Revised Bean Performance Equation for East Baghdad Oil Wells

Abstract

Summary A comparison of the existing correlations for the determination of multiphase fluid-flow performance through a wellhead choke is made. The comparison is based on statistical analysis with production data from 155 well tests, 20 of which are from the East Baghdad oil field. The comparison indicates the relative strengths and weaknesses of each correlation and should aid in the selection of a satisfactory correlation for different applications. ‘No one method is found to be most accurate in all ranges of flow variables. The best overall comparison, however, is obtained with the Gilbert correlation that predicted measured production rates within an average error of 6.19%. This correlation is then revised in two forms to fit the observed data from the East Baghdad oil wells best. Introduction Various developments have been published that present theories and correlations for describing simultaneous liquid and gas flow through an orifice.1–5 Gilbert's1 approach, Poettmann and Beck's4 adaptation of Ros' equation, and Ashford's3 approach have been used by more petroleum engineers than any other approach. The purposes of this paper areto define the range of applicability of these techniques andto find a technique that would best fit the observed production data from the East Baghdad oil field. Therefore, it was necessary to use some published production data3,4 and other production data from five oil wells in the East Baghdad oil field (see Table 1) to test these correlations. Basic Equations Gilbert's Approach. Assuming a knife-edge choke and making several simplifying assumptions with regard to the pressure/volume characteristics of the oil and gas, we can show theoretically thatEquation 1 wherePt = tubing-head pressure,C = constant approximately equal to 600,R = gas/liquid ratio,q = gross liquid rate, andd = bean size. Gilbert's equation assumes that the actual mixture velocities through the bean exceed the speed of sound; therefore, the downstream or flowline pressure has no effect on the rate of upstream pressure. The speed of sound is known to be reached when the upstream pressure is at least twice the downstream pressure. Gilbert noted, however, that his equation was good when the downstream pressure was less than 70% of the upstream pressure. Poettmann and Beck's Adaptation of Ros' Equation. The correlations of Poettmann and Beck4 were intended to aid in the prediction of gas/liquid flow through chokes. Their development followed the original presentation by Ros and was derived for an average orifice discharge coefficient. Poettmann and Beck converted the Ros equation to oilfield units and reduced it to graphic form, resulting in the following expression:Equation 2 whereqo = oil flow rate,Kd = discharge coefficient (1.03),A = cross-sectional area of throat (minimum cross sectional area of the choke),?Ls = density of crude,?g = specific gravity of gas,Rp = producing GOR at standard conditions,pt = tubing-head pressure,VL = volume of liquid per unit mass of total fluid, mL/?LmL = 1/[1+R(?g/?L)]R = [0.00504 Tz(Rp-Rs)]/(Bopt),T = tubing-head temperature,z = compressibility factor of gas at tubing-head pressure and temperature,Rs = solubility of gas in crude at tubing-head pressure and temperature,Bo = oil FVF at tubing-head pressure and temperature, and?L = density of crude. Graphic solution of Poettmann and Beck's equation was based on the selection of a temperature value of 85°F [29°C] and gas specific gravity of 0.6. Good results are obtained from Eq. 2 if there is no water production and if the flow is two-phase at critical flow conditions. Gilbert's Approach. Assuming a knife-edge choke and making several simplifying assumptions with regard to the pressure/volume characteristics of the oil and gas, we can show theoretically thatEquation 1 wherePt = tubing-head pressure,C = constant approximately equal to 600,R = gas/liquid ratio,q = gross liquid rate, andd = bean size. Gilbert's equation assumes that the actual mixture velocities through the bean exceed the speed of sound; therefore, the downstream or flowline pressure has no effect on the rate of upstream pressure. The speed of sound is known to be reached when the upstream pressure is at least twice the downstream pressure. Gilbert noted, however, that his equation was good when the downstream pressure was less than 70% of the upstream pressure. Poettmann and Beck's Adaptation of Ros' Equation. The correlations of Poettmann and Beck4 were intended to aid in the prediction of gas/liquid flow through chokes. Their development followed the original presentation by Ros and was derived for an average orifice discharge coefficient. Poettmann and Beck converted the Ros equation to oilfield units and reduced it to graphic form, resulting in the following expression:Equation 2 whereqo = oil flow rate,Kd = discharge coefficient (1.03),A = cross-sectional area of throat (minimum cross sectional area of the choke),?Ls = density of crude,?g = specific gravity of gas,Rp = producing GOR at standard conditions,pt = tubing-head pressure,VL = volume of liquid per unit mass of total fluid, mL/?LmL = 1/[1+R(?g/?L)]R = [0.00504 Tz(Rp-Rs)]/(Bopt),T = tubing-head temperature,z = compressibility factor of gas at tubing-head pressure and temperature,Rs = solubility of gas in crude at tubing-head pressure and temperature,Bo = oil FVF at tubing-head pressure and temperature, and?L = density of crude. Graphic solution of Poettmann and Beck's equation was based on the selection of a temperature value of 85°F [29°C] and gas specific gravity of 0.6. Good results are obtained from Eq. 2 if there is no water production and if the flow is two-phase at critical flow conditions.