BH pressure calculation - PetroBAK

1 1 calculation OF BOTTOM-HOLE pressure AND SUBMERSIBLE PUMP INTAKE pressure Ildar K. Shayhutdinov In this article the design procedure of a bottom-hole pressure and intake pressure of submersible pump under the fact sheet of operation of well is offered. A feature of the algorithm consists of using the given standard field values of annulus pressure , dynamic level, flow rate and water cut. In article results of calculations are compared to actual measured pressure at the level of pump intake. It is demonstrated, that the applied methodology provides high accuracy of calculation for required parameters. With artificial lift the important parameters of the oil producing wells are the bottom-hole pressure as well as the intake pressure of the submersible pump. The definition accuracy of these parameters is dictated by the necessity to calculate the potential well production opportunities when selecting the appropriate pumping equipment and optimizing well performance.

2 Finding BH pressure thru actual well performance data can be divided in two stages: а) calculation of pressure distribution in annulus (in tubing) and definition of pressure at the pump run-in depth; б) definition of pressure in the well bore at the interval pump intake BH and estimate of BH pressure . Definition of pressure at the pump intake The hardest bit in finding the BH pressure in the producing well is calculation of pressure at the pump run-in depth using actual well performance data. This article considers methodology for calculation of mentioned pressure based on plotting the curve of pressure distribution in annulus. shows the diagram for producing well performance using submersible pump. As a rule, the majority of producing wells for a more reliable pump performance are equipped with gas separators. With gas separator the bigger part of free gas, liberated from crude, under conditions of pump intake is directed into annulus.

3 With absence of gas separator (gas anchor / bottom hole separator) on the pump intake less quantity of free gas is coming into annulus. Gas phase flow process in annulus can be characterized as gas lift operation at zero feed/delivery mode. Theoretical and practical researches of Krylov [1] were devoted to it. Equation for liquid-gas mixture flow in this case is presented the following way 00aQagdldPгж+= (1) гQ - volumetric gas discharge/flow in the annulus, m3/s; ж - fluid density in the annulus (presupposing that fluid in the annulus is presented by oil), kg/m3; 0a - ratio, considering geometrical dimension of fluid passage, m3/s; g gravity acceleration, m/s2. ),(785,0220dDa = (2) D - production casing ID, m; d - tubing OD, m. Diagram, for calculation of ESP performance with oil-gas mix calculation of pressure distribution in annulus is based on numerical calculation of equation (1) with known pressure at the pump run-in depth снP.

4 At that the iteration procedure is implemented and actual and calculated pressure at dynamic level дP are compared. The algorithm for definition of pressure at the pump run-in depth is the following. 1. The following initial data are put in: стжQ - fluid flow rate under standard conditions, m3/day; в - volume ratio of water in production under standard conditions; затP - annulus pressure , MPa; плТ - formation pressure , K; cL - well depth (vertical), m; снH - pump run-in depth (vertical), m; дh - well dynamic level (vertical), m; вd - tubing ID, m; d - tubing OD, m; D - production casing ID, m; нд - density of degassed oil under standard conditions, kg/m3; нд - dynamic viscosity of degassed oil under standard conditions, mPa s; насP - bubble point pressure at formation temperature, MPa; 0G - GOR of oil in place (gas-oil ratio) under normal conditions, m3/m3; го - density of gas, liberated from crude at flash liberation under normal conditions, kg/m3; мayy, - mole fraction of nitrogen and methane in gas at flash liberation.

5 в - water density under standard conditions, kg/m3. Numerical calculation of equation (1) is presented as following ()LgdDdDQPжг = + )(785,0)(785,02222 (3) P - pressure stepping, Pa; L - length delta, m. 2. pressure stepping taken and the sequential pressure values are identified for various depths. For that the general pressure variation range )(затснPР is divided into several intervals, under condition ),(05,0затснPPP = (4) where затP - annular pressure , Pa; снР - assumed pump intake-level pressure (at first approximation is taken at random), Pa. Accordingly recurrence relation defines the calculated pressures = =NiiснiРPP1 (5) 3. The temperature distribution in producing well bore is defined [2]. With known formation temperature the temperature at the pump s run-in depth ( calculation bottom-up ) is calculated thru equation =вплdhSttht1)( (6) To calculate the temperature distribution above the pump intake it is necessary to know the wellhead temperature ( calculation top-down ): 3 вуdHSttHt =1)( (7) In equations (6) and (7) уплtt, - formation and wellhead temperatures accordingly, оС; h - vertical depth, measured from bottom-hole, m; H- vertical depth, measured from wellhead, m; St - non-dimensional Stanton number.

6 Dependence of Stanton number on mass well flow rate is represented as: ,10202,0)40ln(10763,144 + =жqSt (8) where жq - mass well flow rate, t/day. If wellhead temperature data is not available the calculation of temperature distribution above the pump intake can be done using the equation (6), taking as base for measuring the temperature at the pump-setting depth. In this case the value of wellhead temperature is the required parameter and is defined for снcHLh =. But, in case the well is operated using centrifugal, cavity/screw or diaphragm pump the heating of liquid gas mix passing the submersible motor will not be considered. Thus we are getting the temperature distribution in producing well bore. 4. Using the data of fluid properties we find the physical properties of oil, gas, water or water-oil mix under corresponding thermo dynamic conditions ),(iiTP [1,2].

7 5. The volumetric gas-liquid flow parameters снжQ and снгQ are defined in conditions of pump intake [2]. To define gas volume, going into annulus, we need to set the gas separation ratio. For that we recommend to use the following equations, obtained from theoretical and experimental researches [2]: at the level of flowing lift shoe экжфFwQ007,01+= ; (9) at the sucker-rod pump intake экжшFwQ0005,11+= ; (10) at the electrical submersible pump intake '75,0100зжцfwQ+= , (11) where 0 - free gas separation ratio with zero feed/delivery mode 201 =Dd (12) Here жQ - volumetric fluid flow under conditions of pump intake, m3/s; 0w - relative velocity of gas bubbles, m/s. Relative velocity of gas bubbles depends on the water volume ratio in production: at смwв/ 02,0 5,00= ; смwв/ 17,0 5,00=> ; экF - cross sectional area of production casing, m2; 'зf - area of circular clearance between production casing and submersible pump, m2.

8 After calculation of separation ratio the volume згQ of gas flow going into annulus is defined. In case of well operating with ESP the volume of gas flow is calculated the following way: цснгзгQQ = (13) 4 If the centrifugal gas separator is available at the ESP s intake the separation ratio is varying within range 0,6-0,8 (it is recommended to take it as 7,0 ). If the gas anchor / bottom hole separator is available at the SRP s intake the separation ratio is varying within range 0,4-0,6 (it is recommended to take it as 5,0 ). 6. Values of згiгQQ = and iнж = assuming there is oil-gas mix above the pump intake, values set in equation (3) and the well depth delta 1L is found. Hence, at the depth 11 LHhсн = we are having the pressure РPPсн =1. 7. From equations (6)-(8) the temperature 1T is defined at the depth of 1h. Using equation (5) we calculate the sequential pressure step PPP =12.

9 The following calculations are done for the average pressure between 1P and 2P: 2212РРРср+= and for the temperature 1T. Here you can see that at numerical integration of equation (1) the implemented calculations are one step behind in temperature. But it appears that calculation error with such approximation is very minor. The volume of gas flow going into annulus is calculated for taken iР and iТ: снiiснснiзгiгTPTPzzQQ =, (14) where згQ - volume of gas flow in annulus under pump intake conditions, m3/s; снP, снT - taken pump intake pressure and calculated temperature correspondingly; снz, iz - correspondingly the supercompressibility ratios for the pump intake conditions and set iР and iТ. When calculating the density of three-phase mix in the annulus additional complications occur due to necessity to account for dissolved gas liberating from crude. If we presuppose there is no mass exchange/transfer between the fluid in the annulus and the fluid going to the pump intake, then the presence of free gas phase in the annulus will be determined only by the separation at the pump s intake.

10 Then fluid density ж in equation (3) will be equal to oil density iн at set iР and iТ. In reality there is a constant mass transfer/exchange process between the fluid in the annulus and the fluid going to the pump intake. Accounting for fluid density change in the annulus due to dissolved gas liberating from crude is done using the following correlation: )1( нiгжснiнж +=, (15) where iн - oil density in the annulus fluid at iР and iТ, kg/m3; iгжс - gas liquid mix density from crude and gas liberated from it as part of the annulus fluid at iР and iТ, kg/m3; н - volume ratio of oil degassed at iР and iТ (without consideration for free gas phase liberated in conditions of pump intake). It is easy to see that гвгвгвiнiгжс + =)1( , (16) ()()1),(),(),(),(00 0000 00+ =TPTPTPzGTPGTPTPTPzGTPG iiiiндснмiiмiiiiндснмiiмгв , (17) iiiiснрггв ),( = (18) Here гв - volume ratio of gas, liberated at iР and iТ (without consideration for free gas phase liberated in conditions of pump intake); гв - density of gas additionally liberated from crude at iР and iТ, kg/m3; снмG 0 - specific volume of gas liberated in conditions of pump 5intake, modified to normal conditions, m3/t; ),(0 TPGм - specific volume of gas liberated at iР and iТ, modified to normal conditions, m3/t; снрг.