, and efficiency.
The flow rate can then be calculated by:
flowrate = (cylinder volume * N)(spm) (pump efficiency)
where
. cylinder volume=(((pump sleeve inner diameter in inches)^2* π)/4)*pump stroke length in inches (0.00433 in^3/gal)
. N=number of pump cylinders
. (spm)=strokes per minute
2. Take a representative sample from the feed stream and measure the density.
Underflow:
1. Weigh the sampling container. A minimum container size of 5 gal is recommended in order to capture a large sample of solids.
2. Take a representative sample from the underflow (effluent) stream of the solids-control equipment system (Figure 4.1; note that using a smaller container to fill the larger sampling container will not adversely affect the solids sample).

3. Weigh the sampling container and effluent sample.
4. Calculate the weight of the effluent sample: weight of effluent sample = effluent sample and container – weight of container
5. Wet sieve and dry the sieved solids thoroughly. Slowly pour the collected sample through a stack of U.S. Standard Sieve screens with a broad distribution of micron opening sizes (see Section 4.2 for a representative distribution of sieve sizes). A gentle stream of water is used to wash the solids and to assist the sieving process (Figures 4.2 and 4.3). Once the sample has completely passed through the stack of sieves, each sample of solids on each individual sieve must be dried. Drying can be accomplished by placing the sample in a static oven(1) and heating at a maximum temperature of 250°F until all of the water has evaporated. If an oven is unavailable, the samples may also be allowed to slowly air dry.

6. Measure the weight of dry solids captured on each size of sieve screen. These will be the weights of individual dry effluent solids.
1. Weigh the trough that will be used to collect the discard sample.
2. Collect the discard sample off the end of the solids-control equipment(Figure 4.4).

3. Measure the time (in minutes) for which all the discard is collected from the solids-control equipment. This will be the time of discard sample.
4. Weigh the discard sample and trough.
5. Calculate the weight of the discard sample in the trough: wet discard sample weight = discard sample and trough – weight of trough
6. Wet sieve and dry the sieved solids thoroughly.(2)
Take a representative sample from the discarded solids and slowly pour through a stack of U.S. Standard Sieve screens. Use the same sizes of sieves used for the underflow sample, and follow the same procedure: Wash the solids with a gentle stream of water, which also assists the sieving process (Figures 4.2 and 4.3). Once the sample has completely passed through the stack of sieves, dry each sample of solids on each individual sieve. Drying can be accomplished by placing the sample in a static oven(3) and heating at a maximum temperature of 250°F until all of the water has evaporated. If an oven is unavailable, the samples may also be allowed to slowly air dry.
7. Measure the weight of dry solids captured on each size of sieve screen.These will be the weights of individual dry discard solids
Plotting the Cut Point Curve
1. Determine the wet discard flow rate:
2. Determine the effluent flow rate:
effluent flow rate = well flow rate – wet discard flow rate.
3. Calculate the time taken for the effluent sample:
effluent sample time = weight of effluent sample/effluent flow rate.
4. For each U.S. Standard Sieve screen size, determine the rate of solids collected for the discard sample:
5. For each U.S. Standard Sieve screen size, determine the rate of solids collected for the effluent sample:
effluent flow rate = weight of individual dry effluent solids=/effluent sample time.
6. Determine the feed flow rate for each sieve size:
feed flow rate = dry discard flow rate + effluent flow rate.
7. Calculate the percentage of discarded solids for each sieve size:
8. Plot the percentage of discard on the Y axis with the corresponding sieve size (expressed in microns) along the X axis of a graph to produce the cut point curve for the analyzed system. The cut point curve would actually be a series of horizontal lines between sieve sizes. The curve is usually drawn through the center of each segment to
produce a smooth curve.

(1)This method applies to water-base fluids only. For oil-base fluids, proper cleansing and drying of the sample should be administered in order to extract all residual fluids from the solids.

(2)This method applies to water-base fluids only. For oil-base fluids, proper cleansing and drying of the sample should be administered in order to extract all residual fluids from the solids.

(3)This method applies to water-based fluids only. For oil-based fluids, paper cleansing and drying of the sample should be administered in order to extract all residual fluids from the solids.

## CUT POINTS

Cut points are used to indicate the separation characteristics of solids control equipment at a given moment in time. The performance of the equipment, in addition to the condition of the drilling fluid, should be taken into consideration in the assessment of cut point data. Cut point curves are derived from the collected data and indicate, at the actual moment of data collection, the percentage of chance that a particle of a particular size can flow through or be discarded by the solids-control equipment. Therefore, the cut point curve is a function of the physical properties of the solids (i.e., density), particle size distribution of the solids, physical condition of the solids-control equipment (i.e., sealing capabilities), and the drilling-fluid properties.
Cut points may be determined for all drilled-solids removal equipment. The mass flow rate of various-size particles discarded from the equipment is compared with the mass flow rate of the same-size particles presented to the equipment. When testing a particular unit, knowledge of the feed flow rate to the unit and the two discharge flow rates are required. The density of the feed flow multiplied by the volume flow rate provides the mass flow rate into the unit. Discharge mass flow rates are also calculated by multiplying the density of the stream by the volume flow rate. Obviously, the sum of the discharge mass flow rates must be equal to the feed mass flow rate. Usually one of the discharge flow streams is discarded and the other is retained in the drilling fluid.The material balance—both the volume flow rate balance and the mass flow rate balance—should be verified before measuring the particle sizes of the various streams.
Solids-removal equipment removes only a very small fraction of the total flow into the equipment. For example, a 4-inch desilter processing about 50 gpm of drilling fluid will discard only about 1 gpm of material. Since the discarded material is such a small proportion of the total material processed, the difference between the retained stream and the feed stream is difficult to measure. For this reason, more accurate data are acquired by mathematically adding the value of the discarded solid concentrations to that of the retained solids concentration to determine the feed solids concentration.
To determine the mass flow of a particular-size particle in the feed (or retained) stream and the mass flow of the same-size particle in the discard, flow rate measurements and solids concentrations are needed. The discard volume flow rates are normally relatively low, but the feed rates require using a flow meter or a positive displacement pump.
For shale shakers, the feed to the shaker will be the circulating rate coming from the well. Mud pumps must be calibrated to provide an accurate feed rate. While drilling, move the suction from the suction tank to the slug tank and measure the rate of drop of the fluid leaving the slug pit. The fluid in the slug tank will contain liquid and gas (or air), so the volume percentage of (%vol) gas must be subtracted from the volume of fluid leaving the slug tank. The %vol gas is calculated by dividing the difference between the pressurized mud weight and the unpressurized mud weight by the pressurized mud weight and multiplying by 100. If the desilters or centrifuges are fed by centrifugal pumps, some type of flow meter will be required to accurately determine the feed rate. The flow meter could be a large container whose volume is calibrated and a stopwatch. A centrifuge underflow volume flow rate is difficult to measure because of the high concentration of solids. A barrel or other large container can be split vertically and support beams or pipes welded to provide a support when the container is placed across the top of a mud tank. Calibrated lines are painted inside of the container to provide volume measurements. A quantity of water is placed in the container and the container is positioned adjacent to a decanting centrifuge mounted on top of a mud tank. The stopwatch is started when the container is pushed under the centrifuge, and the rate of water level is observed.
The known volume between lines and the time permit calculation of the volume discard rate. Representative samples of the underflow or heavy slurry provide the density measurements of the underflow. After confirming that there is a mass and volume flow balance with the measured values, the particle sizes in the discharge streams are determined.
All of the discard stream may be captured for analysis during a period of several minutes. The contents of the feed stream during that period must be known so that the ratio of discard to feed particle mass can be determined for various particle sizes. The feed stream and retained stream for shakers and desilters, however, would require much larger containers, and it is impractical to try to weigh or measure their volumes directly. Representative samples of the retained stream must be used to determine the mass of various-size particles.
With the centrifuge and the desilters, the particle sizes must be measured with an instrument that discerns particle sizes as small as 1 micron. With the shaker measurements, sieves may be used because the cut point range will be within the range of screens standardized by the American Society for Testing and Materials (ASTM). A variety of different laboratory devices are available that measure small-diameter particles. Instruments using lasers are popular in many laboratories.
The discard sample will contain the solids and the liquid phase of the drilling fluid. With the shale shaker discard, the mass of solids retained on each ASTM test screen may be measured directly by weighing the solids after they are dried. With the desilter underflow and the centrifuge underflow (or heavy slurry) discharge, the density of the solids must be used to determine the mass percentage of solids.
Cut points for shale shakers are measured by determining the particle size distribution of the feed and discard streams with the use of a stack of U.S. Standard Sieves. The flow rate of each stream is determined, and the mass flow rate for each sieve size in each stream is calculated. The mass flow rate of the discard stream for each sieve size is divided by the mass flow rate for the same size introduced into the equipment in the feed stream.
Using this method, the feed-stream sample represents a small fraction of the total overall flow. This can create a problem with material balances. A better method is to sample the discard and underflow streams. Combining these two solids distributions will yield a more accurate cut point curve. This method can be used on solids-control equipment in which the feed-stream flow rate is greater than the discard stream.