IMPROVED MATERIAL BALANCE EQUATION OF SHALE GAS RESERVES AND PRODUCTION

Abstract

Langmuir adsorption isotherm has been used extensively when incorporating gas desorption into gas Material Balance Equation (MBE) framework. However, it over-estimates adsorbed gas reserves at higher pressures without adsorption saturation pressure (P_s ). Previous researches developed modified Z-factors incorporating gas desorption, rendering them complex for routine calculations. Therefore, this study was designed to improve shale gas MBE by developing an isotherm that defines the onset of adsorption saturation pressure, and modifying single-porosity Z-factor to a simpler but accurate dual-porosity free gas Z-factor. A new adsorption isotherm involving pressure (P), P_s, maximum adsorbed volume (V_max ), and adsorbate-adsorbent resistance parameter (n) was developed using kinetic approach. The developed and Langmuir isotherms were used in modelling secondary adsorption data of different adsorbents, and the qualities of fit were statistically assessed. The modified Z-factor incorporates ratio of dual porosity to initial matrix porosity (ϕ_mat^' ), and it was statistically correlated with existing dual-porosity Z-factor. The improved MBE is a function of the developed isotherm and the modified Z-factor. Using adsorption and reservoir data of some shale gas formations obtained from literature, variation of cumulative gas production (G_p ) with pressure depletion (∆P) were determined. Effect of fracture porosity (ϕ_frac ) on G_p was determined. Free and total gas production decline rate models were derived from well production history and average change of G_p with pressure depletion from initial reservoir pressure to wellbore flowing pressure. The results were statistically correlated. The developed isotherm, V={█(V_max {P/P_s +(1-P/P_s ) (P/P_s )^n },&for P<P_s i.e.undersaturated adsorption@V_max,&for P≥P_s i.e.saturated adsorption)} shows that V_max is maintained during pressure depletion to P_s, below which gas desorption begins. For secondary low-pressure methane adsorption data of a shale sample from 190 to 2,005 psia at 25 oC, a V_max of 0.0450 mmol/g at a P_s of 2,005 psia and Langmuir volume of 0.0548 mmol/g at infinite P_s were predicted by the developed and Langmuir isotherms with R2 values of 0.997 and 0.989, respectively. The modified Z-factor is Z∙{1-(1-ϕ_frac+ϕ_frac/(ϕ_mat^' ))((C_w 〖S_w〗_i+C_( matrix))/〖S_g〗_i )∙∆P}^(-1)where Z, C_w, 〖S_w〗_i, C_( matrix) and 〖S_g〗_i are Z-factor at P, water compressibility, initial water saturation, matrix compressibility and initial gas saturation, respectively. For a shale formation, correlating the modified Z-factor with Aguilera Z-factor yields a R2 value of 1.00. With pressure drawdown from 3,500 to 2,285 psig, technically recoverable reserves of 489 Tscf would be depleted in form of free gas G_p; the corresponding developed isotherm-based and Langmuir isotherm-based total gas G_p were estimated as 509.26 and 564.09 Tscf, respectively. Increase in ϕ_frac was found to increase G_p. Using a production history of 59 months as base case, the developed isotherm-based decline rate model results offered better correlation than Langmuir isotherm-based model results, with Root Mean Square Errors (RMSE) of 6.680 and 52.646 Mscf/d, respectively. A production forecast of 30 years, using the production history and its projection as base case, yields corresponding RMSE of 5.333 and 42.774 Mscf/d, respectively. An improved adsorption isotherm that defines the onset of adsorption saturation pressure was established, Z-factor was modified for dual-porosity and an improved material balance equation was formulated for a better production forecast.