AMNA Gumati, HIROSHI Takahshi

Graduate School of Environmental Studies, Tohoku University, 6-6-20 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, Japan, E-mail: amna@algumati.com

EXPERIMENTAL STUDY AND MODELING OF PRESSURE LOSS FOR FOAM-CUTTINGS MIXTURE FLOW IN HORIZONTAL PIPE*

AMNA Gumati, HIROSHI Takahshi

Graduate School of Environmental Studies, Tohoku University, 6-6-20 Aramaki-Aza-Aoba, Aoba-ku, Sendai 980-8579, Japan, E-mail: amna@algumati.com

In this study, we first sought to elucidate foam rheology to describe foam flow behavior, and then to experimentally investigate the pressure losses for both foam and foam-cuttings flow in a horizontal pipe by considering both varied foam qualities of 80%, 85% and 90% and foam velocities. Also, a two-layer numerical model to predict pressure loss was developed based on experimental observations of cuttings behavior. Results show that the foam behaves like a power-law fluid. Furthermore, and the pressure loss significantly increases as foam velocity increases, while the delivered cuttings concentration dramatically decreases. Moreover, results indicate that both the pressure loss and the delivered cuttings concentration increase with foam quality. Comparisons between the experimental results and numerical model predictions show satisfactory agreement.

foam rheology, pressure loss, horizontal pipe, cuttings concentration, two-layer model

Introduction

Foam has been used in many applications in the oil and gas industry, especially in underbalanced drilling, where the pressure of drilling fluid is kept at a value smaller than the formation pore pressure. Foam has been proved to be a strong candidate as a drilling fluid in underbalanced drilling because of its variable density and good cuttings transport ability. Additionally, in many field cases, foam has been shown to provide significant benefits, including reduction of operational difficulties such as stuck pipe, loss of fluid circulation, minimization of formation damage and an increase in drilling rate[1].

Foam is defined as a large volume of gas dispersed in a small volume of liquid containing a foaming agent (surfactant), where the continuous phase is liquid and the discrete phase is gas. Foam is classified according to its quality, which is defined as gas volume ratio to the total volume of foam, and foam is characterized into dry and wet foam according to its texture, i.e., the bubble size and bubble size distribution. To achieve successful drilling operations under underbalanced conditions, foam rheology, pre-ssure loss and cuttings transport behavior should be fully understood to minimize the risks and costs associated with foam drilling, especially in horizontal foam drilling.

In literature, different studies of rheological foam flow behavior have been reported in recent years to model the rheological characterization of foam, but there is disagreement among researchers to select the best model for describing the foam flow behavior[2]. This is mainly because of the complexity of foam and the differences of analytical approaches and experimental setups. Basically, two different approaches for characterizing foam rheology have been reported: (1) quality-based method and (2) volume equalized method. In the quality-based approach, foam is treated as a single phase fluid and it is characterized separately for different foam qualities, while in the volume equalized approach, foam normalizes the quality values and it is characterized by using parameters valid for all quality values[3].

Moreover, the determination of pressure loss has also been found to be a very important aspect in horizontal foam drilling[4]. Therefore, appropriate measurement of pressure loss is one of the key features of a successful underbalanced operation. Furthermore, a better understanding of cuttings transport with foam is important for accurate prediction of pressure lossesand safe/secure drilling operations. To our knowledge, few studies have been reported in the literature concerning the investigation of pressure loss and cuttings transport phenomena with foam in horizontal drilling, and even less is known about the behavior of foam flow and the foam-cuttings mixture flow in horizontal drilling[5-12].

Therefore, the objective of the present study is firstly to experimentally investigate the pressure losses for both single phase (foam) and multiphase flow (foam-cuttings) in a horizontal pipe at ambient conditions, and secondly, to propose a numerical model to predict the pressure loss for multiphase flow in the horizontal pipe. Although during on-site drilling operations, cuttings are transported through the annulus, a space between the wellbore and drill pipe, a single pipe is used in this research as the first step. However, the effects of an inner pipe on the pressure loss and cuttings transport behavior will be investigated in the next study.

Fig.1 Schematic of the experimental apparatus

1. Experimental apparatus and procedures

1.1Experimental apparatus

Experiments were conducted on flow equipment consisting of a test section, a pump, an air compressor, a foam generator, flow meters, a cuttings injection tank, and a collection tank. Figure 1 shows a schematic of the experimental apparatus. The test section is a 5 m long acrylic pipe with a 50 mm diameter. A pump with a maximum capacity of 60 l/min is used to inject the liquid phase (mixture of water and surfactant) into the test section and a compressor with a maximum capacity of 250 l/min is used to supply air.

Both liquid and gas flow rates are measured by using flow meters. The foam generator consists of a stainless cylinder packed with glass beads 3 mm in diameter and is set at the entrance of the test section to provide better mixing between the gas phase and the liquid phase.

Pressure loss was measured by a manometer. Cuttings were injected at the inlet of the test section, where they merged with the foam flow. The collection tank provided with a separation system was used to collect the delivered cuttings and the foam.

In this experiment, a commercial surfactant (KAFoam) was used. Three foam qualities of 80%, 85% and 90% were considered to investigate the effect of foam quality on the pressure loss. In order to stimulate the drilled cuttings, spherical glass beads with a diameter of 7 mm and a density of 2 500 kg/m3were used. All experiments were performed at room temperature and pressure. Table 1 shows the test matrix of this study.1.2Test procedures

Table 1 Test matrix

The experimental procedures are divided into the following stages:

(1) The liquid phase was prepared by mixing tap water with a foam agent (surfactant) at a concentration of 0.5% in the liquid tank.

(2) Both the air compressor and liquid pump were started to generate foam with the desired foam quality and flow rate, the foam then flowing into the test section. After the flow rate became stable, pressure loss for foam flow was recorded.

(3) Once the flow rates were stable, cuttings were injected into the test section, and simultaneously frictional pressure loss of foam-cuttings flow was recorded.

(4) The delivered cuttings were collected and weighed to calculate the cuttings concentration.

(5) Finally, the whole system was shut down.

2. Foam rheology

A full understanding of the rheological behavior of foam is required to estimate the pressure losses in pipes. To explain the rheological behavior of foam, a conventional method (quality-based) was adopted in this study. The discharged foam from the test section was tested by a rotational viscometer. Rheology tests were conducted for different foam qualities of 80%, 85% and 90% to determine foam rheological properties. Foam quality is defined as follows

whereΓis the foam quality, andVolgandVolLare gas and liquid volumes, respectively.

In our previous work[9], although we examinedrheological properties of foam, the foam generation method was totally different, hence, we carried out the measurement of rheological properties to confirm the best model for describing foam behavior. This is mainly because the foam generation method has a significant effect on foam rheology. Figure 2 shows the foam generated in this experiment.

Fig.2 Foam used in this study

The rheological results were analyzed to decide the most appropriate rheological model for describing the foam flow behavior. Pre-defined rheological models of power-law fluid and Bingham plastic fluid were assumed to determine the foam rheological parameters relevant to our previous study. The rheological equations of these models are expressed as follows:

Power law fluid

whereτis shear stress,γshear rate,yτyield stress,kconsistency index andna fluid behaviour index.

Table 2 Correlation coefficients for each rheological model

The curve fitting technique was used to select the most appropriate model. Table 2 shows the correlation coefficients for both the power-law model and Bingham model fluids. According to the correlation coefficients, it is confirmed that the power-law model is the best to explain the foams flow behavior. This result is in good agreement with our previous result[9].

Fig.3 Relationship between shear stress and shear rate

Figure 3 shows the relationships between shear stress and shear rate for foam qualities of 80%, 85% and 90%. It can be seen that the higher foam quality presents higher shear stress at constant shear rate, which means a higher effective viscosity. A summary of the rheological parameters are given in Table 3. Furthermore, it is known that foam texture (i.e., bubble size, shape and bubble size distribution) has an effect on foam rheology. Therefore, in order to measure the bubble size and bubble size distribution, the image analysis of the image captured by a digital microscope was used.

Table 3 Rheological parameters

Fig.4 Image of foams structure

Figure 4 shows the images of foam captured through a vision port of the microscope for three different foam qualities of 80%, 85% and 90%. Figure 4(a) shows the image for foam quality of 80%. It can be seen that foam bubbles are small in size and circular in shape and that there is no interaction between bubbles. The average diameter of bubbles was about 116 m.

Figure 4(b) shows the image for foam quality of 85%. In this image, large bubbles were observed with shapes other than circles. Interaction between the bubbles was observed and the average size of the bubbles was about 150 m. Figure 4(c) shows the image for foam quality of 90%. Bubbles were observed to be greater in size and their circularity is less than a perfect circle, which is due to a high content of gas that tends to interact between bubbles. The average size of the bubbles was about 167 m.

It is clear that as the foam quality increases, the average bubble size increases and the circularity of the foam decreases, which are due to the increase of gas content in the foam structure. Since the foam rheology changes with foam texture, it is considered that the foam texture will change with time. Thus, the effect of foam stability on the rheological behavior of foam was investigated. An evaluation of foam stability was performed by an adaptation of a rheological measurement as a function of time in ambient conditions. The foam was collected in a visual graduated cylinder, and then rheological measurements were conducted at 10 min, 20 min, 30 min, 60 min, 90 min and 120 min. Since the liquid phase is denser than the gas phase, consequently, the foam has a strong tendency to break down.

Fig.5 Foam stability

Figure 5 illustrates a significant rheological variation for foam quality of 80% as a function of time. In the present study, the change of foam rheology due to the shear during transportation was not investigated. However, it was confirmed that foam rheology changed with time, which was due to foam collapsing into its components after a short time period.

It should be noted that we attempted to keep the foam rheology constant while pressure losses were measured with generating foam for each single experiment. Therefore, the effect of the change in foam rheology on the pressure losses was negligible in this experiment.

3. Experimental results and discussion

Figure 6 shows the pressure losses for foam flow in a pipe with different foam qualities of 80%, 85% and 90%. The pressure losses were measured under variable foam velocities. As shown in this figure, the pressure loss increases with the increase of foam velocity. It is obvious that foam quality has a major effect on the pressure loss, i.e., the higher foam quality tends to increase the pressure loss by making bubbles more active where mechanical and chemical interaction occurs between the bubbles.

Fig.6 Pressure loss for foam flow

Also, the increase of the pressure loss is basically due to the increase of foam viscosity. The solid line in Fig.6 represents the pressure losses for water flow. The pressure losses for foam flow are much greater than those for water flow, although the density of foam is much smaller than that of water. A possible explanation for this result is that the viscosity of foam is much greater than that of water, accordingly, the effect of the viscosity on the pressure loss is significant.

Fig.7 Relationship between the Reynolds number and friction factor

Figure 7 presents the relationship between the Reynolds number and friction factor for foam flow with different qualities.

On the basis of foam rheological results and the experimental results of the pressure losses for foam flow, the friction factor and Reynolds number were estimated for the foams by the following equations:

whereλis the friction factor, Δp/ΔLthe pressure loss,Dthe pipe diameter,ρfthe foam density,Vfthe foam velocity,Rethe Reynolds number andμfthe effective viscosity.

[10]The effective foam viscosity can be estimated by

Also, Fig.7 shows that the flow regime of the foam in this experiment is a laminar flow. Moreover, it shows that the experimental data fall on a unique line regardless of foam quality. A solid line in this figure represents the theoretical values of friction factor for laminar flow which was calculated by the following equation

Since all the experimental data lie on the theoretical line and show good agreement with the theoretical results, it was confirmed that the test section was hydraulically smooth and the measuring system of the pressure loss was correct.

Fig.8 Pressure loss for multiphase flow of foam quality 80%

Figures 8 through 10 show both the experimental and the calculated results of the pressure losses of multiphase flow (foam-cuttings) for foam qualities of 80%, 85% and 90%. The solid lines in these figures indicate the calculated results of the pressure loss which will be explained in the next section.

Figure 8 shows the pressure losses for foam quality of 80%. The pressure losses were distributed in a certain range, even if the foam velocity was the same value. This is due to the difference in cuttings concentration. It should be mentioned that it was difficult to control the cuttings concentration at a constant value because of the limitation of the experimental apparatus, and as a result, the cuttings concentration is varying, and then the pressure losses change. The delivered volumetric cuttings concentration ranged from 18% to 23.5% for foam quality of 80%.

Fig.9 Pressure loss for multiphase flow of foam quality 85%

Figure 9 shows the results of pressure losses for foam quality of 85%. The trend was the same as the one in Fig.8. In this case, however, the delivered volumetric cuttings concentration ranged from 15% to 25%.

Fig.10 Pressure loss for multiphase flow of foam quality 90%

Figure 10 shows the results of pressure losses for foam quality of 90%. The delivered volumetric cuttings concentration varied from 13.5% to 27%. These figures clearly indicate that pressure loss is a function of both foam velocity and foam quality. Therefore, thepressure loss increases with the increase of both foam velocity and quality.

The effect of foam velocity on the delivered volumetric cuttings concentration is shown in Fig.11.

Fig.11 Effect of foam velocity on cuttings concentration

In order to estimate the cuttings transport efficiency, the concentrations of the delivered volumetric cuttings were calculated. It can be seen that as foam velocity increases, the concentration of the delivered volumetric cuttings decreases, i.e., more cuttings are transported and less is accumulated in the pipe. Moreover, it is observed that the delivered volumetric cuttings concentration increases with the increase of foam quality at the same foam velocity. Thus, the foam quality has a positive effect on the efficiency of the cuttings transport.

4. Numerical modeling for pressure loss

We previously proposed a three-layer numerical model to predict the pressure losses for foam-cuttings mixture flow[9].

However, in the range of this experiment, only two layers were observed in foam-cuttings flow in the horizontal pipe. Therefore, a two-layer model was developed based on our previous three-layer numerical model[9]to predict the pressure loss for the foamcuttings flow. The two-layer model consists of the upper layer, which is only foam flow, and lower layer, which is a moving bed of cuttings and foam. The model was derived from mass and momentum conservation equations. Figure 12 illustrates the two-layer model concept.

Fig.12 Schematic of the two-layer model

4.1Major assumptions

In order to simplify the model analysis, the following assumptions were considered in developing the mathematical model:

(1) The foam flow is isothermal and steady state.

(2) The foam flow is a laminar flow.

(3) Cuttings are uniform in size and spherical with constant diameter and density.

(4) Physical and rheological properties are constant for a given foam quality.

(5) There is no slip between the cuttings and the foam.

4.2Mass balance equations

Under steady state flow conditions, mass balance can be written for the solid phase and the fluid phase as follows, respectively:

whereVis the mean velocity,Cthe mean concentration,Qfthe foam flow rate andAthe crosssectional area. The subscriptsf,mbandtrepresent the upper layer, foam, moving bed layer and total mean, respectively.

4.3Momentum balance equations

Force balances can be written for the two layers according to a free body diagram, as shown in Fig.12. Then the sum of the forces acting on the upper layer is as follows The sum of forces acting on the lower layer is given as follows

whereτfmbthe interfacial shear stress between the upper layer and the moving bed..fτthe upper layer shear stress,Sfthe upper layer perimeter,Sfmbthe perimeter between the moving bed layer and the upper layer andFmbthe force acting on the bottom of the pipe.

The shear stress at the pipe wall is expressed by the following equation

wherefρis the foam density andffis fanning friction factor for the upper layer.

The interfacial shear stress,τfmb, between the upper layer and the moving bed layer is given by

wherebρis the effective density of the moving layer, which is evaluated as

wherecρa(bǔ)ndfρa(bǔ)re the densities of the cuttings particle and foam, respectively.Cmbis assumed to be 0.52 by considering pack in cubic form.

On the basis of the laminar flow for power-law fluid through the pipe, the correlations for the fanning friction factor were chosen. The following equations estimate the fanning friction factor for the upper layer and the interfacial friction factor between the upper layer and the moving bed layer, respectively[9].

whereRegenis the generalized Reynolds number,dcthe cuttings particle diameter andDthe pipe diameter. The generalized Reynolds number of the upper layer was used for bothffandffmb.Fmbis the friction force among the lower layer, the friction between the moving bed layer and the pipe wall, it is expressed by the next equation according to[9]

wherehmbis the moving bed height,kdthe dry coefficient of friction when a moving bed is considered with value of 0.27, andφ..an internal friction angle.

4.4Calculation procedure

A computer program was compiled based on the proposed model by using Matlab. In order to solve the model, the moving bed height (hmb) was initially assumed to determine the geometrical parameters (Af,Amb,At,Sf,Sfmb,θmb) of both layers. Then, the velocities (Vt,Vmb,Vf) were calculated from Eqs.(8), (9) and (10) by assuming the total cuttings concentration (Ct), i.e., for simplicity. Since the velocities in the system were determined, the friction factors in the upper layer and moving bed layer (ff,ffmb) were calculated from Eqs.(16) and (17), and consequently, the shear stresses (fτ,τfbm) were calculated from Eqs.(13) and (14). Then, the friction force (Fmb) was calculated from empirical Eq.(19).

By using the momentum equations (Eqs.(11) and (12)) to calculate the pressure loss (Δp/ΔL) for the upper layer and the moving bed layer, iteration was needed to solve these equations. Hence, the value of the moving bed height (hmb) was modified in each iteration according to the difference between the pressure losses of the upper layer and the moving bed layer until the pressure losses converged. However, to confirm that the difference was satisfied, the calculation was repeated until the errors in the momentum equations (Eqs.(11) and (12)) were smaller than 10?4.

Fig.13 Calculated results of pressure loss for various foam qualities

The solid lines in Figs.8-10 show model results. Obviously, the calculated results agree well with the experimental results. Therefore, it is confirmed that the two-layer numerical model is reasonable. Figure 13 shows the results of predicted pressure loss using the two-layer model.It is clear that foams with higher quality result in higher pressure loss, which is due to the increase of the rheological properties, and that the effects of foam quality on pressure loss is more pronounced in this figure. The simulation is performed for the database described in Table 4.

Table 4 Parameters used in the simulation

5. Conclusions

Experimental and numerical modeling studies have been conducted for single flow and multiphase flow. Firstly, experimental tests were carried out on different foam qualities of 80%, 85% and 90%, and different foam velocities. Then, a two-layer model was developed to predict the pressure loss for foamcuttings flow in a horizontal pipe based on the experimental observation of both single flow (foam) and multiphase flow (foam-cuttings). The conclusions are as follows:

(1) The power-law model is applicable for the foams used in this study. The foam quality has a significant effect on the average bubble size and the circularity of the foam, i.e., average bubble size increases as foam quality increases while the circularity decreases since the gas content increases in the foam.

(2) The pressure losses for both single flow and multiphase (foam-cuttings) flow increase with a rise in foam velocity. Furthermore, higher foam quality results in greater pressure losses, which is due to an increase in foam rheological properties.

(3) The increase of foam velocity decreases the delivered cuttings concentration in the pipe, thus, foam velocity plays a significant role in cuttings transport, i.e., the lower the cuttings concentration, the better cuttings transport efficiency.

(4) It was demonstrated that the higher the foam quality, the better the cuttings transport efficiency, i.e., an increase of the delivered cuttings concentration at the same foam velocity when the foam quality is raised.

(5) The results of the two-layer model are in good agreement with the experimental results. Moreover, the effect of the foam quality on the pressure losses is more pronounced in the predicted results.

Acknowledgement

The authors would like to thank Japan Oil, Gas and Metals National Corporation (JOGMEC) for their partial financial support of this research.

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May 26, 2010, Revised May 19, 2011)

* Biography: AMNA Gumati (1976-), Female, Ph. D.

2011,23(4):431-438

10.1016/S1001-6058(10)60133-3