本研究主要是針對屬於共軛格拉茲問題的薄膜氣體吸收系統進行理論分析，利用正交展開法求得系統中氣體溶質於氣、液兩相內之二維濃度分佈式，所推導出之解題流程適用於平板及套管之順流與逆流系統。當使用分離變數法將系統之偏微分方程式化簡為常微分方程式以求解其特徵函數時，吾等對平板及套管系統分別取前六項及前七項特徵值(包含 )，以此項數計算的結果相當符合入、出口處之邊界條件。研究中也推導出氣體溶質在氣-液薄膜接觸器內，於氣、液兩相中之平均濃度分佈、質傳係數、吸收速率及吸收效率等物理量之數學表示式。 以本論文所推導之理論為基礎，對二氧化碳之物理吸收作廣泛的討論，結果發現，不論是何種類型之吸收，增加液體的流率或減少氣體的流率皆能增加二氧化碳之吸收效率，而各種濃度變化的趨勢，也都能符合吾等之預期。此外，由平板吸收實驗所得之結果更可以確定本論文所提出的數學模型之正確性。 本論文最大的貢獻為無須經過冗長費時的實驗即可求出整個吸收系統的質傳係數以及氣體溶質之二維濃度分佈式，對影響薄膜吸收的各種變因有更進一步的認識。 In the present dissertation the orthogonal expansion techniques has been employed to solve the conjugated Graetz problems in various membrane gas absorptions, where the theoretical solutions for the solute concentrations in gas and liquid phases. The theoretical analysis aforementioned may be applied to the gas-liquid contactor operating in co-current. The solution, which is calculated on the basis of the first six eigen values from the system of plate and the first seven ones (including ) from the system of sleeve, respectively, is adequate to the boundary condition of entrance and exit for the co-current or countercurrent flow systems when a corresponding eigen function is acquired by simplifying a partial differential equation into an ordinary differential equation with the method of variable separation. The research also introduces the mathematical functions for the average distribution of concentration, mass transfer coefficients, absorbing rates and absorbing efficiency of the gas solutes in the gas and liquid phases in the gas-liquid membrane contactor. There are also comprehensive discussions on the physical absorption of carbon dioxide on the basis of the present research. It is found that not only the added rates of liquid but also the reduced rates of gas may improve the absorbing rates of carbon dioxide, regardless of the types of absorption. However, the trends on the variations of concentration meet researchers’ anticipation. Furthermore, the effects from the experiments on the absorption issue of plate are in support of the correct mathematical model introduced in the present dissertation. The introduced mathematical model is advantageous to acquire the mass transfer coefficients for the whole system of absorption and the two-dimensional distribution of concentration for the gas solutes without undue experiments, which provides further knowledge on the variables relative to the membrane absorption.