Prediction of natural gas hydrate formation region in wellbore during deepwater gas well testing*

WANG Zhi-yuan (王志远), SUN Bao-jiang (孙宝江), WANG Xue-rui (王雪瑞), ZHANG Zhen-nan (张振楠)

School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, China,

Email:wangzy1209@126.com

Prediction of natural gas hydrate formation region in wellbore during deepwater gas well testing*

WANG Zhi-yuan (王志远), SUN Bao-jiang (孙宝江), WANG Xue-rui (王雪瑞), ZHANG Zhen-nan (张振楠)

School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, China,

Email:wangzy1209@126.com

(Received November 1, 2013, Revised February 26, 2014)

Wellbore temperature field equations are established with considerations of the enthalpy changes of the natural gas during the deep-water gas well testing. A prediction method for the natural gas hydrate formation region during the deep-water gas well testing is proposed, which combines the wellbore temperature field equations, the phase equilibrium conditions of the natural gas hydrate formation and the calculation methods for the pressure field. Through the sensitivity analysis of the parameters that affect the hydrate formation region, it can be concluded that during the deep-water gas well testing, with the reduction of the gas production rate and the decrease of the geothermal gradient, along with the increase of the depth of water, the hydrate formation region in the wellbore enlarges, the hydrate formation regions differ with different component contents of natural gases, as compared with the pure methane gas, with the increase of ethane and propane, the hydrate formation region expands, the admixture of inhibitors, the type and the concentrations of which can be optimized through the method proposed in the paper, will reduce the hydrate formation region, the throttling effect will lead to the abrupt changes of temperature and pressure, which results in a variation of the hydrate formation region, if the throttling occurs in the shallow part of the wellbore, the temperature will drop too much, which enlarges the hydrate formation region, otherwise, if the throttling occurs in the deep part of the wellbore, the hydrate formation region will be reduced due to the decrease of the pressure.

deep-water gas well testing, temperature and pressure fields, hydrate, throttling effect

Introduction

During the deep-water gas well testing, there is normally a certain amount of water in the gas produced, and it is likely to form the natural gas hydrate in the environment of low temperature and high pressure in the wellbore. After the hydrate is formed, it will occlude the circulation channel of the natural gas, resulting in serious accidents[1-3]. Therefore, during the deep-water gas well testing, it is important to pay attention to the formation of the hydrate and to take measures for the prevention of the hydrate forming.

However, during the deep-water gas well testing, besides the formation phase state of the hydrate, the formation region is also an important factor in the design of the injection position and the determination of the required concentrations of the inhibitors. Wang et al.[10,11]predicted the formation region of the natural gas hydrate during the deep-water drilling and the well control process. But so far, the prediction of the hydrate formation region during the deep-water well testing has not been much studied. Three aspects are involved in the prediction of the hydrate formation region in the wellbore during the deep-water well testing: the temperature field distribution, the pressure field distribution, and the phase state conditions of the natural gas hydrate formation. In this paper, considering the throttling effect (Joule-Thomson effect) in the testing pipe of variable diameter, as well as the work done by the volume variation during the gas flowing, using the concept of enthalpy, the temperature field equation of the wellbore during the deep-water gas well testing is established. A method for the prediction of the natural gas hydrate formation region during the deep-water gas well testing is proposed, combining the phase state conditions of the natural gas hydrate formation and the calculation of the pressure field. Furthermore, a sensitivity analysis of the parameters that affect the hydrate formation region is made in this paper.

1. Models of natural gas hydrate formation region prediction

1.1 Temperature field equations

The solutions for the temperature and the pressure of the wellbore are the basis of a precise prediction of the natural gas hydrate formation region. Ramey (1962) established a temperature prediction model for incompressible fluid or ideal gas, which has a far-reaching influence on solving the wellbore temperature field, and in which the wellbore temperature and the formation temperature are combined, and the concept of the total heat transfer coefficient is introduced. Willhite (1967) proposed a calculation method for the total heat transfer coefficient, which found a wide application. Wu and Pruess (1990) obtained an analytical solution of the temperature field model of the wellbore based on the consideration of the thermal parameters of various formations. Romero (1998) put forward a method for the temperature prediction in deepwater drilling. Hasan et al.[12-14]carried out an enormous amount of work in a series of papers on the temperature field calculation of the wellbore, and the methods for the wellbore temperature calculation were well accepted and with a good accuracy.

During the deep-water gas well testing, one may find throttling problems in the testing pipe of variable diameter, due to the high flowing velocity of gas. Because of the compressibility of gas, the work done by the volume variation will lead to changes of enthalpy, therefore, this paper takes up the issue of the enthalpy changes, to deal with the throttling problems as well as the work done by the volume variation, and sets up the temperature field equation of the wellbore during the deep-water gas well testing.

In the temperature field calculation model, the following assumptions are made.

(1) Gas is in a one-dimensional steady flow in the wellbore.

(2) The heat transfer is steady in the wellbore when the gas production rate is stable during the deepwater gas well testing.

(3) The heat loss in the direction of the wellbore can be ignored, only the radial heat loss is considered.

(4) The relationship between the formation temperature and the depth is linear, and this ratio coefficient (the temperature gradient) is known.

Figure 1 shows the heat transfer in the wellbore. According to the above assumptions, the enthalpy change is considered when the gas flows, to establish the temperature equation as

where H is the enthalpy of the gas,gis the acceleration of gravity,θis the included angle between the wellbore axis and the horizontal direction,v is the gas velocity,z is the well depth,w is the mass flow, rtois the outer radius of the pipe,rtiis the inner radius of the pipe,Utois the overall heat transfer coefficient,keis the formation heat conduction coefficient,TDis the dimensionless temperature (Kabir et al. 1996),Teiis the formation temperature,Tfis the temperature in the pipe,ρis the density,λis the friction coefficient, dimensionless.

Utodepends on the thermal resistance from the fluid in the pipe to the surrounding formation, including the thermal resistance of the forced convection heat transfer of the inner wall, the thermal resistance of the pipe wall, the convection and radiation heat transfer resistance of the annular liquid or gas, along with the thermal resistance of the casing wall as well as the cement ring. It is expressed as (Willhite 1967)

where htois the heat convection coefficient,ktis the heat conduction coefficient of the pipe,hcis the heat transfer coefficient of the annulus convection,hris the heat transfer coefficient of the annulus radiation, rcois the outer radius of the casing,rciis the inner radius of the casing,kcasis the heat conduction coefficient of the casing,rwbis the external diameter of the wellbore,kcemis the heat conduction coefficient of the cement ring.

Equation (1) is for the formation environment below the mud line, however, in the sea water environment, the process of the heat loss is different from that in the formation, therefore, the overall heat transfer coefficient in the sea water is different from that in the formation, and the second item on the left side of Equation (1) should be adjusted correspondingly, and the expression of the temperature field should be rewritten as

where rrois the external diameter of the riser,Urois the overall heat transfer coefficient with the outer surface of the riser as the datum plane,Tseais the temperature of the sea water.

The first term on the left side of Eq.(1) is the overall energy change of the gas, which includes four parts: the enthalpy, the kinetic energy, the potential energy, and the work done by the external force (i.e., term of friction), the second term is the heat exchange between the fluids in and outside the wellbore. The heat exchange between the gas in the wellbore and the surrounding environment is equal to the overall energy change, hence, the sum of these two terms is zero.

whereV is the specific volume,T0,P0are the temperature and the pressure at the triple point,Ti,Piare the present temperature and pressure,Cpis the specific heat capacity,βis the thermal expansion coefficient,P is the pressure of the gas in the pipe.

The first term on the right side of Eq.(4) is the internal energy, which mainly represents the effect of the temperature change during the flow movement of the natural gas on the enthalpy of the system, the second term is the flow work, which mainly represents the effects of the pressure and volume changes on the enthalpy of the system during the flow movement of the natural gas. However, when the fluid in the wellbore is liquid, the effect of the fluid volume change on the enthalpy is usually ignored.

Equation (4) is rewritten in the differential form, as follows

The enthalpy of the gas changes all the time in the whole wellbore. While at the position where the internal diameter of the testing pipe varies, the gas flow is regarded as an adiabatic process within the relatively shorter distance of the variable diameter before and after the variation point. Therefore, the enthalpy values before and after the throttling position are equal, that is to say,dH=0.The expression of the adiabatic throttle coefficient can be derived from Eq.(5) as

where µjis the adiabatic throttle coefficient (Joule-Thomson coefficient).

Another expression of the enthalpy can be derived from Eqs.(5) and (6)

When the expression of the enthalpy in Eq.(7) is substituted into Eq.(1) and the friction term λρv2/ 4rtiin Eq.(1) is ignored, the wellbore temperature field equation is obtained, which is the same as the equation established by Hasan and Kabir (1994).

1.2 Pressure field equations

The pressure is obtained by solving simultaneously the steady equations of the gas, the expression of the gas flow velocity, and the expression of the gas density

where qscis the gas flow in the standard state,Zgis the gas compressibility factor,rgis the relative density.

1.3 Equations for prediction of natural gas hydrate phase state

To predict the formation region of the natural gas hydrate, the formation conditions of the hydrate should be known, which include the temperature and the pressure in the testing pipe when the hydrate is being formed. The hydrate is formed when the pressure at a certain position in the testing pipe is higher than that of the hydrate formation and the temperature is lower than that of the hydrate formation. A chemical balance is reached between the water phase, the gas phase, and the lattice in the hydrate lattice system. The equations for the phase equilibrium are obtained based on the thermodynamic equilibrium theory (Van delwalls and Platteeuw (1959)).

where Δµ0is the difference between the chemical potential in the unoccupied lattice and the pure water at the reference state,Ris the gas constant,THis the hydrate-formation temperature,ΔH0is the difference between the enthalpy in the unoccupied lattice and the pure water,ΔCKis the difference between the heat capacity in the unoccupied lattice and the pure water,pHis the hydrate-formation pressure, ΔVis the difference between the molar volume in the unoccupied lattice and the pure water,fwis the fugacity of the water in the solution,fwris the fugacity of the water at the reference state (TH,pH),lis the total number of hydrate species,Miis the ratio of the number of cavities of typei to the number of water molecules in the hydrate phase,L is the total number of gas types,θijis the fraction of the cavities of type i occupied by a gas molecule of type j,xwis the mole fraction of the water,ywis the water activity coefficient in the solution.

1.4 Model verification

The prediction accuracy of the hydrate formation region in the wellbore during the deep-water gas well testing depends on the prediction accuracy of the temperature and pressure fields as well as the hydrate phase state. In this paper, Eqs.(9) and (10) are used forthe hydrate phase state prediction and these two equations have been verified by experiments. Now our focus is on the accuracy of the temperature and the pressure in the wellbore.

The temperature and pressure fields of the gas wells in the South Sea of China during the gas testing are calculated, and the results are compared with the measured values, and it is shown that the agreement is good. Take one of the wells as an example. The basic parameters of the well are shown in Table 1, and the comparisons of the calculation and measured values are shown in Table 2.

2. Sensitivity analysis of hydrate formation region in the wellbore during deep-water gas well testing

According to the calculation methods of the wellbore temperature and pressure fields as well as the prediction methods of the hydrate phase state, a sensitivity analysis of the factors affecting the hydrate formation region is made through a software developed for the prediction of the hydrate formation region in the wellbore during deep-water gas well testing.

It is a well in the south sea, and the well structure as well as the data related to the testing pipe is as shown in Fig.2.

2.1 The influence of gas output on hydrate formation region

Figure 3 shows the prediction of the hydrate formation region in the wellbore under the conditions given by Table 3, and different gas production rates (Qg). Thex axis represents temperature(T)and they axis represents depth (D). The area surrounded by the hydrate phase curve and the temperature curve is the hydrate formation region. The temperature gradually decreases from the well bottom to the wellhead, whenQgis low, the temperature in the wellbore drops rapidly due to the complete heat exchange between the slowly flowing fluid and the surrounding environment, on the other hand, the larger theQgis, the less slowly the temperature drops, and the temperature in the wellhead would rise with the increase ofQg.

With the increase of Qg, the temperature at every position in the wellbore rises gradually. The increase of the temperature is unfavorable for the hydrate formation, therefore, for a same well, the hydrate formation region is smaller with a higherQg. Under these conditions in this case, the hydrate formation region is 0 m-1 675 m whenQgis 5×104m3/d, the hydrate formation region is 0 m-1 335 m whenQgis 105m3/d, and there is no longer hydrate being formed, when the output is 6×105m3/d. Hence, the hydrate formation should be paid more attention to during the testing process of lowQg.

2.2 Effect of gas components on hydrate formation region

Figure 4 shows the prediction of the hydrate formation region under the conditions given by Table 3 and various gas components, as shown in Fig.5. When the gas is pure methane (100% Methane), the hydrate formation region is 0 m-612 m, when the gas contains 10% ethane (90% Methane+10% Ethane), the hydrate formation region is 0 m-845 m, when the gas contains 20% ethane (80% Methane+20% Ethane), the hydrate formation region is expanded to 0 m-899 m. Therefore, the hydrate formation region will expand when the gas generated contains ethane, and the higher the percenttage of ethane is contained, the larger the hydrate formation region will be. Likewise, when the gas contains propane, the hydrate formation region will expand. When the gas contains ethane or propane with the same mole fraction, the hydrate formation region is larger for the case of propane, that is to say, it is easier for propane to produce hydrate than for ethane. As a matter of fact, with the increase of the hydrocarbon of a large molecular weight in the generated gas, the hydrate formation region will increase gradually.

2.3 Influence of geothermal gradient on hydrate formation region

Figure 5 shows the prediction of the hydrate formation region under the conditions given by Table 3 and various geothermal gradients, in which the dotted line is the curve for the hydrate phase state, and the rests are the wellbore temperature field curves with various geothermal gradients (1.0oC/100 m, 1.5oC/ 100 m, 2.0oC/100 m, 2.5oC/100 m and 3.0oC/100 m).

Under these conditions, the hydrate formation region is 0 m-2 100 m when the geothermal gradient is 1.0oC/100 m, when the geothermal gradient is 1.5oC/100 m, the hydrate formation region is reduced to 0 m-1 010 m, and there is no longer hydrate formation produced if the geothermal gradient is higher than 2.0oC/100 m. With the increase of the geothermal gradient, the temperature difference between the well bottom and the wellhead increases as well, and the hydrate formation region decreases gradually, this is because the temperature of the formation rises, which makes the temperature of the wellbore rise as well, and it is unfavorable for the hydrate formation. Hence, during the deep-water gas well testing, if the geothermal gradient is small, the formation of the hydrate should be paid more attention to.

2.4 Influence of water depth on hydrate formation region

Figure 6 shows the prediction of the hydrate formation region under the conditions given by Table 3 and various sea water depths, in which the double point lines are the curves for the hydrate phase state, and the rests are the curves for the wellbore temperature with different sea water depths (250 m, 500 m, 750 m and 1 000 m).

Under these conditions, when the water depth is 1 000 m, the hydrate formation region is 0 m-1 224 m, when the water depth is 750 m, the hydrate formation region is 0 m-623 m, and there is no hydrate formed with the water depth of 500 m and 250 m. With the increase of the sea water depth, the hydrate formation region expands gradually. This is because with the increase of the water depth, the temperature near the submarine mud line becomes low, in the meantime, the cooling of the sea water in the wellbore takes a longer time, which makes the temperature in the wellbore drop, which is favorable for the hydrate formation. Therefore, with the increase of the water depth, the hydrate formation becomes more active.

2.5 Effect of inhibitors on hydrate formation region

The effect of different inhibitors on the hydrate formation region is analyzed when the gas production rate is 2×105m3/d, and other data are shown in Table 3. Figure 7 and Fig.8 present the predictions of the hydrate formation region with different concentrations of NaCl or methanol, respectively. With the increase of the concentration for NaCl or methanol, the hydrate formation region reduces gradually, and there is no more hydrate formed in the wellbore when the concentration of NaCl and methanol reduces under 20% and 15%, respectively.

Figure 9 and Fig.10 demonstrate the predictions of the hydrate formation region with respect to various salt and alcohol inhibitors. As shown in Fig.9, withthe same mass concentration, the hydrate formation region is the smallest for the inhibitor of NaCl, followed by that for the inhibitor of KCl, and that for the inhibitor of CaCl2is the largest, which demonstrates that among these three common salt inhibitors, the effect of NaCl is the best. As shown in Fig.10, the hydrate formation region for the inhibitor of glycol is smaller than that for the inhibitor of methanol with a small difference. With the methodology in this paper, the types and the concentrations of hydrate inhibitors during the deep-water gas well testing can be chosen.

2.6 Influence of throttling effect on hydrate formation region

During the deep-water gas well testing, the throttling can be observed in the testing pipe of variable diameter, and it is shown that the pressure and the temperature at positions where the diameter varies change abruptly, which can lead to a change of the hydrate formation region in the wellbore.

Figures 11 and Fig.12 show the hydrate formation region under the conditions of Table 3, with different depths of throttling devices, and diameter ratios of 15:1, 14:1, 12:1 and 1:1,. When the gas flows upwards, the diameter ratio means the ratio between the inner diameter of the upstream at the variable diameter position and that of the downstream.

At the same depth, with the increase of the variable diameter ratio, the curves for the temperature in the wellbore and for the hydrate phase state both move to the left, which demonstrates that the temperature and pressure values in the wellbore decrease because of the throttling effect. However, the hydrate formation region is reduced when the throttle devices with the same variable diameter ratio are set at the deep position near the wellbore bottom, and the hydrate formation region will expand otherwise.

As shown in Fig.11, when the down hole throttling device is located at the depth of 768m, with the variable diameter ratio of 1:1 (which means not variable), the hydrate formation region is 0 m-610 m, when the variable diameter ratio is 15:1, the hydrate formation region in the wellbore expands to 0 m-768 m. As shown in Fig.12, when the down hole throttling device is located at the depth of 2 500 m, with the variable diameter ratio of 1:1, the hydrate formation region is also 0 m-610 m, however, when the variable diameter ratio is 15:1, the wellbore will not create the conditions for the formation of the hydrate.

Therefore, the hydrate formation region is expanded when the variable diameter of the testing pipe is at the shallow position; otherwise, the hydrate formation region is reduced,. This phenomenon can be used to prevent the formation of the hydrate. The variable diameter at a shallow position of the testing pipe should be avoided during the deep-water gas well testing.

3. Conclusions

(1) A prediction method for the natural gas hydrate formation region, during the deep-water gas well testing is proposed, which combines the temperature field equations established with considerations of the enthalpy changes of the natural gas, the phase state conditions for the natural gas hydrate formation as well as the calculation equation for the pressure field.

(2) With the increase of the gas production rate, the hydrate formation region decreases gradually. The hydrate formation region disappears when the gas production rate is over 6×105m3/d under the condition described in this paper.

(3) Different components of the natural gas have different abilities to form the hydrate, if other components with large molecular weight are mixed with methane, it will be much easier to generate the hydrate.

(4) Different inhibitors have different inhibitory effects, and the higher the concentration of the inhibitor is, the better effect it will produce. In a practical well testing, the types and the concentration of hydrate inhibitors can be determined by the method proposed in this paper.

(5) The hydrate formation in deep water, especially, in depth over 600 m, should be a very concernedissue for the reason that the hydrate formation region enlarges with the increase of the water depth.

(6) The throttling effect will lead to abrupt changes of temperature and pressure. If the throttling occurs at the shallow part of the wellbore, the temperature would drop dramatically and the hydrate formation region will be enlarged. On the contrary, if the throttling occurs at the deep part of the wellbore, the hydrate formation region is reduced because of the reduced pressure due to the throttling.

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10.1016/S1001-6058(14)60064-0

* Project supported by the National Natural Science Foundation of China (Grant Nos. 51104172, U1262202), the Program for Changjiang Scholars and Innovative Research Team in University (Grant No. IRT1086).

Biography: WANG Zhi-yuan (1981-), Male, Ph. D.,

Associate Professor