Prediction of Well Bore Temperatures during Ultra-Deep Drilling

Transcription

1 Prediction o Well Bore Temperatures during Ultra-Deep Drilling Fanhe Meng, Aiguo Yao*, Shuwei Dong Faculty o Engineering China University o Geosciences Wuhan, Hubei, , China Abstract In order to carry out a series o key basic researches, a scientiic ultra-deep drilling plan is being undertaken in China. Wellbore temperature is one o the key actors during the drilling process. In this paper, we establish a two-dimensional transient numerical model to predict the ultra-deep well bore temperature distributions during circulation and shut-in stages. The simulation results indicate that the cooling eort o drilling luid circulation is very obvious, especially during the inception phase. Drilling luid viscosity has great inluence on the temperature distributions during circulation stage: the lower the viscosity, the higher the bottom hole temperature. Drilling luid displacement and inlet temperature have little eect on the bottom hole temperature. During the shut-in stage, the well bore temperature recovery is a slow process. Keywords - Scientiic drilling; Ultra-deep well; Transient temperature; Finite dierence method I. INTRODUCTION Continental scientiic drilling is a direct technique to reveal the composition and structure o the continental crust, veriy the results o geophysical explorations. It can also provide inormation on the Earth s natural resources, the global climate and environmental changes and the processes causing earthquakes. It is acknowledged as a telescope entering the interior o the Earth [1]. Thereore, many countries have carried out the deep exploration program since 1970s [2]. In the ormer Soviet Union, 11 ultra deep wells were drilled and the amous one m depth Kola SG 3 ultra deep well, which world's deepest one o all time. KTB-which stands or German Continental Deep Drilling Program completed a m pilot hole and a 9101 m main hole in 1990s, through which lots o achievements have been obtained [3]. In China, building on the success o the Chinese Continental Scientiic Drilling Project (CCSD), a national scientiic program titled as Deep Exploration Technology and Experimentation (ab. as SinoProbe) has been implemented since As part o the project, ultra-deep drilling technology (>10000 m) will be developed based on pilot drilling and experimental work. During the ultra-deep drilling process, the downhole high-temperature problem is not inevitable. With a geothermal gradient o 3 /100 m, the m downhole temperature can reach about 300. But KTB s experience shows that drilling luid circulation can strongly inluence the wellbore temperatures [4]. However, these dynamic temperature distributions are very important since they can be used in the ollowing activities: drilling luid rheology, cementing program design, wellbore and casing stability evaluation, downhole tool selection, etc. Thereore, how to predict the transient wellbore temperatures during the drilling process becomes a key problem. In 1941, Farris developed many charts or depicting the bottomhole temperature during cementing periods [5]. Then, based on the ield measurements o Farris, the American Petroleum Institute (API) developed new empirical correlations or estimating circulating temperatures or cementing. But some research has observed that the API method always overestimates circulating luid temperatures or deep wells [6]. Besides, this method is originally developed or the oil drilling industry, which diers notably rom scientiic drilling technology. To solve this problem, two approaches have been emerged to estimate the wellbore temperatures: analytical and numerical. The classical analytical method was developed by Ramey [7], which assumed that heat transer in the well bore is steady state, while heat transer in the ormation is unsteady radial conduction. In general, this method is applicable to system geometries o lesser complexity, such as the case o a single casing string and single temperature gradient. While the numerical method can tackle more complex problems which involves solving the governing heat transer equations numerically using a inite dierence scheme. Raymond proposed the irst numerical model or predicting wellbore temperatures during drilling luid or cement circulation [8]. Keller et al. extended Raymond s method. In their model, the presence o multiple casing strings and energy sources were included [9]. Wooley developed the irst transient computer program-geotemp or prediction o bottomhole temperature [10]. Beirute developed a simulator or estimation o temperatures during circulation and shut-in stage [11]. The altemating-direction-implicit method was used to obtain the solutions. The comparison o the simulation results with ield data provided good agreement. GARCIA et al. developed the program TEMLOPI v1.0 or predicting temperatures in and around geothermal wells [12]. And then they proposed the method o estimating wellbore temperatures under lost circulation conditions [13]. Osisanya and Harris established a two-dimensional and ully transient model to prediction o wellbore temperatures and the solution was obtained by Crank-Nicolson method [14]. With the eatures o accurate, reliable and economic, numerical simulators are considered to be the best method to predict the transient temperature distributions in scientiic ultra-deep wells. However, seldom research has been DOI /IJSSST.a ISSN: x online, print

2 emphasized in this area beore. The transient heat transer model need to be established in order to predict wellbore temperatures during the whole drilling process. II. PHYSICAL MODEL During the scientiic drilling process, the stage can be mainly divided into two ones: circulation and shut-in. The circulation stage can be basically described in three main phases: drilling luid lows down the drill string, through the bit, and up to the surace (Fig. 1) Fig. (1). Physical Model o Drilling Fluid Circulation In dierent stages and phases, the downhole temperatures depend on the dierent heat transer processes. In general, the ormation temperature increases with depth. Thereore, the temperature o drilling luid always increases during the lowing down process. The heated drilling luid lows up to the surace, and exchanges heat with the surrounding materials and ormation. This system acts very much like a counter-low heat exchanger. However, during the shut-in stage, the wellbore system (luids, casing, cement and ormation) gradually reaches the thermal equilibrium mainly by heat conduction. III. FUNDAMENTAL ASSUMPTIONS To derive the energy equations or describing the overall thermal behaviour o the wellbore system, certain assumptions need to be considered. 1. The scientiic drilling is almost vertical. And it is assumed to be an axisymmetric problem. 2. Drilling luid is incompressible and no luid losses to the ormation. 3. Heat transer or the drilling luid is only by convection, since axial and radial conduction has little eect on wellbore temperature distributions [15]. 4. Ignoring the inluence o adaptors on the wellbore geometry. 5. No phase change occurs. IV. MODEL DEVELOPMENT As the dierent heat transer mechanisms, the circulation and shut-in stages need to be treated dierently. With respect to the overall circulation process, ive heat transer regions can be identiied: (a) the drill pipe; (b) the drill pipe wall; (c) the annulus; (d) the wellbore wall; and (e) the surrounding ormation. For shut-in stage, only axial and radial conduction was considered. Based on the energy conservation law, a set o governing equations were developed. A. Circulation Stage 1. Drill Pipe Model For a control volume inside the pipe, heat lows in by convective o the luid column, convection with the inner drill pipe wall and the luid raction energy source. Thereore, the model can be expressed as equation (1), where the right-hand term represents the accumulation o energy. T p 2 Tp Q p mqcm 2 r pihpi ( Tw Tp ) mcm rpi (1) where Q energy source term o unit length inside p m and cm are the density and heat capacity o the drill pipe; drilling luid, respectively; q low rate; Tp and Tw are the temperatures o inside drill pipe luid and drill pipe wall, respectively; z length in wellbore direction; rpi inner radius o drill pipe; hpi convection coeicient o inside drill pipe wall; and t time. 2. Drill Pipe Wall Model The heat transer model o drill pipe wall can be expressed as equation (2). The irst let term respects the vertical conduction in the drill pipe. And the last two ones respect the convection between the drill pipe and the luid inside and outside the string. 2 T 2rpohpo 2r h w pi pi w ( Ta Tw ) ( Tw Tp ) 2 rpo rpi rpo rpi (2) Tw wcw where w, w and cw are the thermal conductivity, density and heat capacity o drill pipe, respectively; rpo outer radius o drill pipe; hpo convection coeicient o outer drill pipe wall; and Ta temperature o annulus luid. 3. Annular Model To calculate the temperature distribution o annulus, the main heat transer mechanisms need to be considered, including: (a) heat generated by luid raction and drill string rotation; (b) heat convection up the annulus; (c) radial convection between the annulus luid and the surrounding drill string and ormation. Thereore, the model is expressed as ollows. Ta Qa mqcm 2 ra hb ( Tb Ta ) 2 r pohpo ( Ta Tw ) (3) Ta mcm ( ra rpo ) where Qa energy source term o unit length inside the annulus; ra radius o wellbore wall; hb DOI /IJSSST.a ISSN: x online, print

3 convection coeicient o wellbore wall; and Tb temperature o the interace between annulus and borehole wall. 4. Wellbore Wall Model The axial conduction and internal energy change can be neglected or a suiciently small control volume o wellbore wall. Based on the energy balance, heat transers by radial conduction and convection should be equal. Thereore, the ollowing equation is derived. T ( ) r r hb[ T ( ra, z) Ta ] a r (4) where thermal conductivity o ormation; r is the radial distance rom wellbore; and T temperature o ormation. 5. Formation Model According to casing program, the ormation region could be casing strings, cement or rock ormations. The twodimensional heat conduction model in cylindrical coordinate system can be used to calculate the temperature distributions in this region. The model is written as ollows. T T 1 T c T r r r (5) where and c are the density and heat capacity o ormation, respectively. B. Shut-in Stage For shut-in conditions, the two-dimensional heat conduction model in cylindrical coordinates can also be adopted during the thermal recovery process. The temperature distributions are governed by the equation. Tx Tx 1 Tx xcx Tx r r r x (6) where the subscript x represents the dierent regions. C. Initial and Boundary Conditions To solve the above governing equations, the proper initial and boundary conditions should be derived. For circulation stage, the undisturbed static temperatures can be used as the initial condition. In mathematical language they are expressed as: Tx ( z, t 0) Gz (7) where Ts surace ormation temperature; and G is the geothermal gradient. As the inlet luid temperature can be measured, the boundary condition or the drill luid can be written as equation (8). Tp ( z 0, t) T in (8) where Tin drilling luid inlet temperature. The boundary conditions or the ormation can be described as: the temperatures are constant at ormation surace, ar away rom the wellbore, and a suicient distance below the wellbore. T ( z 0, r, t) T ( z, r, t) Gz (9) T ( z H, r, t) G( H ) where H total vertical depth o the well. For shut-in stage, the initial temperature distributions decided by the circulation history. The boundary condition equation (9) still applies in this condition V. NUMERICAL SOLUTION For numerically solving the heat transer model, the twodimensional space was divided into inite vertical and radial elements. For each element, the governing equations are written. And then these partial dierential equations were solved by the inite dierence method (FDM). The implicit orm was used since it is unconditionally stable. Although a serious o algebraic equations can be obtained ater the model discretized, a single generalized vector orm can be obtained or equations o each region, expressed as: n n n Ai, jt i 1, j Bi,jT i, j Ci,jT i 1, j Di,j (10) where subscripts i and j correspond to the depth coordinate and radial coordinate respectively; superscript n represents the time level; A, B, C are the coeicient matrixs; and D matrix o the constants. Then a Matlab program was established to calculate these tridiagonal matrix systems. With this simulator, the next time level temperatures o each region can be calculated in sequence using the previous iteration results, until the error range can be accepted. VI. CASE STUDY A. Simulation Parameters In order to validate the proposed model and evaluate the eect o operating parameters on temperature distributions, a 7000m scientiic deep well was simulated. The casing program is shown in Fig. (1), and the geometry data is detailed in Table 1. The undisturbed bottom-hole temperature is 200. The volume low rate o drilling luid was assumed constant at 0.03 m3/s, with a surace inlet temperature o 25. The water-based drilling luid viscosity is 0.03 Pa s. The required thermos-physical properties are detailed in Table 2. DOI /IJSSST.a ISSN: x online, print

4 TABLE 1. CASING PROGRAM Parameter First cement First casing Second casing Third cement Third casing Outer diameter (mm) Inner diameter (mm) Depth (m) 0~300 0~300 0~ ~6000 0~6000 Component Density (Kg/m 3 ) TABLE 2. THERMOPHYSICAL PROPERTIES Speciic heat hapacity (J/(kg )) Thermal conductivity (W/(m )) Drilling luid Casing Cement Formation B. Results The eect o circulation time on the bottomhole luid temperature is shown in Fig. (2). As can be seen, drilling luid circulation has a great inluence on the wellbore temperatures, especially during the 2 hours ater circulation starting, just as the KTB s experience. The bottomhole luid temperature drops rom 200 to 135 quickly. However, with the circulation time increases, the inluence becomes gradually weakened. Ater 4 hours o circulation, the bottomhole luid temperature almost no longer changes. This phenomenon has great signiicance or the operation o downhole instruments during the scientiic ultra-deep drilling process. In this case, the instruments can be lowered ater a period o circulation or keep circulating during lowered to ensure the saety. 10 hours o shut-in, the bottomhole luid temperature gradually increases rom 128 to 135. Fig. (3). Eect o Shut-in Time on The Bottomhole Fluid Temperature Fig. (2). Eect o Circulation Time on The Bottomhole Fluid Temperature As logging and cementing operated soon ater the circulation stopped, the thermal recovery during shut-in stage is also very important. Assumed that the initial condition o shut-in stage temperature distribution ater 10 hours o circulation, the temperature recovery o the bottomhole luid is shown in Fig. (3). The thermal recovery is a slow process because conduction only way or heat transer and the thermal conductivity o ormation is relatively small. Ater To ind out the importance o drilling luid viscosity, simulation work was conducted with only viscosity was allowed to change while all others held constant. The result is shown in Fig. (4). By data analysis, maximum dierences o about 21.6 are ound at the bottom o the well ater 10 hours o circulation. These temperature dierences indicate that the viscosity o drilling luid strongly inluences the wellbore temperature distributions. These dierences are directly due to the convection coeicient which is a unction o viscosity. Generally, the luid viscosity decreases, the heat transer coeicient increases. Under the circulation conditions, the higher convective coeicient tends to increase the heat exchange between the luid and the ormation. In addition, the inluence o downhole conditions need to be considered i the drilling luid viscosity changes with temperature or pressure greatly. DOI /IJSSST.a ISSN: x online, print

5 Fig. (4). Eect o Drilling Fluid Viscosity on The Wellbore Temperature Field The eect o drilling luid displacement on the bottomhole luid temperature is shown in Fig. (5). During the initial phase, the higher luid displacement leads to the lower bottomhole temperature. This is mainly duo to cooling eect o luid circulation. More heat can be transerred orm downhole to surace i the luid displacement is higher. Ater a period o circulation, the bottomhole luid temperature begins to stabilize and the inluence o displacement becomes weakened. During the scientiic ultra-deep drilling process, the eect o higher luid displacement can be used to cool down the bottomhole, but the working conditions, such as pump perormance and borehole wall stability, should also be considered. Fig. (5). Eect o Drilling Fluid Displacement on The Bottomhole Fluid Temperature The eect o drilling luid inlet temperature on the wellbore temperature ield is shown in Fig. (6). As can be seen, the dierences o these two temperature proiles get smaller with the depth increase ater 10 hours o circulation. Moreover, the lower part o these temperature proiles are almost the same. Thereore, the cooling eect o inlet luid temperature on bottomhole is not obvious during the scientiic ultra-deep drilling process. Fig. (6). Eect o Drilling Fluid Inlet Temperature on The Wellbore Temperature Field VII. CONCLUSIONS A two-dimensional and ully transient numerical model has been established to predict the wellbore temperatures during the whole scientiic ultra-deep drilling process. Based on the inite dierence method, a simulator has been developed. By simulating analysis, the ollowing conclusions can be drawn. 1. The drilling luid circulation strongly aects the wellbore temperature distributions. The cooling eect o circulation is obvious during the inception phase. Ater a period o circulation, the bottomhole luid temperature almost no longer changes. 2. The disturbed wellbore temperature distributions caused by circulation can not be easily recovered. The thermal recovery is a slow process during shut-in stage. 3. The drilling luid viscosity has a signiicant eect upon the bottomhole wellbore temperature under circulation conditions. The lower the viscosity, the higher the bottomhole temperature. 4. The drilling luid displacement can aect the temperature distributions only at the inception phase o circulation. The higher displacement has a aster cooling eect at the bottom. 5. The inlet drilling luid temperature partially aects the wellbore temperature proiles. And the upper part is more easily inluenced than others. REFERENCES [1] J. S. Yang, Z. Q. Xu, and Z. L. Tang, Continental scientiic drilling: site selection and pilot holes, Acta. Geoscientica. Sin., vol. 32, pp , [2] S. W. Dong, T. D. Li, R. Gao, and Q. T. Lv, International progress in probing the earth's lithosphere and deep interior: a review, Acta. Geological. Sin., vol. 84, No. 6, pp , [3] R. Emmermann and J. Lauterjung, The German continental deep drilling program KTB: overview and major results, J. Geophys. Res., vol. 102, No. B8, pp , [4] H. Wilhelm, Undisturbed temperature in the main drillhole o the German Continental Deep Drilling Program predicted rom temperature logs recorded ater shut-in, Geothermics, vol. 29, No. 3, pp , [5] R. F. Farris, A practical evaluation o cements or oil wells, Drilling and Production Practice, DOI /IJSSST.a ISSN: x online, print

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