Small Business, Bit Impact.

“I know you always want to have an MBA degree.” My brother called me from Kentucky in August. “There is this program specially designed for small business owners like you. Try it. It is free if admitted.”

This 10-minute conversation with my dear brother caused me a 4-month commitment to the Goldman Sachs 10,000 Small Business Program this fall. After an on-line application, an on-site interview and one week of Hurricane Harvey, I was admitted to this program (Houston site) in the middle of September 2017.

We have 20 scholars, as called by the organizer, in this session. The purpose of the program is to teach busy businessmen to grow their business. Unlike degreed programs, which are costly, length and faculty-focused, the Goldman Sachs 10,000 Small Business Program is a gift, fast paced and peer-focused. It is not only free, but they also provide breakfast and lunch. My classmates are all business owners, but I am the only one in petroleum engineering area. I guess that this does not matter, as all business share the similar process.

One day, a lady instructor showed us a slide loaded with the information of US firms. To my surprise, there are nearly 30 million companies in US. She continued to the next slide showing the number of employees of these companies. It was even more shocking: among those 29+ million companies in US, more than 80% are no-employee firms. Ever wonder how many US firms hiring more than 500 people? The answer is 18,219. So, for those of you who are working for big companies, you should feel privileged, because only 0.06% of all the US companies hire more than 500 people.

However, if you are working for companies with only a few or a couple of hundred employees or you are running one of similar sizes, please do not be discouraged, because together, we are the largest employer in the US economy.

A few weeks into the program, I have been inspired by the creative way of their teaching. We paired up to do presentation and discuss. We used super-sized Post-It to brainstorm our ideas on new opportunities. We are encouraged to generate ideas for other business owners. I already got some ideas how to generate ideas within our company. Keep learning and keep practicing, I told myself.

Goldman Sachs 10,000 Small Business Program

Goldman Sachs 10,000 Small Business Program

Circulation Sub Series—4: Case Study Part II of II

3. Effect of Flow Rate

To study the sensitivity of flow rate on a circulation sub’s performance, 3 cases were chosen: one is without a circulation sub, and the other two have 1 (in2) and 2 (in2) of TFA, respectively. As we increase the flow rate from 1 to 10 (bpm), bypass ratios for both cases decrease. One might wonder why the bypass ratio decreases as flow rate increases. Does not the circulation sub play a bigger role in tougher conditions such as a high flow rate situation? Here is the reason behind the reverse change: the pressure drop across circulation sub nozzles (Path B) is proportional to the square of the flow rate, regardless of the rheological model. The frictional pressure loss along Path A is proportional to the flow rate to the power of 1.75 for Newtonian fluids in turbulent flow conditions. When the flow rate increases, it is relatively easier for fluid to flow along Path A than Path B. Therefore, at higher flow rates, the bypass ratio is smaller.

Figure 10: Circulation Sub Bypass Ratio vs Flow Rate

Figure 10: Circulation Sub Bypass Ratio vs Flow Rate

However, even with the slightly decreased bypass ratio at higher flow rate, the presence of a circulation sub greatly reduces pump pressure and bottom hole ECDs, as illustrated in Figure 11 and Figure 12. The benefits become more pronounced at higher flow rates. As noted before, the inclusion of a circulating sub makes a dramatic impact up to a certain TFA, in this case 1 square inch.

Figure11: Pump Pressure vs Flow Rate

Figure 11: Pump Pressure vs Flow Rate

Figure12: Bottom Hole ECD vs Flow Rate

Figure 12: Bottom Hole ECD vs Flow Rate

4. Effect of Viscosity

Since viscosity has a small impact on the analysis, the circulation sub’s nozzles have been changed to 2 x 10 (1/32in) for this portion of the analysis, which yields a TFA of 0.153 (in2) for our base case.

The flow split at a circulation sub is the result of flowing fluid seeking the path of least resistance and pressure balance. The frictional pressure loss along Path A is a function of fluid viscosity, density, flow rate and flow path geometry. If the flow is laminar, the pressure loss is proportional to the fluid viscosity for Newtonian fluid. The resistance of path B is dominated by the pressure drop across nozzles, where the viscous frictional effects are essentially negligible. As fluid viscosity increases, it is more difficult for fluid to flow through Path A. The bypass ratio will increase as illustrated by Figure 13. Both pump pressure and bottom hole ECD increase as fluid viscosity becomes higher. However, they would be much higher if no circulation sub is present.

Figure 13: Circulation Sub Bypass Ratio vs Fluid Viscosity

Figure 13: Circulation Sub Bypass Ratio vs Fluid Viscosity

Figure 14: Pump Pressure vs Fluid Viscosity

Figure 14: Pump Pressure vs Fluid Viscosity

Figure 15: Bottom Hole ECD vs Fluid Viscosity

Figure 15: Bottom Hole ECD vs Fluid Viscosity

5. Effect of Fluid Density

If the flow is turbulent, the pressure loss along Path A is proportional to the fluid density to the power of 0.75 for a Bingham plastic fluid. On the other hand, the pressure drop across Path B is proportional to the fluid density. As the fluid density increases, it is relatively more difficult for fluid to flow through Path B. The bypass ratio will decrease when fluid density increases as illustrated by Figure 16. The pump pressure increases as fluid density increases. The bottom hole ECD increases because both hydrostatic pressures and frictional pressure loses increase with greater fluid density.

Figure 16: Circulation Sub Bypass Ratio vs Fluid Density

Figure 16: Circulation Sub Bypass Ratio vs Fluid Density

Figure 17: Pump Pressure vs Fluid Density

Figure 17: Pump Pressure vs Fluid Density

Figure 18: Bottom Hole ECD vs Fluid Density

Figure 18: Bottom Hole ECD vs Fluid Density

The above case study is performed for a particular wellbore cleanup scenario. In order to have a better understanding of your particular case, it is recommended to use engineering software to take into account of well configurations and fluid properties to optimize circulation sub performance.

Circulation Sub Series—3: Case Study Part I of II

Case Study

Engineers may have some basic ideas on how to optimize the design parameters of a circulation sub to achieve their goals. For example, increasing the total flow area of a circulation sub will increase the bypass flow rate, reduce pump pressure, etc. This case study will quantify the impacts of various circulation sub parameters and fluid properties on pump pressure and ECD for a wellbore cleanup operation. We used a wellbore cleanup hydraulics software to perform this case study. Numerical methods are employed to obtain the correct flow split percentage at the location of the circulation sub. The flow split is obtained such that the summation of the frictional pressure losses inside the pipe below the circulation sub and in the annulus below the circulation sub should be equal to the pressure loss through the circulation sub nozzles.

Figure 2 shows the wellbore configuration used for the example calculation. This is the basic case, from which we will perform sensitivity studies on each of 5 parameters. Note that the flow rate is left blank because it is run at several values for all stages.

Figure2: Example Case

Figure2: Example Case

Figure3: Flow Paths

Figure3: Flow Paths

1. Effect of Total Flow Area (TFA)

Circulation sub’s adjustable nozzles enable you to define how the flow is split between the annulus and the pipe interiors. By adjusting the TFA of the circulation sub, you can control the amount of fluid that is diverted.

The flow split at a circulation sub is determined as the fluid chooses the path of least resistance. The rates of flow through the circulation sub and down the string are determined when these two flow paths reach a pressure balanced state. When fluid inside pipe travels to the circulation sub, it faces 2 choices. The first one is to flow downward through the pipe and up the annulus. Let us call this Flow Path A. The alternative path is sideways through the circulation sub’s nozzles. We will call this Flow Path B.

As illustrated by Figure 3, Flow Path A involves a long, but wide conduit, while Flow Path B is an array of short constrictions (nozzles).

The circulating fluid does not have a preference as which path to flow. When the fluid passes the circulation sub, it senses the resistances of both paths and chooses the split of fluid so that it yields an overall minimum resistance.

The frictional pressure loss, or flow resistance, along Path A is a function of fluid viscosity, density, flow rate, pipe ID, hole ID, pipe OD and flow path length. On the other hand, the resistance of Path B is dominated by the pressure drop across the nozzles, which is reversely proportional to the square of the TFA of those nozzles. As we increase the TFA of a circulation sub, it becomes much easier for fluid to flow through Path B. As a result, less fluid will flow through Path A and the frictional pressure losses in the lower pipe and annular sections will be reduced. Whatever the percentage of flow split, the pump pressure and ECD of the system are both reduced by the fluid bypass.

In our example, we increase the TFA from 0, representing a case of no circulation sub, to 2 (in2). Figure 4 shows increased fluid bypass ratios as the TFA increases for 3 flow rates, 2 (bpm), 4 (bpm) and 6 (bpm). The circulating sub bypass ratio is the percentage of flow exiting the string through the circulating sub nozzles, as opposed to the bit.

Figure4: Circulation Sub Bypass Ratio vs TFA

Figure4: Circulation Sub Bypass Ratio vs TFA

Accompanying these increased bypass ratios, both the pump pressure and bottom hole ECD reduce rapidly at beginning and more gradually later, as shown in Figure 5 and 6, respectively. The pump pressure is reduced by almost 80% when TFA is increased from 0 (in2) to 1 (in2) for a flow rate of 6 (bpm). Meanwhile, for the same flow rate, bottom hole ECD is reduced by 7.6%. Further increase of TFA from 1 (in2) to 2 (in2) yields only marginal reduction.

Figure5: Pump Pressure vs TFA

Figure5: Pump Pressure vs TFA

Figure6: Bottom Hole ECD vs TFA

Figure6: Bottom Hole ECD vs TFA

2. Effect of Circulation Sub Depth