A Model for Predicting the Density of Oil-Base Muds at High Pressures and Temperatures

Abstract

Summary. A compositional material-balance model was used to predict the densities of diesel- and mineral-oil-based muds at elevated pressures and temperatures. We measured the densities of diesel oil, two mineral oils, and calcium chloride solutions from 78 to 350 deg F and from 0 to 15,000 psig. The measured densities were used in an existing compositional psig. The measured densities were used in an existing compositional material-balance model to predict the densities of 11 - and 17-lbm/gal oil-based muds. We also measured the densities of these muds at elevated pressures and temperatures and compared them with the predicted values. pressures and temperatures and compared them with the predicted values. The results show excellent agreement between measured and predicted densities. The experimental density data were used to predict downhole densities and static wellbore pressures for the oil-based muds. Results show that the mineral-oil muds are not only more compressible than the diesel-oil muds, but also more susceptible to thermal expansion. Therefore, all the oil-based muds tend to give essentially the same static-wellbore-pressure profile. Introduction Oil-based muds are widely used to drill deep, hot wells. Because the muds compress under pressure and expand with temperature, their downhole densities may be quite different from their surface densities, which are typically measured during drilling operations. To plan well control adequately, to prevent lost circulation, and to analyze fracture-gradient test data accurately, one must be able to predict the densities of these muds at elevated pressures and temperatures. McMordie et al. investigated the effects of pressure and temperature on the densities of water- and diesel-oil-based muds. Hoberock et al. presented a technique for predicting downhole densities for water- and diesel-oil-based muds that uses a compositional material-balance model. Thus, the effects of pressure and temperature on mud densities have been studied previously for water- and diesel-oil-based muds. The effects of pressure and temperature on the relatively new, less toxic, mineral-oil-based muds, however, have not been reported. This study complements the previous studies by providing new experimental data for these new previous studies by providing new experimental data for these new oilbased muds. The objective of this study was to investigate the possibility of using Hoberock et al.'s compositional material-balance model to predict the densities of diesel- and mineral-oil-based muds at elevated predict the densities of diesel- and mineral-oil-based muds at elevated pressures and temperaturen the basis of laboratory density pressures and temperaturen the basis of laboratory density measurements of the liquid components of the muds. To achieve this objective, we first measured the densities of diesel oil, two popular mineral oils, and various concentrations of calcium chloride popular mineral oils, and various concentrations of calcium chloride solutions at elevated pressures and temperatures. Next, we used the measured densities and the compositional model to predict the densities of the oil-based muds of known composition. Finally, we measured the densities of the muds at elevated pressures and temperatures and compared the results with the predicted values. This paper presents our results, which show excellent agreement between paper presents our results, which show excellent agreement between predicted and measured densities. predicted and measured densities. Compositional Model Hoberock et al.'s compositional material-balance model was derived as follows. Suppose that the oil-based mud consists of the base oil, salt water, solid weighting material, and chemicals. At ambient pressure and temperature, the volume and weight of the mud are V=Vo+Vw+Vs+Vc...............(1) and W=poVo+pwVw+psVs+pcVc.......(2) After the mud is subjected to a higher temperature and pressure, the volume changes, predominantly because of the expansion or contraction of the base oil and the salt water (the compressibility and the thermal expansion of the solids are essentially negligible). Therefore, the new -mud volume is Vi=Vo+Vw+Vs+Vc+ Vo+ Vw......(3) From mass conservation, Vo=(poVo/poi)-Vo...........(4) and Vw=(pwVw/pwi)-Vw...........(5) The mud density at elevated pressure and temperature can be obtained with Eqs. 2 and 3: poVo+pwVw+psVs+pcVc p(p, T)=.......(6) p(p, T)=.......(6) Vo+Vw+Vs+Vc+ Vo+ Vw Once Eqs. 4 and 5 are substituted and the volume fraction of the various constituents at ambient pressure and temperature is defined, Eq. 6 may be written as pofvo+pwfvw+psfvs+pcfvc..(7) p(p, T)= . p(p, T)= . (Po) (Pw)1+fvo (- 1)+fvw(-1)(poi) (pwi) Eq. 7, Hoberock et al.'s compositional model, shows that the mud density at elevated pressure and temperature can be predicted from a knowledge of the mud composition, the density of the mud constituents at ambient temperature and pressure, and the density of the liquid constituents at elevated pressure and temperature. To test the model, we measured the density of the base oils and salt water at elevated pressures and temperatures with high-pressure PVT equipment and used Eq. 7 to predict the densities of several PVT equipment and used Eq. 7 to predict the densities of several oil-based muds of known composition. We also measured the densities of the muds and compared them with the predicted results. Experimental Equipment and Procedure Fig. 1 is a schematic of the experimental equipment used to perform the density measurements. The test cell was a blind PVT cell perform the density measurements. The test cell was a blind PVT cell rated at 20,000 psig and 600 deg. F and installed in an air bath whose temperature could be controlled to within +/-1 deg. F. The test sample, which was held in a lead jacket, was compressed by a positive-displacement pump capable of generating a pressure up to 20,000 positive-displacement pump capable of generating a pressure up to 20,000 psig. Because the pump compressed the test sample by a psig. Because the pump compressed the test sample by a compressible hydraulic fluid, it was necessary to calibrate the equipment to correct the test results for the compressibility of the hydraulic fluid. This was done by running a compressibility test with a steel plug in place of the test sample. Because a steel plug is essentially plug in place of the test sample. Because a steel plug is essentially incompressible, the observed volume change at each pressure was attributed entirely to the compressibility of the hydraulic oil. The test sequence was as follows. P. 141